AN ABSTRACT OF THE THESIS OF
Yanshui Yin for the degree of Doctor of Philosophy in Fisheries Science presented on
September 28, 2001. Title: Sensitivity of the Stock Synthesis Assessment Model: a Simulation
Approach.
Abstract approved:
Redacted for Privacy
David B. Sampson
Stock assessments for many U.S. Pacific coast groundfish stocks are developed using
the catch-at-age method known as Stock Synthesis. In this work a simulation package was
developed and used to evaluate the sensitivity of the Stock Synthesis program. More
specifically, the evaluation focused on the impacts of input data errors and stock
characteristics on the accuracy and precision of Synthesis estimates. Factors examined
included the length of the time series of data, the rate of natural mortality, the shape of the
fishery and survey selectivity curves, the trend in the rate of fishing mortality, the recruitment
pattern, and errors in the observed data for annual catch, fishing effort, fishery and survey age
composition, and survey biomass indices. First, the study evaluated the sensitivity of the Stock
Synthesis program applied to populations with simple multinomial age compositions. The
length of the data series and sample size were the two most influential factors. Second, the
study focused on populations with compound multinomial age composition, in which the age
composition data were over-dispersed relative to simple multinomial samples. When the
fishery age composition actually followed a compound multinomial distribution, the estimates
produced by the Stock Synthesis program, which assumed simple multinomial distributions
with maximum sample sizes of 400 fish, were moderately more biased and more variable.
When applying Synthesis to populations whose age compositions follow compound
multinomial distributions, the results from the experiments indicated that a common
configuration, in which age sample sizes in the likelihood specification are limited to 400 fish
per sample, probably gives age composition data too much emphasis. The experiments
indicated that using 200 as the upper limit provided more accurate results than using 400.
Third, the actual stock assessment of yellowfin sole (Limanda
Aspera)
was taken as a case
study and it was found that more accurate assessment results could be achieved from a better
balance in the amount of sampling effort allocated to age composition data versus survey
biomass estimates.
©Copyright by Yanshui Yin
September 28, 2001
All Rights Reserved.
Sensitivity of the Stock Synthesis Assessment Model: a Simulation Approach
i;'i
Yanshui Yin
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Doctor of Philosophy
Completed September 28, 2001
Commencement June 2002
Doctor of Philosophy thesis of Yanshui Yin presented on Septembers 28, 2001.
APPROVED:
Redacted for Privacy
Major Professor, representing Fisheries Science
Redacted for Privacy
Chair of Department of Fisheries and Wildlife
Redacted for Privacy
Dean of Gradflate School
I understand that my thesis will become part of the permanent collection of Oregon State
University libraries. My signature below authorizes the release of my thesis to any reader
upon request.
Redacted for Privacy
Yin, Author
ACKNOWLEDGMENTS
Thanks go to Professor Sampson for providing with an apprenticeship to modem stock
assessment modeling; the work could not have been undertaken without the skills and
experience acquired as a research assistant on a project dealing with stock assessments along
the U.S. Pacific coast. Dr. Richard Methot is thanked for his helpful discussions on the Stock
Synthesis Program. Professor Thomas is thanked for providing an efficient algorithm in
partitioning a population into strata. Thanks also go to Oregon Sea Grant for partially
supporting the author's graduate program.
TABLE OF CONTENTS
Chapter One: Stock Assessment and the Stock Synthesis Model ..............................................
1
1.1 Introduction .....................................................................................................................
1
1.2 The Stock Synthesis Model ............................................................................................. 3
1.3 Potential Issues with the Stock Synthesis Model ............................................................
7
1.4 Research Objectives ........................................................................................................
9
Chapter Two: Sensitivity of the Stock Synthesis Program on Populations with Simple
Multinomial Age Compositions................................................................................................ 12
2.1 Introduction Simple Multinomial Age Composition and Stock Synthesis ................. 12
2.2 Methods .........................................................................................................................
13
2.3 Results .......................................................................................................................... 39
2.4. Discussion .................................................................................................................... 52
Chapter Three: Compound Multinomial Age Compositions and Assessments with the Stock
SynthesisProgram .................................................................................................................... 55
3.1 Introduction ................................................................................................................... 55
3.2 Methods ......................................................................................................................... 56
3.3 Results ............................................................................................................................ 98
3.4 Discussion ................................................................................................................... 119
Chapter Four: The Rational Allocation of Sampling Effort for Assessing the Stock of
Yellowfin Sole with the Stock Synthesis Program................................................................. 123
4.1 Introduction ................................................................................................................. 123
4.2 Methods ........................................................................................................................ 124
4.3 Results .........................................................................................................................
141
4.4 Discussion ................................................................................................................... 146
ChapterFive: Summary ......................................................................................................... 149
References ............................................................................................................................... 154
TABLE OF CONTENTS (Continued)
APPENDICES
AppendixA: Terminology ..................................................................................................... 158
Appendix B: Creating a Generic Fisheries Simulation Package for a Monte Carlo
Evaluation of the Stock Synthesis program ..................................................... 161
Appendix C: Common Simulation Methodology and Stock Synthesis Configurations........ 199
LIST OF FIGURES
Figure
2.1
gç
The maturity at age schedule for the simulated stocks: (a) the short-lived
stock (M =0.4/yr), where the slope is at 2.0 and the inflection age is at 3.
(b) the long-lived stock (M0.2/yr), where the slope is at 1.0 and the
inflection age is at 5
20
2.2.
The configuration for fishery and survey selectivity. The selectivity curve
was defined by a double logistic function
21
2.3.
Initial age composition for M = 0.2. (a) constant recruitment. (b) variable
recruitment
22
Initial age composition for M = 0.4. (a) constant recruitment. (b) variable
recruitment
23
The distributions of relative bias for the seven estimates across the 128
treatments
37
The distribution of relative bias of the median for the seven estimates
across the 128 treatments
38
The distribution of relative variability for the seven estimates across the
128 treatments
39
2.4.
2.5.
2.6.
2.7.
2.8.
Example histograms from experimental treatment 1 of variables output by
the Stock Synthesis program and used as dependent experimental variables 40
2.9.
Experiments on sensitivity to initial parameter values for treatment 36 and
treatment 109. The dashed line represents the true ending biomass
51
3.1.
An example comparison of data variability between compound
multinomial age samples (CM) and simple multinomial age samples when
applied to a same population (SM)
59
3.2.
Experiment Al example histograms (from experimental treatment 1) of
variables output by the Stock Synthesis program and used as dependent
experimental variables
96
3.3.
Experiment A2 example histograms (from experimental treatment one) of
variables output by the Stock Synthesis program and used as dependent
experimental variables
97
3.4.
Sensitivity to initial parameter values for treatment 40 and treatment 77 of
experiment Al. The dashed line represents the true ending biomass
109
LIST OF FIGURES (Continued)
Figure
3.5
Sensitivity to initial parameter values for treatment 40 and treatment 89 of
experiment A2. The dashed line represents the true ending biomass
110
3.6.
Main effects on the relative bias of ending biomass estimates from the
Stock Synthesis program after combining the results of experiments B 1
andB2
3.7
Main effects on the relative bias of ending biomass estimates from the
Stock Synthesis program after combining the results of experiments Cl
116
andC2
116
4.1.
Weight-at-age of yellowfin sole, with maximum age at 20 years
126
4.2.
Maturity-at-age curve, with inflect age at 10 years
128
4.3.
The initial non-equilibrium age composition at the start of 1964. The fish
numbers are in millions and the ages are in years
128
Fishery selectivity and survey selectivity. For fishery selection curve the
inflection age = 8.8 years and the slope = 1.0 / yr. For survey selection
curve the inflection age = 5.4 years and the slope = 1.4 / yr
129
Example histograms (from experimental treatment 1) of variables output
by the Stock Synthesis program and used as response experimental
variables.
139
Diagnostic plots of the residual versus fitted values for the two response
variables. The three clumps correspond to the three levels of the survey
CV factor, with the high CV producing less accurate estimates
140
4.7.
Example surface plot of relative RMSE of ending biomass
145
4.8.
Example surface plot of relative RIVISE of ending exploitable biomass
145
4.4.
4.5.
4.6.
LIST OF TABLES
Table
2.1.
Fractional factorial experimental design
16
2.2.
Configurations of the low vs. high levels for the nine controlling variables
19
2.3.
Alias structure of the fractional factorial design
26
2.4.
Relative bias for the 128 experimental treatments
28
2.5.
Relative variability for the 128 experimental treatments
31
2.6.
Relative median bias for the 128 experimental treatments
34
2.7.
ANOVA tables from the fractional factorial experiment
42
2.8.
Analysis of relative bias
45
2.9.
Analysis of relative median bias
47
2.10.
Analysis of relative variability
48
3.1.
Fractional factorial experimental design
61
3.2.
Low vs. high levels for the nine controlling variables
64
3.3.
Parameter values associated with the two levels of natural mortality M
65
3.4.
Alias structure of the fractional factorial design
66
3.5.
Designs of experiments BI, B2, Cl, and C2
70
3.6.
Design of experiment D
71
3.7.
Relative bias for the 128 experimental treatments in experiment Al
72
3.8.
Relative variability for the 128 experimental treatments in experiment Al
75
3.9.
Relative bias of the median for the 128 treatments in experiment Al
78
3.10.
Relative bias for the 128 experimental treatments in experiment A2
81
3.11.
Relative variability for the 128 experimental treatments in experiment A2
84
3.12.
Relative bias of the median for the 128 treatments in experiment A2
87
3.13.
ANOVA tables from fractional factorial experiment Al
90
LIST OF TABLES (Continued)
Table
3.14.
ANOVA tables from fractional factorial experiment A2
93
3.15.
Analysis of relative bias for experiment Al
101
3.16.
Analysis of relative bias for experiment A2
102
3.17.
Analysis of relative variability for experiment Al
104
3.18.
Analysis of relative variability for experiment A2
105
3.19.
Analysis of relative median bias for experiment Al
106
3.20.
Analysis of relative median bias for experiment A2
107
3.21.
Analysis of relative bias for experiments Bi, B2, Cl, and C2
113
3.22.
Analysis of relative variability for experiments Bi, B2, Cl, and C2
114
3.23.
Comparisons of coefficients for relative bias of ending biomass from
experiment Bi and B2
115
Comparisons of coefficients for relative bias of ending biomass from
experiment Cl and C2
115
3.24.
3.25.
Comparisons of coefficients for relative bias of ending biomass from
experimentBl and Cl
117
3.26.
Comparisons of coefficients for relative bias of ending biomass from
experiment B2 and C2
117
3.27.
Paired T test on relative variability of ending biomass
117
3.28.
Analysis of relative bias for experiment D
118
3.29.
Analysis of relative variability for experiment D
118
4.1.
Yearly recruitment and fishing mortality values estimated in the 1998
assessment
127
4.2.
Initial values for the parameters of the non-equilibrium age composition at
the start of 1964 and yearly recruitments from 1964 to 1998
130
Design of experiment on the combination of input data errors in last three
years
134
4.3.
LIST OF TABLES (Continued)
Table
4.4.
Relative bias, variability, and RIVISE of the 81 experimental treatments
137
4.5.
Analysis of variance for relative RMSE of ending biomass estimates
144
4.6.
Analysis of variance for relative RMSE of ending exploitable biomass
estimates
144
LIST OF APPENDIX FIGURES
Figure
B.1.
Illustration of the Stock Synthesis Program
161
B.2.
Flowchart of the Evaluation Process
163
B.3.
Document-view architecture illustration
166
B.4.
Objects and classes used by the SDI application
167
B.5.
A Schematic Illustration of a Fishery System
169
B.6.
Class Organizations
171
B.7.
Screen Shot of Stock Program
171
B.8.
Class Declaration of CStockApp
172
B.9.
Partial Listing of Method Initlnstance()
172
B.1O.
Class Declaration of CStockDoc
174
B.11.
Class Declaration of C Info
175
B.12.
A C Info Dialog Box Invoked Inside a Graphical View
176
B.13.
Class Declaration of CRecruitDlg
177
B.14.
Font Saving Method Called by Windows
178
B. 15.
Dynamic Creation of Control Objects
178
B.16.
Dynamic Creation of Control Windows
179
B.17.
Screen Shots of CRecruitDlg Windows with Dynamic Control
Creation
180
B.18.
Class Declaration of CSlctView
181
B.19.
Screen Dump of CSlctview windows
183
B.20.
Class Declaration of CTextView
184
B.21.
Method OnKeyDown() of Class CTextView (partial listing)
185
B.22.
Method change Font() of Class CTextView
186
LIST OF APPENDIX FIGURES (Continued)
Figure
B.23
Screen Shot of CTextView Window
186
B.24.
Class Declaration of CMainFrame
187
B.25.
Screen Shot of Font Selection Process
188
B.26.
Disabling and Enabling of Menu Item Command
189
B.27.
Message Handlers for UI Update
189
B.28.
Method OnSimulationStart () of Class CMinFrame
190
B.29.
Method OnSimulationTextfile() of Class CMainFrame
191
B.30.
Code Fractions of Command Line Parsing
192
B.31.
Code Fraction of Input File Parsing
193
B.32.
Declaration of Class tritrix
194
B .33.
Random Number Generator for a Normal Distribution
195
B.34.
Partial Listing of Codes for Numerical Simulation
196
B.35.
Code Fraction for Creating Template Parameter files
197
B.36.
Code Fraction for Modifying Template Parameter File into Actual Output
File
197
B.37.
Code Fraction for Searching Values of Type "RECRUIT" and "SUM-BIO" 198
Sensitivity of the Stock Synthesis Assessment Model: a Simulation Approach
Chapter One: Stock Assessment and the Stock Synthesis Model
1.1 Introduction
Fisheries managers and fisherman generally appreciate that fish resources are not
unlimited and their exploitation should be regulated. To efficiently manage exploited fish
resources, managers need to know the status of the resources, particularly whether they are
increasing or decreasing, and why. This is one of the maj or reasons that stock assessment
plays a key role in fisheries management (Megrey 1989). However, despite considerable effort
by management agencies, most of the major fish stocks whose status is known are either
overexploited or fully utilized (National Marine Fisheries Services 1993). Inaccurate
assessment information is one of the factors that can contribute to improper utilization of fish
resources, either because the information is biased or was derived from an inappropriate
assessment model (Myers and Cadigan 1995b). For example, estimates of fish biomasg, from
which catch quotas are derived, may be inaccurate if they are based on models that are not
robust to errors in the input data (Pope 1997, Ralston 1989). In the face of decreasing
resources, reliable stock assessment information has become more crucial (Richards and
Megrey 1994); better understanding of the behavior of stock assessment models will lead to
better estimates of biomass.
Stock assessment models in fisheries science differ considerably in complexity. In the
early years (50's and 60's) of stock assessment, the mathematical models that were developed
usually were simple in form and rigid in assumptions (Megrey 1989). The stock production
model (Schaefer 1954, 1957) and the dynamic pool model (Beverton and Flolt 1957) are
typical representatives of this category. In the 70's, 80's, and 90's, with the introduction of
modern computers, more complex models were developed. Most of these models include age-
structure for the fish populations and are mathematically sophisticated, make less rigid
assumptions about the fish stocks, and involve considerable amount of calculations. Examples
of this large category of assessment models include cohort analysis (Pope 1972), the separable
models of Doubleday (1976) and Pope and Shepherd (1984), the model of Dupont (1983), and
the CAGEAN program (Deriso et al. 1985).
As stock assessment models became more complicated, the number of model
parameters increased, with the result that input errors may have considerable impact on
assessment results. Also, no matter how complicated a model is, it still depends on some
simplifying assumptions about the nature of the fish stock it is applied to. It is natural to ask
what will happen if these assumptions are violated. Evaluating the sensitivity of a model to
input errors or violated assumptions is essential to the understanding and wise application of
those models. Because of the nature of fish resources, it is impractical to conduct the
sensitivity analyses by actual experiments. Firstly, we will never know exactly the status of the
stock being modeled or the actual errors associated with the input data; secondly, it would be
too costly to perform the experiments even if we could do so. Although sensitivity analyses
can be done analytically on some less complicated models, it is very difficult, if not impossible,
to analytically evaluate the sensitivity of modem age-structured models. This is obab1y the
major reason why most sensitivity analyses of complex stock assessment models have been
done using simulation techniques (Francis 1993; Kimura 1989; Pelletier and Gros 1991;
Prager 1988; Restrepo et al. 1992; Sampson 1993).
'Please see Appendix A for fishery specific terminology.
1.2 The Stock Synthesis Model
The evolution of model building in stock assessment reflects a trend towards greater
awareness of the uncertainties associated with fishery data and an increasing willingness and
ability to deal with these uncertainties. As pointed out by some authors (e.g., May et al. 1978;
Roff 1983; Walters 1986), the future success of fisheries management will primarily depend
upon having assessment models that are flexible enough to integrate various data resources
that have different degrees of uncertainty. Stock assessment scientists have made considerable
efforts to develop models that satisfy the above requirements. For example, Foumier and
Archibald (1982) and Deriso et al (1985) started the analytical approach that integrates the
analysis of fishery catch-at-age data and survey estimates of abundance in their age-structured
models. Methot (1990, 2000) further elaborated the approach with increased flexibility and
developed the Stock Synthesis program. The program has adequate flexibility to deal with
variable data. Based on the maximum likelihood method of parameter estimation, the program
is very complex and also is very powerful in the variety of situations it can accommodate. As
its name implies, the model can integrate different kinds of data and has relatively flexible
requirements on the type and form of input data (Methot 1990). For example, even with catchat-age data that are not consecutive year by year, as required by Virtual Population Analysis
(Gulland, 1977) and its derivatives, this model can simultaneously analyze data on catch
biomass, age composition, stock abundance, and fishing effort from multiple fisheries and
multiple surveys. Perhaps because of this flexibility and adaptability, this model is currently a
major tool used in assessing the stocks of groundfish along the U. S. west coast and in some
other areas (Dom et al. 1991; NPFMC 2000; Porch et al. 1994; Sampson 1994).
Mathematically, the Stock Synthesis program models the dynamics of an agestructured fish population using standard deterministic equations for survival, catch, and
growth (Methot 1990, 2000). The number of fish that survive in a given year class is assumed
to follow an exponential decay function,
Nya = Ny_i,a_l exp[(M +Sa_i F5_1)]
where
Pv,a
(1)
is the number of fish at the start of year y that are a years old, M is the instantaneous
rate of natural mortality, Saj is the selectivity coefficient for age a-i fish, and F,1 is the
instantaneous rate of fishing mortality in yeary-1 for fully selected ages. The selectivity
coefficients allow for age-specific rates of mortality due to fishing. The number of fish in the
oldest age class is accumulated in accordance with survivorship (equation 1) and is given by
NyT = Ny_1,T exp[ -(M + ST F_1)] + Ny_I,T_1 exp[ -(M + ST_I F_1)]
(2)
where T denotes the oldest age, or Terminal age.
The Stock Synthesis program accommodates a range of methods for representing
selectivity. One typical example is the double-logistic function,
Sa
{l+exp[b1(aal)]}1 {1+exp[b2(aa2fl}1
Smax
(3)
where a i and hi are respectively the slope and the inflection age for the ascending portion of
the "dome-shaped" curve, b2 and t2 are respectively the slope and the inflection age for the
descending portion of the curve, and
Sm
is the maximum value of the numerator over the
range of ages in the modeled stock. When parameter b2 is positive, equation 3 will generate a
dome-shaped selectivity curve; when the value of b2 is 0, the selectivity function will give an
asymptotic curvature.
The catch in numbers of age a fish in yeary is given by the following catch equation,
cya
NyaSaFy
{1exp[(M+SaFy)]}
M+SaEy
(4)
The catch in weight for age a (yield at age) is given by
= Cya Wa
(5)
where W denotes the average weight of age a fish in the fishery, which is given by the von
Bertalanffy growth function,
Wa
=W {1exp[k(aa0)]}'
where W is the weight at infinite age, k is the growth coefficient,
a0
is a constant, and b is the
length-weight power coefficient, the value of which is usually around 3.0.
The weight-length relationship can be represented by
W=c
where L denotes length, and b and c are conversion coefficients.
The total catch biomass in year y is given by
'ya
(6)
The Stock Synthesis program, as with all catch-at-age methods, requires additional
auxiliary information for tuning the analysis in the form of independent survey indices of stock
biomass or numerical abundance, or data series for fishing effort or catch per unit effort (Pope
and Shepherd 1982, Shepherd and Nicholson 1991). If survey biomass data are used and the
survey is conducted at the beginning of the year, then the expected value of the survey
biomass index is given by
E[B'] = Q'Nya W'a S'a
(7)
where Q' denotes the survey catchability coefficient, W'a is the average fish weight at age in
the survey, S'a is the survey selectivity coefficient for age a fish. If fishing effort data (J) are
used, the expected value of the effort is related to the rate of fishing mortality by
(8)
F =QE[f3j
where Q denotes the fishery catchability coefficient.
The iterative fitting process of the Stock Synthesis program is based on maximizing
the value of the total log-likelihood function for a set of parameters that define the population
structure and dynamics. The log-likelihood function measures the goodness-of-fit between the
observed data and the values predicted by the model given the parameter values. The total loglikelihood (Ltotai) consists of several components,
Ltotal
=L1e1
(9)
J
where L denotes log-likelihood attributed by typej data. Because different data types can be
subject to different levels of observation error, emphasis factors (e) are assigned to the
individual components.
Suppose age determination is exact and that simple random samples of fish are
obtained from the fishery and survey, then the age composition data are distributed as
multinomial random variables and the log-likelihood component for these data is given by
Lage >y {Pya log(E[pya])_pya log(pya)}
y
(10)
a
where J is the number of fish in the sample for yeary, p, is the observed proportion at age in
the sample for year y, and E[pJ is the true proportion at age in the sample for year y.
Assuming the survey biomass and fishing effort estimates both are lognormally
distributed, the log-likelihood components for these data are given by
I
Lsurvey = _log(s)__-_ )log
and
2
B'
1
E[B'y]J
(11)
Leffort = 1Og()----
1og
fl
2
E[f]j
(12)
respectively, where B',, is the observed survey biomass in year y and E[B'I is its expected
value,f,, is the observed fishing effort in year y and E[f] is its expected value. o and
aF are
respectively the true, log-scale standard deviation for observed survey biomass and observed
fishing effort.
Even though
Ls,irve,,
and
Lefprt
in equations (11) and (12) are called "log-likelihood
components", they are not exactly the log-likelihood function of lognormal distribution. The
generic format of log-likelihood function for lognormal distribution looks like:
X +O.5a2
L-1og(a)log
2a2
E(X)
In equations (11) and (12), the term O.52 is ignored.
1.3 Potential Issues with the Stock Synthesis Model
Because Stock Synthesis takes data from multiple sources and analyzes them
simultaneously, the accuracy of Synthesis estimates is inevitably subject to the errors and the
structures of these diverse data sources. Because the model is based on the analysis on the
dynamics of an age-structured population, estimates from Stock Synthesis might also be
influenced by the biology of a fish stock and the characteristics of the fishery. For example,
data for total annual catch, fishery age composition, fishing effort, and survey indices of
abundance are all subject to observation errors and may have different length of time series.
Different fisheries may have different fishing intensity on their fish stocks; some fish species
may grow slowly and live longer and others might grow fast and have a shorter life span.
Determining the impact of these various factors on the accuracy of Stock Synthesis estimates
will help better understand the performance of Synthesis under various scenarios.
Although flexible, the Stock Synthesis model, like other assessment models, depends
on some simplifying assumptions that could adversely influence the reliability of its estimates.
Because estimates of sampling error associated with observed age composition data are
usually unavailable, the Stock Synthesis model assumes that the annual age composition
samples follow multinomial distributions. With this distribution, the greatest relative accuracy
occurs in the most frequently caught age classes and the variances of age composition within
and among years are determined by the size of each annual age composition sample. There is
evidence that most variability in age compositions of commercially-exploited species results
from significant variation between boat trips (Crone 1995), which implies that annual age
composition data obtained from samples combined among trips will follow some form of
compound multinomial distribution (Smith and Maguire 1983) instead of the simple
multinomial distribution that the Stock Synthesis model assumes.
When sample size is large, it is possible that the fitting process of the Stock Synthesis
is dominated by small incongruities between observed and predicted age compositions. To
avoid the possibility of over-fitting the age composition data, users often configure the model
to assume the maximum sample size to be 400 fish per sample as suggested by Foumier and
Archibald (1982). This practice implicitly treats composition data from a lightly sampled stock
as being the same quality as data from a heavily sampled stock, ignoring the high possibility
that the latter are more accurate than the former. The relative size of ageing error variances can
be critical for inference, in which case, the use of a subjective factor is inappropriate (Myers
and Cadigan 1995a).
The Stock Synthesis assumes that the errors associated with the catch data (total
weight of fish caught) are much less than those associated with other data types such as age
composition or survey indices of abundance. Although actual landings data are reasonably
accurate for many fisheries, the data for the discarded portion of the total catch are usually a
rough guess. For some fisheries, the discarded portion can be substantial (Pikitch et al.1988),
with the result that the errors in estimates of total catch data can be considerable. In addition,
the predicted catch biomass depends on the assumed values for average weight-at-age, which
are also subject to errors.
Like other modern age-structured models, the Stock Synthesis Program separates each
coefficient of fishing mortality at age into a time-specific factor (the rate of fishing mortality
on the fully exploited age classes) and an age-specific factor (a selectivity coefficient that
measures the relative vulnerability of the particular age class). In addition, the selectivity
coefficients are often assumed to be constant through time. Sampson (1993) has shown that
the assumption of constant selectivity, which is assumed in many applications of the Stock
Synthesis model, can result in seriously biased estimates of stock size. Also, research survey
data, which are often used for 'tuning" the catch-at-age analysis, can be highly variable
(Sampson and Stewart 1994). The possibility that errors in survey data will be inflated by the
Stock Synthesis needs to be explored.
1.4 Research Objectives
The research described in this thesis evaluated the influence of random sampling
errors in fishery and survey data on the accuracy of stock assessment estimates from the Stock
Synthesis program. In addition, a stock assessment with Synthesis applied to an example
commercial fishery was simulated under various scenarios to find ways for improving the
accuracy of the estimates from Synthesis.
10
In chapter two, I use Monte Carlo simulation to evaluate the sensitivity of the Stock
Synthesis program on populations with simple multinomial age compositions. More
specifically, I evaluate the impacts of input data errors and stock characteristics on the
accuracy and precision of Synthesis estimates. Factors examined include the length of the data
time series, the rate of natural mortality, the fishery and survey selectivity curves, the trend in
the rate of fishing mortality, the recruitment pattern, and errors in observed annual catch,
fishing effort, fishery and survey age composition, and survey biomass indices.
In chapter three, I focus on populations with compound multinomial age composition
and conduct simulation experiments similar to those used in chapter two. By comparing the
results with those from chapter two, I measure differences in Synthesis's performance with
populations having different error structure for the age composition data. The comparison also
measures the robustness of Synthesis with regard to violation of the assumed error structure,
since compound multinomial age composition is not the distribution assumed in Stock
Synthesis.
In chapter four, I take an actual stock assessment of yellowfin sole
(Limanda aspera)
as a case study. I use simulation to evaluate whether more accurate assessment results could be
achieved from a better balance in the amount of sampling effort allocated to age composition
data versus survey biomass estimates.
The experiments in chapters two, three and four all involve large amounts of
simulation. To get the necessary tools for the experiments, I developed a simulation package
consisting of three of C++ programs: the Stock Definer, the Data Simulator, and the Statistical
Analyzer. A fishery system of interest can be specified with the Stock Definer program. The
Data Simulator simulates the dynamics of the fishery system and produces auxiliary data used
by the Stock Synthesis program. The Statistical Analyzer summarizes the output data
produced by the Stock Synthesis program. In addition, I also created some utility programs
that generated batch commands to automate the running of any particular experiment. Details
of the simulation package are in Appendix B.
12
Chapter Two: Sensitivity of the Stock Synthesis Program on Populations with Simple
Multinomial Age Compositions
2.1 Introduction Simple Multinomial Age Composition and Stock Synthesis
The Stock Synthesis program (Methot 1990, 2000) incorporates diverse information
and attempts to reconstruct both the dynamics of an exploited fish population and the
processes by which we observe the population and its fishery. A major strength of Stock
Synthesis is its ability to accommodate input data from multiple sources having different
degrees of uncertainty. For example, this model can simultaneously analyze data on catch
biomass, age composition, stock abundance, and fishing effort, each of which might be from
different sources and is subject to different levels of error.
Since the Stock Synthesis model takes data from multiple sources and analyzes them
simultaneously, estimates from Synthesis may be subject to the errors and the structures of
these diverse data sources. Based on the analysis of the dynamics of an age-structured
population, the model might also be sensitive to the biology of the fish stock and the
characteristics of the fishery. For example, data for total annual catch, fishery age
composition, fishing effort, and survey indices of abundance are all subject to observation
errors and may have different length of time series. Different fisheries may have different
fishing intensity on their fish stocks; some fish species may grow slowly and live longer and
others might grow fast and have a shorter life span. Determining the impact of these various
factors on the accuracy of Stock Synthesis estimates will let us better understand the
performance of Synthesis under various scenarios and help identify which inputs were most in
13
need of improvement. The results may also serve as references for analysis and improvements
on other age-structured models that use a similar integrated approach as the Stock Synthesis.
In this study we evaluated the sensitivity of the Stock Synthesis program applied to
populations for which the age composition data follow simple multinomial distributions as
assumed by the Stock Synthesis program. With this distribution, the greatest relative accuracy
occurs in the most frequently caught age classes and the variances of the age composition data
within and among years are determined by the size of each annual age composition sample.
We used Monte Carlo simulation (Rubinstein 1981) to determine the impacts of input data
errors and stock characteristics on the accuracy and precision of Synthesis estimates.
2.2 Methods
The brute-force approach we used in this simulation study is relatively straightforward:
we defined a stock and its fishery with known characteristics, generated random data sets
based on the defined fishery system, analyzed the data sets with Synthesis, and then compared
the estimates from Synthesis with the true values.
2.2.1 Software Tools
We created a simulation package (Appendix B) to be used as the tools for this study.
Our package consists of three C++ programs, namely the Stock Definer, the Data Simulator,
and the Statistical Analyzer. A fishery system of our interest can be specified with the Stock
Definer program. The Data Simulator program simulates the dynamics of a fishery system
and produces the random data used by the Stock Synthesis program. The Statistical Analyzer
14
program summarizes the output data produced by the Stock Synthesis program and compares
them with the true values.
A typical fishery system that can be specified with the Stock Definer is composed of a
fish stock, a fishery operating on the stock, a survey monitoring the status of the stock, and a
series of sampling activities conducted by fisheries scientists. The definition of a fish stock
involves the specification of parameters that define the biological traits of the fish stock, e.g.,
average weight-at-age, maturity-at-age, natural mortality, recruitment, and etc. The Stock
Definer also allows one to quantify the parameters that define the processes by which we
observe the stock and its fishery, e.g., fishing mortality, catchability, fishery selectivity, survey
selectivity, sampling frequency and sample size both for the fishery and the survey. The end
result of the Stock Definer is a text file used as the input to the Data Simulator prgram.
Both deterministic and non-deterministic (stochastic) methods are used by the Data
Simulator in the simulation of a fishery system. The deterministic method simulates the
dynamics of an age-structured fish population using the same deterministic equations that
underlie Methot's Stock Synthesis program (described in Chapter one). The stochastic method
takes the true demographic data produced by the deterministic method and generates random
data sets that can be analyzed directly by the Stock Synthesis program. The expected values
for the random data sets are the same as given by the deterministic equations.
The Statistical Analyzer program scans the output files of Synthesis and summarizes
the Synthesis estimates into a series of statistics. It then compare these statistics with their
corresponding true values and generates comparison results that reflect the relative accuracy
and precision of Synthesis's estimates.
The production, testing, and debugging of the simulation package was a very involved
process. Appendix B provides further details about the design, implementation, and
documentation of the simulation package.
15
2.2.2 Simulation and Stock Synthesis Configurations for this Stuy
The hypothetical fish stocks used in this study were all configured to have simple
multinomial age composition and their corresponding sampling processes all follow the
multinomial distribution. The age composition data for both fishery and survey were generated
without age-reading error. The age composition data were inaccurate only because of the
random sampling process and not because of incorrect age determinations. The Stock
Synthesis program was then configured to treat age composition data in accord with the way
they were generated (with multinomial sampling error but without age-reading error).Many
aspects of the data configurations were also used with the data generated for the experiments
in the next chapters. These shared data features are summarized in Appendix C.
2.2.3 Experimental Desigp
Our study simultaneously examined the effects of nine factors on the performance of
the Stock Synthesis program through an experiment created with a fractional factorial design.
Random data sets were generated in accordance with a one-fourth fraction of the 2 factorial
design (Table 2.1).
For each of the 128 experimental treatments, we applied the Data Simulator four times,
each time generating 200 replicate data sets that were analyzed with Stock Synthesis. We used
the term batch to describe each of these four collections of 200 data sets. Actually, all 800
data sets within the four batches were replicates because they were based on the same true
values and generated with the same degrees of random error. For example, the observed catch
data for each year were all based on the same true catch data and randomly generated with
16
Table 2.1. Fractional factorial experimental design. The factors are described in the text and in
Table 2.2.
Treatment NumYrs SmplSize EffortCV SurvCV NatlMort FishMort CatchCV FishSel
1
8
100
20%
20%
0.2
0.01
10%
dome
2
16
100
20%
20%
0.2
0.01
10%
asym
3
8
400
20%
20%
0.2
0.01
10%
dome
4
16
400
20%
20%
0.2
0.01
10%
asym
5
8
100
80%
20%
0.2
0.01
10%
asym
6
16
100
80%
20%
0.2
0.01
10%
dome
7
8
400
80%
20%
0.2
0.01
10%
asym
8
16
400
80%
20%
0.2
0.01
10%
dome
9
8
100
20%
80%
0.2
0.01
10%
asym
10
11
12
13
14
15
16
17
18
19
20
16
8
16
8
16
8
16
8
16
8
16
21
8
22
23
24
25
26
27
28
29
30
16
8
16
8
16
8
16
8
16
31
8
32
33
16
34
16
8
35
8
36
16
37
8
38
39
40
16
8
16
41
8
42
16
8
43
44
45
100
400
400
100
100
400
400
100
100
400
400
100
100
400
400
100
100
400
400
100
100
400
400
100
100
400
400
100
100
400
400
100
100
16
400
400
8
100
20%
20%
20%
80%
80%
80%
80%
20%
20%
20%
20%
80%
80%
80%
80%
20%
20%
20%
20%
80%
80%
80%
80%
20%
20%
20%
20%
80%
80%
80%
80%
20%
20%
20%
20%
80%
80%
80%
80%
80%
80%
80%
80%
20%
20%
20%
20%
20%
20%
20%
20%
80%
80%
80%
80%
80%
80%
80%
80%
20%
20%
20%
20%
20%
20%
20%
20%
80%
80%
80%
80%
80%
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
dome
asym
dome
dome
asym
dome
asym
dome
asym
dome
asym
asym
dome
asym
dome
asym
dome
asym
dome
dome
asym
dome
asym
asym
dome
asym
dome
dome
asym
dome
asym
dome
asym
dome
asym
asym
RecVar
const
const
van
van
van
van
const
const
const
const
van
van
van
van
const
const
van
van
const
const
const
const
van
van
van
van
const
const
const
const
van
van
van
van
const
const
const
const
van
van
van
van
const
const
const
17
Table 2.1 (continued)
Treatment NumYrs SmplSize EffortCV SurvCV NatiMort FishMort CatchCV FishSel RecVar
46
16
100
80%
80%
0.2
0.03
10%
dome
const
47
8
400
80%
80%
0.2
0.03
10%
asym
van
48
16
400
80%
80%
0.2
0.03
10%
dome
van
49
8
100
20%
20%
0.4
0.03
10%
asym
const
50
16
100
20%
20%
0.4
0.03
10%
dome
const
51
8
400
20%
20%
0.4
0.03
10%
asym
van
52
53
54
55
56
57
16
400
8
100
100
58
59
60
16
16
400
400
61
62
63
8
16
100
100
8
64
65
66
67
68
69
70
16
400
400
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
16
8
16
8
8
8
16
8
16
8
16
100
100
100
100
400
400
100
100
8
16
400
400
8
100
100
16
8
16
8
16
8
16
8
16
8
16
8
16
8
16
89
8
90
16
8
91
400
400
400
400
100
100
400
400
100
100
400
400
100
100
400
400
100
100
400
20%
80%
80%
80%
80%
20%
20%
20%
20%
80%
80%
80%
80%
20%
20%
20%
20%
80%
80%
80%
80%
20%
20%
20%
20%
80%
80%
80%
80%
20%
20%
20%
20%
80%
80%
80%
80%
20%
20%
20%
20%
20%
20%
20%
20%
80%
80%
80%
80%
80%
80%
80%
80%
20%
20%
20%
20%
20%
20%
20%
20%
80%
80%
80%
80%
80%
80%
80%
80%
20%
20%
20%
20%
20%
20%
20%
20%
80%
80%
80%
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.4
0.4
0,4
0.4
0.4
0.4
0.4
0.4
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
dome
dome
asym
dome
asym
dome
asym
dome
asym
asym
dome
asym
dome
asym
dome
asym
dome
dome
asym
dome
asym
dome
asym
dome
asym
asym
dome
asym
dome
asym
dome
asym
dome
dome
asym
dome
asym
dome
asym
dome
van
van
van
const
const
const
const
van
van
van
van
const
const
van
van
const
const
const
const
van
van
van
van
const
const
const
const
van
van
const
const
van
van
van
van
const
const
const
const
van
18
Table 2.1 (continued)
Treatment NumYrs SmplSize EffortCV SurvCV NatiMort FishMort CatchCV FishSel RecVar
92
16
400
20%
80%
0.4
0.01
20%
asym
van
93
8
100
80%
80%
0.4
0.01
20%
asym
van
94
16
100
80%
80%
0.4
0.01
20%
dome
van
8
95
400
80%
80%
0.4
0.01
20%
asym
const
96
16
400
80%
80%
0.4
0.01
20%
dome
const
97
8
100
20%
20%
0.2
0.03
20%
dome
const
98
16
100
20%
20%
0.2
0.03
20%
asym
const
99
8
400
20%
20%
0.2
0.03
20% dome
van
100
16
400
20%
20%
0.2
0.03
20%
asym
van
101
8
100
80%
20%
0.2
0.03
20%
asym
van
102
103
104
105
106
107
108
109
110
16
100
8
400
400
16
8
16
100
100
16
400
400
8
16
100
100
8
111
8
112
113
114
115
116
117
118
119
120
16
121
8
122
123
124
125
126
127
128
16
8
16
400
400
100
100
16
400
400
8
16
100
100
8
8
16
8
16
8
16
8
16
400
400
100
100
400
400
100
100
400
400
80%
80%
80%
20%
20%
20%
20%
80%
80%
80%
80%
20%
20%
20%
20%
80%
80%
80%
80%
20%
20%
20%
20%
80%
80%
80%
80%
20%
20%
20%
80%
80%
80%
80%
80%
80%
80%
80%
20%
20%
20%
20%
20%
20%
20%
20%
80%
80%
80%
80%
80%
80%
80%
80%
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
dome
asym
dome
asym
dome
asym
dome
dome
asym
dome
asym
dome
asym
dome
asym
asym
dome
asym
dome
asym
dome
asym
dome
dome
asym
dome
asym
van
const
const
const
const
van
van
van
van
const
const
van
van
const
const
const
const
van
van
van
van
const
const
const
const
van
van
same CV (coefficient of variation) following lognormal distributions; The fishery age
composition data were all generated as simple multinomial random variables based on the true
catch-at-age proportions and the same sample size as defined at each treatment. We used four
batches of 200 rather than one batch of 800 to produce "replicates" for sample summary
19
statistics and to make our analysis better conforms to the ANOVA assumptions. For example,
the average values of the 200 replicates should be fairly normally distributed even though the
individual replicate values are not.
The nine controlling variables (Table 2.2) were: (I) the number of years in the data
series (NumYrs); (2) the size of annual age composition samples (SmplSize); (3) the
coefficient of variation for the annual fishing effort data (EffortCV); (4) the coefficient of
variation for the annual survey biomass data (SurvCV); (5) the instantaneous rate of natural
mortality (NatMort); (6) the annual increment in the rate of fishing mortality (FishMort); (7)
the coefficient of variation for the annual catch data (CatchCV); (8) fishery selectivity
(FishSel); and (9) annual recruitment (RecVar).
Table 2.2 Configurations of the low vs. high levels for the nine controlling variables.
Name
NumYrs
SmplSize
EffortCV
SurvCV
NatMort
FishMort
CatchCV
FishSel
RecVar
Factor
Description
number of years of data.
sample size for age composition.
fishing effort variability.
survey biomass variability.
natural mortality increment.
fishing mortality.
catch data variability.
fishery selectivity,
recruitment variability,
Value Configuration
at low level (-1)
at high level (+1)
8
16
100
400
20%
20%
0.2
0.01
10%
dome shaped
constant
80%
80%
0.4
0.03
20%
asymptotic shaped
variable
The level of natural mortality was also associated with several other stock parameters.
When natural mortality M was at the low value of 0.2/yr, the stock was long-lived, and the
initial and terminal age classes were 4 and 20 years. When M was at the high value of 0.4/yr,
the stock was short-lived, and the initial and terminal age classes were 2 and 10 years. The
20
maturity-at-age curve for the short-lived fish is steeper than that for the long-lived one and
shifted towards younger ages (Figure 2.1).
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
1
2
4
3
5
6
7
8
10
9
Age (yr)
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Age (yr)
Figure 2.1 The maturity at age schedule for the simulated stocks: (a) the short-lived stock (M
=0.4/yr), where the slope is at 2.0 and the inflection age is at 3. (b) the long-lived stock
(M0.2/yr), where the slope is at 1.0 and the inflection age is at 5.
100%
.
U
10%
0%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
2
3
4
5
6
7
8
9
10
4
6
8
10
Age (yr)
12
14
16
18
20
14
16
18
20
Age (yr)
100%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
.'
.
.
U)
0%
2
3
4
5
6
7
Age (yr)
8
9
10
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
4
6
8
10
12
Age (yr)
Figure 2.2. The configuration for fishery and survey selectivity. The selectivity curve was defined by a double logistic function. The four
parameters of the function are: a], the 1st inflection age; bi, the Vt slope; a2, the 2 inflection age; b2, the 2' slope. Configurations for both
levels of natural mortality (M) are listed here: (a) fishery selectivity when M = 0.4, where a] = 4.0, bi = 1.0, a2 = 8.0, b2 = 1.0 for the domeshaped, and a]4.0, b]1.0, b20.0 for the asymptotic curve; (b) fishery selectivity when M = 0.2, where a] = 6.0, b] = 1.0, a2 = 16.0, b2 =
1.0 for the dome-shaped, and a] = 6.0, bi = 1.0, b2 = 0.0 for the asymptotic curve; (c) survey selectivity when M = 0.4, where a1 3.0, bi =
1.5, b2 = 0.0; (d) survey selectivity when M = 0.2, where a] = 5.0, bi = 1.5, b2 = 0.
22
3500
0
0
(a)
3000 1r
2500
'oLj1r1r
7
8
9
10
11
12
13
14
15
16
17
18
19
20+
Age (yr)
4000
0
(b)
3500
3000
2500
2000
0
1500
1000
____ ____
500
0
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Age (yr)
Figure 2.3. Initial age composition for M = 0.2. (a) constant recruitment. (b) variable
recruitment
20-'-
23
3500
(a)
3000
2500
2000
o 1500
1
I
0____I
2
3
4
5
6
8
7
9
10+
Age (yr)
4000
0
(b)
3500 1
3000
- 2500
2000
1500
1000
500
r
ol
2
3
4
I__I
6
7
8
Age (yr)
Figure 2.4 Initial age composition for M = 0.4. (a) constant recruitment. (b) variable
recruitment
24
The coefficients for the selectivity relationships also depend on the level of natural mortality.
When M was 0.4/yr, the true ascending and descending inflection ages for the fishery selection
function were 4 and 8 years, and the true ascending inflection age for the survey selection
function was 3 years. When M was 0.2/yr, the true ascending and descending inflection ages
for the fishery selection function were 6 and 16 years, and the true ascending inflection age for
the survey selection function was 5 years. The shape of the selectivity curve for the survey was
always asymptotic, but the selectivity curve for the fishery was either "domed" or asymptotic
(Figure 2.2).
The two types of recruitment we used were constant versus variable recruitment. For
simulations with constant recruitment, the annual recruitment was 3,000 fish (in thousands)
and the initial age composition at the start of the first year was at equilibrium. The Stock
Synthesis was then configured to estimate the initial equilibrium age composition. Equilibrium
here means the age composition would not change from year to year because survival and
recruitment had been constant for a sufficiently long period. In an unexploited stock, for
example, the number of age i fish
(N1)
in the equilibrium age composition simply follows a
exponential decay function of the form of
N = 3000 exp (-i M), where M is the instantaneous natural mortality. For simulations with
variable recruitment, the average annual recruitment was also 3,000 fish, but the annual
recruitment values varied with the sequence of 3,500, 4,000, 1,200, 4,200, 3,000, 3,200, 1,700,
3,200 (repeat if necessary). The Stock Synthesis program was then configured to estimate the
initial non-equilibrium age composition (Figure 2.3, 2.4).
Even though we used a fractional factorial design, all nine main effects were
separately estimable (Table 2.3) in our experiment, assuming that fifth and higher order
interactions were zero. In other words, none of the main effects were "aliased" with any fourth
and lower order interactions. However, the interactions were not separately estimable. For
25
example, the two way interaction between the number of years and the sample size was
"aliased" with the four way interaction among survey biomass variabilityx natural mortality
x
fishery selectivity x recruitment variability, meaning the value estimated for the two way
interaction included the value for the four way interaction (Box et al. 1978). Usually one
would expect high-order interactions to be small relative to low-order interactions.
The Stock Synthesis program routinely produces a wide variety of estimates, e.g.,
estimates for the annual series of biomass, fishing mortality, catch, and recruitment In this
study we focused on seven categories of Synthesis outputs. These outputs include the
estimates for the first year for total biomass, the estimates for the last year for total biomass,
exploitable biomass, rate of fishing mortality, recruitment, the ratio of the total biomass for the
last year versus the total biomass for the first year, and the
F35%
catch.
F35%
is defined as the
value of fishing mortality that would reduce the spawning stock biomass per recruit to 35% of
the level that would exist with no fishing. The F35% catch is the predicted catch biomass when
F35%
is applied to a stock. For each experimental treatment and output type, we calculated the
relative bias and relative variability for each of the four batches (each batch contained 200 data
sets). We measured relative bias both in the forms of relative bias of the mean and relative bias
of the median. The relative bias of the mean within each batch of 200 estimates was defined as:
1
(estimatedvalue1
200L
truevalue
(1)
J
The relative bias of the median within each batch of 200 estimates was defined as:
The median of the 200 estimated values true value
true value
We calculated the median as the average of the
100th
(2)
and 101st ordered values. The relative
variability within each batch of 200 estimates was measured using the coefficient of variation.
We summarized the results for each experimental treatment by calculating the mean relative
26
Table 2.3. Alias structure of the fractional factorial design
Alias Structure* (up to order 4)
A: NumYr, B: SmplSize, C: EffortCV, D: SurvCV, E: NatMort, F: FishMort, G: CatchCV,
H: FishSel, J: RecVar
Grand mean
A
B
C
D
E
F
G
H
J
AB + DEHJ
AC + DFGH
AD + BEHJ + CFGH
AE + BDHJ
AF + CDGH
AG + CDFH
AH + BDEJ + CDFG
AJ + BDEH
BC + EFGJ
BD + AEHJ
BE + ADHJ + CFGJ
BF + CEGJ
BG + CEFJ
BH + ADEJ
BJ + ADEH + CEFG
CD + AFGH
CE + BFGJ
CF + ADGH + BEGJ
CG + ADFH + BEFJ
CH+ADFG
CJ + BEFG
DE + ABHJ
DF + ACGH
DG + ACFH
DH + ABEJ + ACFG
Di + ABEH
EF + BCGJ
EG + BCFJ
EH + ABDJ
EJ + ABDH + BCFG
FG + ACDH + BCEJ
FH+ACDG
FJ + BCEG
GH + ACDF
GJ + BCEF
HJ + ABDE
*The main effects are ahased with
5th
and higher order interactions, which are assumed 0.
27
bias and mean coefficient of variation across the four batches. Bias and variation are the two
components of the mean squared error (MSE), which is one commonly used measure of
accuracy,
MSE = av [(X- trueX)2 ] = bias2
For each of the
21
+
variance.
(3).
measurements, we conducted a separate fractional analysis of variance
using the Minitab statistics program (Release 13.1 for Windows).
2.2.4
Sensitivity to Initial Parameter Values
In the main experiment, we used the true values as the initial parameter values.
However, likelihood functions can have multiple maxima, thus the choice of initial parameter
values may influence whether or not the search algorithm actually finds a local rather than the
global maximum. For a given data set, Synthesis users sometimes randomize the initial
parameter values many times and choose the results from the run that produces the maximum
likelihood value. To examine the influence of initial parameter values on the performance of
Synthesis, we conducted a randomization experiment on treatment 36 and treatment 109. In
the main experiment, treatment 36 had the best result in terms of minimum relative bias and
relative variability for the estimate of ending biomass. Its relative bias was only
relative variability (CV) was 0.098. Treatment
109,
0.002
and the
on the other hand, had the worst results for
the estimate of ending biomass. Its relative bias was 0.440 and the relative variability was
0.749.
In the randomization experiment, for each of the two treatments (treatment 36 and
treatment
109),
we generated 100 random data sets. For each random data set generated, we
ran the Stock Synthesis program 100 times, each time using a different set of randomized
initial parameter values, with each parameter varying uniformly within ± 40% of its true value.
28
Table 2.4. Relative bias for the 128 experimental treatments.
Treatment end Bio end F end Rec
1
0.1394
0.0121
0.1669
2
0.0081
0.0204 0.0267
3
0.0971 -0.0075
0.1154
4
0.0121
0.0096 0.0206
5
0.2132 0.0513 0.2558
0.0485
6
0.0073
0.0387
7
0.0969 0.0270 0.1216
8
0.0171
0.0150 0.0208
9
0.1732 0.0828 0.2144
10
0.0174 0.0359 0.0052
11
0.0840 0.0760 0.1124
12
0.0110 0.0043 0.0115
13
0.4270 0.0199 0.4778
14
0.1822 0.1019
0.2299
15
0.0626 0.0286 0.0842
16
0.0685 0.0707 0.0951
17
0.1104 0.1324 0.1323
18
0.0388 0.0091
0.0589
19
0.0816 0.0448 0.0876
20
0.0080 0.0070 0.0156
21
0.1855
0.1023 0.2422
22
0.0660 0.0367 0.0753
23
0.0540 0.1057 0.0732
24
0.0277 0.0233 0.0302
25
0.1480 0.1290 0.1690
26 0.0516
0.0437 0.0358
27
0.0823
0.0639 0.0943
28
0.0329
0.0098 0.0358
29
0.1118 0.4818 0.1409
30 0.1114 0.1476 0.1508
31
0.0547 0.1705
0.0678
32
0.1075 0.0206 0.1290
33
0.0393
0.0305
0.0487
34 -0.0088 0.0513 -0.0052
35
0.0325 0.0113 0.0410
36
0.0017 0.0115 -0.0003
37
0.1053 0.0199 0.1390
38
0.0155 0.0029 0.0142
39
0.0501
0.0093 0.0627
40
0.0061
0.0121
0.0070
41
0.1163 0.0230 0.1512
42
0.0188 0.0146 0.0264
43
0.0207 0.0103
0.0305
44 0.0023
0.0186 0.0104
45
0.3667
0.2395
0.5099
46 -0.0244
0.1689 -0.0273
start Bio end exB
0.0866 0.1268
0.0013
0.0042
0.0600
0.0907
0.0016 0.0104
0.1107
0.2004
0.0373
0.0437
0.0493 0.0910
0.0060 0.0141
0.0859 0.1602
0.0151
0.0093
0.0393
0.0764
0.0084
0.0094
0.2772 0.4077
0.0288
0.1721
0.0383
0.0607
0.0083 0.0626
0.0931
0.1152
0.0196 0.0410
0.0547 0.0830
0.0025
0.0064
0.1079 0.1778
0.0537 0.0706
0.0276
0.0484
0.0093
0.0288
0.0885
0.1448
0.0577
0.0569
0.0460 0.0813
0.0146 0.0337
0.0759 0.1178
0.0214 0.1062
0.0308
0.0547
0.0179 0.1040
0.0118
0.0296
0.0113 -0.0135
0.0113
0.0308
0.0000 0.0003
0.0508 0.0960
0.0018
0.0174
0.0212
0.0460
0.0002
0.0063
0.0604 0.1017
0.0072
0.0203
0.0084
0.0174
0.0008
0.0028
0.1151
0.3304
-0.0047 -0.0279
F35 catch endB/startB
0.1530
0.0241
0.0066
0.0057
0.1068
0.0140
0.0127
0.0089
0.2364
0.0373
0.0524
0.0043
0.1074
0.0168
0.0173
0.0085
0.1910
0.0217
0.0184
-0.0024
0.0945
0.0025
0.0130
-0.0006
0.4646
0.0427
0.2073
0.1163
0.0677
0.0056
0.0775
0.0421
0.1116
-0.0059
-0.0082
0.0189
0.0863
0.0007
0.0096
0.0040
0.0565
0.0207
0.0642
0.0027
0.0489
-0.0055
0.0297
0.0124
-0.0091
0.0477
0.0876
0.0360
0.1172
0.0720
0.0605
0.1241
0.0476
-0.0097
0.0385
0.0034
0.1297
0.0231
0.0607
0.0093
0.1387
0.0222
0.0263
0.0018
0.4423
-0.0271
0.0081
-0.0123
0.0003
0.0114
-0.0413
0.0633
-0.0124
0.0730
0.0171
-0.0193
0.0117
0.0018
0.0315
0.0142
0.0182
0.0063
0.0273
0.0129
0.0064
0.0021
0.0923
-0.0226
29
Table 2.4. (continued)
Treatment end Bio
end F
end Rec
start Bio end exB
47
0.1878
0.1065
0.2539
0.0578
0.1712
0.2290
0.0521
48
0.0047
0.0295
0.0070
0.0031
0.0027
0.0075
0.0007
49
0.0527
0.0381
0.0637
0.0238
0.0498
-0.0593
0.0186
50
0.0059
0.0246
0.0013
0.0160
0.0123
0.0046
-0.0076
51
0.0242
0.0292
0.0362
0.0094
0.0225
0.0229
0.0046
52
0.0097
0.0099
0.0136
0.0018
0.0103
0.0104
0.0087
53
0.0914
0.1101
0.0831
0.0648
0.1023
0.0983
0.0013
54
0.0234
0.0098
0.0362
0.0219
0.0333
-0.0009
0.0039
55
0.0683
0.0197
0.0763
0.0393
0.0714
0.0758
0.01 17
56
0.0162
0.0037
0.0224
0.0021
0.0174
0.0209
0.0145
57
0.1250
0.0840
0.1340
0.0809
0.1315
0.1330
0.0094
58
0.0313
-0.0014
0.0425
0.0177
0.0419
0.0083
0.0159
59
0.0433
0.0535
0.0574
0.0222
0.0447
0.0506
0.0019
60
0.0153
0.0123
0.0200
-0.0025
0.0139
0.0180
0.0194
61
0.2846
0.3072
0.3940
0.0943
0.2504
0.0942
0.0668
62
-0.0068
0.2324
-0.0168
0.0287
0.0051
-0.0118
-0.0401
63
0.1373
0.0824
0.1682
0.0534
0.1353
0.1608
0.0278
64
0.0223
0.0408
0.0289
0.0023
0.0232
0.0272
0.0190
65
0.1632
0.0050
0.2258
0.0847
0.1530
0.1772
0.0336
66
0.0356
0.0011
0.0498
0.0320
0.0264
0.0368
-0.0010
67
0.1190
-0.0107
0.1334
0.0608
0.1170
0.1298
0.0279
68
0.0163
0.0080
0.0168
0.0033
0.0149
0.0172
0.0111
69
0.1948
0.0363
0.2622
0.1164
0.1786
0.2119
0.0347
70
0.0301
0.0222
0.0415
0.0092
0.0296
0.0318
0.0173
71
0.1023
0.0126
0.1273
0.0625
0.0981
0.1119
0.0123
72
0.0239
0.0092
0.0365
0.0002
0.0212
0.0271
0.0212
73
0.4026
-0.0234
0.4840
0.2566
0.3772
0.4360
0.0448
74
0.0443
0.0034
0.0773
0.0098
0.0389
0.0479
0.0301
75
0.0795
-0.0153
0.0995
0.0469
0.0781
0.0870
0.0143
76
0.0337
-0.0033
0.0413
0.0057
0.0322
0.0396
0.0234
77
0.3291
0.4752
0.4259
0.1649
0.3074
0.3647
-0.0085
F35
catch endB/startl3
78
0.0279
0.1267
0.0463
0.0175
0.0153
0.0271
-0.0068
79
0.0776
0.2601
0.1091
0.0371
0.0702
0.0860
-0.0279
80
0.0358
0.0004
0.0400
0.0144
0.0361
0.0419
0.0154
81
0.1549
0.0519
0.1705
0.1037
0.1591
0.0516
0.0093
82
0.0770
0.0002
0.0606
0.0659
0.0843
0.073 1
0.0036
83
0.0932
0.0417
0.1034
0.0538
0.0933
0.0989
0.0041
84
0.0361
-0.0126
0.0417
0.0123
0.0363
0.0389
0.0189
85
0.1389
0.1917
0.1520
0.1086
0.1456
0.1448
-0.0073
86
0.0353
0.0362
0.0445
0.0155
0.0379
0.0054
0.0174
87
0.1146
0.0266
0.1143
0.0780
0.1165
0.1231
0.0064
88
0.0129
0.0263
0.0227
0.0055
0.0127
0.0135
0.0039
89
0.2251
0.1921
0.2489
0.1724
0.2283
0.2287
-0.0166
90
0.0484
0.0149
0.0588
0.0182
0.0500
0.0264
0.0256
91
0.1035
0.1102
0.1180
0.0626
0.1045
0.1114
-0.0044
92
0.0368
-0.0005
0.0379
0.0094
0.0362
0.0435
0.0232
30
Table 2.4. (continued)
Treatment end Bio
end F
end Rec
start Bio end ex1
93
0.1485
0.5525
0.2091
0.0728
0.1316
-0.0630
-0.0260
94
0.1143
0.2083
0.1150
0.0712
0.1207
0.1209
-0.0015
95
0.1275
0.1780
0.1583
0.0667
0.1224
0.1348
-0.0097
96
0.0563
0.0588
0.0573
0.0198
0.0563
0.0619
0.0174
97
0.0584
0.0270
0.0831
0.0264
0.0460
0.0699
0.0178
98
0.0144
-0.0032
0.0176
0.0066
0.0180
0.0171
0.0107
99
0.0533
-0.0028
0.0659
0.0257
0.0498
0.0622
0.0 175
100
0.0120
-0.0074
0.0146
-0.0020
0.0098
0.0175
0.0165
101
0.0952
0.0379
0.1420
0.0300
0.0840
0.1104
0.0420
102
-0.0039
0.0706
0.0047
0.0127
-0.0082
-0.0020
-0.0169
103
0.0443
0.0360
0.0558
0.0136
0.0413
0.0527
0.0153
104
0.0101
0.0129
0.0141
0.0046
0.0089
0.0135
0.0058
105
0.1436
0.0289
0.2046
0.0489
0.1324
0.1657
0.0490
106
-0.0070
0.0610
0.0172
0.0014
-0.0143
-0.0090
-0.0067
107
0.1262
0.0117
0.1625
0.0423
0.1178
0.1509
0.0440
108
0.0068
0.0018
0.0094
0.0004
0.0051
0.0122
0.0074
109
0.4402
0.0252
0.5803
0.2063
0.4266
0.5257
0.0991
110
0.0884
0.0965
0.1078
0.0138
0.0848
0.1167
0.0760
111
0.0500
0.0050
0.0644
0.0202
0.0461
0.0619
0.0213
112
0.0184
0.0447
0.0262
0.0033
0.0172
0.0264
0.0177
113
0.1314
0.0317
0.1295
0.1075
0.1436
0.1323
0.0016
114
0.0289
-0.0236
0.0340
0.0216
0.0385
0.0106
0.0121
115
0.0427
0.0032
0.0478
0.0220
0.0448
0.0508
0.0064
116
0.0139
-0.0025
0.0154
-0.0015
0.0140
0.0160
0.0177
117
0.0914
0.0448
0.1242
0.0387
0.0871
-0.0174
0.0289
118
0.0166
0.0201
0.0160
0.0263
0.0268
0.0172
-0.0081
119
0.0570
0.0289
0.0694
0.0213
0.0543
0.0578
0.0205
120
0.0216
0.0068
0.0246
0.0053
0.0222
0.0273
0.0167
121
0.1702
0.0396
0.2258
0.0691
0.1611
0.0301
0.0512
122
0.0185
0.0136
0.0261
0.0260
0.0272
0.0221
-0.0059
123
0.0914
0.0216
0.1108
0.0326
0.0872
0,1024
0.0271
124
0.0262
-0.0046
0.0307
0.0023
0.0282
0.0324
0.0255
125
0.2066
0.2819
0.2349
0.1164
0.2122
0.2345
-0.0001
126
0.1256
0.0605
0.1747
0.0208
0.1288
0.1297
0.1065
127
0.1264
0.0517
0.1522
0.0608
0.1294
0.1485
0.0247
128
0.0725
-0.0053
0.0922
-0.0004
0.0697
0.0971
0.0765
-0.0244
-0.0236
-0.0273
-0.0047
-0.0279
-0.0630
-0.0413
0.4402
0.5525
0.5803
0.2772
0.4266
0.5257
0.1163
0.0816
0.0586
0.1014
0.0413
0.0787
0.0791
0.0159
mm
max
average
F35
catch endB/startB
31
Table 2.5. Relative variability for the 128 experimental treatments.
Treatment end Bio
1
0.3980
2
0.1500
3
0.3399
4
0.1399
5
0.5763
6
0.2243
7
0.3669
8
0.1389
9
0.5945
10
0.2076
11
0.4526
12
0.1517
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
0.6831
0.5267
0.2951
0.3953
0.5770
0.2011
0.4101
0.1414
0.6158
0.3262
0.4109
0.2138
0.6060
0.3204
0.4155
0.2154
0.7388
0.4827
0.4449
0.3724
0.2438
0.1369
0.2163
0.0976
0.3359
0.1636
0.2172
0.1349
0.3726
0.1832
0.1690
0.1395
0.8276
0.2794
end F
0.3469
0.1813
0.2903
0.1566
0.4561
0.2605
0.3507
0.1797
0.4381
0.2327
0.3707
0.1786
0.6372
0.5673
0.3064
0.3650
0.4738
0.2384
0.3356
0.1699
0.4911
0.3459
0.3852
0.2532
0.4720
0.3249
0.3733
0.2383
0.7981
0.5498
0.4889
0.3745
0.2581
0.1790
0.2253
0.1414
0.3532
0.2130
0.2527
0.1843
0.3555
0.2071
0.1990
0.1681
0.7410
0.3578
end Rec
0.6141
0.3587
0.4266
0.2152
0.7922
0.3787
0.4575
0.2181
0.7379
0.3862
0.5370
0.2118
0.9004
0.6894
0.3903
0.4767
0.6380
0.3170
0.4407
0.1858
0.7398
0.4085
0.4818
0.2354
0.7106
0.3760
0.4785
0.2490
0.8714
0.6249
0.4971
0.4399
0.4383
0.2964
0.3116
0.1699
0.5417
0.3337
0.2915
0.1902
0.5278
0.3414
0.2533
0.2013
1.0586
0.4235
start I3io
0.2726
0.0610
0.2153
0.0371
0.3601
0.1150
0.2045
0.0517
0.3488
0.0955
0.2408
0.0553
0.4811
0.1014
0.1790
0.0653
0.4793
0.1421
0.2908
0.0619
0.4156
0.2341
0.2414
0.1219
0.4158
0.2399
0.2456
0.1094
0.5347
0.1448
0.3099
0.0823
0.1141
0.0601
0.0846
0.0341
0.1784
0.0456
0.1097
0.0338
0.2072
0.0479
0.0817
0.0311
0.3436
0.0570
end exB
0.4104
0.1505
0.3436
0.1376
0.5838
0.2372
0.3639
0.1425
0.5920
0.2150
0.4421
0.1570
0.6896
0.5144
0.3031
0.3824
0.5905
0.2266
0.4183
0.1465
0.6301
0.3363
0.4082
0.2175
0.6321
0.3282
0.4167
0.2182
0.7583
0.4881
0.4467
0.3650
0.2483
0.1381
0.2095
0.1007
0.3552
0.1561
0.2225
0.1293
0.3837
0.1744
0.1775
0.1315
0.7992
0.2930
f35 catch endB/startB
0.4331
0.1389
0.1657
0.1284
0.3709
0.1167
0.1558
0.1216
0.6172
0.1978
0.2478
0.1472
0.4009
0.1560
0.1622
0.1053
0.6488
0.2170
0.2328
0.1543
0.4983
0.1891
0.1736
0.1150
0.7318
0.2151
0.5912
0.4217
0.3316
0.1148
0.4496
0.3141
0.5877
0.1426
0.3228
0.1357
0.4341
0.1190
0.1569
0.1135
0.7937
0.2007
0.3405
0.1599
0.4696
0.1669
0.2331
0.1339
0.8401
0.2059
0.3303
0.1634
0.4523
0.1690
0.2348
0.1426
0.7911
0.2675
0.5917
0.3812
0.4794
0.1666
0.4256
0.3014
0.2860
0.1510
0.1721
0.1260
0.2526
0.1379
0.1262
0.0936
0.4035
0.1672
0.2035
0.1603
0.2633
0.1142
0.1755
0.1325
0.4352
0.1743
0.2248
0.1841
0.2082
0.0982
0.1721
0.1408
0.9509
0.4136
0.3812
0.2588
32
Table 2.5. (continued)
Treatment
47
48
49
50
51
52
53
54
55
56
57
58
end Bio
0.6301
0.1555
0.2714
0.1708
0.2384
0.1181
0.4878
0.1605
0.2918
0.1363
0.5059
0.1777
59
60
0.3279
0.1415
61
0.7931
0.3978
0.5120
0.2171
0.5261
0.2051
0.3600
0.1403
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
0.5070
0.2018
0.3789
0.1729
0.7315
0.2511
0.3070
0.2333
0.9104
0.3458
0.5855
0.1982
0.5770
0.3404
0.4307
0.2024
0.6171
0.2203
0.4100
0.1817
0.7852
0.2692
0.5293
0.2412
end F
0.5077
0.2074
0.2990
0.2165
0.2347
0.1586
0.4375
0.2368
0.3075
0.1874
0.4440
0.2262
0.3209
0.1717
0.7395
0.4972
0.4621
0.2760
0.3701
0.2689
0.3291
0.2269
0.4612
0.2944
0.3721
0.2687
0.5201
0.2623
0.2862
0.2518
0.9677
0.4188
0.6303
0.3019
0.4267
0.3335
0.3582
0.2298
0.5936
0.3233
0.4302
0.2797
0.5690
0.2989
0.4472
0.2604
end Rec
0.7593
0.2221
0.4166
0.2824
0.2970
0.1554
0.5514
0.2666
0.3288
0.1812
0.5546
0.2892
0.3635
0.1882
0.9715
0.5027
0.6119
0.2619
0.7048
0.3918
0.4380
0.2131
0.7127
0.3767
0.4527
0.2394
0.9404
0.4139
0.3991
0.2990
1.1204
0.5112
0.6760
0.2583
0.6798
0.3991
0.4874
0.2216
0.6694
0.3319
0.4403
0.2242
0.8735
0.3910
0.5714
0.2889
start Bio
0.2383
0.0390
0.1593
0.1256
0.1103
0.0706
0.3568
0.0855
0.1721
0.0425
0.3587
0.0808
0.2033
0.0460
0.3486
0.1390
0.2159
0.0607
0.3339
0.1109
0.2105
0.0667
0.3541
0.0783
0.2432
0.0616
0.5155
0.0779
0.1955
0.0603
0.5487
0.1243
0.3104
0.0767
0.4198
0.2730
0.2679
0.1242
0.4981
0.1420
0.2937
0.0775
0.6232
0.1359
0.3728
0.0814
end exB
0.6064
0.1591
0.2971
0.1822
0.2408
0.1215
0.5038
0.1746
0.2996
0.1386
0.5273
0.1898
0.3346
0.1406
0.7680
0.4060
0.5064
0.2199
0.5414
0.2108
0.3584
0.1455
0.5345
0.2009
0.3834
0.1694
0.7343
0.2467
0.3173
0.2267
0.9024
0.3588
0.5670
0.2050
0.6098
0.3460
0.4344
0.2057
0.6252
0.2404
0.4159
0.1853
0.7946
0.2817
0.5318
0.2397
f35 catch endB/startB
0.7387
0.3171
0.2086
0.1432
0.4876
0.1551
0.2074
0.1309
0.2905
0.1402
0.1464
0.1018
0.5284
0.1768
0.2630
0.1542
0.3336
0.1300
0.1753
0.1331
0.5465
0.1796
0.2728
0.1739
0.3702
0.1456
0.1781
0.1446
1.0352
0.5150
0.6030
0.2817
0.5592
0.2223
0.3871
0.1566
0.5474
0.2283
0.4173
0.1974
0.7734
0.2772
0.3345
0.2556
0.9821
0.3978
0.6494
0.2306
0.7335
0.3426
0.4664
0.2074
0.6493
0.3075
0.4363
0.2052
0.8124
0.3395
0.5613
0.2654
0.4251
0.3445
0.2667
0.2030
0.1789
0.1402
0.1488
0.1065
0.1566
0.1640
0.1266
0.1452
0.1990
0.2181
0.1090
0.2012
0.3486
0.2493
0.2582
0.1460
0.1763
0.1440
0.1659
0.1247
0.1781
0.1504
0.1288
0.1412
0.2103
0.2113
0.1663
0.2057
33
Table 25. (continued)
Treatment end Bio
end F
end Rec
start Bio
end exB
93
0.7282
0.9220
0.8758
0.4370
0.7215
0.9972
0.3512
94
0.5727
0.6532
0.6498
0.2954
0.5804
0.6238
0.3486
95
0.6040
0.5620
0.6878
0.3546
0.5941
0.6608
0.2313
96
0.3358
0.3920
0.3685
0.1430
0.3391
0.3712
0.2250
97
0.2838
0.2885
0.4606
0.1648
0.3097
0.3267
0.1496
98
0.1564
0.2131
0.3190
0.0679
0.1466
0.1727
0.1607
99
0.2221
0.2564
0.2991
0.1254
0.2251
0.2556
0.1154
100
0.1359
0.2095
0.1851
0.0592
0.1306
0.1551
0.1411
101
0.3534
0.3932
0.5282
0.1638
0.3571
0.4171
0.2014
102
0.1819
0.3139
0.3421
0.0782
0.1868
0.2424
0.1579
103
0.2806
0.3357
0.3735
0.1197
0.2717
0.3316
0.1734
104
0.1175
0.2486
0.1769
0.0588
0.1237
0.1580
0.1043
105
0.4753
0.3630
0.6935
0.1952
0.4655
0.5410
0.2714
106
0.1946
0.2364
0.3434
0.0719
0.1967
0.2287
0.1909
107
0.4279
0.3518
0.5413
0.1653
0.4085
0.4928
0.2538
108
0.1456
0.2047
0.2026
0.0596
0.1487
0.1704
0.1401
109
0.7491
0.6643
0.9524
0.4353
0.7823
0.8383
0.2772
110
0.4156
0.4915
0.5485
0.0694
0.3979
0.5274
0.4139
111
0.2056
0.3070
0.2928
0.1156
0.2154
0.2528
0.1080
112
0.2615
0.3236
0.3354
0.0601
0.2472
0.3247
0.2639
113
0.4787
0.4185
0.4978
0.3759
0.4948
0.4956
0.1550
114
0.1472
0.2372
0.2590
0.0977
0.1622
0.2409
0.1482
115
0.2794
0.2947
0.3138
0.1674
0.2856
0.3122
0.1316
116
0.1338
0.2063
0.1746
0.0651
0.1362
0.1568
0.1348
117
0.3761
0.4168
0.4887
0.2102
0.3959
0.5869
0.1924
118
0.1990
0.3128
0.2988
0.1312
0.2124
0.2466
0.1558
119
0.2870
0.3397
0.3516
0.1377
0.2841
0.3582
0.1659
120
0.1481
0.2739
0.1879
0.0814
0.1514
0.1935
0.1287
121
0.5627
0.4163
0.7046
0.2963
0.5815
0.8189
0.2606
122
0.2484
0.2742
0.3316
0.1419
0.2610
0.2870
0.2033
123
0.3864
0.3329
0.4608
0.1689
0.3820
0.4461
0.2187
124
0.1881
0.2247
0.2242
0.0704
0.1909
0.2201
0.1836
125
0.7348
0.6986
0.8070
0.4463
0.7627
0.8295
0.2983
126
0.4029
0.5073
0.5230
0.0941
0.3993
0.5300
0.3948
127
0.4488
0.4619
0.5002
0.2680
0.4565
0.5091
0.1862
128
0.2731
0.3334
0.3300
0.0660
0.2658
0.3471
0.2751
mm
max
average
f35
catch endB/startB
0.0976
0.1414
0.1554
0.0311
0.1007
0.1262
0.0936
0.9104
0.9677
1.1204
0.6232
0.9024
1.0352
0.4251
0.3468
0.3567
0.4486
0.1873
0.3509
0.4042
0.1879
34
Table 2.6. Relative median bias for the 128 experimental treatments.
Treatment
end Bio
0.0323
0.0001
0.0187
-0.0055
0.0159
0.0120
0.0250
-0.0021
-0.0169
31
-0.0190
0.0050
0.1299
0.0334
0.0035
-0.0273
-0.0416
0.0092
-0.0176
-0.0053
-0.0020
-0.0140
-0.0184
0.0004
-0.0390
-0.0204
-0.0199
0.0036
-0.0965
0.0123
-0.0465
end F
-0.0304
0.0000
-0.0134
-0.0023
-0.0054
-0.0171
-0.0179
-0.0034
0.0196
0.0045
0.0411
-0.0125
-0.1161
-0.0284
-0.0143
0.0170
0.0509
-0.0097
0.0170
-0.0034
0.0054
0.0119
0.0402
-0.0023
0.0313
0.0136
0.0063
-0.0097
0.1295
-0.0125
0.0384
32
0.0221
-0.0267
0.0154
0.0050
-0.0221
-0.0015
-0.0042
0.0358
-0.0100
0.0109
-0.0083
0.0292
0.0097
0.0037
-0.0086
0.0100
-0.0705
0.0069
0.0273
0.0063
0.0315
-0.0063
0.0000
-0.0263
-0.0144
-0.0067
-0.0053
-0.0098
-0.0002
-0.0054
-0.0010
0.0000
0.1055
0.0289
33
-0.0218
-0.0420
-0.0078
-0.0122
0.0105
-0.0490
0.0109
-0.0015
0.0361
-0.0246
0.0057
-0.0013
0.0188
-0.1102
-0.0072
0.0095
0.0016
-0.0002
0.0170
0.0000
0.0068
-0.0001
0.0151
0.0037
-0.0013
0.0008
-0.0032
-0.0066
0.0150
-0.0094
-0.0230
-0.0003
-0.0035
0.0276
0.0035
-0.0012
-0.0080
0.0125
0.0162
-0.0035
-0.0071
0.0155
-0.0768
0.0074
-0.0277
0.0061
-0.0045
0.0457
-0.0042
0.0078
-0.0079
0.0302
0.0029
0.0058
-0.0089
0.0064
-0.0894
0.0059
-0.0281
-0.0002
-0.0019
0.0194
-0.0066
0.0069
-0.0058
0.0139
0.0032
-0.0001
-0.0065
0.0285
-0.0570
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
34
35
36
37
38
39
40
41
42
43
44
45
46
-0.0131
end Rec
-0.0116
-0.0073
0.0068
-0.0009
-0.0067
-0.0396
0.0091
-0.0093
-0.0563
-0.0365
-0.0331
-0.0093
0.1296
0.0180
0.0003
-0.0315
-0.0480
0.0128
-0.0292
-0.0028
0.0131
-0.0197
-0.0409
0.0043
-0.0559
-0.0370
-0.0253
0.0056
-0.1355
-0.0195
-0.0588
start Bio
0.0167
-0.0020
0.0115
0.0003
-0.0036
0.0211
0.0099
0.0042
-0.0124
0.0048
-0.0173
0.0055
0.1040
0.0147
0.0075
0.0014
-0.0341
-0.0003
-0.0197
-0.0014
-0.0129
0.0043
-0.0228
-0.0015
-0.0250
0.0001
-0.0129
0.0010
-0.0648
0.0033
-0.0279
end exB
0.0248
-0.0067
0.0115
-0.0044
0.0060
0.0109
0.0222
-0.0027
-0.0231
-0.0194
-0.0243
-0.0006
0.1049
0.0220
0.0027
-0.0259
-0.0452
0.0103
-0.0115
-0.0078
-0.0130
-0.0082
-0.0301
-0.0021
-0.0560
-0.0183
-0.0207
0.0032
-0.0951
0.0016
-0.0404
f35 catch endB/startB
0.0336
0.0106
-0.0050
-0.0042
0.0172
0.0017
-0.0027
-0.0020
0.0270
0.0152
0.0193
-0.0105
0.0275
0.0093
-0.0017
-0.0006
-0.0161
0.0019
-0.0142
-0.0083
-0.0172
-0.0086
0.0041
-0.0057
0.1525
0.0386
0.0494
0.0318
0.0020
-0.0026
-0.0310
-0.0141
-0.0428
-0.0174
0.0047
0.0128
-0.0168
-0.0066
-0.0090
-0.0035
-0.0653
0.0064
-0.0139
-0.0129
-0.0411
-0.0125
0.0008
0.0081
-0.1408
-0.0149
-0.0180
-0.0233
-0.0249
-0.0016
0.0016
-0.0006
-0.1068
-0.0553
-0.0224
0.0196
-0.0452
-0.0161
35
Table 2.6. (continued)
Treatment
end Bio
end F
end Rec
start Bio
end exB
47
-0.0006
0.0045
-0.0015
-0.0120
-0.0106
0.0030
0.0035
48
-0.0134
0.0190
-0.0290
0.0006
-0.0200
-0.0207
-0.0140
49
-0.0030
0.0009
-0.0333
0.0010
-0.0049
-0.0393
0.0055
50
-0.0261
0.0072
-0.0315
0.0044
-0.0226
-0.0288
-0.0130
51
-0.0158
0.0165
-0.0161
-0.0073
-0.0211
-0.0249
-0.0090
52
0.0027
-0.0053
-0.0010
-0.0018
-0.0001
-0.0012
-0.0008
53
-0.0428
0.0509
-0.0652
-0.0355
-0.0468
-0.0366
-0.0 163
54
0.0141
-0.0293
0.0179
0.0162
0.0239
0.0050
-0.0084
55
0.0131
-0.0103
0.0110
0.0127
0.0170
0.0114
-0.0004
56
0.0083
-0.0173
0.0044
0.0002
0.0075
0.0097
0.0045
57
-0.0208
0.0147
-0.0352
-0.0101
-0.0150
-0.0285
-0.0055
58
0.0156
-0.0291
-0.0020
0.0131
0.0167
0.0078
0.0037
59
-0.0297
0.0089
-0.0192
-0.0126
-0.0213
-0.0303
-0.0085
f35
catch endB/startl3
60
0.0061
-0.0048
0.0087
-0.0037
0.0027
0.0064
0.0098
61
-0.0155
0.0116
-0.0040
-0.0056
-0.0234
-0.1771
-0.0130
62
-0.0949
0.1012
-0.1286
0.0099
-0.0806
-0.1299
-0.1026
63
-0.0276
0.0192
-0.0457
-0.0095
-0.0247
-0.0392
-0.0171
64
-0.0013
0.0135
-0.0159
-0.0004
-0.0048
-0.0096
-0.0058
65
0.0260
-0.0420
0.0395
0.0062
0.0104
0.0294
0.0175
66
0.0127
-0.0273
-0.0041
0.0261
0.0028
0.0143
-0.0133
67
0.0337
-0.0482
0.0345
0.0109
0.0315
0.0330
0.0160
68
0.0056
-0.0074
-0.0062
0.0007
0.0039
0.0085
0.0072
69
0.0389
-0.0375
0.0475
0.0111
0.0178
0.0371
0.0173
70
0.0069
-0.0136
-0.0096
0.0082
0.0144
0.0053
0.0035
71
-0.0012
-0.0429
0.0077
0.0074
-0.0052
-0.0019
-0.0012
72
0.0058
-0.0273
-0.0023
-0.0019
0.0048
0.0084
0.0116
73
0.1170
-0.1161
0.0867
0.0646
0.0810
0.1184
0.0276
74
0.0096
-0.0261
-0.0002
0.0045
0.0068
0.0058
0.0074
75
0.0040
-0.0420
0.0127
0.0024
0.0004
0.0039
0.0091
76
0.0001
-0.0324
-0.0096
-0.0009
-0.0030
-0.0011
0.0040
77
-0.0698
0.0848
-0.0937
-0.0383
-0.0736
-0.0773
-0.0411
78
-0.0302
0.0455
-0.0566
0.0042
-0.0481
-0.0321
-0.0311
79
-0.0065
0.0455
-0.0414
-0.0080
-0.0119
-0.0157
-0.0196
80
0.0102
-0.0489
0.0030
0.0096
0.0053
0.0147
-0.0007
81
-0.0210
-0.0063
-0.0118
-0.0216
-0.0200
-0.0750
-0.0047
82
0.0185
-0.0375
-0.0232
0.0165
0.0254
0.0200
-0.0058
83
-0.0108
0.0000
-0.0220
-0.0104
-0.0165
-0.0192
0.0013
84
0.01 19
-0.0210
0.0163
-0.0001
0.0104
0.0140
0.0121
85
-0.0473
0.0384
-0.0452
-0.0296
-0.0373
-0.0534
-0.0248
86
0.0046
-0.0159
-0.0026
-0.0026
0.0016
-0.0053
0.0034
87
0.0083
-0.0455
-0.0024
0.0171
0.0022
0.0084
0.0033
88
0.0037
-0.0142
0.0039
0.0023
0.0028
-0.0062
-0.0003
89
-0.0519
0.0491
-0.0779
-0.0415
-0.0568
-0.0639
-0.0220
90
-0.0033
-0.0278
-0.0141
-0.0043
-0.0033
-0.0099
-0.0027
91
-0.0296
0.0304
-0.0440
-0.0239
-0.0284
-0.0260
-0.0 164
92
-0.0064
-0.0290
-0.0202
0.0059
0.0008
-0.0056
0.0054
36
Table 2.6. (continued)
Treatment
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
mill
max
average
end Bio
-0.0682
-0.0285
-0.0567
-0.0151
0.0009
-0.0004
0.0285
0.0059
0.0326
-0.0210
0.0032
0.0001
0.0036
-0.0245
0.0148
-0.0033
0.0993
0.0140
0.0251
-0.0124
0.0126
0.0224
-0.0075
0.0082
0.0026
-0.0035
0.0085
0.0082
0.0249
-0.0194
0.0078
-0.0012
-0.0645
0.0434
0.0190
0.0304
end F
0.0955
-0.0051
0.0321
-0.0182
-0.0098
-0.0200
-0.0250
-0.0228
-0.0317
0.0123
-0.0134
-0.0267
-0.0013
0.0370
-0.0357
-0.0127
-0.1210
-0.0180
-0.0366
0.0050
-0.0433
-0.0560
-0.0335
-0.0207
-0.0210
-0.0293
-0.0170
-0.0224
-0.0411
-0.0034
-0.0107
-0.0147
0.0750
-0.0572
-0.0250
-0.0358
end Rec
-0.0788
-0.0770
-0.0731
-0.0182
-0.0099
-0.0090
0.0241
-0.0031
0.0214
-0.0368
-0.0148
-0.0022
-0.0216
-0.0123
-0.0006
-0.0084
0.1046
-0.0274
0.0216
-0.0207
0.0086
-0.0001
-0.0203
-0.0040
-0.0022
-0.0264
0.0075
0.0063
0.0231
-0.0248
0.0102
-0.0015
-0.0938
0.0512
0.0176
0.0305
start Bio
-0.0547
0.0040
-0.0350
-0.0061
-0.0059
0.0021
0.0117
-0.0043
0.0093
0.0078
0.0002
0.0043
0.0016
0.0017
0.0093
0.0002
0.0521
0.0100
0.0088
0.0025
0.0176
0.0198
-0.0057
-0.0053
0.0032
0.0145
0.0045
-0.0018
0.0098
0.0170
0.0013
-0.0013
-0.0205
0.0147
-0.0049
-0.0021
end exB
-0.0848
-0.0237
-0.0569
-0.0129
-0.0157
0.0047
0.0182
0.0041
0.0291
-0.0264
0.0039
-0.0012
-0.0060
-0.0268
0.0227
-0.0051
0.0759
0.0153
0.0178
-0.0073
0.0084
0.0277
-0.0073
0.0045
0.0001
-0.0030
0.0109
0.0102
0.0102
-0.0203
0.0038
0.0049
-0.0772
0.0595
0.0195
0.0308
f35 catch endB/startB
-0.2590
-0.0348
-0.0393
-0.0516
-0.0628
-0.0237
-0.0198
-0.0123
0.0007
0.0085
-0.0021
-0.0059
0.0229
0.0139
0.0068
0.0029
0.0338
0.0300
-0.0288
-0.0187
0.0113
0.0002
-0.0005
0.0005
0.0043
0.01 19
-0.0281
-0.0223
0.0104
0.0056
-0.0114
-0.0098
0.1375
0.0540
0.0079
0.0115
0.0294
0.0151
-0.0197
-0.0224
-0.0039
-0.0152
0.0200
0.0007
-0.0100
-0.0048
0.0137
0.0126
-0.0503
0.0037
-0.0044
-0.0156
-0.0015
0.0144
0.0050
0.0054
-0.0753
0.0157
-0.0209
-0.0352
0.0066
0.0114
0.0068
-0.0011
-0.0786
-0.0353
0.0326
0.0454
0.0243
0.0129
0.0320
0.0323
-0.0965
0.1299
-0.1210
0.1295
-0.1355
0.1296
-0.0123
-0.0648
0.1040
0.0004
-0.0951
0.1049
-0.0044
-0.2590
0.1525
-0.0094
-0.0016-0.0050
-0.1026
0.0540
-0.0024
37
60.00%
end Bio
1
40.00%
20.00%
0.00%
q,
,
c:,(b
ç,b'
ç
end F
60.00%
40.00%
[1n,__
20.00%
0.00% ___
El
D
-
'
s:
60.00%
end Rec
40.00%
20.00%
U
0.00%
'
5bn
80.00%
Q,
U no
?
c
ç'
ç;<7
o
ç(3
QcO
start Bio
60.00%
40.00%
20.00%
0.00%
n
'
t>
ç;>
c:t
end exB
60.00%
40.00%
20.00%
Ii
_______
0.00% ____
?
?'
'
c;'
2rt
D
F35 catch
60.00%
40.00%
20.00%
0.00%
t'
ç\
)
80.00%
60.00%
40.00%
20.00%
0.00%
ç:,1
ç
ç;'
çD
c°
endBlstartB
-_
I,
LI
'
1:
c:
D - _____
c:;'
c'
Qb
- -_____
çb
<)
Figure 2.5. The distributions of relative bias for the seven estimates across the 128 treatments.
treatments. 128
the across estimates seven the for median the of bias relative of distribution The 2.6. Figure
c.
endB/startB
c:y
c:y
cD
$
c
-
c
0%
I10°
120%
B B
I c'
130%
catch F35
c
c1'
--=
5:'
p,
0%
20%
40%
exB end
.
-
ç
*
_____
- - -
-
H
ç)')
ç'
çtf
0%
20%
40%
Bio start
9'
60%
ç)
U
=
0%
Rec end
c
1
20%
40%
60%
fl
-
U
0%
20%
40%
endF
çD
60%
çD
_cDLJ
0%
20%
40%
[1
Bio end
60%
38
39
40.0%
endB/startB
35.0%
30.0%
5 catch
B
25.0%
20.0%
15.0%
10.0%
5.0%
0.00/c
OddUo 000a)_
Figure 2.7. The distribution of relative variability for the seven estimates across the 128
treatments.
2.3 Results
The seven types of Stock Synthesis estimates that we examined varied greatly in
relative bias and relative variability. Tables 2.4 - 2.6 lists the average values across the four
replicate groups for the 128 treatments. For the measurement of the relative bias of the mean,
the F35% catch estimates showed the largest negative bias (- 6.3%) and ending recruitment
estimates had the largest positive bias (+ 5 8%). Across the 128 treatments, the distributions of
the relative bias were skewed to the right for all seven estimates (Figure 2.5), indicating that
the bigger positive values of relative bias occurred only in a few treatments. For the
measurements of the relative bias of the median, the largest negative bias (-25.9%) and the
largest positive bias (+ 15.3%) both occurred within tlt estimates of the F35% catch. Across the
40
128 treatments, the distributions of the relative bias of the median were fairly tightly centered
about zero for all seven estimates (Figure 2.6), indicating that the Synthesis estimates tended
to be median-unbiased. The relative variability ranged from 0.031 in the estimates of starting
biomass to 1.12 in the estimates of ending recruitment. Across the 128 treatments, the
distributions of the relative variability all were skewed to the right (Figure 2.7).
Ending Biomass
Ending Recruitment
Ending F
Starting Biomass
Figure 2.8. Example histograms from experimental treatment 1 of variables output by the
Stock Synthesis program and used as dependent experimental variables. The dashed lines
indicate the true values. The units for the biomass and recruitment axes are in thousands
Across replicates within a given treatment, the Stock Synthesis estimates of ending
biomass, ending exploitable biomass, ending recruitment, and starting biomass were in general
skewed to the right, whereas the estimates for the ending fishing mortality coefficient were
reasonably symmetric (e.g., Fig. 2.8). Because the analyses of variance were applied to
41
averages of 200 values, the residuals from the analyses were reasonably well approximated by
normal distributions. For the variables that measured relative bias of the mean and relative bias
of the median, diagnostic plots of the residual versus fitted values indicated little evidence of
heterogeneous variability. However, similar plots for the variables that measured relative
variation showed some tendency for residual variability to increase with the magnitude of the
fitted values.
In the analyses of variance, the main effects, two-way interactions, and three-way
interactions were all highly significant (P < 0.01) for all 21 dependent variables (Table 2.7).
However, main effects and interactions did not have same degrees of importance. For example,
the MS (Mean Square) for the main effects for
endBio was
about 10 times larger than the MS
for the two-way interactions and 20 times larger than the MS for the three-way interactions.
Most of the variability in the dependent variables was accounted for by differences in the main
effects. The interactions were significant but much less so than the main effects. In addition,
because the main effects were not aliased with any 4th and lower order interactions (Table 2.3),
the significant interactions have no side effects on the estimates of the main effects.
2.3.1 Effects on Relative Bias
On average across all levels of the nine factors the seven types of estimates that we
examined had slight but statistically significant (P < 0.05) positive bias, ranging from a low of
1.6% for the estimates of the ending/starting biomass ratio to a high of 10% for the estimates
of ending recruitment (Table 2.8). Note that the relative bias of ending/starting biomass ratio
(at 1.6%) was significantly smaller than the other six types of estimate, indicating that
Synthesis produced relatively unbiased estimates for this type of measurement. For the
estimates of ending biomass, ending recruitment, starting biomass, and ending exploitable
Table 2.7. ANOVA tables from the fractional factorial experiment.
Source
DF
SS
Relative bias in ending total biomass.
Main Effects
9
2.217
2-Way Interactions
36
0.932
3-Way Interactions
55
0.55 1
Residual Error
384
0.528
Total
511
4.336
Relative bias in ending F.
Main Effects
9
2.064
2-Way Interactions
36
1.627
3-Way Interactions
55
0.767
Residual Error
384
0.688
Total
511
5.245
Relative bias in ending recruitment.
Main Effects
9
3.550
2-Way Interactions
36
1.536
3-Way Interactions
55
0.816
Residual Error
384
0.834
Total
511
6.889
Relative bias in starting biomass.
Main Effects
9
0.736
2-Way Interactions
36
0.260
3-Way Interactions
55
0.158
Residual Error
384
0.168
Total
511
1.360
Relative bias in ending exploitable biomass.
Main Effects
9
1.980
2-Way Interactions
36
0.814
3-Way Interactions
55
0.525
Residual Error
384
0.517
Total
511
3.942
Relative bias in predicted F35 Catch.
Main Effects
9
2.072
2-Way Interactions
36
1.578
3-Way Interactions
55
0.990
Residual Error
384
0.701
Total
511
5.492
Relative bias in the ratio of ending/starting biomass.
Main Effects
9
0.078
2-Way Interactions
36
0.158
3-Way Interactions
55
0.089
Residual Error
384
0.104
Total
511
0.443
MS
P
F
0.246
0.026
0.010
0.001
179.0
18.8
7.3
<0.001
0.229
0.045
0.014
0.002
128.0
25.2
7.8
<0.001
<0.001
<0.001
0.394
0.043
0.015
0.002
181.5
19.6
6.8
<0.001
<0.001
<0.001
0.082
0.007
0.003
0.000
187.4
16.6
6.6
<0.001
<0.001
<0.001
0.220
0.023
0.010
0.001
163.6
<0.00 1
16.8
7.1
<0.001
<0.001
0.230
0.044
126.1
<0.001
<0.001
0.0 18
0.002
0.009
0.004
0.002
0.000
24.0
9.9
32.1
16.3
6.0
<0.001
<0.00 1
<0.00 1
<0.001
<0.001
<0.001
43
Table 2.7. (continued)
Source
DF
SS
MS
Relative median bias in ending total biomass.
Main Effects
9
0.072
0.008
2-Way Interactions
36
0.243
0.007
3-Way Interactions
55
0.161
0.003
Residual Error
384
0.386
0.001
Total
511
0.885
Relative median bias in ending F.
Main Effects
9
0.122
0.014
2-Way Interactions
36
0.315
0.009
3-Way Interactions
55
0.235
0.004
Residual Error
384
0.513
0.001
Total
511
1.218
Relative median bias in ending recruitment.
MainEffects
9
0.098
0.011
2-Way Interactions
36
0.3 16
0.009
3-Way Interactions
55
0.244
0.004
Residual Error
384
0.549
0.001
Total
511
1.251
Relative median bias in starting biomass.
Main Effects
9
0.03 7
0.004
2-Way Interactions
36
0.076
0.002
3-Way Interactions
55
0.057
0.001
Residual Error
384
0.123
0.000
Total
511
0.303
Relative median bias in ending exploitable biomass.
Main Effects
9
0.058
0.006
2-Way Interactions
36
0.208
0.006
3-Way Interactions
55
0.150
0.003
Residual Error
384
0.395
0.00 1
Total
511
0.833
Relative median bias in predicted F35 catch.
Main Effects
9
0.249
0.028
2-Way Interactions
36
0.543
0.0 15
3-Way Interactions
55
0.325
0.006
Residual Error
384
0.472
0.001
Total
511
1.621
Relative median bias in the ratio of ending/starting biomass.
Main Effects
9
0.033
0.004
2-Way Interactions
36
0.094
0.003
3-Way Interactions
55
0.062
0.001
Residual Error
384
0.147
0.000
Total
511
0.350
F
P
8.0
6.7
2.9
<0.001
<0.001
<0.001
10.1
<0.001
<0.001
<0.001
6.5
3.2
7.6
6.1
3.1
<0.001
<0.001
<0.001
12.7
6.6
3.2
<0.001
<0.001
<0.001
6.2
5.6
2.6
<0.001
<0.001
<0.001
22.5
<0.001
<0.001
12.3
4.8
9.6
6.8
2.9
<0.00 1
<0.001
<0.001
<0.001
44
Table 2.7. (continued)
Source
DF
SS
Relative variability in ending total biomass.
Main Effects
9
14.671
2-Way Interactions
36
2.599
3-Way Interactions
55
0.705
Residual Error
384
0.728
Total
511
18.850
Relative variability in ending F.
Main Effects
9
9.816
2-Way Interactions
36
2.091
3-Way Interactions
55
0.500
Residual Error
384
0.493
Total
511
12.960
Relative variability in ending recruitment.
Main Effects
9
19.493
2-Way Interactions
36
2.728
3-Way Interactions
55
0.845
Residual Error
384
1.201
Total
511
24.406
Relative variability in starting biomass.
Main Effects
9
7.913
2-Way Interactions
36
1.343
3-Way Interactions
55
0.282
Residual Error
384
0.3 15
Total
511
9.919
Relative variability in ending exploitable biomass.
Main Effects
9
14.965
2-Way Interactions
36
2.3 82
3-Way Interactions
55
0.687
Residual Error
384
0.755
Total
511
18.936
Relative variability in predicted F35 catch.
Main Effects
9
19.402
2-Way Interactions
36
3.056
MS
1.630
0.072
0.0 13
0.002
1.091
0.058
0.009
0.001
2.166
0.076
P
F
859.9
38.1
6.8
848.8
45.2
7.1
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
692.5
24.2
4.9
<0.00 1
0.879
0.037
0.005
0.001
1000.0
45.5
6.3
<0.001
<0.001
<0.00 I
1.663
<0.001
0.0 12
845.8
33.7
6.4
2.156
916.6
<0.001
0.085
36.1
<0.001
6.9
<0.00 1
1000.0
120.5
19.6
<0.001
<0.001
<0.001
0.0 15
0.003
0.066
0.002
3-Way Interactions
55
0.892
0.0 16
Residual Error
384
0.903
0.002
Total
511
24.395
Relative variability in the ratio of ending/starting biomass.
Main Effects
9
2.071
0.230
2-Way Interactions
36
0.673
0.019
3-Way Interactions
55
0.167
0.003
Residual Error
384
0.060
0.000
Total
511
2.984
<0.001
<0.00 1
<0.00 1
<0.001
45
Table 2.8. Analysis of relative bias.
Factor
Grand mean
numYrs
smplSize
effortCv
svyCv
natiM
Ftrend
catchCv
Fslct
recVar
numYrs*smplSize
numYrs*effortCv
numYrs*svyCv
numYrs*natlM
numYrs*Ftrend
numYrs*catchCv
numYrs*Fslct
numYrs*recVar
smplSize*effortCv
smplSize*svyCv
smplSize*natlM
smplSize*Ftrend
smplSize*catchCv
smplSize*Fslct
smplSize*recVar
effortCv*svyCv
effortCv*natlM
effortCv*Ftrend
effortCv*catchCv
effortCv*Fslct
effortCv*recVar
svyCv*natlM
svyCv*Ftrend
svyCv*catchCv
svyCv*Fslct
svyCv*recVar
natlM*Ftrend
natlM*catchCv
natlM*Fslct
natlM*recVar
Ftrend*catchCv
Ftrend*Fslct
Ftrend*recVar
catchCv*Fslct
catchCv*rec Var
Fslct*recVar
end Bio
0.0816
-0.0492
-0.0287
0.0155
0.0226
-0.0037
-0.0148
0.0064
0.0044
9.0060
0.0213
-0.0050
-0.0114
0.0121
-0.0035
0.0041
-0.0024
-0.0080
-0.0128
0.0077
0.0062
-0.0017
0.0020
-0.0034
0.0098
-0.0052
0.0055
-0.0088
0.0059
0.0010
end F
0.0586
-0.0266
-0.0270
0.0327
0.0318
0.0169
-0.0144
-0.0024
0.0041
-0.0006
0.0085
-0.0110
-0.0129
-0.0168
0.0131
-0.0033
-0.0134
-0.0004
-0.0169
-0.0160
-0.0102
0.0035
-0.0014
0.0045
0.0056
0.0228
0.0063
-0.0078
0.0060
0.0075
-0.0001
end Rec
0.1014
-0.0612
-0.0363
0.0211
0.0297
-0.0088
-0.0153
0.0081
0.0108
0.0072
0.0270
-0.0080
-0.0155
0.0165
0.0003
-0.0042
0.0036
-0.0037
-0.0108
-0.0162
0.0111
0.0062
-0.0040
-0.0005
-0.0028
0.0130
-0.0054
0.0066
-0.0104
0.0087
-0.0004
start Bio
0.0413
-0.0278
-0.0189
0.0041
0.0073
0.0009
-0.0123
0.0037
-0.0076
0.0035
0.0104
-0.0026
-0.0064
0.0045
0.0066
-0.0031
0.0031
-0.0015
-0.0021
-0.0055
0.0011
0.0049
-0.0015
0.0062
-0.0036
0.0021
-0.0032
0.0027
-0.0037
0.0007
0.0000
-0.0051
0.0069
-0.0066
-0.0035
0.0011
0.0060
-0.0086
0.0095
0.0015
0.0018
0.0018
0.0028
0.0012
0.0066
0.0071
0.0094
-0.0005
0.0068
-0.0057
0.0078
0.0033
0.0053
-0.0103
0.0062
0.0028
0.0021
-0.0029
0.0000
0.0011
0.0000 -0.0130
0.0019
-0.0003
-0.0085
0.0086 -0.0092
-0.0050
0.0016 -0.0102
0.0020
-0.0007
0.0054 -0.0069
0.0054
0.0031
0.0005
0.0007
0.0010
0.0005
-0.0089
0.0044 -0.0117
-0.0038
0.0009 -0.0002
0.0025
-0.0002
-0.0072
0.0039
-0.0080
-0.0055
Bold: Coefficients with t-statistics significant at the P = 0.05 levels
end exB f35 catch endl3/startB
0.0787
0.0791
0.0159
-0.0465
-0.0466
-0.0010
-0.0277
-0.0192
-0.0018
0.0146
0.0175
0.0039
0.0211
0.0245
0.0046
0.0001
-0.0183
-0.0037
-0.0141
-0.0123
0.0035
0.0067
0.0079
0.0016
0.0028
-0.0058
0.0089
0.0056
0.0047
0.0016
0.0194
0.0161
0.0040
-0.0044
-0.0049
0.0023
-0.0106
-0.0109
0.0030
0.0112
0.0228
0.0062
0.0019
0.0001
-0.0066
-0.0038
-0.003 1
0.0012
0.0055
0.0129
0.0048
-0.0020
-0.0002
-0.0003
-0.0074
-0.0085
-0.0016
-0.0117
-0.0120
-0.0017
0.0053
0.0217
0.0042
0.0057
0.0052
0.0000
-0.0017
-0.0024
0.0004
0.0024
0.0133
-0.0049
-0.0036
-0.0012
-0.0004
0.0091
0.0109
0.0024
-0.0053
-0.0073
-0.0009
0.0055
0.0074
0.0024
-0.0085
-0.0095
-0.0032
0.0046
0.0055
0.0029
0.0012
0.0007
0.0011
-0.0050
-0.0079
-0.0004
0.0057
0.0017
0.0056
0.0063
0.0052
0.0022
-0.0017
-0.0085
0.0018
0.0050
0.0005
-0.0083
0.0009
-0.0075
0.0076
0.0023
0.0059
0.0004
0.0059
0.0033
-0.0118
-0.0120
0.0028
0.0065
0.0005
-0.0094
0.0042
-0.0001
0.0047
0.0024
0.0023
0.0007
0.0021
-0.0024
0.0044
0.0026
-0.0003
-0.0022
0.0007
0.0004
0.00 15
-0.0104
46
biomass, the two most influential factors were the number of years and the sample size. In
addition, the estimated coefficients for these two factors were negative for all types of
estimates, indicating that longer data series and larger samples produced less biased estimates.
However, the interaction of the two factors was positively significant, indicating the effects of
the two factors were not simply additive. The main effects of the fishery CPUE variability and
the survey variability were both positively significant across all seven types of estimates,
indicating that their degrees of variability were propagated into the estimates. The main effects
for natural mortality were not significant for two types of estimates and were relatively small
(absolute value of its coefficient < 1%) for five types of estimates, indicating that natural
mortality was not a major contributor by itself. However, there were significant interactions
with this factor for several types of estimates. For example, the interactions between natural
mortality and the number of years of data were significant across all seven types of estimates
and the absolute values of the interaction coefficients were bigger than 1% for seven types of
estimates. The magnitude of the trends in the fishing mortality coefficient produced negatively
significant effects in six out of seven types of estimates (the ending/starting biomass ratio was
the only exception), indicating that increased fishing mortality produced less biased estimates.
The main effects of catch data variability were positively significant for six types of estimates,
implying that increased variability in observed catch data contributed to more biased estimates.
The main effects of fishery selectivity were positively significant for four types of estimates
(ending biomass, ending fishing mortality, ending recruitment, and the ratio between ending
biomass and starting biomass) and negatively significant for two types of estimates (starting
biomass and F35% catch), but mostly relatively small in absolute values (<1%), suggesting that
fishery selectivity was not a major factor for the biases of the estimates. The main effects of
47
Table 2.9. Analysis of relative median bias.
Factor
Grand mean
numYrs
smplSize
effortCv
end Bio
-0.0016
-0.0006
0.0007
-0.0016
0.0041
0.0092
0.0017
0.0036
0.0016
0.0042
0.0022
0.0000
0.0007
0.0116
0.0044
0.0002
0.0068
-0.0018
0.0015
-0.0003
0.0055
0.0014
0.0002
0.0028
0.0035
-0.0019
-0.0015
0.0013
-0.0023
0.0008
0.0008
end F
-0.0050
-0.0028
-0.0034
0.0039
0.0061
0.0066
-0.0018
-0.0104
-0.0015
-0.0031
-0.0010
-0.0010
-0.0012
-0.0116
0.0060
-0.0003
-0.0088
0.0003
-0.0030
-0.0019
-0.0032
0.0000
-0.0004
0.0048
0.0053
0.0038
0.0027
-0.0016
0.0025
0.0007
-0.0017
0.0023
-0.0008
end Rec
-0.0123
-0.0016
0.0056
-0.0026
-0.0054
-0.0078
0.0031
0.0045
0.0024
0.0050
0.0047
-0.0017
0.0004
0.0125
-0.0051
-0.0004
0.0083
-0.0033
0.0013
0.0004
0.0046
0.0015
-0.0015
-0.0049
-0.0043
-0.0032
-0.0014
0.0011
-0.0022
0.0014
0.0007
-0.0040
0.0052
start Bio end exB
0.0004
-0.0044
0.0036
0.0023
-0.0019
0.0022
0.0000
-0.0013
svyCv
-0.0012
-0.0046
natiM
-0.0060
-0.0068
Ftrend
0.0022
0.0029
catchCv
0.0011
0.0033
Fslct
-0.0027
0.0024
recVar
0.0021
0.0030
numYrs*smplSize
-0.0017
0.0002
numYrs*effortCv
0.0005
0.0000
numYrs*svyCv
0.0008
0.0008
numYrs*natlM
0.0058
0.0109
numYrs*Ftrend
-0.0023
-0.0040
numYrs*catchCv
-0.0005
0.0007
numYrs*Fslct
0.0019
0.0071
numYrs*recVar
-0.0007
-0.0008
smplSize*effortCv
0.0006
0.0011
smplSize*svyCv
-0.0010
0.0010
smplSize*natlM
0.0023
0.0044
smplSize*Ftrend
-0.0010
0.0004
smplSize*catchCv
0.0000
0.0008
smplSize*Fslct
0.0012
-0.0033
smplSize*recVar
-0.0033
-0.0030
effortCv*svyCv
-0.0006
-0.0022
effortCv*natlM
-0.0014
-0.0015
effortCv*Ftrend
0.0003
0.0015
effortCv*catchCv
-0.0018
-0.002 1
effortCv*Fslct
-0.0009
0.0012
effortCv*recVar
-0.0003
0.0011
svyCv*natlM
0.0030
-0.0019
-0.0024
svyCv*Ftrend
0.0024
0.0010
0.0028
svyCv*catchCv
0.0000
0.0012
-0.0010
-0.0009
-0.0002
svyCv*Fslct
-0.0003
0.0002
-0.0011
-0.0009
0.0000
svyCv*recVar
0.0057 -0.0066
0.0049
0.0033
0.0055
natlM*Ftrend
0.0052 -0.0062
0.0053
0.0044
0.0048
natlM*catchCv
0.0009
-0.0015
-0.0003
0.0007
0.0012
natlM*Fslct
0.0071
-0.0071
0.0091
0.0041
0.0044
natlM*recVar
0.0052
0.0058 -0.0043
-0.0026 -0.0043
Ftrend*catchCv
0.0044
0.0042
-0.0039
0.0017
0.0041
Ftrend*Fslct
0.0042
-0.0057
0.0031
0.0021
0.0051
Ftrend*rec Var
-0.0008
0.0002 -0.000 1
-0.0006
-0.0008
catchCv*Fslct
-0.0018
0.0037 -0.0028
-0.0007
-0.0007
catchCv*recVar
0.0024
-0.0031
0.0015
0.0012
0.0028
Fslct*recVar
-0.0011
0.0028 -0.00 17
-0.0019
-0.00 15
Bold: Coefficients with t-statistics significant at the P = 0.05 levels
f35 catch
-0.0094
0.0042
0.0071
-0.0033
-0.0075
-0.0175
0.0018
0.0034
-0.0048
0.0022
-0.0020
0.0185
-0.0058
0.0011
0.0133
0.0008
0.0025
0.0033
0.0128
0.0013
0.0007
0.0029
-0.0020
-0.0034
-0.0044
0.0016
-0.0022
-0.0011
0.0010
-0.0058
0.0021
endB/startB
-0.0024
-0.0025
0.0024
-0.0013
-0.0027
-0.0040
0.0009
0.0018
0.0049
0.0007
0.0032
-0.0001
0.0001
0.0056
-0.0038
0.0005
0.0049
-0.0008
0.0005
0.0001
0.0042
0.0005
0.0009
-0.0045
0.0003
-0.0018
-0.0013
0.0012
-0.0003
0.0009
0.0012
-0.0012
0.0017
0.0006
-0.0002
-0.0033
0.0021
0.0060
0.0014
0.0009
-0.0083
0.0063
0.0056
-0.0020
-0.0025
0.0018
-0.0038
0.0017
0.0017
0.0014
0.0001
0.0023
0.0006
0.0039
-0.0028
0.0035
0.0018
-0.0006
-0.0008
0.0013
0.0008
48
Table 2.10. Analysis of relative variability.
Factor
Grand mean
numYrs
smplSize
effortCv
svyCv
natiM
Ftrend
catchCv
Fslct
recVar
numYrs*smplSize
numYrs*effortCv
numYrs*svyCv
numYrs*natlM
numYrs*Ftrend
numYrs*catchCv
numYrs*Fslct
numYrs*recVar
smplSize*effortCv
smplSize*svyCv
smplSize*natlM
smplSize*Ftrend
smplSize*catchCv
smplSize*Fslct
smplSize*recVar
effortCv*svyCv
effortCv*natlM
effortCv*Ftrend
effortCv*catchCv
effortCv*Fslct
effortCv*recVar
svyCv*natlM
svyCv*Ftrend
svyCv*catchCv
svyCv*Fslct
svyCv*recVar
natlM*Ftrend
natlM*catchCv
natlM*Fslct
natlM*recVar
Ftrend*catchCv
Ftrend*Fslct
Ftrend*recVar
catchCv*Fslct
catchCv*recVar
Fslct*rec Var
end Bio
0.3468
0.1205
0.0671
0.0432
0.0670
0.0248
0.0475
0.0127
0.0124
0.0095
0.0289
-0.0022
0.0139
0.0043
0.0138
0.0057
0.0092
0.0064
0.0160
0.0215
-0.0018
0.0080
-0.0032
0.0154
end F
0.3567
-0.0767
-0.0574
0.0662
0.0579
0.0239
-0.0330
0.0224
0.0070
0.0074
0.0164
-0.0089
-0.0136
-0.0037
0.0105
0.0000
-0.0071
-0.0029
-0.0233
-0.0234
-0.0055
0.0059
0.0012
0.0081
0.0008
0.0352
0.0011
-0.0029
0.0014
0.0139
0.0017
0.0025
-0.0043
-0.0015
0.0162
0.0036
-0.0049
-0.0021
-0.0178
-0.0020
-0.0039
-0.0016
-0.0001
-0.0025
0.0018
-0.0046
end Rec
0.4486
-0.1293
-0.1058
0.0472
0.0705
-0.0029
-0.0482
0.0101
0.0225
0.0068
0.0281
-0.0054
-0.0179
start Bio end exB
0.1873
0.3509
-0.0948 -0.1219
-0.0496 -0.0714
0.0109
0.0419
0.0194
0.0643
0.0315
0.0280
-0.0449 -0.0482
0.0117
0.0130
-0.0181
0.0076
0.0068
0.0086
0.0244
0.0304
-0.0079
-0.0015
-0.0174 -0.0131
0.00 13
-0.0050
-0.0040
0.0128
0.0234
0.0133
-0.0057 -0.0042
-0.0064
-0.0125
0.0007 -0.0078
-0.0071
-0.0043 -0.0054
-0.0170
-0.0037 -0.0157
-0.0203
-0.0080 -0.0206
0.0109
-0.0091 -0.0032
0.0096
0.0123
0.0081
-0.0025
-0.0017 -0.0037
0.0130
0.0131
0.0150
0.0021
0.0037
0.0010
0.0019
0.0282
0.0318
0.0070
0.0274
0.0041
-0.0021
-0.0053 -0.0052
0.0068
0.0065
0.0031
0.0069
0.0150
-0.0174
-0.0045 -0.0141
0.0151
0.0157
0.0043
0.0126
-0.0007
-0.0006 -0.0009
-0.0012
-0.0017
0.0018
-0.0028 -0.0016
0.0072
0.0079
0.0015
0.0074
0.0033
0.0057
0.0028
0.0033
0.0201
0.0211
0.0026
0.0172
0.0040
0.0061
0.0011
0.0037
0.0040
-0.0015
-0.0053 -0.0034
0.0014
0.0009
-0.0006
0.0010
0.0247
-0.0164
-0.0167 -0.0214
0.0077
-0.0073
-0.0044 -0.0080
-0.0025
-0.0028
-0.0032 -0.0020
0.0023
0.0043
0.0027
0.0005
0.0027
0.0029
0.0019
0.0027
0.0103
-0.0108
-0.0049 -0.0104
0.0005
0.0013
-0.0005
0.0005
0.0071
-0.0060
-0.0068 -0.0064
Bold: Coefficients with t-statistics significant at the P = 0.05 levels
f35 catch endB/startB
0.4042
0.1879
-0.1332
-0.0038
-0.0849
-0.0263
0.0538
0.0283
0.0774
0.0429
0.0376
0.0053
-0.0378
0.0023
0.0116
0.0060
0.0309
0.0249
0.0124
0.0034
0.0348
0.0018
-0.0006
0.0051
-0.0153
0.0061
-0.0099
0.00 10
0.0138
-0.0045
-0.0067
0.0011
-0.0190
-0.0055
-0.0066
-0.0013
-0.0177
-0.0116
-0.0249
-0.0125
-0.0138
0.0015
0.0062
-0.0025
-0.0032
-0.0003
0.0027
0.0032
0.0013
0.0005
0.0327
0.0200
-0.0046
0.0023
0.0096
0.0014
-0.0135
-0.0083
0.0154
0.0094
-0.0007
0.0013
-0.0015
0.0030
0.0089
0.0029
0.0036
0.0013
0.0228
0.0145
0.0106
0.0021
-0.0036
-0.0006
0.0016
0.0005
-0.0097
-0.0090
-0.0059
-0.0009
-0.0026
0.0024
0.0014
0.0006
0.0019
0.0001
-0.0105
-0.0011
0.0017
0.0004
-0.004 1
0.0002
49
recruit variability were generally small and positively significant for six types of estimates,
indicating that the variable recruitment series slightly increased the bias of Synthesis estimates.
3.2 Effects on Relative Median Bias
The overall average relative bias of the median for all seven types of estimates were
very close to zero (ranging from 1.2% to 0.00%), indicating that Synthesists estimates were
almost median-unbiased (Table 2.9). This may be due to the fact that the distributions of most
estimates were skewed to the right (Figure 2.8).
2.3.3 Effects on Relative Variabili
On average, the overall relative variability of the seven types of Stock Synthesis
estimates ranged from a low of 18.7% for the estimates of starting biomass to a high of 44.9%
for the estimates of ending recruitment (Table 2.10). The number of years in the data series
and the sample size factors produced the first and second most influential effects for most of
the seven types of estimate. In addition, the estimated coefficients for these factors were
always negative, indicating that longer data series and larger sample size produced less
variable estimates. The interaction between these two factors was significantly positive for all
cases, however, indicating that these two effects we not strictly additive. The effects of
fishing effort variability and survey biomass variability were both positively significant for all
seven types of estimates, indicating that these two factors directly influence the variability of
the seven types of estimates. Except for the estimate of the ending/starting biomass ratio, the
magnitude of the trends in the fishing mortality coefficient produced negatively significant
effects on the remaining six types of estimates. In addition, the relative rank of its estimated
coefficient for all the six types of estimates ranged from 3td to
6th
meaning increased fishing
50
mortality significantly reduced the variability of estimates. The main effects of both catch
variability and recruitment variability were all positively significant for all seven types of
estimates, indicating that variable recruitment series and increased variability in observed
catch data both contributed to the increased variability of Synthesis estimates. Finally, all nine
factors produced significant main effects for at least six of the seven types of estimates.
2.3.4 Sensitivity to Initial Parameter Values
Figure 2.9 shows the comparisons of using true initial parameter values versus using
randomized initial parameter values for treatment 36 and treatment 109. For treatment 36,
which had the best result in terms of minimum relative bias and relative variability on the
estimate of ending biomass, using randomized initial parameter values had essentially no
effect on the final estimates of ending biomass. Averaged across the 100 replicates, the
relative bias was at 0.3% for both the randomized and the non-randomized runs. The average
likelihood values were both at 203.35 and the relative variability values were almost identical
(9.7% in the non-randomized versus 9.8% in the randomized). For treatment 109, which had
the worst results in terms of minimum relative bias and relative variability on the estimate of
ending biomass, using randomized initial parameter values produced some differences. Even
though the average likelihood values (averaged across the 100 replicates) were almost
identical (-243.91 for the non-randomized versus 243.90 for the randomized), using
randomized initial parameter values produced slightly bigger relative bias (0.52 versus 0.37)
and relative variability (1.08 versus 0.73). However, a Two-Sample T Test did not show strong
evidence of statistically significant differences (P=0.238).
51
ending bio.
40,000
*
Treatment 36,
Two-Sample T-Test
P-Value: 0.999
*
35,000
30,000
25,000
true initial narameters
rindnmi7M inthil nirnmeterc
ending bio.
*
300,000
Treatment 109,
Two-Sample 1-Test
P-Value: 0.238
*
*
200,000
*
100,000
L-------.-I-
-L-L
0
true initial parameters
randomized intial parameters
Figure 2.9. Experiments on sensitivity to initial parameter values for treatment 36 and
treatment 109. The dashed line represents the true ending biomass.
2.4. Discussion
Results from our experiments were generally in accord with what we anticipated, but
with a small surprise on the effect of fishery selectivity. The effect of fishery selectivity was
relatively small for all seven types of estimates. Asymptotic shaped fishery selectivity
produced less biased estimates for starting biomass and
F35%
catch and less variable estimates
for starting biomass. However, for all other estimates, asymptotic shaped fishery selectivity
resulted in slightly bigger bias and variability. Bence et al. (1993) in a Monte Carlo
investigation of the Stock Synthesis program found that biomass estimates were more accurate
if derived using data from a survey that had an asymptotic rather than domed selectivity curve.
In their simulated populations the fishery selection curve was always domed. In our study the
survey selection curve was always asymptotic.
In a previous Monte Carlo investigation of Synthesis Sampson and Yin (1997)
conducted a smaller but similar experiment on the performance of the Stock Synthesis
program. That experiment was based on a one-eighth fraction of a 28 factorial design and 200
data sets were generated and analyzed for each experimental treatment. In contrast, the
experiment in this study was based on a one-fourth fraction of a 2 factorial design and 800
data sets were generated and analyzed for each experimental treatment. The results of this
bigger experiment were in general in accord with the results of that smaller experiment, but
this experiment detected a few more significant factors. In addition, there were also some
changes in the rank ordering of the relative importance of the main effects on relative bias. For
example, the results from the 1997 study showed that the magnitude of the trends in the
fishing mortality coefficient had no significant (P<5%) effect on the bias of Synthesis
estimates, whereas in this study we found that the effects of the fishing mortality trend were
significant for the biases of all seven types of Synthesis estimates. Similarly, for the
53
recruitment variability factor, the 1997 study did not find any significant (P<5%) effects on the
bias of Synthesis estimates, but the current study showed that the recruitment factors produced
significant effects on relative biases for six of the seven types of Synthesis estimates. For the
measurement of relative variability, the rank ordering of the relative importance of the main
effects matched quite well between the two experiments. For example, for the relative
variability of ending biomass estimates, NumYr, SmplSize, and SurvCV ranked No.1, No.2,
and No.3 respectively both in the 1997 experiment and this experiment. For the measurement
of relative bias, however, the two experiments were not congruent in the rank ordering of the
relative importance of the main effects. For example, for the relative bias of ending biomass
estimates, while SmplSize ranked No.2 in both experiments, NumYr ranked No.1 in this
experiment and No.12 in the 1997 experiment. We think the differences in the results of the
two studies were at least partially due to the differences in experimental sizes. Another
possible cause was the different versions of Synthesis we used. We used a newer version of
Synthesis (1999 release vs. 1997 release) for this study.
The ratio between ending biomass and starting biomass reflects the degree of
depletion for a particular population and has become an important measure of overfishing in
the management of many fisheries (e.g., PFMC 2000). Compared with the other types of
estimates that we examined, the Stock Synthesis program performed particularly better when
estimating this ratio (relative bias: 1.6%, relative variability: 19%). This study indicates that
the estimate of this ratio from the Stock Synthesis program at least can safely give fishery
managers some indication on the exploitation status of the stocks they manage.
Stock Synthesis estimates of ending exploitable biomass and
F35%
catch form the basis
for the annual catch quotas for many groundfish stocks on the U.S. Pacific coast (PFMC
54
1996)2.
This study suggests that increasing the number of years in the data series and
increasing the sample size are very crucial for obtaining less variable results for these two
estimates. For example, the ANOVA model for ending exploitable biomass predicts that the
most variable ending biomass estimates will occur for a treatment with a short data series (8
years), small fishery and survey age composition samples (100 fish per annual sample), high
variability (80%) in the fishing effort and survey biomass indices, low natural mortality (0.2),
an asymptotic fishery selection curve, high variability (20%) in the observed catch data,
constant recruitment, and a low trend in fishing mortality coefficient (0.0 1/ yr). For the
particular set of parameter values we examined the ANOVA model predicts for this worst-case
scenario a 90% coefficient of variation in the estimate of ending exploitable biomass. If we
double the length of data series to 16 years and increase the sample size to 400, the model
predicts that the same coefficient of variation will decrease to 20%.
2
In recent years the PFMC has adopted more conservative fishing rates,
for flatfish.
F40%
F5o% for
rockfish and
55
Chapter Three: Compound Multinomial Age Compositions and Assessments with the Stock
Synthesis Program
3.1 Introduction
The Stock Synthesis program (Methot 1990, 2000) extends the methods of Foumier
and Archibald (1982) and Deriso et al. (1985)10 reconstruct the demographic history of a fish
population from observed changes in the age compositions of the catch coupled with auxiliary
information such as survey indices of population abundance. A remarkable feature of the
program is its ability to process large amounts and different kinds of data. The Stock Synthesis
program is also very flexible with respect to the underlying population dynamics models and
to the number of parameters it can estimate. Since 1990, this program has been a major tool
used in assessing the stocks of groundfish along the U. S. west coast and in some other areas
(Dom et al. 1991; Porch et al. 1994; Sampson 1994).
Although flexible, the Stock Synthesis program, like other assessment models,
depends on some simplifying assumptions that, if violated, could adversely influence the
reliability of its estimates. Because estimates of sampling error associated
with
observed age
composition data are usually unavailable, the Stock Synthesis program assumes that the annual
age composition samples follow multinomial distributions. With this distribution, the greatest
relative accuracy occurs in the most frequently caught age classes and the variances of the age
composition data within and among years are determined by the size of each annual age
composition sample. There is evidence that most variability in age compositions of landings of
commercially-exploited species results from significant variation between boat trips (Crone
1995), which implies that annual age composition data obtained from samples combined
56
among trips will follow some form of compound multinomial distribution (Smith and Maguire
1983) instead of the simple multinomial distribution that the Stock Synthesis program assumes.
The primary objective of this research was to evaluate the robustness of the Stock
Synthesis program when applied tostocks whose annual age composition data follow
compound multinomial distributions. Specifically, we used Monte Carlo simulation techniques
to simultaneously evaluate the influence of nine input factors on the accuracy and precision of
seven types of Synthesis estimates, when the annual age composition data were generated
from compound multinomial distributions. We compared the results with the cases where
annual age compositions strictly obey simple multinomial distribution to isolate the effect of
different assumptions about the model for annual age composition. Synthesis estimates of
ending biomass, ending fishing mortality, ending recruitment, starting biomass, ending
exploitable biomass,
F35%
catches, and the ratio of ending biomass over starting biomass
constituted the seven types of estimates we evaluated (see Appendix A for the definitions of
these variables). The nine input factors we considered were the number of years in the data
series, the sample size for fishery and survey age sampling, the error levels in fishing effort
data, the error levels in survey biomass indices, the level of the natural mortality rate, the level
of trend in the fishing mortality rate, the error levels in the fishery catch data, the shape of
fishery selectivity curve, and the levels of strata coverage (defined in section 3.2.1) in
sampling.
3.2 Methods
The Monte Carlo techniques we used were relatively straightforward and essentially
the same as used for the experiments described in Chapter 2. We generated fishery and survey
data with known characteristics. The simulated data were then analyzed with the Stock
57
Synthesis program and the results from the program were compared with the true values to
evaluate the influence of age composition errors on the accuracy and precision of the Stock
Synthesis results. The experiments here differ from Chapter 2 in that the simulated age
composition data were drawn from strata with differing age compositions to mimic compound
multinomial random variables. Data sets were constructed with two levels of random
measurement error in each of five types of sample data (annual catch, fishery age composition,
fishing effort, survey index of stock biomass, and survey age composition). A series of
experiments was conducted to evaluate the suggestion by Fournier and Archibald (1982) that
age sample sizes in the likelihood specification should be limited to 400 fish per sample, i.e.,
the sample size that Synthesis uses should be the smaller of the actual sample size or 400.
Other factors examined in the experiments included short versus long series of data, domeshaped versus asymptotic fishery selection curves, high versus low trends in fishing mortality,
high versus low rates of natural mortality, and constant versus variable annual recruitment.
3.2.1 Compound multinomial distribution and simulation techniques
A fish population is not evenly spread across its habitat. Often fish tend to occur in
schools and are very patchily distributed. The size and age compositions observed from one
boat's landings of fish are usually very different from those of another boat. Crone (1995) has
shown that most variability in age compositions of landings of commercially exploited species
results from significant variation between boat trips. Thus, it is usually inappropriate to
assume that samples of fish are simple random samples from the fish population. Instead, a
more reasonable assumption might be that a fish population is stratified, each stratum
possessing its own annual age composition. To simulate this phenomenon, we assumed the
fish in a particular age group were randomly divided into strata following a normal distribution.
Note that there is no empirical basis for this algorithm. It is simply a convenient way to
58
randomly assign fish to strata. Let's use N as the number of stratum,
Nx,uk
as the total number
of age k fish, y, as the number of age k fish in stratum i, and o as the variance of the normal
distribution. Now our simulation problem can be rephrased as:
Given that y, Y2
are independent normal
1 to N, simulate the conditional distribution
We can write the above asy
y + (y
distribution model y and the (y
' Y
... YN,
...
y) for i = 1
= rn + (y
(/1k
given that
y = ,11k
N.
ofy1,
(,Uk
y,
..
o) random variates for strata
.
given that y =
y) for i = 1, ..., Nand use the fact that for the normal
y) are independent. Thus, the conditional distribution of
is the same as the distribution of
x1, x2
..... x, . . .XN, where x
Thus, we can simply generate N normal variates with normal
d'), subtract their sample mean, and add /1k.Ifl our actual implementation of the algorithm,
we used the CV(coefficient of variation) to replace o following d' =
(CVx1uk)2.
When simulating the fishery sampling across strata, we introduced the notion of
"strata coverage". When a fish stock is stratified, the fishery sampling for age composition is
not likely to evenly cover each and every stratum. Strata coverage reflects the percentage of
strata that were included in the sampling. For example, 50% strata coverage means
approximately half of the strata were sampled. In our simulation, each stratum was randomly
selected with replacement and the number of fish sampled per selected stratum was given by
s,,
N
where
Sto,ai
is the yearly total number of fish sampled (fishery sample size) and Pco is the strata
coverage in fishery sampling. The fishery age composition data sampled with above
compound multinomial algorithm are more variable than those with simple multinomial
algorithm (e.g., Figure 3.1). In the simulation, the survey strata coverage is always 100%.
59
60.00%
---
50.00%
LTT-°
40.00%
j
-*-____
30.00%
I..
20.00%
-I
10.00%
0.00%
2
3
4
5
6
7
8
9
10
Age
Figure 3.1. An example comparison of data variability between compound multinomial age
samples (CM) and simple multinomial age samples when applied to a same population (SM).
For both compound multinomial age composition and simple multinomial age composition, 20
samples, each containing 100 fish, were generated. The data variability is measured in CV
across the 20 samples.
We developed a simulation package for this research (Appendix B), consisting of
three C++ programs: the Stock Definer, the Data Simulator, and the Statistical Analyzer. The
attributes of a fishery system can be specified with the Stock Definer program. The Data
60
Simulator program simulates the dynamics of the fishery system as defined by the Stock
Definer and produces data sets for input to the Stock Synthesis program. The Statistical
Analyzer program summarizes the output data produced by the Stock Synthesis program and
compares them with the true values.
3.2.2 Stock Synthesis Configuration for this Study
Most fish stocks used in this study were configured to have compound multinomial
age compositions and their corresponding sampling processes all followed the compound
multinomial distribution as described above. The age composition data for both the fishery and
the survey were generated without age-reading error, but with compound-multinomial
sampling error. The Stock Synthesis program was then configured to treat the age composition
data as if they were generated with multinomial sampling error but without age-reading error.
Many of the features of the data configurations were similar to ones used for the experiments
in Chapter one and are described in Appendix C.
3.2.3 Experimental Design
Our study simultaneously examined the effects of nine factors on the performance of the
Stock Synthesis program through two main experiments (Al and A2) that conformed with a
fractional factorial design. The two main experiments follows the same design except that the
recruitment series were always held constant in one experiment and a variable recruitment
series was always used in the other experiment. One of the reasons we couldn't combine the
two experiments into one was that a one-fourth fraction of a 2'° factorial design was too big for
analyzing with the available statistics software. We compared the results of the two
experiments as a way of measuring the effect of more variable data as introduced by variable
61
Table 3.1. Fractional factorial experimental design. The factors are described in the text and in
Table 3.2.
Treatment NumYrs SmplSize EffortCV SurvCV NatlMort FishMort CatchCV FishSel StrtCov
8
400
20%
20%
0.2
0.01
10%
dome
50%
2
16
400
20%
20%
0.2
0.01
10%
asym
50%
3
8
2000
20%
20%
0.2
0.01
10%
dome
100%
4
16
2000
20%
20%
0.2
0.01
10%
asym
100%
5
8
400
80%
20%
0.2
0.01
10%
asym
100%
6
16
400
80%
20%
0.2
0.01
10%
dome
100%
7
8
2000
80%
20%
0.2
0.01
10%
asym
50%
16
8
2000
80%
20%
0.2
0.01
10%
dome
50%
9
8
400
20%
80%
0.2
0.01
10%
asym
50%
10
16
400
20%
80%
0.2
0.01
10%
dome
50%
11
8
2000
20%
80%
0.2
0.01
10%
asym
100%
12
16
2000
20%
80%
0.2
0.01
10%
dome
100%
13
8
400
80%
80%
0.2
0.01
10%
dome
100%
14
16
400
80%
80%
0.2
0.01
10%
asym
100%
15
2000
8
80%
80%
0.2
0.01
10%
dome
50%
16
16
2000
80%
80%
0.2
0.01
10%
asym
50%
17
8
400
20%
20%
0.4
0.01
10%
dome
100%
18
16
400
20%
20%
0.4
0.01
10%
asym
100%
19
8
2000
20%
20%
0.4
0.01
10%
dome
50%
20
16
2000
20%
20%
0.4
0.01
10%
asym
50%
21
8
400
80%
20%
0.4
0.01
10%
asym
50%
22
16
400
80%
20%
0.4
0.01
10%
dome
50%
23
8
2000
80%
20%
0.4
0.01
10%
asym
100%
24
16
2000
80%
20%
0.4
0.01
10%
dome
100%
25
8
400
20%
80%
0.4
0.01
10%
asym
100%
26
16
400
20%
80%
0.4
0.01
10%
dome
100%
27
8
2000
20%
80%
0.4
0.01
10%
asym
50%
28
16
2000
20%
80%
0.4
0.01
10%
dome
50%
29
8
400
80%
80%
0.4
0.01
10%
dome
50%
30
16
400
80%
80%
0.4
0.01
10%
asym
50%
2000
31
8
80%
80%
0.4
0.01
10%
dome
100%
16
2000
32
80%
80%
0.4
0.01
10%
asym
100%
400
33
8
20%
20%
0.2
0.03
10%
asym
100%
16
400
34
20%
20%
0.2
0.03
10%
dome
100%
35
8
2000
20%
20%
0.2
0.03
10%
asym
50%
16
36
2000
20%
20%
0.2
0.03
10%
dome
50%
37
8
400
80%
20%
0.2
0.03
10%
dome
50%
38
16
400
80%
20%
0.2
0.03
10%
asym
50%
2000
39
8
80%
20%
0.2
0.03
10%
dome
100%
16
2000
40
80%
20%
0.2
0.03
10%
asym
100%
41
8
400
20%
80%
0.2
0.03
10%
dome
100%
42
16
400
20%
80%
0.2
0.03
10%
asym
100%
43
8
2000
20%
80%
0.2
0.03
10%
dome
50%
44
16
2000
20%
80%
0.2
0.03
10%
asym
50%
400
45
8
80%
80%
0.2
0.03
10%
asym
50%
62
Table 3.1. (continued)
Treatment NumYrs SmplSize EffortCV SurvCV NatiMort FishMort CatchCV FishSel StrtCov
46
16
400
80%
80%
0.2
0.03
10%
dome
50%
47
8
2000
80%
80%
0.2
0.03
10%
asym
100%
48
16
2000
80%
80%
0.2
0.03
10%
dome
100%
49
8
400
20%
20%
0.4
0.03
10%
asym
50%
50
16
400
20%
20%
0.4
0.03
10%
dome
50%
51
8
2000
20%
20%
0.4
0.03
10%
asym
100%
52
16
2000
20%
20%
0.4
0.03
10%
dome
100%
53
8
400
80%
20%
0.4
0.03
10%
dome
100%
54
16
400
80%
20%
0.4
0.03
10%
asym
100%
55
8
2000
80%
20%
0.4
0.03
10%
dome
50%
56
16
2000
80%
20%
0.4
0.03
10%
asym
50%
57
8
400
20%
80%
0.4
0.03
10%
dome
50%
58
16
400
20%
80%
0.4
0.03
10%
asym
50%
59
8
2000
20%
80%
0.4
0.03
10%
dome
100%
60
16
2000
20%
80%
0.4
0.03
10%
asym
100%
61
8
400
80%
80%
0.4
0.03
10%
asym
100%
16
62
400
80%
80%
0.4
0.03
10%
dome
100%
63
8
2000
80%
80%
0.4
0.03
10%
asym
50%
64
16
2000
80%
80%
0.4
0.03
10%
dome
50%
65
8
400
20%
20%
0.2
0.01
20%
asym
100%
66
16
400
20%
20%
0.2
0.01
20%
dome
100%
67
8
2000
20%
20%
0.2
0.01
20%
asym
50%
68
16
2000
20%
20%
0.2
0.01
20%
dome
50%
69
8
400
80%
20%
0.2
0.01
20% dome
50%
70
16
400
80%
20%
0.2
0.01
20%
asym
50%
71
8
2000
80%
20%
0.2
0.01
20%
dome
100%
72
16
2000
80%
20%
0.2
0.01
20%
asym
100%
73
8
400
20%
80%
0.2
0.01
20%
dome
100%
74
16
400
20%
80%
0.2
0.01
20%
asym
100%
75
8
2000
20%
80%
0.2
0.01
20%
dome
50%
76
16
2000
20%
80%
0.2
0.01
20%
asym
50%
77
8
400
80%
80%
0.2
0.01
20%
asym
50%
78
16
400
80%
80%
0.2
0.01
20%
dome
50%
79
8
2000
80%
80%
0.2
0.01
20%
asym
100%
80
16
2000
80%
80%
0.2
0.01
20% dome
100%
81
8
400
20%
20%
0.4
0.01
20%
asym
50%
82
16
400
20%
20%
0.4
0.01
20% dome
50%
83
8
2000
20%
20%
0.4
0.01
20%
asym
100%
84
16
2000
20%
20%
0.4
0.01
20% dome
100%
85
8
400
80%
20%
0.4
0.01
20% dome
100%
86
16
400
80%
20%
0.4
0.01
20%
asym
100%
87
8
2000
80%
20%
0.4
0.01
20%
dome
50%
88
16
2000
80%
20%
0.4
0.01
20%
asym
50%
89
8
400
20%
80%
0.4
0.01
20%
dome
50%
90
16
400
20%
80%
0.4
0.01
20%
asym
50%
63
Table 3.1. (continued)
Treatment NumYrs SmplSize EffortCV SurvCV NatiMort FishMort CatchCV FishSel StrtCov
91
8
2000
20%
80%
0.4
0.01
20% dome
100%
92
16
2000
20%
80%
0.4
0.01
20%
asym
100%
93
8
400
80%
80%
0.4
0.01
20%
asym
100%
94
16
400
80%
80%
0.4
0.01
20%
dome
100%
95
8
2000
80%
80%
0.4
0.01
20%
asym
50%
96
16
2000
80%
80%
0.4
0.01
20% dome
50%
97
8
400
20%
20%
0.2
0.03
20% dome
50%
98
16
400
20%
20%
0.2
0.03
20%
asym
50%
99
8
2000
20%
20%
0.2
0.03
20% dome
100%
100
16
2000
20%
20%
0.2
0.03
20%
asym
100%
101
8
400
80%
20%
0.2
0.03
20%
asym
100%
102
16
400
80%
20%
0.2
0.03
20% dome
100%
103
8
2000
80%
20%
0.2
0.03
20%
asym
50%
104
16
2000
80%
20%
0.2
0.03
20%
dome
50%
105
8
400
20%
80%
0.2
0.03
20%
asym
50%
106
16
400
20%
80%
0.2
0.03
20%
dome
50%
107
8
2000
20%
80%
0.2
0.03
20%
asym
100%
108
16
2000
20%
80%
0.2
0.03
20%
dome
100%
109
8
400
80%
80%
0.2
0.03
20% dome
100%
110
16
400
80%
80%
0.2
0.03
20%
asym
100%
111
8
2000
80%
80%
0.2
0.03
20% dome
50%
16
112
2000
80%
80%
0.2
0.03
20%
asym
50%
113
8
400
20%
20%
0.4
0.03
20% dome
100%
114
16
400
20%
20%
0.4
0.03
20%
asym
100%
115
8
2000
20%
20%
0.4
0.03
20%
dome
50%
116
16
2000
20%
20%
0.4
0.03
20%
asym
50%
117
8
400
80%
20%
0.4
0.03
20%
asym
50%
118
16
400
80%
20%
0.4
0.03
20%
dome
50%
119
8
2000
80%
20%
0.4
0.03
20%
asym
100%
120
16
2000
80%
20%
0.4
0.03
20% dome
100%
121
8
400
20%
80%
0.4
0.03
20%
asym
100%
16
122
400
20%
80%
0.4
0.03
20%
dome
100%
123
8
2000
20%
80%
0.4
0.03
20%
asym
50%
124
16
2000
20%
80%
0.4
0.03
20% dome
50%
125
8
400
80%
80%
0.4
0.03
20% dome
50%
126
16
400
80%
80%
0.4
0.03
20%
asym
50%
127
8
2000
80%
80%
0.4
0.03
20% dome
100%
16
128
2000
80%
80%
0.4
0.03
20%
asym
100%
recruitment and a bigger CV for the population partitioning in A2. In addition, we used the
two experiments to check the repeatability of the experimental results where the two
64
experiments had slightly different configurations. In both experiments, random data sets were
generated in accordance with a one-fourth fraction of the 2 factorial design (Table 3.1).
Table 3.2. Low vs. high levels for the nine controlling variables
Name
NumYrs
SmplSize
EffortCV
SurvCV
NatMort
FishMort
CatchCV
FishSel
StrtCov
Factor
Description
number of years of data.
sample size for age composition.
fishing effort variability.
survey biomass variability.
natural mortality increment.
fishing mortality.
catch data variability.
fishery selectivity,
Strata coverage.
Value Configuration
at low level (-1)
at high level (+1)
8
400
20%
20%
16
1600/2000*
80%
80%
0.2
0.4
0.01
0.03
10%
20%
dome shaped
asymptotic shaped
50%
100%
*Note: the two main experiments had slightly different values in the high level of sample size.
Experiment Al used 2000 and experiment A2 used 1600. The purpose was to measure the effect
of having different high level sample size values.
For each of the 128 experimental treatments, we applied the Data Simulator four times,
each time generating 200 replicate data sets that were then analyzed with Stock Synthesis. We
use the term ?tbatch!I to describe each of the four 200 data sets. Note that data among the four
batches were subject to two levels of random errors: partitioning error for stratification of the
age compositions and observation error during sampling. The batches differed in partitioning,
but samples within a batch all had the same partitioning. The nine controlling variables were:
(1) the number of years in the data series (NumYrs); (2) the size of annual age composition
sample (SmplSize); (3) the coefficient of variation of annual fishing effort data (EffortCV); (4)
the coefficient of variation of annual survey biomass data (SurvCV); (5) the instantaneous rate
of natural mortality (NatlMort); (6) the annual increment in the rate of fishing mortality
(FishMort); (7) the coefficient of variation of annual catch data (CatchCV); (8) the shape of
the fishery selection curve (FishSel); and (9) the strata coverage (StrtCov). Among the nine
65
controlling variables, sample size was a bit unusual because Synthesis was configured to use a
maximum sample size of 400 in its calculation of the likelihood component for the age
composition data. The configuration of the low and high levels of the nine factors is shown in
Table 3.2.
The level of natural mortality (M) was coupled with several other stock parameters
(Table 3.3). Normally, a long-lived species grows slower, matures at a later age, and has a low
natural mortality coefficient. In contrast, a short-lived species grows faster, matures earlier,
and has a high natural mortality coefficient. Similarly, species with low M and species with
high M will very likely have different fishery and survey selectivity curves. In this study, the
shape of the selectivity curve for the survey was always asymptotic, but the selectivity curve
for the fishery was either 'domed" or asymptotic. Also, for the two main experiments (Al, A2)
involving compound multinomial distributions, the total number of age composition strata for
a stock was always 10. However, for the CVs used to randomly partition an age group into the
10 strata, Al and A2 had slightly different values. The partitioning CV for all the simulation in
Al was 0.3 whereas in A2 it was 0.5. When a bigger CV is used in partitioning the population
Table 3.3. Parameter values associated with the two levels of natural mortality M.
parameters
max. age
mm. age
1St inflection age of fish. Selectivity
2nd inflection age of fish. Selectivity
inflection age of survey selectivity
inflection age of maturity function
slope of maturity function
value when M at 0.2/yr.
20 yr.
4 yr.
6 yr.
value when M at 0.4/yr.
16 yr.
5 yr.
5 yr.
10 yr.
2 yr.
4 yr.
8 yr.
3 yr.
3 yr.
1
2
Table 3.4. Alias structure of the fractional factorial design.
Alias Structure* (up to order 4)
A: NumYr, B: SmplSize, C: EffortCV, D: SurvCV, E: NatMort, F: FishMort, G: CatchCV,
H: FishSel, J: StrtCov
Grand mean
A
B
C
D
E
F
G
H
J
AB + DEHJ
AC + DFGH
AD + BEHJ + CFGH
AE + BDHJ
AF + CDGH
AG + CDFH
AH+BDEJ+CDFG
AJ + BDEH
BC + EFGJ
BD + AEHJ
BE + ADHJ + CFGJ
BF + CEGJ
BG + CEFJ
BH + ADEJ
BJ + ADEH + CEFG
CD + AFGH
CE + BFGJ
CF + ADGH + BEGJ
CG + ADFH + BEFJ
CH + ADFG
CJ + BEFG
DE+ABHJ
DF + ACGH
DG + ACFH
DH + ABEJ + ACFG
DJ + ABEH
EF + BCGJ
EG + BCFJ
EH + ABDJ
EJ + ABDH + BCFG
FG + ACDH + BCEJ
FH + ACDG
FJ + ECEG
GH + ACDF
GJ + BCEF
HJ + ABDE
*The main effects are aliased with 5" and higher order interactions, which are assumed 0.
67
into strata, the age composition within each stratum is likely to be more different than the age
composition of the entire population. Thus, when only a few strata are selected for sampling,
the combined sample age composition data will tend to deviate more from the true populationat-age.
In main experiment Al, all simulations had constant recruitment with the annual
recruitment at 3,000 fish (in thousands), the initial age composition at the start of the first year
was at equilibrium, and Stock Synthesis was configured to estimate the initial equilibrium age
composition. For all simulations in main experiment A2, the average annual recruitment was
also 3,000 fish, but the annual recruitment values varied according to the sequence 3,500,
4,000, 1,200, 4,200, 3,000, 3,200, 1,700, 3,200 (repeated as necessary), and the Stock
Synthesis program was configured to estimate the initial non-equilibrium age composition.
Even though we used a fractional factorial design, all nine main effects were
separately estimable (Table 3.4) in our experiment, assuming that fifth and higher order
interactions were zero. In other words, none of the main effects were "aliased" with any fourth
and lower order interactions. However, the interactions were not separately estimable. For
example, the two-way interaction between the number of years and the sample size was
"aliased" with the four-way interaction among survey biomass variability x natural mortality><
fishery selectivity
x
strata coverage, meaning the value estimated for the two-way interaction
included the value for the four-way interaction (Box et al. 1978). Usually one would expect
high-order interactions to be small relative to low-order interactions.
The Stock Synthesis program routinely produces a wide variety of estimates, e.g.,
estimates for the annual series of biomass, fishing mortality, catch, recruitment, and the
F3500
catch for the last year. In this study we focused on seven categories of Synthesis outputs.
These outputs included the estimates for the first year for total biomass, the estimates for the
last year for total biomass, exploitable biomass, rate of fishing mortality, recruitment, F350.
68
catch, and the ratio of the total biomass for the last year versus the total biomass for the first
year. For each experimental treatment and output type, we calculated the relative bias and
relative variability for each of the four replicated batches (each replicate batch contained 200
data sets). We measured relative bias both in the forms of relative bias of the mean and relative
bias of the median. The relative bias of the mean within each group of 200 estimates was
defined as:
1
200
(estimated value1
true value
)
The relative bias of the median within each group of 200 estimates was defined as:
The median of the 200 estimated values
true value
true value
We calculated the median as the average of the 100thi and 101st ordered values. The relative
variability within each batch of 200 estimates was measured using the coefficient of variation.
We summarized the results for each experimental treatment by calculating the mean relative
bias and mean coefficient of variation across the four replicate groups. For each of the 21
measurements, we conducted a separate fractional analysis of variance using the Minitab
statistics program (Release 13.1 for Windows). After conducting the above analysis separately
for main experiment Al and A2, we compared the results from Al and A2.
3.2.4 Sensitivity to Initial Parameter Values
In the two main experiments, we used the true parameter values as the initial
parameter values. However, likelihood functions can have multiple maxima or the search
algorithm might stop prematurely if the likelihood surface is very flat, thus the choice of initial
parameter values may influence whether or not the search algorithm actually finds a local
rather than the global maximum. For a given data set, Synthesis users sometimes randomize
69
the initial parameter values many times and compare the likelihood values from the runs with
each of the randomized parameter values. To examine the influence of initial parameter values
on the performance of Synthesis, we conducted four randomization experiments on treatment
40 and treatment 77 in Al, and treatment 40 and treatment 89 in A2. In the main experiment
Al, treatment 77 and treatment 40 respectively had the maximum and the minimum variability
in the estimates of ending biomass and exploitable ending biomass. In experiment A2, the
same maximum and minimum occurred respectively in treatment 89 and treatment 40. For
each of the four treatments, we generate 100 random data sets. For each random data set
generated, we ran the Stock Synthesis program 100 times, each time using a different set of
randomized initial parameter values, with each parameter varying uniformly within ± 40% of
its true value.
3.2.5 The Influence of Compound Multinomial Distribution on the Effect of Sample Size
The effects of the major contributing factors (e.g., number of year, sample size, survey
variability, and etc.) on the Synthesis estimates might be very different from the results in
Chapter 2 when the age composition models of the underlying stock differ (compound
multinomial distribution here versus simple multinomial distribution in Chapter 2). In addition,
we only used two levels (low and high) in the values of the factors in the main experiments Al
and A2 but the effects of those factors on relative bias and relative variability may not be
linear. For example, in experiment Al, the low (-1) and high (+1) levels for the factor of
sample size were 400 and 2000 respectively. Would we get different results if we had used
different values for the low and high levels of sample size? To supplement the comparison and
analysis on the effect of stratification and to evaluate the non-linearity of the effects, we
designed four smaller full factorial experiments on three factors, the number of years in the
data series, the size of the age composition samples, and the survey vaiability (Table 3.5).
70
Each experiment was conducted with four batches. Each batch contained 200 Synthesis runs.
Thus, for each of the four (Bi, B2, Cl, C2) experiments, the total Synthesis runs were
8x4x200. In experiments Bi and B2, there was no stratification in the population (simple
multinomial samples), whereas in experiments Cl and C2, the populations were split into 10
strata (compound multinomial samples). The only difference between B 1 and B2 was the
sample size factor. In B 1, the low and high values of sample size were 100 and 400
respectively. In B2, these values were 400 and 1600. Similarly, the only difference between
Cl and C2 was in the sample size values. These designs made it very easy to directly compare
the results from experiment Bi and B2 as well as that from Cl and C2.
Table 3.5. Designs of experiments Bi, B2, Cl, and C2.
Without Stratification
Factor
numYrs
smplSize
svyCv
Experiment B!
Values
Low (-1) High
(+1)
Experiment B2
Values
Low (-1) High
(+1)
8
16
8
400
0.8
16
100
0.2
400
0.2
1600
Factors at Fixed Value:
effortCv
0.5
natiM
0.2
Ftrend
0.02
catchCv
0.1
Fslct
domed
rec Var
const
#Stratum
1
strtaCov
100%
0.8
0.5
0.2
0.02
0.1
domed
const
1
100%
With Stratification
Factor
numYrs
smplSize
svyCv
Experiment Cl
Values
Low (-1)
High
(+1)
Experiment C2
Values
Low (-1) High (+1)
8
16
8
400
0.8
16
100
0.2
400
0.2
1600
0.8
Factors at Fixed Value:
effortCv
0.5
natlM
0.2
Ftrend
0.02
EcatchCv
0.!
Fslct
domed
recVar
const
#Stratum
10
strtaCov
100%
0.5
0.2
0.02
0.1
domed
const
10
100%
71
3.2.6 Effects of Configured Maximum Sample Sizes in the Likelihood Specification
In experiments Al, A2, BI, B2, Cl, C2, we configured Synthesis following the
suggestion by Foumier and Archibald (1982) that age sample sizes in the likelihood
specification should be limited to 400 fish per sample. In other words, the sample size that
Synthesis used was the smaller of the actual sample size or 400. With compound multinomial
distributions, the age composition sample data are more overdispersed relative to simple
multinomial distributions. It is likely that the upper limit of 400 is already too big, i.e., the
increased variability in age composition data might be disproportionately propagated into the
Synthesis estimates. Experiment D (Table 3.6) was designed specifically to evaluate the
effects of different configured maximum sample sizes in the likelihood specification.
Experiment D was a small 2 full factorial. One of the three factors was "synSize", the
maximum sample size configured in the likelihood specification. In experiment D, the sample
size that Synthesis used was the smaller of the actual sample size or the value of synSize. We
used 200 and 400 as the low and high levels for the synSize factor.
Table 3.6 Design of experiment D.
Factor
numYrs
synSize*
svyCv
Factors at Fixed Value:
smplSize
effortCv
natlM
Ftrend
catchCv
Fslct
recVar
#Stratum
strtaCov
Values
Low(-1)
High(--1)
8
16
200
0.2
400
0.8
400
0.5
0.2
0.02
0.1
domed
const
10
50%
*synSize: the maximum sample size used by Synthesis
72
Table 3.7. Relative bias for the 128 experimental treatments in experiment Al.
Treatment end Bio
1
0.0622
0.0073
2
3
0.0157
4
0.0086
0.0309
5
6
0.0073
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
0.0171
0.0042
end F
-0.0054
0.0087
0.0055
0.0003
0.0261
0.0158
0.0175
0.0008
0.0662
0.0217
0.0287
-0.0055
0.0156
0.0713
0.0136
0.0255
0.0213
0.0357
0.0112
0.0105
0.0722
0.0482
0.0364
0.0059
0.1196
0.0486
0.0633
0.0150
0.0511
0.1333
0.0580
0.0141
0.0243
0.0177
0.0029
0.0034
-0.0138
0.0160
-0.0069
0.0754
0.0120
0.0887
0.0199
0.1351
0.0540
0.0314
0.0519
0.0648
-0.0071
0.0464
0.0059
0.0008
-0.0169
-0.0056
0.0013
0.0498
0.0142
0.0843
0.0290
0.2839
0.0150
0.0329
0.0521
0.0165
-0.0001
0.0202
0.0032
0.0476
0.0102
0.0206
0.0080 0.0061
0.0504 -0.0109
0.0267
0.0112
0.0199 0.0038
0.0130 0.0005
0.1068 0.1556
0.0129
0.0321
end Rec
0.0760
0.0288
0.0192
0.0177
0.0511
0.0063
0.0204
-0.0045
0.1060
0.0248
0.1000
0.0208
0.1646
0.0684
0.0392
0.0619
0.0816
-0.0023
0.0506
0.0055
0.0124
-0.0033
-0.0113
-0.0010
0.0670
0.0308
0.0918
0.0357
0.3161
0.0287
0.0396
0.0586
0.0320
0.0082
0.0213
0.0051
0.0634
0.0191
0.0257
0.0060
0.0718
0.0478
0.0323
0.0201
0.1497
0.0218
start Bio
0.0347
-0.0034
0.0091
0.0028
0.0134
-0.0020
0.0089
0.0006
0.0344
-0.0017
0.0477
0.0072
0.0754
0.0050
0.0169
0.0083
0.0288
-0.0157
0.0308
0.0011
-0.0082
-0.0262
-0.0042
-0.0005
0.0221
-0.0156
0.0474
0.0079
0.1690
-0.0072
0.0173
0.0075
0.0042
-0.0056
0.0071
-0.0006
0.0188
-0.0002
0.0122
0.0007
0.0192
-0.0010
0.0071
0.0019
0.0326
-0.0028
end exE F35 catch
0.0574
0.0719
0.0005
0.0074
0.0152
0.0182
0.0062
0.0098
0.0245
0.0348
0.0015
0.0102
0.0150
0.0193
0.0025
0.0060
0.0650
0.0854
0.0056
0.0149
0.0864
0.0987
0.0184
0.0236
0.1324
0.1541
0.0453
0.0622
0.0290
0.0357
0.0476
0.0590
0.0670
0.0781
-0.0202
-0.0046
0.0464
0.0508
0.0004
0.0086
-0.0102
-0.0390
-0.0198
-0.0124
-0.0086
-0.0047
0.0011
0.0045
0.0389
0.0430
0.0132
0.0213
0.0807
0.0935
0.0291
0.0338
0.2884
0.3162
0.0022
0.0118
0.0346
0.0382
0.0463
0.0625
0.0096
0.0195
-0.0063
0.0005
0.0176
0.0251
0.0018
0.0044
0.0447
0.0612
0.0028
0.0089
0.0196
0.0249
0.0049
0.0090
0.0480
0.0648
0.0158
0.0305
0.0179
0.0245
0.0094
0.0188
0.0929
0.1304
0.0056
0.0189
endB/startB
0.0162
0.0101
0.0025
0.0051
0.0050
0.0076
0.0015
0.0030
0.0059
0.0108
0.0098
0.0110
0.0230
0.0364
0.0071
0.0359
0.0178
0.0080
0.0048
0.0038
-0.0011
0.0076
-0.0067
0.0008
-0.0085
0.0226
-0.0001
0.0141
0.0384
0.0101
-0.0019
0.0364
0.0056
0.0058
0.0074
0.0039
0.0231
0.0107
0.0070
0.0076
0.0229
0.0285
0.0092
0.0118
0.0169
0.0150
73
Table 3.7 (continued)
Treatment end Bio end F
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
0.0777
0.01 10
0.0213
-0.0098
0.0190
0.0045
0.0354
-0.0001
0.0225
0.0010
0.1077
0.0089
0.0519
0.0144
0.1505
0.0223
0.0801
0.0195
0.0597
0.0117
0.0652
0.0042
0.0977
0.0061
0.0138
0.0134
0.0982
0.0308
0.0347
0.0373
0.1365
0.0402
0.0959
0.0190
0.0459
-0.0019
0.0498
0.0127
0.0831
-0.0028
0.0379
0.0096
0.2029
0.0250
0.1040
0.0357
end Rec start Bio end exB
0.0196 0.1003
0.0260 0.0697
0.0096 0.0123
0.0041
0.0104
0.0353 0.0370 -0.0003 0.0084
0.0262 -0.0009 -0.0205 -0.0157
0.0056 0.0183
0.0087 0.0164
0.0023 0.0021
0.0011
0.0040
0.0209 0.0550
0.0079 0.0346
0.0282 0.0054 -0.0059 -0.0132
-0.0003
0.0270
0.0142 0.0252
0.0119 -0.0041
0.0009 -0.0039
-0.0015 0.1347
0.0424 0.1126
0.0274 0.0158 -0.0064 -0.0036
0.0046 0.0564
0.0245 0.0550
0.0119 0.0164
0.0014 0.0066
0.1240 0.1965
0.0466 0.1311
0.0620 0.0364 -0.0118 0.0171
0.0691
0.1131
0.0301
0.0722
0.0227 0.0190
0.0044 0.0202
0.0232 0.0876
0.0270 0.0516
0.0049 0.0117
0.0004 0.0081
-0.0087
0.0740
0.0333
0.0625
0.0026 0.0035
0.0003
0.0030
-0.0346 0.1219
0.0566 0.0945
0.0149 0.0013 -0.0017 0.0020
0.0097 0.0170
0.0071
0.0126
-0.0072 0.0175
0.0023 0.0130
-0.0043
0.1425
0.0516 0.0945
0.0193 0.0435
0.0025 0.0246
0.0015 0.0484
0.0186 0.0343
-0.0009
0.0442
0.0043
0.0337
0.2210 0.1809
0.0648
0.1242
0.0104 0.0587
0.0038 0.0347
0.0115
0.1226
0.0497 0.0883
-0.0016 0.0181
0.0079 0.0177
0.0596 0.0636
0.0149 0.0378
0.0432 0.0079 -0.0234 -0.0017
0.0193
0.0573
0.0294 0.0456
0.0050 0.0176
0.0033 0.0118
0.0358 0.0849
0.0477 0.0849
0.0287 0.0104 -0.0133 -0.0149
-0.0012 0.0500
0.0231
0.0392
0.0048 0.0046
0.0017 0.0056
0.0578 0.2224
0.1207 0.2054
0.0400 0.0304 -0.0056 0.0144
0.0462 0.1246
0.0623
0.1041
0.0154 0.0377
0.0074 0.0306
F35 catch endB!startB
0.0957
0.0289
0.0122
0.0069
0.0083
0.0158
-0.0065
0.0115
0.0235
0.0050
0.0064
0.0035
0.0465
0.0192
0.0000
0.0068
0.0258
0.0043
0.0020
0.0004
0.1329
0.0402
0.0038
0.0174
0.0627
0.0131
0.0197
0.0140
0.1636
0.0415
0.0338
0.0327
0.0951
0.0186
0.0264
0.0130
0.0659
0.0111
0.0152
0.0097
0.0725
0.0108
0.0050
0.0030
0.1107
0.0276
0.0073
0.0073
0.0165
0.0039
0.0164
0.0104
0.1111
0.0232
0.0343
0.0237
0.0390
0.0065
0.0432
0.0288
0.1523
-0.0123
0.0507
0.0289
0.1091
0.0142
0.0232
0.0092
0.0435
0.0076
0.0028
0.0189
0.0561
0.0013
0.0158
0.0068
0.0937
0.0172
0.0008
0.0101
0.0431
0.0078
0.0128
0.0076
0.2264
0.0268
0.0278
0.0265
0.1170
0.0017
0.0411
0.0235
74
Table 3.7 (continued)
Treatment end Bio
93
0.0546
94
0.0883
95
0.0809
96
0.0548
97
0.0410
98
0.0178
99
0.0218
100
0.0112
101
0.0258
102
0.0188
103
0.0262
104
0.0127
105
0.0868
106
0.0067
107
0.0795
108
0.0099
109
0.0832
110
0.0404
111
0.0219
112
0.0484
113
0.0474
114
0.0070
115
0.0386
116
0.0187
117
118
119
120
121
122
123
124
125
126
127
128
max
mm
average
0.0299
0.2270
0.0513
0.0560
0.0381
end F
0.3311
0.0463
0.0904
0.0116
-0.0153
0.0026
-0.0129
0.0109
0.0229
0.0091
-0.0095
-0.0210
0.0264
0.0155
0.0211
-0.0098
0.0071
0.0414
0.0021
0.0069
-0.0078
0.0070
-0.0137
-0.0083
0.0234
0.0240
0.0169
-0.0039
0.0440
0.0048
0.0302
-0.0019
0.0158
0.0471
0.0100
-0.0037
0.2839
-0.0169
-0.0346
0.0121
0.0077
0.0164
0.0125
0.0814
0.0241
0.0709
0.3311
0.04060.0246
end Rec
0.0788
0.1055
0.1055
0.0623
0.0560
0.0265
0.0274
0.0078
0.0473
0.0267
0.0277
0.0164
0.1183
0.0172
0.1100
0.0154
0.1153
0.0582
0.0216
0.0606
0.0514
0.0073
0.0485
0.0200
0.0256
0.0147
0.0188
0.0115
0.1206
0.0402
0.0875
0.0384
0.2791
0.0627
0.0731
0.0465
0.3161
-0.0113
0.0525
start Bio
0.0229
0.0037
0.0441
0.0134
0.0161
0.0003
0.0110
0.0050
0.0089
-0.0026
0.0120
0.0037
0.0287
-0.0028
0.0281
0.0006
0.0316
-0.0020
0.0101
0.0030
0.0165
-0.0070
0.0220
0.0069
0.0002
-0.0065
0.0085
0.0029
0.0265
-0.0172
0.0307
0.0035
0.0991
-0.0058
0.0242
0.0069
end exB F35 catch
0.0432
0.0234
0.0887
0.1060
0.0717
0.0850
0.0549
0.0637
0.0399
0.0519
0.0125
0.0195
0.0221
0.0279
0.0082
0.0103
0.0190
0.0280
0.0134
0.0254
0.0235
0.0325
0.0119
0.0220
0.0765
0.1045
0.0004
0.0103
0.0718
0.0948
0.0082
0.0155
0.0824
0.1034
0.0326
0.0508
0.0215
0.0276
0.0423
0.0603
0.0503
0.0622
-0.0056
0.0129
0.0390
0.0473
0.0137
0.0250
0.0014
-0.0058
0.0043
0.0109
0.0137
0.0179
0.0119
0.0170
0.0669
0.0832
0.0182
0.0367
0.0681
0.0816
0.0268
0.0389
0.2314
0.2749
0.0372
0.0669
0.0571
0.0683
0.0305
0.0532
0.1690
-0.0262
0.0142
0.2884
-0.0202
0.0363
0.3162
-0.0390
0.0470
endB/startB
-0.0361
0.0623
-0.0039
0.0289
0.0205
0.0204
0.0076
0.0083
0.0119
0.0221
0.0109
0.0095
0.0257
0.0107
0.0231
0.0106
0.0367
0.0450
0.0090
0.0490
0.0206
0.0166
0.0063
0.0138
0.0066
0.0151
0.0048
0.0098
0.0228
0.0433
0.0079
0.0274
0.0640
0.0614
0.0174
0.0335
0.0640
-0.0361
0.0149
75
Table 3.8. Relative variability for the 128 experimental treatments in experiment Al.
Treatment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
end Bio
0.2321
0.1111
0.1417
0.1020
0.2396
0.1180
0.1737
0.0721
0.4056
0.1536
0.3561
0.1156
0.4472
0.3270
0.1848
0.2582
0.3405
0.1184
0.2433
0.1076
0.2400
0.1471
0.1643
0.0968
0.4410
0.2360
0.4384
0.2089
0.6132
0.3491
0.2981
0.2659
0.1851
0.0900
0.1660
0.0743
0.1615
0.0924
0.0878
0.0675
0.1940
0.1596
0.1331
0.1480
0.5428
0.1671
end F
0.2381
0.1373
0.1634
0.1273
0.2501
0.1648
0.2019
0.1314
0.3583
0.1848
0.3369
0.1492
0.3576
0.3722
0.2077
0.2841
0.2968
0.1504
0.2453
0.1359
0.2618
0.1840
0.1950
0.1515
0.3721
0.2505
0.3500
0.2184
0.5755
0.3797
0.3119
0.2640
0.1883
0.1335
0.1649
0.1214
0.2072
0.1443
0.1369
0.1260
0.2270
0.1753
0.1559
0.1630
0.5016
0.2235
end Rec
0.3213
0.2028
0.1813
0.1435
0.3177
0.1968
0.2267
0.1243
0.5152
0.2566
0.4148
0.1602
0.5564
0.4067
0.2373
0.3093
0.3831
0.1760
0.2745
0.1455
0.2958
0.1868
0.1935
0.1230
0.5166
0.2787
0.4899
0.2418
0.6769
0.4157
0.3271
0.3051
0.2651
0.1595
0.2227
0.1263
0.2635
0.1712
0.1366
0.1013
0.2963
0.2468
0.1935
0.2023
0.6845
0.2544
start Bio
0.1493
0.0378
0.0892
0.0310
0.1341
0.0493
0.0972
0.0358
0.2170
0.0580
0.1966
0.0384
0.2775
0.0571
0.1141
0.0458
0.2440
0.0606
0.1710
0.0440
0.1544
0.1014
0.1036
0.0572
0.2621
0.1233
0.2526
0.0885
0.4274
0.0872
0.1977
0.0576
0.0778
0.0365
0.0678
0.0307
0.0854
0.0341
0.0530
0.0292
0.0947
0.0324
0.0655
0.0311
0.1993
0.0390
end exB
0.2412
0.1083
0.1478
0.0991
0.2382
0.1233
0.1713
0.0756
0.3958
0.1581
0.3517
0.1192
0.4593
0.3197
0.1908
0.2508
0.3425
0.1258
0.2451
0.1101
0.2499
0.1507
0.1680
0.0979
0.4450
0.2412
0.4385
0.2124
0.6127
0.3483
0.3040
0.2626
0.1824
0.0922
0.1604
0.0753
0.1707
0.0895
0.0927
0.0647
0.2044
0.1477
0.1394
0.1393
0.5213
0.1712
F35 catch
0.2587
0.1220
0.1577
0.1118
0.2639
0.1367
0.1920
0.0835
0.4434
0.1760
0.3871
0.1333
0.4983
0.3710
0.2079
0.2946
0.3604
0.1349
0.2591
0.1188
0.3377
0.1585
0.1787
0.1068
0.5003
0.2561
0.4766
0.2292
0.6596
0.4102
0.3232
0.3017
0.2158
0.1119
0.1923
0.0916
0.1982
0.1160
0.1076
0.0882
0.2371
0.1922
0.1620
0.1793
0.6425
0.2231
endB/startB
0.0882
0.0977
0.0585
0.0890
0.1103
0.0885
0.0810
0.0515
0.1769
0.1185
0.1573
0.0930
0.1390
0.2782
0.0762
0.2196
0.1059
0.0937
0.0847
0.0874
0.1068
0.0843
0.0706
0.0621
0.1750
0.1525
0.1634
0.1428
0.1876
0.2855
0.1094
0.2193
0.1181
0.0847
0.1063
0.0698
0.0896
0.0890
0.0480
0.0659
0.1105
0.1611
0.0783
0.1493
0.3016
0.1575
76
Table 3.8 (continued)
Treatment
end Bio
end F
end Rec
start Bio end exB
47
0.3154
0.3332
0.3955
0.1163
0.3013
0.3731
0.1940
48
0.0905
0.1560
0.1463
0.0290
0.0924
0.1237
0.0855
49
0.1863
0.2062
0.2583
0.0966
0.1912
0.2558
0.1131
50
0.1091
0.1442
0.1714
0.0606
0.1120
0.1331
0.0971
51
0.1628
0.1666
0.2024
0.0730
0.1597
0.1897
0.1013
52
0.0932
0.1295
0.1325
0.0389
0.0944
0.1125
0.0850
53
0.2126
0.2473
0.2655
0.1340
0.2194
0.2412
0.1023
54
0.0876
0.1476
0.1464
0.0448
0.0927
0.1180
0.0872
55
0.1488
0.1886
0.1893
0.0990
0.1566
0.1671
0.0657
56
0.0767
0.1326
0.1237
0.0355
0.0790
0.0965
0.0723
57
0.3543
0.3237
0.4107
0.2072
0.3648
0.4018
0.1545
58
0.1559
0.1836
0.2195
0.0501
0.1568
0.2155
0.1613
59
0.2547
0.2456
0.2888
0.1377
0.2597
0.2919
0.1218
60
0.1362
0.1658
0.1713
0.0367
0.1341
0.1696
0.1393
61
0.5418
0.5023
0.6473
0.2287
0.5336
0.6476
0.2857
62
0.2435
0.3111
0.3072
0.0705
0.2465
0.3138
0.2236
63
0.3804
0.3749
0.4704
0.1523
0.3718
0.4514
0.2180
64
0.1957
0.2461
0.2516
0.0495
0.1938
0.2494
0.1773
65
0.3211
0.2826
0.4091
0.1850
0.3177
0.3441
0.1390
66
0.1339
0.2141
0.2176
0.0646
0.1360
0.1466
0.1021
67
0.3083
0.2595
0.3583
0.1741
0.3056
0.3292
0.1348
68
0.1120
0.2064
0.1522
0.0567
0.1132
0.1213
0.0854
69
0.2511
0.3153
0.3286
0.1718
0.2623
0.2759
0.0890
70
0.1059
0.2341
0.1999
0.0579
0.1059
0.1206
0.0822
71
0.1350
0.2415
0.1676
0.1017
0.1397
0.1499
0.0465
72
0.0976
0.2303
0.1352
0.0576
0.0972
0.1127
0.0691
73
0.3389
0.3266
0.4599
0.2179
0.3523
0.3697
0.1226
74
0.2359
0.2430
0.3207
0.0618
0.2301
0.2584
0.2013
75
0.2195
0.2332
0.2738
0.1401
0.2263
0.2387
0.0895
76
0.2291
0.2405
0.2721
0.0579
0.2226
0.2488
0.2000
77
0.6427
0.5911
0.7821
0.3537
0.6297
0.6998
0.2609
78
0.2325
0.3184
0.3206
0.0824
0.2418
0.2706
0.1727
79
0.3683
0.3986
0.4326
0.2053
0.3605
0.4008
0.1637
80
0.1245
0.2539
0.1632
0.0622
0.1281
0.1463
0.0887
81
0.3552
0.3175
0.4086
0.2225
0.3625
0.3953
0.1409
82
0.1859
0.2451
0.2196
0.1163
0.1918
0.1955
0.1191
83
0.3064
0.2801
0.3445
0.1836
0.3083
0.3282
0.1262
84
0.1463
0.2167
0.1692
0.0756
0.1484
0.1559
0.1017
85
0.3419
0.3841
0.3772
0.2579
0.3507
0.3592
0.0997
86
0.1183
0.2347
0.1737
0.0743
0.1274
0.1302
0.0859
87
0.2116
0.2784
0.2425
0.1609
0.2135
0.2213
0.0687
88
0.1013
0.2359
0.1428
0.0625
0.1038
0.1147
0.0757
89
0.5763
0.4762
0.6174
0.4197
0.5821
0.6101
0.1683
90
0.2367
0.2628
0.3011
0.0875
0.2392
0.2676
0.1963
91
0.4626
0.3778
0.5055
0.3005
0.4660
0.4970
0.1510
92
0.2348
0.2438
0.2675
0.0669
0.2315
0.2581
0.1992
F35
catch
endB/startB
77
Table 3.8 (continued)
Treatment
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
max.
mm.
average
end Bio
0.5985
0.3690
0.4330
0.2634
0.1635
0.1265
0.1417
0.1142
0.1724
0.1085
0.1432
0.0786
0.4018
0.1432
0.3690
0.1266
0.2611
0.2655
0.1380
0.2116
0.2449
0.1208
0.2273
0.1153
0.1903
0.1227
0.1455
0.0947
0.4081
0.2024
0.3929
0.1816
0.5316
0.2825
0.2614
0.2013
end F
0.6237
0.4365
0.4649
0.3217
0.2431
0.1978
0.2017
0.1910
0.2612
0.2485
0.2315
0.2305
0.3230
0.2163
0.3043
0.1947
0.3455
0.3384
0.2517
0.2875
0.2674
0.2060
0.2334
0.2026
0.2799
0.2421
0.2381
0.2340
0.3422
0.2251
0.3279
0.2232
0.5286
0.3504
0.3298
0.2753
end Rec
0.6971
0.4173
0.5050
0.2993
0.2564
0.1933
0.1866
0.1436
0.2489
0.1846
0.1885
0.1249
0.5175
0.2253
0.4566
0.1703
0.3730
0.3514
0.1909
0.2762
0.2825
0.1725
0.2619
0.1519
0.2493
0.1813
0.1794
0.1200
0.4846
0.2523
0.4619
0.2234
0.6156
0.3639
0.3002
0.2504
start Bio
0.3391
0.1545
0.2548
0.1114
0.0997
0.0591
0.0885
0.0557
0.0940
0.0597
0.0876
0.0573
0.1597
0.0608
0.1451
0.0540
0.1345
0.0584
0.0891
0.0587
0.1538
0.0669
0.1288
0.0619
0.1135
0.0766
0.0930
0.0610
0.1868
0.0845
0.1726
0.0649
0.3091
0.0709
0.1512
0.0606
0.2661
0.1712
0.1235
0.1458
0.1118
0.1703
0.1104
0.1417
0.0816
0.3891
0.1454
0.3551
0.1301
0.2740
0.2524
0.1425
0.1991
0.2514
0.1238
0.2296
0.1137
0.1985
0.1267
0.1483
0.0970
0.4113
0.2057
0.3886
0.1824
0.5415
0.2758
0.2659
0.1972
0.3007
0.2493
0.6427
0.0675
0.2285
0.6237
0.1214
0.2613
0.7821
0.1013
0.2894
0.4274
0.0290
0.1153
0.6297
0.0647
0.2295
0.6998
0.0835
0.2617
end exB F35 catch
0.5934
0.6748
0.3766
0.4057
0.4269
0.4797
0.2911
0.1916
0.1398
0.1611
0,1224
0.2046
0.1475
0.1644
0.1072
0.4581
0.1722
0.4214
0.1431
0.3222
0.3281
0.1706
0.2640
0.2689
0.1376
0.2510
0.1306
0.2760
0.1545
0.1650
0.1218
0.4868
0.2326
0.4546
0.2121
0.5984
0.3576
endB/startB
0.2515
0.2465
0.1829
0.1747
0.0908
0.1356
0.0752
0.1194
0.1055
0.0955
0.0815
0.0633
0.2349
0.1378
0.2234
0.1258
0.1345
0.2675
0.0731
0.2198
0.1209
0.1226
0.1142
0.1171
0.1075
0.1043
0.0787
0.0740
0.2215
0.1876
0.2208
0.1757
0.2123
0.2856
0.1220
0.2037
0.3016
0.0465
0.1348
78
Table 3.9. Relative bias of the median for the 128 treatments in experiment Al.
Treatment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
end Bio
0.0207
0.0020
0.0025
0.0081
-0.0038
-0.0032
0.0049
-0.0003
-0.0133
-0.0056
0.0136
0.0126
0.0086
0.0090
0.0134
0.0135
-0.0119
-0.0215
0.0075
0.0045
-0.0258
-0.0338
-0.0099
-0.0066
-0.0779
-0.0182
-0.0382
-0.0047
0.0761
-0.0578
-0.0346
0.0056
-0.0095
-0.0021
0.0122
-0.0050
0.0263
0.0057
0.0171
0.0075
0.0187
0.0110
0.0000
0.0047
-0.0391
-0.0092
end F
-0.0152
-0.0046
-0.0054
-0.0119
0.0107
0.0011
-0.0027
-0.0074
0.0152
0.0017
-0.0134
-0.0159
0.0089
-0.0006
-0.0009
-0.0080
-0.0116
0.0193
-0.0143
0.0006
0.0491
0.0386
0.0098
-0.0040
0.0759
0.0210
0.0545
0.0000
-0.0938
0.0540
0.0304
0.0023
0.0250
0.0043
-0.0116
-0.0036
-0.0326
0.0017
-0.0174
0.0007
-0.0308
-0.0007
-0.0031
-0.0135
0.0629
0.0036
end Rec
0.0225
0.0105
0.0001
0.0120
-0.0007
-0.0082
-0.0086
-0.0085
-0.0306
-0.0083
0.0064
-0.0009
0.0098
-0.0068
0.0068
0.0036
0.0068
-0.0102
0.0065
0.0004
-0.0379
-0.0274
-0.0272
-0.0095
-0.0874
-0.0115
-0.0500
-0.0064
0.0859
-0.0557
-0.0365
-0.0068
0.0029
-0.0053
0.0000
-0.0022
0.0358
0.0054
0.0151
0.0011
0.0358
0.0150
0.0072
-0.0034
-0.0575
-0.0094
start Bio
0.0045
-0.0042
-0.0017
0.0041
-0.0045
-0.0027
0.0026
-0.0005
-0.0118
-0.0039
0.0087
0.0060
0.0038
-0.0003
0.0057
0.0056
-0.0240
-0.0202
0.0061
-0.0008
-0.0309
-0.0340
-0.0097
-0.0027
-0.0454
-0.0326
-0.0229
-0.0001
0.0461
-0.0174
-0.0273
-0.0007
-0.0046
-0.0077
0.0025
-0.0004
0.0092
-0.0001
0.0103
0.0005
0.0105
-0.0019
0.0003
0.0015
-0.0195
-0.0034
end exB
0.0139
-0.0083
-0.0030
0.0058
-0.0119
-0.0086
0.0060
-0.0015
-0.0182
-0.0097
0.0140
0.0074
0.0037
-0.0005
0.0042
0.0164
-0.0106
-0.0380
0.0106
-0.0097
-0.0427
-0.0372
-0.0179
-0.0056
-0.0789
-0.0200
-0.0485
0.0002
0.0814
-0.0636
-0.0366
-0.0049
-0.0130
-0.0135
0.0120
-0.0023
0.0207
0.0017
0.0132
0.0039
0.0103
0.0051
0.0007
0.0031
-0.0420
-0.0138
F35 catch endB/startB
0.0249
0.0103
0.0001
0.0052
0.0019
0.0007
0.0071
0.0038
-0.0040
-0.0045
0.0012
0.0033
0.0079
0.0000
0.0025
0.0028
-0.0145
-0.0019
-0.0032
-0.0026
0.0136
0.0032
0.0156
0.0066
0.0106
0.0057
0.0091
0.0111
0.0168
0.0065
0.0180
0.0108
0.0002
0.0179
-0.0201
0.0040
0.0094
0.0022
0.0060
0.0015
-0.0389
-0.0064
-0.0289
0.0027
-0.0069
-0.0070
-0.0047
-0.0020
-0.0954
-0.0294
-0.0208
0.0071
-0.0348
-0.0181
-0.0057
-0.0003
0.0864
0.0313
-0.0694
-0.0238
-0.0335
-0.0089
0.0043
-0.0040
-0.0117
0.0002
-0.0052
0.0046
0.0122
-0.0003
-0.0033
-0.0007
0.0335
0.0167
0.0079
0.0090
0.0183
0.0068
0.0093
0.0075
0.0259
0.0095
0.0150
0.0134
0.0005
0.0032
0.0067
0.0015
-0.0481
-0.0254
-0.0098
-0.0043
Table 3.9 (continued)
Treatment
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
end Bio
0.0240
0.0047
-0.0074
-0.0169
0.0029
-0.0003
0.0058
-0.0072
0.0139
-0.0026
0.0247
-0.0054
0.0047
0.0066
0.0022
-0.0084
-0.0126
-0.0033
-0.0037
0.0013
-0.0024
-0.0022
0.0436
-0.0003
0.0003
0.0063
0.0156
-0.0018
0.0042
0.0074
-0.0637
-0.0001
0.0159
0.0112
-0.0447
-0.0179
0.0024
-0.0013
0.0017
-0.0113
-0.0048
0.0070
-0.0001
-0.0087
-0.0302
0.0047
end F
-0.0326
-0.0048
0.0259
0.0139
-0.0031
-0.0048
-0.0058
0.0178
-0.0130
0.0043
-0.0299
0.0156
-0.0147
-0.0012
0.0281
0.0139
0.0268
-0.0089
-0.0036
-0.0193
-0.0295
-0.0148
-0.0714
-0.0148
-0.0036
-0.0296
-0.0393
-0.0011
-0.0161
-0.0261
0.0804
-0.0358
-0.0723
-0.0364
0.0304
0.0028
0.0000
-0.0261
-0.0161
0.0000
-0.0366
-0.0256
-0.0339
0.0080
-0.0179
0.0102
end Rec
0.0100
-0.0021
0.0020
-0.0102
-0.0050
-0.0074
0.0301
-0.0026
0.0088
-0.0116
0.0423
-0.0037
-0.0056
0.0045
-0.0255
-0.0094
-0.0086
-0.0066
-0.0005
-0.0060
-0.0117
-0.0096
0.0608
-0.0176
0.0000
0.0102
0.0150
-0.0006
0.0023
0.0180
-0.0734
0.0027
0.0275
0.0071
-0.0438
-0.0172
-0.0094
0.0021
0.0123
-0.0001
0.0142
0.0035
0.0234
-0.0150
-0.0160
-0.0038
start Bio
0.0085
0.0042
-0.0097
-0.0214
0.0009
0.0008
-0.0097
-0.0064
0.0054
0.0001
-0.0039
-0.0073
0.0006
-0.0002
-0.0181
-0.0134
0.0009
0.0029
-0.0098
-0.0015
-0.0025
0.0004
0.0320
-0.0023
0.0019
0.0002
0.0059
-0.0006
0.0023
0.0022
-0.0296
-0.0025
0.0073
0.0065
-0.0310
-0.0353
-0.0041
-0.0035
-0.0046
-0.0167
-0.0035
-0.0002
-0.0124
-0.0141
-0.0088
0.0044
end exB
0.0260
0.0054
-0.0140
-0.0235
-0.0003
-0.0020
0.0042
-0.0215
0.0156
-0.0073
0.0157
-0.0195
0.0033
-0.0052
-0.0231
-0.0127
-0.0086
-0.0026
-0.0146
-0.0016
-0.0015
0.0019
0.0444
-0.0030
-0.0015
0.0056
0.0140
-0.0041
-0.0043
0.0014
-0.0689
-0.0044
0.0126
0.0101
-0.0490
-0.0241
-0.0071
-0.0055
0.0113
-0.0235
-0.0024
0.0006
0.0157
-0.0185
-0.0236
-0.0025
F35 catch endB/startB
0.0295
0.0134
0.0008
0.0018
-0.0122
0.0078
-0.0114
0.0057
0.0017
-0.0015
0.0002
0.0016
0.0105
0.0191
-0.0062
0.0057
0.0160
0.0035
-0.0027
-0.0012
0.0465
0.0273
-0.0061
0.0075
0.0093
0.0015
0.0087
0.0062
-0.0210
-0.0028
-0.0072
-0.0020
-0.0137
-0.0045
-0.0003
-0.0016
-0.0097
0.0001
-0.0010
0.0038
-0.0006
0.0028
-0.0005
0.0018
0.0538
0.0247
-0.0018
0.0043
0.0026
0.0013
0.0089
0.0051
0.0223
0.0105
-0.0027
0.0049
-0.0039
0.0043
0.0067
0.0207
-0.0710
-0.0354
0.0046
0.0067
0.0215
0.0128
0.0166
0.0050
-0.0490
-0.0029
-0.0214
0.0127
0.0024
-0.0018
0.0001
0.0036
0.0089
0.0168
-0.0081
0.0042
0.0031
0.0075
0.0076
0.0074
0.0117
0.0251
-0.0103
0.0038
-0.0314
-0.0032
0.0024
0.0053
Table 3.9 (continued)
Treatment
122
123
124
125
126
127
128
end Bio
-0.1026
0.0134
-0.0014
0.0116
0.0291
0.0119
0.0098
0.0087
0.0125
0.0164
0.0220
0.0129
0.0034
-0.0008
0.0044
0.0045
0.0308
0.0143
0.0092
0.0238
0.0126
-0.0002
0.0078
0.0085
-0.0087
-0.0021
0.0041
0.0065
-0.0020
0.0074
-0.0087
0.0144
0.0618
0.0049
0.0086
0.0179
end F
0.1134
-0.0227
-0.0098
-0.0301
-0.0438
-0.0221
-0.0317
-0.0026
-0.0071
-0.0245
-0.0330
-0.0481
-0.0103
-0.0067
-0.0018
-0.0325
-0.0255
-0.0204
-0.0250
-0.0365
-0.0388
-0.0176
-0.0362
-0.0257
-0.0080
-0.0106
-0.0085
-0.0322
0.0134
-0.0320
0.0045
-0.0284
-0.0915
-0.0120
-0.0451
-0.0353
end Rec
-0.1167
0.0069
-0.0119
0.0088
0.0278
0.0109
0.0062
0.0025
0.0298
0.0157
0.0148
0.0101
-0.0049
-0.0130
0.0019
0.0041
0.0463
0.0008
0.0116
0.0198
0.0014
-0.0082
0.0047
0.0052
-0.0120
-0.0047
0.0040
0.0001
0.0076
0.0102
-0.0221
0.0180
0.1033
0.0102
0.0184
0.0183
start Bio
-0.0609
-0.0179
-0.0070
0.0002
0.0101
-0.0011
0.0077
0.0060
0.0052
-0.0043
0.0084
0.0048
-0.0047
-0.0052
0.0070
0.0003
0.0133
-0.0040
0.0027
0.0022
-0.0026
-0.0087
0.0081
0.0048
-0.0081
-0.0088
-0.0007
0.0008
-0.0039
-0.0218
0.0027
0.0011
0.0158
-0.0092
0.0014
0.0095
end exB
-0.0997
0.0118
-0.0193
0.0155
0.0261
0.0085
0.0075
0.0037
0.0023
0.0102
0.0175
0.0111
-0.0149
-0.0028
0.0038
0.0023
0.0245
0.0064
0.0080
0.0182
0.0151
-0.0159
0.0083
0.0069
-0.0232
-0.0036
-0.0006
0.0061
-0.0168
-0.0009
-0.0094
0.0107
0.0565
-0.0020
0.0067
0.0028
F35 catch endB/startB
-0.1250
-0.0321
0.0226
0.0277
-0.0065
-0.0063
0.0216
0.0163
0.0400
0.0146
0.0130
0.0168
0.0143
0.0064
0.0062
0.0033
0.0179
0.0059
0.0147
0.0187
0.0253
0.0057
0.0193
0.0066
-0.0026
0.0051
-0.0005
0.0010
-0.0077
0.0015
0.0077
-0.0003
0.0373
0.0215
0.0062
0.0113
0.0092
0.0044
0.0232
0.0154
0.0212
0.0173
0.0020
0.0038
0.0104
0.0018
0.0152
0.0035
-0.0191
-0.0011
0.0033
0.0028
0.0042
0.0012
0.0097
0.0093
-0.0028
-0.0005
0.0150
0.0266
-0.0145
-0.0084
0.0248
0.0057
0.0832
0.0432
0.0115
0.0229
0.0203
0.0062
0.0246
0.0098
max.
mill.
average
0.0761
-0.1026
0.0007
0.1134
-0.0938
-0.0076
0.1033
-0.1167
-0.0002
0.0461
-0.0609
-0.0035
0.0814
-0.0997
-0.0036
0.0864
-0.1250
0.0020
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
0.0432
-0.0354
0.0047
P
81
Table 3.10. Relative bias for the 128 experimental treatments in experiment A2.
Treatment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
end Bio
0.0493
0.0006
0.0443
0.0137
0.0221
0.0118
0.0089
0.0130
0.1439
0.0166
0.0949
0.0188
0.1661
0.0445
0.0562
0.0512
0.0153
0.0022
0.0319
0.0221
0.0064
-0.0207
0.0044
-0.0003
0.0968
0.0121
0.0919
0.0187
0.0747
0.0733
0.0321
0.0540
0.0249
0.0031
0.0286
0.0063
0.0346
0.0049
0.0146
0.0063
0.0550
0.0252
0.0464
0.0084
0.1490
0.0053
end F
0.0123
0.0190
-0.0089
-0.0011
0.0322
0.0158
0.0242
0.0038
0.0456
0.0196
0.0743
0.0039
0.0634
0.0917
0.0342
0.0515
0.0905
0.0378
0.0400
0.0035
0.0831
0.0462
0.0284
0.0106
0.0909
0.0520
0.0772
0.0334
0.3046
0.1101
0.1225
0.0543
0.0128
0.0142
0.0039
0.0031
0.0089
0.0126
0.0098
0.0072
0.0156
0.0043
0.0026
0.0150
0.1460
0.0500
end Rec
0.0495
0.0021
0.0476
0.0147
0.0333
0.0162
0.0054
0.0183
0.1917
0.0242
0.1138
0.0129
0.1833
0.0728
0.0764
0.0586
0.0396
0.0113
0.0527
0.0355
0.0439
-0.0065
0.0013
0.0050
0.1356
0.0439
0.1122
0.0172
0.0939
0.0954
0.0153
0.0640
0.0326
-0.0012
0.0424
0.0020
0.0483
0.0091
0.0146
0.0019
0.0853
0.0339
0.0670
-0.0021
0.1797
-0.0064
start Bio
0.0286
-0.0009
0.0275
0.0062
0.0120
0.0023
0.0095
0.0083
0.0702
0.0036
0.0503
0.0075
0.0964
0.0045
0.0331
0.0112
-0.0060
-0.0094
0.0160
0.0103
-0.0070
-0.0391
0.0055
-0.0010
0.0449
-0.0201
0.0505
0.0075
0.0303
0.0028
0.0241
0.0126
0.0075
0.0002
0.0109
0.0048
0.0123
0.0019
0.0071
0.0070
0.0234
0.0036
0.0211
0.0071
0.0493
-0.0010
end exB F35 catch
0.0461
0.0580
-0.0080
0.0025
0.0414
0.0511
0.0065
0.0169
0.0136
0.0259
0.0068
0.0150
0.0068
0.0106
0.0076
0.0147
0.1291
0.1610
0.0089
0.0210
0.0857
0.1080
0.0154
0.0238
0.1610
0.1899
0.0309
0.0517
0.0516
0.0645
0.0446
0.0598
0.0128
0.0314
-0.0195
-0.0047
0.0330
0.0414
0.0095
0.0181
-0.0186
-0.1208
-0.0198
-0.0102
-0.0028
0.0005
-0.0004
0.0064
0.0693
0.0024
0.0087
0.0257
0.0746
0.0385
0.0192
0.0243
0.0756
0.0953
0.0501
0.0535
0.0307
0.0409
0.0410
0.0663
0.0162
0.0304
-0.0062
0.0080
0.0225
0.0347
0.0009
0.0095
0.0312
0.0461
-0.0033
0.0064
0.0117
0.0186
0.0010
0.0085
0.0451
0.0717
0.0128
0.0333
0.0440
0.0577
0.0076
0.0122
0.1322
0.1848
-0.0006
0.0120
endB/startB
0.0074
0.0004
0.0081
0.0066
0.0021
0.0073
-0.0070
0.0036
0.0245
0.0093
-0.0009
0.0084
0.0159
0.0281
0.0037
0.0293
0.0083
0.0111
0.0028
0.0111
0.0060
0.0178
-0.0065
-0.0008
0.0142
0.0262
0.0051
0.0046
-0.0105
0.0573
-0.0155
0.0320
0.0115
0.0029
0.0108
0.0018
0.0142
0.0034
0.0050
-0.0003
0.0172
0.0223
0.0154
0.0021
0.0371
0.0048
82
Table 3.10 (continued)
Treatment
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
end Bio
0.0944
0.0070
0.0207
-0.0090
0.0285
0.0131
0.0123
0.0050
0.0422
0.0021
0.0840
0.0184
0.0562
0.0151
0.1005
0.0616
0.1344
0.0407
0.0656
0.0150
0.0821
0.0140
0.0777
0.0166
0.0158
0.0160
0.1683
0.0484
0.0976
0.0290
0.0799
0.0464
0.0662
0.0414
0.0554
0.0021
0.0682
0.0268
-0.0180
0.0100
0.0123
0.0192
0.1384
0.0404
0.1562
0.0485
end F
0.0777
0.0143
0.0489
0.0326
0.0046
-0.0021
0.0587
0.0287
-0.0102
0.0223
0.0844
0.0318
0.0325
0.0186
0.2298
0.0468
0.1004
0.0378
0.0194
-0.0100
0.0031
-0.0163
0.0185
0.0187
0.0090
0.0076
0.0221
-0.0035
0.0113
0.0233
0.3230
0.0479
0.1142
-0.0174
0.0702
0.0333
0.023 1
0.0062
0.1300
0.0422
0.0303
0.0030
0.1819
0.0203
0.0511
0.0072
end Rec
0.1331
0.0074
0.0190
0.0041
0.0237
0.0063
0.0212
0.0053
0.0579
-0.0017
0.1101
0.0305
0.0610
0.0004
0.1339
0.0881
0.1739
0.0469
0.0873
0.0112
0.0926
0.0143
0.0869
0.0167
0.0138
0.0158
0.2196
0.0623
0.1187
0.0249
0.1066
0.0576
0.0853
0.0514
0.0741
-0.0019
0.0740
0.0206
0.0069
0.0390
0.0053
0.0258
0.1795
0.0534
0.1700
0.0508
start Bio
0.0333
0.0017
0.0018
-0.0232
0.0158
0.0099
-0.0069
-0.0009
0.0254
0.0085
0.0337
-0.0019
0.0304
0.0115
0.0270
-0.0126
0.0511
0.0097
0.0318
0.0026
0.0472
0.0075
0.0461
0.0064
0.0116
0.0095
0.0919
0.0046
0.0590
0.0083
0.0361
0.0112
0.0326
0.0186
0.0230
-0.0247
0.0390
0.0091
-0.0286
-0.0101
0.0061
0.0106
0.0673
0.0002
0.1006
0.0121
end exB F35 catch
0.0821
0.1165
0.0025
0.0105
-0.0007
-0.0691
-0.0134
-0.0057
0.0160
0.0353
0.0099
0.0201
0.0168
0.0239
-0.0143
0.0026
0.0431
0.0510
-0.0088
0.0028
0.0786
0.1072
-0.0020
-0.0003
0.0593
0.0689
0.0014
0.0219
0.0633
-0.0278
0.0550
0.0884
0.1117
0.0714
0.0343
0.0573
0.0570
0.0729
0.0094
0.0224
0.0786
0.0899
0.0122
0.0182
0.0688
0.0902
0.0074
0.0187
0.0122
0.0205
0.0120
0.0170
0.1593
0.1922
0.0377
0.0572
0.0955
0.1102
0.0247
0.0330
0.0646
0.0935
0.0393
0.0539
0.0589
0.0736
0.0395
0.0482
0.0326
-0.0648
0.0018
0.0130
0.0592
0.0654
0.0222
0.0355
-0.0163
-0.0084
-0.0127
0.0061
0.0133
0.0203
0.0068
0.0214
0.1387
0.1633
0.0190
0.0109
0.1603
0.1735
0.0358
0.0570
endB/startB
0.0198
0.0047
0.0124
0.0156
0.0068
0.0033
0.0094
0.0067
0.0100
-0.0058
0.0214
0.0218
0.0057
0.0051
0.0160
0.0703
0.0337
0.0267
0.0104
0.0105
0.0095
0.0049
0.0154
0.0095
-0.0014
0.0059
0.0247
0.0395
0.0096
0.0157
-0.0244
0.0257
-0.0094
0.0189
0.0096
0.0235
0.0046
0.0140
-0.0018
0.0200
-0.0022
0.0082
0.0110
0.0356
0.0049
0.0322
83
Table 3.10 (continued)
Treatment
end Bio
0.0727
0.0477
0.0339
0.0712
0.0313
0.0055
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
0.1208
0.0120
0.1265
0.0471
0.0607
0.0585
0.0454
0.0114
0.0696
0.0206
0.0210
0.0021
0.0205
0.0191
0.0902
0.0200
0.1517
0.0276
0.1505
0.1053
0.0665
0.0836
end F
0.2933
0.1189
0.2557
0.0274
0.0198
0.0063
-0.0095
-0.0086
0.0100
0.0269
-0.0140
-0.0137
0.0082
0.0056
0.0032
-0.0061
0.0040
0.0620
-0.0011
0.0121
0.0154
0.0125
-0.0162
-0.0130
0.0588
0.0269
0.0017
-0.0174
0.0689
0.0271
0.0078
-0.0035
0.1534
0.0546
0.0606
-0.0070
max.
mm.
average
0.1683
-0.0207
0.0448
0.3230
-0.0174
0.0409
93
94
95
96
97
98
99
100
101
0.0401
0.0174
0.0219
0.0044
0.0240
0.0192
0.1496
0.01 14
end Rec
0.1073
0.0639
0.0469
0.0736
0.0522
0.0031
0.0481
0.0190
0.0350
-0.0073
0.0345
0.0217
0.2000
0.0108
0.1485
0.0002
0.1744
0.0721
0.0701
0.0786
0.0653
0.0131
0.0823
0.0167
0.0407
0.0138
0.0286
0.0030
0.1217
0.0217
0.1896
0.0288
0.1802
0.1293
0.0703
0.1090
start Bio
0.0229
-0.0153
0.0248
0.0247
0.0112
0.0044
0.0133
0.0060
0.0049
-0.0012
0.0102
0.0091
0.0481
0.0044
0.0433
0.0070
0.0565
0.0031
0.0290
0.0090
0.0109
0.0015
0.0399
0.0138
0.0003
-0.0149
0.0113
0.0095
0.0277
-0.0157
0.0628
0.0107
0.0554
0.0013
0.0372
0.0070
end exB F35 catch
0.0426
-0.0676
0.0479
0.0655
0.0214
-0.0285
0.0685
0.0827
0.0261
0.0385
-0.0040
0.0088
0.0369
0.0503
0.0126
0.0226
0.0136
0.0278
-0.0002
0.0086
0.0187
0.0329
0.0152
0.0284
0.1298
0.1815
0.0042
0.0208
0.1079
0.1474
0.0106
0.0193
0.1191
0.1589
0.0342
0.0594
0.0599
0.0732
0.0480
0.0756
0.0487
0.0625
-0.0109
0.0087
0.0705
0.0856
0.0135
0.0260
-0.0095
-0.0835
-0.0072
0.0138
0.0083
0.0196
0.0184
0.0303
0.0617
0.0048
0.0136
0.0320
0.1286
0.0931
0.0243
0.0397
0.1548
0.1879
0.0731
0.0919
0.0688
0.0804
0.0653
0.1118
0.2196
-0.0073
0.0566
0.1006
-0.0391
0.0161
0.1610
-0.0198
0.0362
0.1922
-0.1208
0.0438
endB/startB
-0.0150
0.0415
-0.0434
0.0306
0.0116
0.0039
0.0196
0.0138
0.0122
0.0059
0.0094
0.0103
0.0584
0.0078
0.0402
0.0058
0.0397
0.0473
0.0209
0.0513
0.0201
0.0123
0.0154
0.0093
0.0161
0.0180
0.0053
0.0095
0.0266
0.0380
0.0464
0.0173
0.0323
0.1104
0.0041
0.0805
0.1104
-0.0434
0.0148
Table 3.11. Relative variability for the 128 experimental treatments in experiment A2.
Treatment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
end Bio
0.2646
0.1165
0.1996
0.1049
0.1957
0.1268
0.1730
0.0885
0.4858
0.1676
0.4881
0.1402
0.5125
0.3319
0.3038
0.3039
0.3310
0.1298
0.2722
0.1140
0.2267
0.1543
0.1759
0.1108
0.4510
0.2537
0.4193
0.2220
0.5935
0.3768
0.3716
0.2992
0.1764
0.0952
0.1850
0.0794
0.1984
0.1079
0.1116
0.0751
0.2599
0.1572
0.2051
0.1528
0.5354
0.1860
end F
0.2626
0.1430
0.2011
0.1367
0.2229
0.1778
0.1997
0.1431
0.4006
0.1922
0.3669
0.1675
0.4444
0.3761
0.2987
0.3281
0.3337
0.1602
0.2754
0.1433
0.2589
0.1935
0.2086
0.1466
0.3838
0.2629
0.3765
0.2335
0.6325
0.4205
0.4287
0.3370
0.1831
0.1371
0.1806
0.1267
0.2320
0.1535
0.1593
0.1360
0.2691
0.1788
0.2289
0.1655
0.5471
0.2547
end Rec
0.3451
0.2038
0.2451
0.1501
0.2850
0.2091
0.2289
0.1496
0.5749
0.2640
0.5881
0.1927
0.6288
0.4315
0.3778
0.3668
0.3608
0.1940
0.3267
0.1748
0.3026
0.2061
0.2202
0.1452
0.5276
0.2979
0.4962
0.2674
0.6456
0.4528
0.3906
0.3589
0.2640
0.1703
0.2515
0.1501
0.2937
0.1949
0.1700
0.1321
0.3667
0.2466
0.2790
0.2462
0.6677
0.2794
start Bio
0.1766
0.0407
0.1267
0.0329
0.1169
0.0573
0.1004
0.0421
0.2694
0.0687
0.2573
0.0508
0.3260
0.0583
0.1905
0.0524
0.2657
0.0707
0.1961
0.0534
0.1630
0.1159
0.1148
0.0704
0.2780
0.1610
0.2441
0.1143
0.4371
0.0928
0.2740
0.0632
0.0755
0.0378
0.0751
0.0317
0.1078
0.0338
0.0644
0.0302
0.1295
0.0331
0.1018
0.0323
0.1998
0.0435
end exB
0.2737
0.1148
0.2020
0.1031
0.1982
0.1306
0.1734
0.0920
0.4758
0.1743
0.4702
0.1445
0.5198
0.3221
0.3083
0.2958
0.3304
0.1400
0.2781
0.1186
0.2462
0.1586
0.1820
0.1122
0.4556
0.2579
0.4215
0.2249
0.6000
0.3707
0.3765
0.2940
0.1711
0.0965
0.1790
0.0812
0.2060
0.1000
0.1140
0.0723
0.2664
0.1449
0.2143
0.1407
0.5177
0.1892
F35 catch
0.2862
0.1304
0.2193
0.1173
0.2151
0.1464
0.1909
0.1019
0.5331
0.1890
0.5373
0.1600
0.5640
0.3783
0.3364
0.3474
0.3412
0.1928
0.2887
0.1576
0.4664
0.1661
0.2077
0.1205
0.6182
0.2716
0.5337
0.2421
0.6288
0.463 1
0.3934
0.3457
0.2071
0.1216
0.2146
0.1006
0.2370
0.1349
0.1362
0.0967
0.3112
0.1924
0.2453
0.1866
0.6314
0.2499
endB/startB
0.0945
0.0985
0.0772
0.0899
0.0878
0.0913
0.0793
0.0623
0.1911
0.1244
0.1913
0.1059
0.1726
0.2850
0.1122
0.2572
0.0988
0.1007
0.0900
0.0938
0.0948
0.0888
0.0773
0.0655
0.1803
0.1483
0.1776
0.1479
0.2064
0.3224
0.1288
0.2560
0.1153
0.0872
0.1181
0.0767
0.1024
0.1068
0.0597
0.0739
0.1372
0.1585
0.1122
0.1543
0.3127
0.1725
85
Table 3.11 (continued)
Treatment
end Bio
end F
end Rec
start Bio
47
0.4519
0.4007
0.5673
0.1607
0.4301
0.5365
0.2602
48
0.1179
0.1735
0.1893
0.0342
0.1195
0.1580
0.1070
49
0.1978
0.2179
0.2809
0.1061
0.2070
0.3955
0.1180
50
0.1182
0.1511
0.1952
0.0708
0.1174
0.1466
0.1035
51
0.1770
0.1911
0.2275
0.0821
0.1760
0.2205
0.1107
52
0.0927
0.1282
0.1382
0.0433
0.0932
0.1139
0.0839
53
0.2527
0.2886
0.3026
0.1783
0.2568
0.2793
0.1053
54
0.0961
0.1626
0.1654
0.0482
0.1022
0.1510
0.0912
55
0.1889
0.2181
0.2255
0.1287
0.1888
0.2116
0.0758
0.0881
end exB
F35
catch
endB/startB
56
0.0900
0.1399
0.1593
0.0400
0.0905
0.1216
57
0.4323
0.3818
0.5014
0.2870
0.4377
0.4764
0.1629
58
0.1640
0.2126
0.2421
0.0563
0.1640
0.2648
0.1639
59
0.3174
0.3055
0.3611
0.1922
0.3229
0.3568
0.1369
60
0.1407
0.1594
0.1922
0.0399
0.1382
0.1733
0.1457
61
0.5396
0.5515
0.6770
0.2080
0.5143
0.7385
0.3168
62
0.2924
0.3488
0.3469
0.0930
0.2936
0.3726
0.2557
63
0.4797
0.4828
0.6101
0.1842
0.4513
0.6019
0.2844
64
0.2495
0.2999
0.3173
0.0665
0.2484
0.3203
0.2220
65
0.3330
0.2801
0.4146
0.1890
0.3288
0.3590
0.1456
66
0.1354
0.2120
0.2137
0.0684
0.1393
0.1477
0.0989
67
0.3451
0.2929
0.4150
0.1946
0.3400
0.3718
0.1448
68
0.1218
0.2016
0.1680
0.0606
0.1252
0.1329
0.0903
69
0.2911
0.3508
0.3718
0.1989
0.2984
0.3180
0.1007
70
0.1110
0.2355
0.2151
0.0605
0.1104
0.1253
0.0853
71
0.1765
0.2616
0.2206
0.1254
0.1807
0.1925
0.0651
72
0.0941
0.2155
0.1438
0.0531
0.0927
0.1067
0.0711
73
0.5121
0.4042
0.6047
0.3365
0.5169
0.5532
0.1663
74
0.2397
0.2502
0.3234
0.0652
0.2319
0.2623
0.2093
75
0.3778
0.3292
0.4640
0.2376
0.3815
0.4109
0.1343
76
0.2415
0.2408
0.3113
0.0600
0.2332
0.2653
0.2091
77
0.5513
0.7346
0.6583
0.2982
0.5371
0.6112
0.2685
78
0.2521
0.3371
0.3606
0.0913
0.2600
0.2916
0.1869
79
0.4579
0.4560
0.5311
0.2500
0.4457
0.5020
0.1965
80
0.1630
0.2650
0.2258
0.0695
0.1666
0.1875
0.1205
81
0.3597
0.3205
0.4187
0.2327
0.3771
0.5563
0.1479
82
0.1972
0.2352
0.2466
0.1301
0.2031
0.2029
0.1155
83
0.3411
0.2945
0.3990
0.2009
0.3408
0.3893
0.1454
84
0.1656
0.2202
0.2004
0.0896
0.1671
0.1741
0.1071
85
0.3325
0.3868
0.3703
0.2672
0.3330
0.3447
0.1067
86
0.1190
0.2387
0.1765
0.0796
0.1269
0.1669
0.0856
87
0.2405
0.3027
0.2643
0.1872
0.2427
0.2504
0.0748
88
0.1164
0.2297
0.1870
0.0748
0.1226
0.1438
0.0841
89
0.6748
0.5270
0.7102
0.5060
0.6880
0.7023
0.1880
90
0.2533
0.2744
0.3295
0.0919
0.2549
0.3490
0.2128
91
0.5366
0.4422
0.5778
0.3785
0.5407
0.5668
0.1645
92
0.228 1
0.2431
0.2758
0.0736
0.2269
0.2529
0.1933
86
Table 3.11 (continued)
Treatment
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
max.
mm.
average
end Bio
0.5573
0.4002
0.5143
0.3000
0.2138
0.1262
0.1893
0.1136
0.1718
0.1143
0.1623
0.0946
0.4462
0.1545
0.4125
0.1330
0.3586
0.2968
0.2257
0.2481
0.3062
0.1285
0.2682
0.1248
0.1890
end Rec
0.6630
0.4553
0.6105
0.3413
0.3014
0.2029
0.2485
0.1559
0.2481
0.1886
0.2302
0.1626
0.5805
0.2423
0.5058
0.1937
0.4871
0.3917
0.2921
0.3257
0.3576
0.1781
0.3028
0.1711
0.2699
0.2055
0.2198
0.1425
0.5375
0.2702
0.5203
0.2565
0.6576
0.4356
0.4069
0.3104
start Bio
0.2970
0.1820
0.2828
0.1391
0.1201
0.0609
0.1062
0.0575
0.0976
0.0618
0.0933
0.0553
0.1716
0.0613
0.1604
0.0560
0.1792
0.1640
0.1040
0.4304
0.2136
0.4274
0.1936
0.6042
0.3491
0.3710
0.2388
end F
0.6968
0.4706
0.5869
0.3948
0.2430
0.1981
0.2108
0.1905
0.2452
0.2509
0.2488
0.2299
0.3559
0.2381
0.3266
0.2065
0.4032
0.3767
0.2921
0.3347
0.2866
0.2094
0.2735
0.2063
0.2746
0.2637
0.2468
0.2502
0.3622
0.2561
0.3539
0.2403
0.5604
0.4270
0.4109
0.3262
0.6748
0.0751
0.2569
0.7346
0.1267
0.2879
0.7102
0.1321
0.3272
0.5060
0.0302
0.1325
0.1341
0.0611
0.1272
0.0584
0.2084
0.0695
0.1654
0.0648
0.1188
0.0807
0.1016
0.0642
0.1851
0.0987
0.1793
0.0750
0.3764
0.0790
0.2364
0.0648
end exB
0.5329
0.4018
0.5011
0.2986
0.2193
0.1234
0.1914
0.1108
0.1731
0.1162
0.1591
0.0968
0.4267
0.1586
0.3945
0.1365
0.3622
0.2819
0.2304
0.2330
0.3076
0.1333
0.2755
0.1242
0.1976
0.1332
0.1674
0.1078
0.4194
0.2164
0.4182
F35 catch
0.7008
0.4405
0.6143
0.3313
0.2458
0.1370
0.2148
0.1245
0.2017
0.1562
0.1911
0.6162
0.3379
0.3764
0.2300
0.1286
0.5122
0.1894
0.4723
0.1568
0.4297
0.3766
0.2703
0.3134
0.3288
0.1857
0.2953
0.1501
0.4248
0.1780
0.2115
0.1362
0.6047
0.2536
0.5837
0.2323
0.6748
0.5002
0.4187
0.3023
0.6880
0.0723
0.2564
0.7385
0.0967
0.3064
0.1921
endB/startB
0.2744
0.2673
0.2386
0.2013
0.1148
0.1340
0.0999
0.1198
0.1012
0.0990
0.0935
0.0803
0.2619
0.1476
0.2451
0.1269
0.1811
0.3010
0.1147
0.2501
0.1288
0.1271
0.1179
0.1292
0.1106
0.1128
0.0925
0.0819
0.2456
0.1971
0.2485
0.1799
0.2325
0.3537
0.1500
0.2470
0.3537
0.0597
0.1496
87
Table 3.12. Relative bias of the median for the 128 treatments in experiment A2.
Treatment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
end Bio
-0.0011
-0.0036
0.0136
0.0095
0.0071
0.0002
-0.0062
0.0065
0.0265
0.0030
-0.0204
0.0099
0.0019
-0.0084
0.0094
0.0035
-0.0292
-0.0123
-0.0191
0.0126
-0.0200
-0.0380
-0.0028
-0.0043
-0.0178
-0.0262
-0.0032
-0.0123
-0.0739
-0.0034
-0.0374
0.0029
0.0023
-0.0028
0.0081
0.0018
0.0002
-0.0009
0.0035
0.0047
-0.0027
0.0128
0.0249
-0.0105
0.0074
-0.0169
end F
-0.0063
0.0006
-0.0205
-0.0119
0.0036
0.0034
0.0089
-0.0091
-0.0134
-0.0017
0.0339
-0.0091
0.0241
0.0097
0.0080
0.0063
0.0268
0.0341
0.0143
-0.0080
0.0589
0.0358
0.0188
0.0051
0.0393
0.0188
0.0384
0.0017
0.0848
-0.0063
0.0286
0.0017
-0.0022
0.0060
-0.0116
-0.0077
-0.0143
0.0007
0.0009
-0.0079
0.0013
-0.0156
-0.0174
0.0038
0.0031
0.0043
end Rec
-0.0191
-0.0109
0.0119
0.0048
-0.0060
-0.0054
-0.0288
0.0061
0.0436
-0.0099
-0.0386
0.0016
-0.0185
-0.0093
-0.0153
-0.0053
-0.0214
-0.0034
-0.0063
0.0254
0.0055
-0.0291
-0.0190
-0.0116
0.0095
-0.0013
-0.0214
-0.0105
-0.0799
0.0031
-0.0479
-0.0145
-0.0103
-0.0097
0.0107
-0.0102
-0.0029
-0.0099
-0.0010
-0.0023
-0.0014
0.0113
0.0360
-0.0370
-0.0359
-0.0410
start Bio
0.0001
-0.0017
0.0102
0.0056
-0.0006
-0.0010
0.0011
0.0054
0.0093
0.0014
-0.0105
0.0059
-0.0051
-0.0054
0.0027
0.0068
-0.0457
-0.0109
-0.0158
0.0078
-0.0326
-0.0524
-0.0031
-0.0060
-0.0268
-0.0465
0.0016
-0.0090
-0.0853
-0.0068
-0.0281
0.0058
-0.0016
-0.0011
0.0010
0.0066
-0.0005
0.0012
-0.0006
0.0061
0.0014
0.0023
0.0133
0.0066
-0.0013
-0.0007
end exB
-0.0066
-0.0133
0.0100
-0.0009
0.0001
-0.0014
-0.0070
0.0008
0.0132
-0.0103
-0.0319
0.0073
-0.0109
-0.0246
0.0018
-0.0006
-0.0332
-0.0317
-0.0108
0.0004
-0.0604
-0.0383
-0.0158
-0.0065
-0.0468
-0.0299
-0.0240
-0.0106
-0.0723
-0.0215
-0.0333
-0.0091
-0.0046
-0.0162
0.0050
-0.0053
-0.0087
-0.0112
0.0025
-0.0017
-0.0115
0.0026
0.0163
-0.0035
-0.0016
-0.0193
F35 catch endB/startB
0.0033
0.0005
-0.0024
-0.0013
0.0166
0.0064
0.0083
0.0013
0.0149
-0.0011
0.0009
0.0059
-0.0071
-0.0094
0.0087
-0.0006
0.0262
0.0144
0.0083
0.0002
-0.0176
-0.0184
0.0135
-0.0011
-0.0093
-0.0016
-0.0118
-0.0065
0.0046
-0.0036
-0.0029
0.0013
-0.0182
0.0065
-0.0022
0.0109
-0.0167
-0.0019
0.0216
0.0086
-0.0549
0.0040
-0.0232
0.0151
-0.0002
-0.0078
0.0007
-0.0021
-0.0744
0.0104
-0.0097
0.0200
-0.0397
-0.0001
-0.0103
-0.0058
-0.0731
-0.0129
-0.0212
0.0045
-0.0291
-0.0079
0.0029
-0.0061
0.0051
0.0074
-0.0056
-0.0053
0.0135
0.0075
0.0049
0.0001
0.0094
0.0080
-0.0026
-0.0058
0.0102
0.0044
0.0057
-0.0025
-0.0034
-0.0046
0.0169
0.0150
0.0297
0.0088
-0.0083
-0.0151
0.0158
0.0006
-0.0189
-0.0108
Table 3.12 (continued)
Treatment
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
end Bio
-0.0169
-0.0056
-0.0063
-0.0128
0.0112
0.0080
-0.0301
-0.0016
0.0211
-0.0026
-0.0297
0.0106
-0.0063
0.0117
-0.0510
0.0154
0.0039
0.0022
-0.0057
0.0095
0.0088
0.0061
0.0097
0.0114
0.0068
0.0134
0.0100
0.0127
0.0262
-0.0018
-0.0054
0.0183
0.0190
0.0194
-0.0201
-0.0247
0.0094
0.0051
-0.0603
0.0001
-0.0162
0.0145
-0.0558
0.0081
-0.0059
0.0083
end F
0.0161
-0.0031
0.0339
0.0180
-0.0094
-0.0099
0.0223
0.0132
-0.0259
0.0103
0.0388
0.0036
-0.0045
0.0151
0.0924
-0.0031
0.0045
-0.0103
-0.0116
-0.0313
-0.0179
-0.0364
-0.0313
-0.0006
-0.0268
-0.0102
-0.0339
-0.0386
-0.0196
0.0006
0.0259
0.0011
0.01 16
-0.0551
0.0509
0.0176
-0.0045
-0.0171
0.0554
0.0267
-0.0161
-0.0136
0.0536
-0.0057
-0.0313
-0.0233
end Rec
-0.0430
-0.0110
-0.0156
-0.0116
-0.0013
0.0035
-0.0368
-0.0055
0.0251
-0.0141
0.0029
0.0083
-0.0062
-0.0093
-0.0678
0.0323
-0.0202
0.0004
-0.0019
-0.0091
-0.0121
-0.0018
0.0114
0.0014
-0.0124
0.0089
0.0205
0.0158
0.0154
-0.0241
-0.0519
-0.0032
-0.0362
0.0298
-0.0350
-0.0354
-0.0122
-0.0126
-0.0495
0.0292
-0.0189
0.0039
-0.0517
0.0055
-0.0086
-0.0002
start Bio
-0.0032
0.0016
-0.0122
-0.0243
0.0056
0.0076
-0.0330
-0.0033
0.0104
0.0051
-0.0380
-0.0016
-0.0016
0.0112
-0.0312
-0.0189
0.0038
0.0072
-0.0057
0.0034
0.0074
0.0061
0.0076
0.0057
0.0041
0.0081
0.0087
0.0020
0.0086
0.0040
-0.0065
0.0051
0.0067
0.0134
-0.0179
-0.0379
-0.0003
0.0047
-0.0689
-0.0128
-0.0209
0.0073
-0.0755
-0.0052
-0.0101
0.0072
end exB
-0.0205
-0.0118
-0.0327
-0.0192
-0.0005
0.0060
-0.0205
-0.0263
0.0165
-0.0099
-0.0244
-0.0085
-0.0077
-0.0051
-0.0716
0.0029
-0.0103
-0.0054
-0.0038
0.0012
0.0090
0.0071
0.0008
0.0023
0.0040
0.0129
-0.0063
0.0006
0.0135
-0.0043
-0.0081
0.0109
0.0144
0.0175
-0.0464
-0.0291
0.0024
0.0013
-0.0586
-0.0230
-0.0144
-0.0004
-0.0562
-0.0106
-0.0053
0.0027
F35 catch endB/startB
-0.0124
-0.0191
-0.0072
-0.0028
-0.0335
0.0086
-0.0088
0.0132
0.0129
0.0064
0.0097
-0.0018
-0.0204
0.0067
-0.0027
0.0048
0.0283
0.0064
-0.0030
-0.0116
-0.0182
0.0101
0.0047
0.0094
0.0010
-0.0052
0.0123
0.0009
-0.1579
-0.0266
0.0266
0.0307
-0.0436
-0.0047
0.0092
-0.0031
-0.0019
-0.0025
0.0170
0.0077
0.0071
-0.0017
0.0125
0.0029
0.0137
0.0057
0.0104
0.0095
0.0110
-0.0006
0.0162
0.0036
0.0203
0.0161
0.0217
0.0186
0.0213
0.0069
-0.0115
-0.0098
0.0038
-0.0118
0.0149
0.0090
0.0101
-0.0012
0.0272
0.0119
-0.0731
0.0004
-0.0174
0.0160
0.0126
-0.0001
0.0138
0.0033
-0.0576
-0.0092
0.0044
0.0194
-0.0083
0.0031
0.0175
0.0062
-0.0524
0.0000
-0.0024
0.0200
0.0054
-0.0022
0.0165
0.0126
89
Table 3.12 (continued)
Treatment
end Bio
end F
catch
endB/startB
93
-0.0396
0.0482
-0.0779
-0.0278
-0.0625
-0.1443
-0.0239
94
-0.0276
0.0085
-0.0278
-0.0447
-0.0340
-0.0158
0.0043
95
-0.0638
0.0464
-0.0827
-0.0274
-0.0698
-0.0957
-0.0448
96
0.0254
-0.0517
0.0133
0.0067
0.0231
0.0260
0.0162
97
-0.0058
-0.0054
0.0110
-0.0014
-0.0161
-0.0014
0.0067
98
-0.0049
-0.0142
-0.0148
-0.0003
-0.0126
0.0044
-0.0039
0.0034
0.0129
0.0250
0.0145
end Rec
start Bio
end exB
F35
99
0.0174
-0.0304
0.0080
100
0.0137
-0.0233
0.0080
0.0010
0.0046
0.0194
0.0119
101
0.0073
-0.0201
0.0021
-0.0032
-0.0043
0.0093
0.0119
102
-0.0045
-0.0125
-0.0209
-0.0045
-0.0038
0.0063
0.0026
103
0.0035
-0.0277
-0.0034
0.0017
-0.0009
0.0099
0.0047
104
0.0178
-0.0301
0.0053
0.0080
0.0122
0.0208
0.0067
105
0.0395
-0.0335
0.0455
0.0130
0.0203
0.0511
0.0201
106
-0.0022
-0.0291
-0.0110
0.0017
-0.0081
-0.0012
0.0001
107
-0.0008
-0.0232
-0.0038
0.0135
0.0042
0.0102
-0.0017
108
-0.0050
-0.0248
-0.0237
0.0059
-0.0035
-0.0035
-0.0092
109
0.0445
-0.0576
0.0465
0.0196
0.0333
0.0469
0.0270
110
0.0002
-0.0075
0.0007
0.0014
0.0040
-0.0020
-0.0021
111
0.0261
-0.0317
0.0259
0.0168
0.0244
0.0291
0.0110
112
0.0301
-0.0284
0.0324
0.0062
0.0228
0.0311
0.0142
113
-0.0169
-0.0237
-0.0052
-0.0274
-0.0133
-0.0107
0.0141
114
-0.0017
-0.0164
-0.0053
0.0007
-0.0227
0.0073
0.0041
115
0.0140
-0.0335
0.0148
0.0134
0.0206
0.0207
0.0090
116
0.0167
-0.0375
0.0030
0.0095
0.0077
0.0264
0.0018
117
-0.0001
0.0339
-0.0077
-0.0088
-0.0307
-0.0260
0.0114
118
-0.0119
-0.0137
-0.0018
-0.0196
-0.0185
0.0019
0.0095
119
0.0133
-0.0246
0.0096
0.0070
-0.0035
0.0062
0.0028
120
0.0144
-0.0522
-0.0115
0.0080
0.0131
0.0185
0.0043
121
-0.0185
0.0125
-0.0353
-0.0111
-0.0438
-0.0932
-0.0061
122
-0.0072
0.0084
-0.0180
-0.0215
-0.0080
-0.0005
0.0138
123
0.0402
-0.0321
0.0317
0.0375
0.0197
-0.0160
0.0185
124
0.0011
-0.0286
-0.0076
0.0081
0.0042
0.0101
-0.0002
125
-0.0296
0.0156
-0.0228
-0.0227
-0.0183
-0.0287
0.0135
126
0.0422
-0.0238
0.0363
0.0008
0.0121
0.0250
0.0498
127
-0.0014
0.0058
-0.0267
-0.0130
-0.0044
-0.0046
-0.0005
128
0.0581
-0.0683
0.0612
0.0037
0.0452
0.0872
0.0589
max.
mm.
average
0.0581
0.0924
0.0612
0.0375
0.0452
0.0872
0.0589
-0.0739
-0.0683
-0.0827
-0.0853
-0.0723
-0.1579
-0.0448
-0.0006
-0.0019
-0.0069
-0.0048
-0.0085
-0.0025
0.0036
90
Table 3.13. ANOVA tables from fractional factorial experiment Al.
Source
DF
Relative bias in ending total biomass.
Main Effects
9
2-Way Interactions
36
3-Way Interactions
55
Residual Error
384
Total
511
Relative bias in ending F.
SS
MS
F
P
0.560
0.289
0.172
0.178
0.062
0.008
0.003
0.000
134.2
17.3
6.8
<0.001
<0.001
<0.001
0.049
0.009
0.003
0.000
118.2
21.2
7.7
<0.001
<0.001
<0.001
0.099
0.010
0.004
131.0
5.1
<0.001
<0.001
<0.001
143.9
22.4
8.2
<0.001
<0.001
<0.001
0.062
0.009
0.003
0.000
137.1
19.5
7.1
<0.001
<0.001
<0.001
0.076
0.011
0.005
0.001
127.5
18.8
7.9
<0.001
<0.001
<0.001
0.004
0.001
0.000
0.000
35.0
<0.001
<0.001
<0.001
1.227
MainEffects
9
0.445
2-Way Interactions
36
0.320
3-Way Interactions
55
0.177
Residual Error
384
0.16 1
Total
511
1.148
Relative bias in ending recruitment.
MainEffects
9
0.894
2-Way Interactions
36
0.369
3-Way Interactions
55
0.212
Residual Error
384
0.291
Total
511
1.803
Relative bias in starting biomass.
Main Effects
9
0.170
2-Way Interactions
36
0.106
3-Way Interactions
55
0.059
Residual Error
384
0.050
Total
511
0.398
Relative bias in ending exploitable biomass.
Main Effects
9
0.560
2-Way Interactions
36
0.319
3-Way Interactions
55
0.177
Residual Error
384
0.174
Total
511
1.256
Relative bias in predicted F35 catch.
Main Effects
9
0.683
2-Waylnteractions
36
0.402
3-Way Interactions
55
0.259
Residual Error
384
0.228
Total
511
1.611
Relative bias in the ratio of ending/starting biomass.
Main Effects
9
0.039
2-Way Interactions
36
0.039
3-Way Interactions
55
0.024
Residual Error
384
0.047
Total
511
0.153
13.5
0.00 1
0.019
0.003
0.001
0.000
8.8
3.6
Table 3.13 (continued)
Source
DF
SS
MS
Relative variability in ending total biomass.
Main Effects
9
6.625
0.736
2-Way Interactions
36
1.613
0.045
3-Way Interactions
55
0.366
0.007
Residual Error
384
0.185
0.000
Total
511
8.832
Relative variability in ending F.
Main Effects
9
3.906
0.434
2-Way Interactions
36
0.980
0.027
3-Way Interactions
55
0.228
0.004
Residual Error
384
0.104
0.000
Total
511
5.237
Relative variability in ending recruitment.
Main Effects
9
8.051
0.895
2-Way Interactions
36
1.815
0.050
3-Way Interactions
55
0.441
0.008
Residual Error
384
0.315
0.001
Total
511
10.679
Relative variability in starting biomass.
Main Effects
9
2.604
0.289
2-Way Interactions
36
0.668
0.019
3-Way Interactions
55
0.153
0.003
Residual Error
384
0.066
0.000
Total
511
3.512
Relative variability in ending exploitable biomass.
Main Effects
9
6.594
0.733
2-Way Interactions
36
1.483
0.041
3-Way Interactions
55
0.345
0.006
Residual Error
384
0.186
0.000
Total
511
8.648
Relative variability in predicted F35 catch.
Main Effects
9
8.178
0.909
2-Way Interactions
36
1.876
0.052
3-Way Interactions
55
0.385
0.007
Residual Error
384
0.232
0.001
Total
511
10.719
Relative variability in the ratio of ending/starting biomass.
Main Effects
9
1.368
0.152
2-Waylnteractions
36
0.410
0.011
3-Way Interactions
55
0.081
0.001
Residual Error
384
0.022
0.000
Total
511
1.887
F
P
2000.0
92.8
<0.001
<0.001
<0.001
13.8
2000.0
100.5
15.3
<0.001
<0.001
<0.00 1
1000.0
61.5
9.8
<0.001
<0.001
<0.001
2000.0
<0.001
<0.001
<0.001
108.6
16.3
2000.0
84.9
12.9
2000.0
86.4
11.6
3000.0
198.6
25.5
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
<0.001
92
Table 3.13 (continued)
Source
DF
SS
MS
Relative median bias in ending total biomass.
Main Effects
9
0.054
0.006
2-Way Interactions
36
0.086
0.002
3-Way Interactions
55
0.070
0.001
Residual Error
384
0.145
0.000
Total
511
0.378
Relative median bias in ending F.
MainEffects
9
0.161
0.018
2-Waylnteractions
36
0.112
0.003
3-Way Interactions
55
0.123
0.002
Residual Error
384
0.2 19
0.00 1
Total
511
0.653
Relative median bias in ending recruitment.
Main Effects
9
0.070
0.008
2-Way Interactions
36
0.151
0.004
3-Way Interactions
55
0.095
0.002
Residual Error
384
0.279
0.00 1
Total
511
0.619
Relative median bias in starting biomass.
Main Effects
9
0.031
0.003
2-Way Interactions
36
0.027
0.001
3-Way Interactions
55
0.023
0.000
Residual Error
384
0.04 1
0.000
Total
511
0.130
Relative median bias in ending exploitable biomass.
Main Effects
9
0.076
0.008
2-Way Interactions
36
0.092
0.003
3-Way Interactions
55
0.070
0.001
Residual Error
384
0.146
0.000
Total
511
0.401
Relative median bias in predicted F35 catch.
Main Effects
9
0.079
0.009
2-Way Interactions
36
0.138
0.004
3-Way Interactions
55
0.100
0.002
Residual Error
384
0.189
0.000
Total
511
0.530
Relative median bias in the ratio of ending/starting biomass.
Main Effects
9
0.0 13
0.001
2-Way Interactions
36
0.02 8
0.001
3-Way Interactions
55
0.019
0.000
Residual Error
384
0.069
0.000
Total
511
0.133
F
P
15.8
6.4
3.4
<0.001
<0.001
<0.001
31.3
5.5
3.9
<0.001
<0.001
<0.001
10.8
5.8
2.4
<0.001
<0.001
<0.001
31.8
7.0
3.8
<0.001
<0.001
<0.001
22.2
6.7
3.3
<0.00 1
17.9
7.8
<0.001
<0.001
<0.001
3.7
8.0
4.3
1.9
<0.001
<0.001
<0.00 1
<0.001
<0.001
93
Table 3.14. ANOVA tables from fractional factorial experiment A2.
Source
DF
Relative bias in ending total biomass.
Main Effects
9
2-Way Interactions
36
SS
MS
F
P
0.572
0.230
0.113
0.286
0.064
0.006
0.002
85.5
8.6
2.8
<0.00 1
132.9
17.9
4.6
<0.001
<0.001
<0.001
80.9
7.3
2.5
<0.001
<0.001
<0.001
84.9
11.0
2.8
<0.001
<0.001
0.059
0.006
0.002
0.001
81.2
8.7
2.7
<0.001
<0.001
<0.001
0.064
0.016
0.005
0.001
59.4
4.8
<0.001
<0.001
<0.001
0.007
0.002
0.001
0.000
28.3
8.7
3.0
<0.001
<0.001
<0.001
3-Waylnteractions
55
Residual Error
384
Total
511
1.228
Relative bias in ending F.
Main Effects
9
1.088
2-Way Interactions
36
0.587
3-Way Interactions
55
0.230
Residual Error
384
0.349
Total
511
2.306
Relative bias in ending recruitment.
Main Effects
9
0.949
2-Way Interactions
36
0.342
3-Way Interactions
55
0.175
Residual Error
384
0.500
Total
511
2.006
Relative bias in starting biomass.
Main Effects
9
0.159
2-Way Interactions
36
0.082
3-Way Interactions
55
0.032
Residual Error
384
0.080
Total
511
0.360
Relative bias in ending exploitable biomass.
Main Effects
9
0.534
2-Way Interactions
36
0.228
3-Way Interactions
55
0.108
Residual Error
384
0.28 1
Total
511
1.178
Relative bias in predicted F35 catch.
Main Effects
9
0.5 80
2-Way Interactions
36
0.591
3-Way Interactions
55
0.284
Residual Error
384
0.417
Total
511
1.905
Relative bias in the ratio of ending/starting biomass.
Main Effects
9
0.060
2-Way Interactions
36
0.074
3-Way Interactions
55
0.039
Residual Error
384
0.09 1
Total
511
0.274
<0.001
<0.001
0.00 1
0.121
0.016
0.004
0.00 1
0.105
0.010
0.003
0.00 1
0.018
0.002
0.00 1
0.000
15.1
<0.00 1
94
Table 3.14 (continued)
Source
DF
SS
MS
Relative median bias in ending total biomass.
Main Effects
9
0.073
0.008
2-Way Interactions
36
0.080
0.002
3-Way Interactions
55
0.041
0.001
Residual Error
384
0.227
0.001
Total
511
0.445
Relative median bias in ending F.
Main Effects
9
0.198
0.022
2-Way Interactions
36
0.096
0.003
3-Way Interactions
55
0.056
0.001
Residual Error
384
0.381
0.001
Total
511
0.759
Relative median bias in ending recruitment.
Main Effects
9
0.04 1
0.005
2-Way Interactions
36
0.134
0.004
3-Way Interactions
55
0.096
0.002
Residual Error
384
0.462
0.00 1
Total
511
0.766
Relative median bias in starting biomass.
Main Effects
9
0.092
0.0 10
2-Way Interactions
36
0.059
0.002
3-Way Interactions
55
0.017
0.000
Residual Error
384
0.062
0.000
Total
511
0.236
Relative median bias in ending exploitable biomass.
Main Effects
9
0.106
0.012
2-Way Interactions
36
0.069
0.002
3-Way Interactions
55
0.031
0.001
ResidualError
384
0.211
0.001
Total
511
0.434
Relative median bias in predicted F35 catch.
Main Effects
9
0.181
0.020
2-Way Interactions
36
0.205
0.006
3-Way Interactions
55
0.104
0.002
Residual Error
384
0.33 8
0.001
Total
511
0.856
Relative median bias in the ratio of ending/starting biomass.
Main Effects
9
0.0 13
0.001
2-Way Interactions
36
0.026
0.001
3-Way Interactions
55
0.025
0.000
Residual Error
384
0.103
0.000
Total
511
0.180
F
P
13.7
3.8
<0.001
<0.001
0.105
1.3
22.2
2.7
1.0
<0.001
<0.001
0.443
3.8
<0.00 1
3.1
1.5
<0.001
0.026
63.4
<0.001
<0.001
<0.001
10.1
1.9
21.5
3.5
1.0
22.9
6.5
2.2
<0.001
<0.001
0.423
<0.001
<0.001
<0.001
5.4
2.7
<0.001
1.7
0.003
<0.00 1
95
Table 3.14 (continued)
Source
DF
SS
Relative variability in ending total biomass.
Main Effects
9
8.246
2-Way Interactions
36
1.533
3-Way Interactions
55
0.334
Residual Error
384
0.221
Total
511
10.363
Relative variability in ending F.
Main Effects
9
5.706
2-Way Interactions
36
1.274
3-Way Interactions
55
0.295
Residual Error
384
0.150
Total
511
7.453
Relative variability in ending recruitment.
Main Effects
9
9.443
2-Way Interactions
36
1.672
3-Way Interactions
55
0.401
Residual Error
384
0.391
Total
511
11.940
Relative variability in starting biomass.
Main Effects
9
3.554
2-Way Interactions
36
0.744
3-Way Interactions
55
0.144
Residual Error
384
0.078
Total
511
4.531
Relative variability in ending exploitable biomass.
Main Effects
9
8.068
2-Way Interactions
36
1.376
3-Way Interactions
55
0.319
Residual Error
384
0.207
Total
511
10.001
Relative variability in predicted F35 catch.
MainEffects
2-Way Interactions
3-Way Interactions
Residual Error
9
36
55
384
11.557
1.778
0.428
0.320
14.125
MS
F
P
0.916
0.043
0.006
2000.0
73.9
<0.001
<0.001
<0.001
10.5
0.001
0.634
0.035
0.005
0.000
2000.0
90.4
13.7
<0.001
<0.001
<0.001
1.049
1000.0
45.7
7.2
<0.001
<0.001
<0.001
0.395
0.021
0.003
0.000
2000.0
<0.001
<0.001
<0.001
0.896
0.038
0.006
0.001
2000.0
70.8
1.284
0.049
0.008
2000.0
<0.001
<0.001
<0.001
2000.0
<0.001
<0.001
<0.001
0.046
0.007
0.001
102.1
12.9
10.8
59.3
9.3
<0.001
<0.001
<0.001
0.00 1
Total
511
Relative variability in the ratio of ending/starting biomass.
Main Effects
9
1.774
0.197
2-Way Interactions
36
0.492
0.014
3-Way Interactions
55
0.109
0.002
Residual Error
384
0.033
0.000
Total
511
2.414
157.1
22.7
96
Ending Biomass
Ending F
1110
10
Ending Recruitment
Starting Biomass
160
200
120
150
80
100
40
50
0
0
U
Figure 3.2. Experiment Al example histograms (from experimental treatment 1) of variables
output by the Stock Synthesis program and used as dependent experimental variables. The
dashed lines indicate the true values. The units for the biomass and recruitment axes are in
thousands
97
Ending Biomass
Ending F
200
I L)
150
90
100
60
50
30
50
100
150
0.0
0.1
0.2
0.
Starting Biomass
Ending Recruitment
160
120
90
80
60
40
30
4
8
12
80
110
140
Figure 3.3. Experiment A2 example histograms (from experimental treatment one) of variables
output by the Stock Synthesis program and used as dependent experimental variables. The
dashed lines indicate the true values. The units for the biomass and recruitment axes are in
thousands
98
3.3 Results
In the two main experiments Al and A2, the seven types of Stock Synthesis estimates
that we examined varied considerably in relative bias and relative variability. The average
values across the four replicate groups for the 128 treatments are listed in Tables 3.7 3.9 for
Al and Tables 3.10 - 3.12 for A2. For the measurement of relative bias of the mean both in Al
and A2, the
F35% catch
estimates showed the largest negative bias (-3.9% in Al and -12% in
A2) and ending fishing mortality estimates (+33% in Al and +32% in A2) had the largest
positive bias. The measurement of relative bias of the median produced similar occurrences of
positive and negative maximums in Al and A2. Both in Al and A2, the largest negative
median bias occurred within the
F35%
catch estimates (-12.5% in Al and-15.8% in A2) and the
largest positive median bias showed in the estimates of ending fishing mortality (+1 1.3% in
Al and +9.2% in A2). While the minimum relative variability was in the estimates of starting
biomass both for Al and A2 (2.9% in Al and 3.0% in A2), the maximum relative variability
occurred in the estimates of ending recruitment (78%) for Al and in the estimates of F35%
catch (74%) for A2.
For both experiments Al and A2, the Stock Synthesis estimates of ending biomass,
ending exploitable biomass, ending recruitment, and starting biomass were in general skewed
to the right, whereas the estimates for the ending fishing mortality coefficient were reasonably
symmetric (e.g., Fig. 3.2 and Fig. 3.3). For the variables that measured relative bias of the
mean and relative bias of the median, diagnostic plots of the residual versus fitted values
indicated little evidence of heterogeneous variability. However, similar plots for the variables
that measured relative variation showed some tendency for residual variability to increase with
the magnitude of the fitted values.
In the analyses of variance for both experiments Al and A2, the main effects, two-way
interactions, and three-way interactions were all highly significant (P < 0.01) for the 14
dependent variables in the measurement of relative bias and relative variability (Tables 3.133.14). However, main effects and interactions did not have same degrees of importance. In
experiment Al, for example, the MS (Mean Square) for the main effects for the measurement
of relative variability in ending total biomass was about 16 times larger than the MS for the
two-way interactions and 110 times larger than the MS for the three-way interactions.
Experiment A2 showed similar pattern. For example, in A2, the MS for the main effects for
the measurement of relative variability in ending total biomass was about 21 times larger than
the MS for the two-way interactions and 150 times larger than the MS for the three-way
interactions. Thus, Tables 3.13 and 3.14 indicated that most of the variability in the dependent
variables was accounted for by differences in the main effects. The interactions were
significant but much less important than the main effects. In addition, since the main effects
were not aliased with any fourth or lower order interactions (Table 3.4), the significant
interactions have no side effects on the analyses of main effects.
.3.1 Effects on Relative Bias
On average across all levels of the nine factors the seven types of estimates that we
examined had slight but statistically significant (P < 0.05) positive bias (Table 3.15 and Table
3.16). For experiment Al, these average biases ranged from a low of 1.4% for the estimates of
starting biomass to a high of 5.3% for the estimates of ending recruitment. For experiment A2,
the values ranged from a low of 1.5% for the estimates of ending/starting biomass ratio to a
high of 5.7% for the estimates of ending recruitment. The results from both experiment Al and
A2 showed that the factor for survey variability and the factor for the number of years in the
data series were the top two most influential effects, indicating that longer data series and less
variable survey indices of biomass produced less biased estimates.
Increasing sample size help reduced the relative bias for most types of estimates in
both Al and A2. But its effect was not as big as that of increasing the number of years in the
data series and reducing survey variability. This doesn't necesrily mean the sample size
factor is not important. In the previous chapter (Chapter two), where experiments were
conducted on populations with simple multinomial age composition and the low/high levels of
sample size were 100/400 fish, we found the sample size factor was one of the top two most
important factors on the measurement of relative bias. Remember, in experiments Al, A2, as
well as the experiments in chapter two, Synthesis was always configured to use a maximum
value of 400 for the age composition sample size. This means that the Synthesis constraint on
sample size was never binding for the Chapter Two experiments and was always binding for
experiment Al, where the low/high levels of sample size were 400/2000 fish, and experiment
A2, where the low/high levels of sample size were 400/1600 fish. This constraint probably had
a greater influence on the high levels of the sample size factor, which in turn made the effect
of sample size non-linear. However, because different age composition models were used
(simple multinomial distribution in Chapter Two versus compound multinomial distribution
here), the direct comparison between the results here and that of Chapter Two won't give us
conclusive evidence. Besides the Synthesis constraint, the age composition model may have
been a contributing factor. Experiments Bl, B2, Cl, and C2 were specifically designed to
address this issue and the discussion of their results (below) will examine the exact cause.
Between experiment Al and A2, as we expected, the effect of sample size in Al on average
was bigger than in A2. In Al we used a bigger value in the high level of sample size (2000)
and the population partitioning was less variable (CV at 0.3).
101
Table 3.15. Analysis of relative bias for experiment Al.
Factor
Grand mean
numYrs
smplSize
effortCv
svyCv
natiM
Ftrend
catchCv
Fslct
strtaCov
numYrs*smplSize
numYrs*effortCv
numYrs*svyCv
numYrs*natlM
numYrs*Ftrend
numYrs*catchCv
numYrs*Fslct
numYrs*strtaCov
smplSize*effortCv
smplSize*svyCv
smplSize*natlM
smplSize*Ftrend
smplSize*catchCv
smplSize*Fslct
smplSize*strtaCov
effortCv*svyCv
effortCv*natlM
effortCv*Ftrend
effortCv*catchCv
effortCv*Fslct
effortCv*strtaCov
svyCv*natlM
svyCv*Ftrend
svyCv*catchCv
svyCv*Fslct
svyCv*strtaCov
natlM*Ftrend
natlM*catchCv
natlM*Fslct
natlM*strtaCov
Ftrend*catchCv
Ftrend*Fslct
Ftrend*strtaCov
catchCv*Fslct
catchCv*strtaCov
Fslct*strtaCov
end Bio
end F
end Rec
start Bio
0.0407
0.0246
0.0525
0.0142
-0.0228
-0.0075
-0.0283
-0.0154
-0.0086
-0.0140
-0.0142
-0.0011
0.0039
0.0086
0.0044
0.0011
0.0203
0.0134
0.0254
0.0076
0.0034
0.0100
0.0028
0.0007
-0.0049
-0.0089
-0.0047
-0.0044
0.0052
-0.0031
0.0062
0.0021
-0.0019
0.0132
-0.0009
-0.0026
-0.0029
-0.0001
-0.0032
-0.0019
0.0100
0.0010
0.0116
0.0061
0.0005
-0.0035
-0.0003
-0.0002
-0.0082
-0.0074
-0.0104
-0.0057
-0.0036
-0.0032
-0.0033
-0.0031
0.0027
0.0046
0.0023
0.0040
0.0000
-0.0029
-0.0009
-0.0011
0.0046
-0.0106
0.0039
0.0036
0.0041
-0.0014
0.0042
0.0023
-0.0052
-0.0061
-0.0059
-0.0027
-0.0056
-0.0058
-0.0064
-0.0028
-0.0003
-0.0031
0.0002
0.0012
0.0010
0.0040
0.0008
0.0014
-0.0004
-0.0009
0.0004
0.0000
0.0084
-0.0078
0.0088
0.0042
0.0025
-0.0004
0.0025
0.0020
0.0063
0.0073
0.0076
0.0020
-0.0004
0.0017
0.0004
-0.0002
0.0018
-0.0009
0.0025
0.0008
-0.0020
-0.0001
-0.0022
-0.0009
-0.0019
0.0057
-0.0015
-0.0016
-0.0013
0.0001
-0.0016
-0.0009
0.0057
0.0023
0.0059
0.0029
-0.0019
-0.0042
-0.0012
-0.0023
-0.0007
0.0011
0.0000
-0.0009
0.0017
0.0076
0.0026
-0.0004
-0.0020
-0.0016
-0.0016
-0.0017
0.0011
-0.0058
0.0017
0.0004
0.0013
0.0003
0.0013
0.0006
-0.0082
0.0005
-0.0098
-0.0034
-0.0033
0.0029
-0.0041
-0.0025
-0.0006
-0.0038
-0.0010
-0.0005
0.0039
-0.0030
0.0043
0.0022
0.0011
-0.0003
0.0012
0.0008
-0.0010
0.0009
-0.0014
-0.0001
-0.0010
0.0017
-0.0006
-0.0002
0.0024
-0.0013
0.0029
0.0017
Bold: Coefficients with t-statistics significant at the P = 0.05 levels.
end exB
0.0363
-0.0233
-0.0067
0.0037
0.0197
0.0034
-0.0053
0.0055
-0.0050
-0.0030
0.0102
0.0007
-0.0081
-0.0042
0.0024
0.0001
0.0054
0.0041
-0.0052
-0.0057
-0.0003
0.0012
-0.0007
0.0094
0.0025
0.0061
-0.0004
0.0018
-0.0019
-0.0021
-0.0012
0.0060
-0.0021
-0.0009
0.0010
-0.0021
0.0010
0.0013
-0.0096
-0.0036
-0.0005
0.0037
0.0009
-0.0009
-0.0011
0.0023
f35 catch endB/startB
0.0470
0.0149
-0.0243
0.0025
-0.0090
-0.0041
0.0043
0.0014
0.0235
0.0057
0.0030
0.0004
-0.0037
0.0032
0.0063
0.0023
-0.0043
-0.0012
-0.0030
-0.0002
0.0104
0.0008
0.0013
0.0012
-0.0094
0.0028
-0.0024
0.0012
0.0018
-0.0023
0.0005
0.0022
0.0065
0.0034
0.0046
0.0008
-0.0054
-0.0002
-0.0065
-0.0004
0.0007
-0.0013
0.0006
-0.0014
-0.0005
-0.0003
0.0116
0.0036
0.0026
-0.0003
0.0076
0.0019
-0.0010
-0.0003
0.0027
0.0011
-0.0023
-0.0002
-0.0025
-0.0005
-0.0014
0.0002
0.0063
0.0011
-0.0010
0.0017
-0.0010
0.0001
0.0021
0.0004
-0.0032
0.0005
0.0018
0.0011
0.0016
0.0004
-0.0108
-0.0028
-0.0032
-0.0008
-0.0003
0.0012
0.0045
0.0017
0.0010
0.0003
-0.0012
-0.0007
-0.0017
-0.0007
0.0029
0.0004
102
Table 3.16. Analysis of relative bias for experiment A2.
Factor
Grand mean
numYrs
smplSize
effortCv
svyCv
natiM
Ftrend
catchCv
Fslct
strtaCov
numYrs*smplSize
numYrs*effortCv
numYrs*svyCv
numYrs*natlM
numYrs*Ftrend
numYrs*catchCv
numYrs*Fslct
numYrs*strtaCov
smplSize*effortCv
smplSize*svyCv
smplSize*natlM
smplSize*Ftrend
smplSize*catchCv
smplSize*Fslct
smplSize*strtaCov
effortCv*svyCv
effortCv*natlM
effortCv*Ftrend
effortCv*catchCv
effortCv*Fslct
effortCv*strtaCov
svyCv*natlM
svyCv*Ftrend
svyCv*catchCv
svyCv*Fslct
svyCv*strtaCov
natlM*Ftrend
natlM*catchCv
natlM*Fslct
natlM*strtaCov
Ftrend*catchCv
Ftrend*Fslct
Ftrend*strtaCov
catchCv*Fslct
catchCv*strtaCov
Fslct*strtaCov
end Bio
end F
end Rec start Bio
0.0448
0.0409
0.0566
0.0161
-0.0213
-0.0196
-0.0281
-0.0136
-0.0024
-0.0189
-0.0078
0.0038
-0.0018
0.0178
-0.0011
-0.0028
0.0242
0.0226
0.0299
0.0089
-0.0005
0.0166
0.0004
-0.0033
-0.0011
-0.0143
-0.0018
-0.0023
0.0071
-0.0034
0.0080
0.0027
0.0036
0.0071
0.0061
0.0004
-0.0018
-0.0035
-0.0025
-0.0010
0.0044
0.0058
0.0056
0.0029
0.0085
-0.0080
0.0113
0.0032
-0.0099
-0.0125
-0.0122
-0.0071
0.0041
-0.0096
0.0057
0.0003
-0.0012
0.0087
-0.0030
0.0023
-0.0007
-0.0031
-0.0017
-0.0012
0.0018
-0.0051
0.0017
0.0021
0.0021
0.0022
0.0030
0.0007
-0.0034
-0.0073
-0.0035
-0.0012
-0.0058
-0.0043
-0.0075
-0.0023
0.0045
-0.0075
0.0030
0.0055
0.0011
0.0022
0.0026
0.0003
0.0009
-0.0025
0.0006
0.0006
0.0015
0.0016
0.0020
-0.0001
0.0006
0.0024
-0.0015
0.0003
0.0047
0.0136
0.0051
0.0005
-0.0006
0.0031
-0.0001
-0.0015
0.0064
-0.0051
0.0079
0.0027
-0.0051
0.0022
-0.0054
-0.0024
-0.0011
0.0072
0.0004
-0.0010
-0.0013
-0.0011
-0.0009
-0.0004
0.0025
0.0057
0.0013
0.0009
0.0003
-0.0068
0.0013
-0.0017
0.0010
0.0001
0.0018
0.0000
0.0030
0.0063
0.0048
-0.0014
0.0000
-0.0040
0.0009
0.000 1
0.0047
-0.0057
0.0041
0.0031
0.0015
-0.0002
0.0008
0.0008
-0.0001
-0.0061
-0.0004
0.0015
-0.0025
0.0004
-0.0038
-0.0011
0.0010
-0.0065
0.0021
-0.0004
0.0032
-0.0016
0.0034
0.0010
-0.0022
0.0025
-0.0032
-0.0010
-0.0024
0.0017
-0.0018
-0.0019
-0.0002
-0.0009
0.0005
-0.0005
-0.0016
0.0005
-0.0014
-0.0006
Bold: Coefficients with t-statistics significant at the P = 0.05 levels
end exB
0.0362
-0.0212
0.0002
-0.0020
0.0229
-0.0022
-0.0018
0.0071
-0.0020
-0.0017
0.0042
0.0083
-0.0093
0.0038
-0.0011
-0.0008
0.0030
0.0019
-0.0035
-0.0055
0.0050
0.0012
0.0011
0.0031
0.0006
0.0045
-0.0008
0.0062
-0.0053
-0.0015
-0.0009
0.0023
-0.0001
0.0012
0.0019
-0.0003
0.0044
0.0015
-0.0037
-0.0023
0.0008
0.0029
-0.0021
-0.0027
0.000 1
-0.0016
f35 catch endB/startB
0.0438
0.0148
-0.0152
0.0041
0.0024
-0.0040
-0.0022
0.0003
0.0251
0.0067
-0.0109
0.0017
0.0010
0.0047
0.0080
0.0033
-0.0089
0.0019
0.0008
-0.0003
0.0015
-0.0006
0.0105
0.0050
-0.0093
0.0040
0.0139
0.0045
-0.0019
-0.0041
-0.0004
0.0021
0.0108
0.0019
0.0017
0.0010
-0.0031
-0.0008
0.0078
0.0017
0.0109
0.0014
0.0007
0.0002
0.0012
0.0004
0.0089
0.0005
0.0025
-0.0002
0.0051
0.0020
-0.0012
0.0007
0.0071
0.0029
-0.0051
-0.0012
-0.0020
-0.0003
-0.0021
-0.0006
-0.0007
0.0007
0.0009
0.0034
0.0011
0.0010
0.0008
0.0028
-0.0039
0.0003
0.0052
0.0013
0.0013
0.0001
-0.0127
-0.0001
0.0000
-0.0009
0.0022
0.0028
0.0044
0.0019
-0.0027
-0.0009
-0.0028
0.0004
-0.0003
0.0003
0.0008
-0.0008
103
The main effect for the factor of fishing effort variability revealed itself differently in
experiments Al and A2. In Al the coefficients of this factor were positive and statistically
significant for all seven types of estimates, indicating that larger fishing effort variability
would result in bigger positive bias for all seven types of estimates. In experiment A2 the
coefficients for this factor were mostly statistically insignificant. However, the interactions
between fishing effort variability and survey variability were positive and mostly significant in
both experiments Al and A2.
Higher fishing mortality seemed to help reduce the positive bias of estimates in both
experiments Al and A2. Increased variability in the fishery catch data did increase the bias for
all types of estimates with the exception of the estimate of ending fishing mortality. The
effects of the fishery selectivity factor were relatively small both in Al and A2.
3.3.2 Effects on Relative Variability
For the overall average relative variability of the seven types of Stock Synthesis
estimates, the estimates of starting biomass and the estimates of ending recruitment
respectively had the lowest and highest values both in experiments Al and A2 (Tables 3.173.18). In experiment Al, these values ranged from 11.5% to 28.9%. In experiment A2, the
ranges were between 13.3% and 32.7%. The results from both experiments Al and A2
indicated that the factor for survey variability and the factor for the number of years in the data
series were the top two most influential effects, indicating that longer data series and less
variable survey indices of biomass produced less variable estimates. The main effects of
sample size and fishing mortality were also fairly big, indicating that increased sample size
and increased fishing mortality would considerably reduce the estimated variability. The main
effects of fishing effort variability, natural mortality, and variability in fishery catch data were
in general as we expected. Higher values of these three factors all contributed to higher
104
Table 3.17. Analysis of relative variability for experiment Al.
Factor
Grand mean
numYrs
smplSize
effortCv
svyCv
natlM
Ftrend
catchCv
Fslct
strtaCov
numYrs*smplSize
numYrs*effortCv
numYrs*svyCv
numYrs*natlM
numYrs*Ftrend
numYrs*catchCv
numYrs*Fslct
numYrs*strtaCov
smplSize*effortCv
smplSize*svyCv
smplSize*natlM
smplSize*Ftrend
smplSize*catchCv
smplSize*Fslct
smplSize*strtaCov
effortCv*svyCv
effortCv*natlM
effortCv*Ftrend
effortCv*catchCv
effortCv*Fslct
effortCv*strtaCov
svyCv*natlM
svyCv*Ftrend
svyCv*catchCv
svyCv*Fslct
svyCv*strtaCov
natlM*Ftrend
natlM*catchCv
natlM*Fslct
natlM*strtaCov
Ftrend*catchCv
Ftrend*Fslct
Ftrend*strtaCov
catchCv*Fslct
catchCv*strtaCov
Fslct*strtaCov
end F
end Rec start Bio end exB f35 catch endB/startB
0.2285
0.2613
0.2894
0.1153
0.2295
0.2617
0.1348
-0.0692
-0.0427
-0.0744
-0.0546
-0.0698
-0.0750
0.0012
-0.0339
-0.0281
-0.0492
-0.0189
-0.0350
-0.0407
-0.0162
0.0060
0.0279
0.0080
0.0016
0.0059
0.0113
0.0030
0.0693
0.0503
0.0769
0.0225
0.0677
0.0795
0.0422
0.0264
0.0194
0.0157
0.0205
0.0278
0.0297
0.0088
-0.0300
-0.0199
-0.0275 -0.0254
-0.0309
-0.0238
0.0022
0.0135
0.0288
0.0125
0.0122
0.0136
0.0123
0.0072
0.0193
0.0099
0.0238 -0.0038
0.0154
0.0245
0.0219
-0.0050
-0.0035
-0.0081
-0.0033
-0.0048
-0.0069
-0.0022
0.0165
0.0124
0.0177
0.0115
0.0167
0.0194
0.0022
0.0044
0.0001
0.0043
-0.0001
0.0045
0.0057
0.0034
-0.0176
-0.0139 -0.0217
-0.0178
-0.0174
-0.0178
0.0045
-0.0106
-0.0083
-0.0088
-0.0093
-0.0105
-0.0120
0.0002
0.0108
0.0065
0.0099
0.0166
0.0105
0.0107
-0.0025
-0.0033
0.0027
-0.0038
-0.0022
-0.0034
-0.0032
0.0017
-0.0111
-0.0077 -0.0137 -0.0027
-0.0100
-0.0148
-0.0055
0.0033
0.0024
0.0028
0.0023
0.0032
0.0040
0.0005
-0.0167
-0.0128
-0.0176
-0.0059
-0.0166
-0.0196
-0.0090
-0.0139
-0.0118 -0.0154 -0.0062
-0.0137
-0.0151
-0.0058
-0.0007
-0.0024
0.0053
-0.0042
-0.0012
-0.0021
0.0009
0.0065
0.0044
0.0074
0.0063
0.0065
0.0055
0.0001
0.0012
0.0019
0.0010
0.0009
0.0009
0.0022
0.0007
0.0077
0.0049
0.0074
0.0065
0.0081
0.0060
0.0017
0.0004
0.0007 -0.0003
0.0021
0.0004
0.0012
-0.0018
0.0214
0.0205
0.0235
0.0058
0.0204
0.0242
0.0143
-0.0007
0.0018
0.0006
-0.0014
-0.0008
-0.0007
0.0012
0.0024
0.0011
0.0036
0.0014
0.0023
0.0036
0.0004
-0.0104
0.0019
-0.0105
-0.0015
-0.0101
-0.0107
-0.0079
0.0025
0.0055
0.0034
0.0000
0.0020
0.0034
0.0030
-0.0024
-0.0013
-0.0036
-0.0010
-0.0023
-0.0032
-0.0012
0.0118
0.0092
0.0112
0.0062
0.0118
0.0127
0.0053
-0.0055
-0.0056
-0.0044
-0.0061
-0.0058
-0.0034
0.0010
-0.0005
-0.0066
0,0009
-0.0007
-0.0005
-0.0006
0.0007
0.0184
0.0140
0.0209
0.0024
0.0163
0.0208
0.0142
-0.0036
-0.0021
-0.0030
-0.0020
-0.0032
-0.0025
-0.0012
-0.0042
-0.0038 -0.0023
-0.0051
-0.0038
-0.0035
0.0003
0.0024
0.0001
0.0024
0.0003
0.0024
0.0020
0.0010
-0.0212
-0.0132 -0.0185
-0.0115
-0.0190
-0.0187
-0.0094
-0.0014
-0.0015 -0.0014
-0.0019
-0.0015
-0.0027
0.0000
-0.0029
-0.0022
-0.0044
-0.0015
-0.0028
-0.0028
0.0012
0.0030
-0.0002
0.0024
0.0030
0.0024
0.0034
0.0008
-0.0009
-0.0005
-0.0017
0.0002
-0.0010
-0.0014
-0.0007
-0.0002
-0.0030
0.0006
0.0010
-0.0003
-0.0008
0.0003
-0.0003
0.0007
0.0004
-0.0006
-0.0003
0.000 1
0.0000
-0.0006
0.0001
-0.0014
0.0004
-0.0006
-0.0022
-0.0007
Bold: Coefficients with t-statistics significant at the P = 0.05 levels
end I3io
105
Table 3.18. Analysis of relative variability for experiment A2.
Factor
Grand mean
numYrs
SmplSize
effortCv
svyCv
natiM
Ftrend
catchCv
Fslct
strtaCov
numYrs*smplSize
numYrs*effortCv
numYrs*svyCv
numYrs*natlM
numYrs*Ftrend
numYrs*catchCv
numYrs*Fslct
numYrs*strtaCov
smplSize*effortCv
smplSize*svyCv
smplSize*natlM
smplSize*Ftrend
smplSize*catchCv
smplSize*Fslct
smplSize*strtaCov
effortCv*svyCv
effortCv*natlM
effortCv*Ftrend
effortCv*catchCv
effortCv*Fslct
effortCv*strtaCov
svyCv*natlM
svyCv*Ftrend
svyCv*catchCv
svyCv*Fslct
svyCv*strtaCov
natlM*Ftrend
natlM*catchCv
natlM*Fslct
natlM*strtaCov
Ftrend*catchCv
Ftrend*Fslct
Ftrend*strtaCov
catchCv*Fslct
catchCv*strtaCov
Fslct*strtaCov
end Bio
end F
end Rec start Bio
0.2569
0.2879
0.3272
0.1325
-0.0825
-0.0542
-0.0860
-0.0648
-0.0257
-0.0252
-0.0354
-0.0164
0.0060
0.0351
0.0082
-0.0012
0.0832
0.0673
0.0916
0.0289
0.0231
0.0222
0.0131
0.0225
-0.0282
-0.0213
-0.0240
-0.0277
0.0158
0.0282
0.0144
0.0123
0.0089
0.0058
0.0171
-0.0147
-0.0051
-0.0063
-0.0088
-0.0027
0.0095
0.0090
0.0099
0.0084
0.0116
0.0011
0.0122
0.0027
-0.0245
-0.0200
-0.0284 -0.0220
-0.0046
-0.0064
-0.0031
-0.0072
0.0095
0.0104
0.0077
0.0163
-0.0056
0.0027 -0.0054
-0.0032
-0.0024
-0.0036 -0.0069
0.0048
0.0010
0.0029
-0.0010
0.0018
-0.0102
-0.0117
-0.0118
-0.0025
-0.0102
-0.0112
-0.0100
-0.0042
-0.0025
-0.0006
0.0013
-0.0047
0.0029
0.0037
0.0028
0.0044
-0.0003
0.0005
-0.0006
0.0010
0.0118
0.0048
0.0125
0.0090
0.0009
0.0003
-0.0009
0.0030
0.0237
0.0284
0.0248
0.0047
0.0026
0.0044
0.0029
-0.0004
0.0091
0.0011
0.0095
0.0049
-0.0129
0.0021
-0.0133
-0.0027
0.0032
0.0087
0.0049
0.0001
-0.0021
-0.0022
-0.0016
-0.0009
0.0086
0.0098
0.0069
0.0048
-0.0061
-0.0080
-0.0042
-0.0077
-0.0008
-0.0045 -0.0003
-0.0009
0.0156
0.0150
0.0189
-0.0027
-0.0014
-0.0036
0.0000
-0.0008
0.0007
-0.0017
0.0019
-0.0026
0.0038
-0.0004
0.0037
0.0009
-0.0195
-0.0129
-0.0141
-0.0140
-0.0040
0.0005
-0.0050 -0.0029
-0.0035
-0.0042
-0.0052
-0.0016
0.0048
0.0009
0.0049
0.0045
-0.0017
0.0000
-0.0020 -0.0003
-0.0037
-0.0009
-0.0039
-0.0011
-0.0007
-0.0006
-0.0004 -0.0004
-0.0008
-0.0026
-0.0011
-0.0002
Bold: Coefficients with t-statistics significant at the P = 0.05 levels.
end exB f35 catch endB/startB
0.2564
0.3064
0.1496
-0.0824
-0.0949
-0.0018
-0.0266
-0.0378
-0.0130
0.0052
0.0106
0.0075
0.0803
0.0950
0.0508
0.0245
0.0381
0.0083
-0.0297
-0.0204
0.0043
0.0156
0.0159
0.0087
0.0047
0.0275
0.0219
-0.0057
-0.0109
-0.0033
0.0099
0.0139
0.0003
0.0116
0.0141
0.0065
-0.0237
-0.0246
0.0024
-0.0048
-0.0114
0.0025
0.0095
0.0097
-0.0027
-0.0055
-0.0054
0.0007
-0.0011
-0.0135
-0.0041
0.0020
0.0038
-0.0008
-0.0100
-0.0127
-0.0074
-0.0099
-0.0087
-0.0055
-0.0028
-0.0110
0.0001
0.0031
0.0017
-0.0006
-0.0001
-0.0002
-0.0009
0.0116
0.0034
0.0030
0.0017
0.0017
-0.0022
0.0225
0.0264
0.0189
0.0017
0.0020
0.0032
0.0091
0.0125
0.0023
-0.0126
-0.0129
-0.0086
0.0027
0.0029
0.0038
-0.0018
-0.0026
-0.0015
0.0082
0.0083
0.0054
-0.0063
-0.0027
0.0011
-0.0009
-0.0006
0.0008
0.0120
0.0181
0.0156
-0.0014
0.0028
-0.0011
0.0005
0.0017
0.0010
0.0038
0.0042
0.0010
-0.0174
-0.0036
-0.0061
-0.0042
-0.0095
-0.0010
-0.0028
-0.0019
0.0008
0.0038
0.0039
0.0017
-0.0012
-0.0021
-0.0009
-0.0039
-0.0039
0.0003
-0.0009
-0.0014
0.0001
-0.0008
-0.0060
-0.0013
106
Table 3.19. Analysis of relative median bias for experiment Al.
Factor
Grand mean
numYrs
smplSize
effortCv
svyCv
natiM
Ftrend
catchCv
Fslct
strtaCov
numYrs*smplSize
numYrs*effortCv
numYrs*svyCv
numYrs*natlM
numYrs*Ftrend
numYrs*catchCv
numYrs*Fslct
numYrs*strtaCov
smplSize*effortCv
smplSize*svyCv
smplSize*natlM
smplSize*Ftrend
smplSize*catchCv
smplSize*Fslct
smplSize*strtaCov
effortCv*svyCv
effortCv*natlM
effortCv*Ftrend
effortCv*catchCv
effortCv*Fslct
effortCv*strtaCov
svyCv*natlM
svyCv*Ftrend
svyCv*catchCv
svyCv*Fslct
svyCv*strtaCov
natlM*Ftrend
natlM*catchCv
natlM*Fslct
natlM*strtaCov
Ftrend*catchCv
Ftrend*Fslct
Ftrend*strtaCov
catchCv*Fslct
catchCv*strtaCov
Fslct*strtaCov
end Bio
0.0007
0.0001
0.0032
0.0015
-0.0008
-0.0054
0.0057
0.0023
-0.0050
-0.0003
0.0019
-0.0009
0.0025
0.0010
-0.0024
0.0021
0.0066
0.0025
0.0004
0.0003
0.0009
-0.0024
-0.0005
0.0063
0.0005
0.0001
0.0003
0.0002
0.0005
-0.0017
end F
-0.0076
-0.0006
-0.0060
-0.0009
0.0017
0.0050
-0.0044
-0.0106
0.0107
0.0011
-0.0013
-0.0006
-0.0023
0.0002
0.0017
-0.0015
-0.0080
-0.0018
-0.0022
-0.0007
-0.0001
end Rec
start Bio
-0.0002
-0.0035
-0.0012
-0.0007
0.0006
0.0047
0.0012
0.0010
-0.0014
-0.0003
-0.0042
-0.0048
0.0061
0.0029
0.0033
0.0008
-0.0081
-0.0021
-0.0003
-0.0007
0.0030
0.0014
-0.0018
-0.0002
0.0023
0.0011
0.0013
0.0006
-0.0031
-0.0013
0.0009
-0.0001
0.0097
0.0040
0.0021
0.0011
0.0007
-0.0009
0.0014
0.0000
-0.0001
0.0023
0.00 17
-0.0030
-0.0007
-0.0003
0.0009
0.0000
-0.0072
0.0072
0.0023
-0.0016
0.0006
0.0008
-0.0002
-0.0006
-0.0001
-0.0004
0.0005
0.0003
-0.0002
0.0009
-0.0003
-0.0020
0.0025
-0.0003
0.0010
-0.0030
-0.0014
-0.000 1
0.0009
-0.0004
-0.0008
0.0008
-0.0003
0.0014
0.0004
0.0012
-0.0015
0.0021
-0.0001
-0.0001
0.0004
0.0015
-0.0006
-0.0026
0.0035
-0.0041
-0.0009
0.0002
-0.0008
-0.0008
-0.0005
0.0031
-0.0037
0.0029
0.0023
0.0008
-0.0012
0.0008
0.0002
-0.0023
0.0048
-0.0037
0.0000
-0.0024
0.0020
-0.0039
-0.0018
0.0021
-0.0017
0.0013
0.0008
0.0021
-0.0012
0.0022
0.0012
0.0012
-0.0006
0.0010
0.0007
-0.0005
0.00 14
-0.0002
-0.000 1
-0.0003
0.0013
-0.0001
0.0005
0.0024
-0.0023
0.0037
0.0014
Bold: Coefficients with t-statistics significant at the P = 0.05 levels
end exB f35 catch endB/startB
-0.0036
0.0020
0.0047
-0.0005
0.0003
0.0011
0.0047
0.0035
-0.0017
0.0015
0.0017
0.0002
-0.0008
-0.0012
-0.0004
-0.0059
-0.0052
-0.0005
0.0050
0.0062
0.0018
0.0026
0.0028
0.0022
-0.0075
-0.0079
-0.0036
-0.0009
-0.0008
0.0000
0.0021
0.0022
0.0007
-0.0003
-0.0007
-0.0001
0.0027
0.0030
0.0012
0.0001
0.0015
0.0001
-0.0022
-0.0025
-0.0009
0.0021
0.0024
0.0011
0.0066
0.0085
0.0040
0.0019
0.0026
0.0008
0.0003
0.0013
0.0010
-0.0001
0.0004
0.0008
0.0005
0.0011
-0.0017
-0.00 12
-0.0028
-0.0013
-0.0012
-0.0007
-0.0003
0.0068
0.0082
0.0034
0.0005
0.0008
0.0000
0.0000
-0.0002
-0.0002
0.0002
-0.0002
-0.0002
0.0002
-0.0003
0.0005
0.0004
0.00 13
0.0008
-0.0019
-0.0022
-0.0010
-0.0002
0.0000
0.0004
0.0010
0.0011
0.0003
0.0006
0.0015
0.0006
-0.0004
0.0000
0.0008
-0.0024
-0.0036
-0.0010
0.0003
-0.0002
0.0001
0.0026
0.0039
0.0008
0.0012
0.0016
0.0007
-0.0044
-0.0036
-0.0024
-0.0026
-0.0027
-0.0011
0.0014
0.0025
0.0002
0.0025
0.0020
0.0013
0.0007
0.0010
0.0007
-0.0011
-0.00 10
-0.0005
0.0000
-0.0002
-0.0004
0.0023
0.0028
0.0006
107
Table 3.20. Analysis of relative median bias for experiment A2
Factor
Grand mean
numYrs
smplSize
effortCv
svyCv
natiM
Ftrend
catchCv
Fslct
strtaCov
numYrs*smplSize
numYrs*effortCv
numYrs*svyCv
numYrs*natlM
numYrs*Ftrend
numYrs*catchCv
numYrs*Fslct
numYrs*strtaCov
smplSize*effortCv
smplSize*svyCv
smplSize*natlM
smplSize*Ftrend
smplSize*catchCv
smplSize*Fslct
smplSize*strtaCov
effortCv*svyCv
effortCv*natlM
effortCv*Ftrend
effortCv*catchCv
effortCv*Fslct
effortCv*strtaCov
svyCv*natlM
svyCv*Ftrend
svyCv*catchCv
svyCv*Fslct
svyCv*strtaCov
natlM*Ftrend
natlM*catchCv
natlM*Fslct
natlM*strtaCov
Ftrend*catchCv
Ftrend*Fslct
Ftrend*strtaCov
catchCv*Fslct
catchCv*strtaCov
Fslct*strtaCov
end Bio
-0.0006
0.0038
0.0061
-0.0009
end F
end Rec start Bio end exB f35 catch endB/startB
-0.00 19
-0.0069
-0.0048
-0.0085
-0.0025
0.0036
-0.0066
0.0045
0.0030
0.0039
0.0090
0.0023
-0.0091
0.0026
0.0082
0.0089
0.0086
-0.0024
0.0029
-0.0032
-0.0016
-0.0009
-0.0022
-0.0009
0.0001
0.0017
-0.0014
-0.0001
-0.0002
-0.0039
-0.0005
-0.0068
0.0089
-0.0038
-0.0081
-0.0084
-0.0112
0.0012
0.0044
-0.0064
0.0045
0.0042
0.0045
0.0048
0.0019
0.0038
-0.0107
0.0024
0.0017
0.0044
0.0041
0.0028
0.0030
0.0037
0.0004
0.0039
-0.0015
-0.0037
-0.0009
-0.0006
-0.0008
-0.0007
-0.0007
-0.0004
0.0002
-0.0001
-0.0008
0.0009
-0.0002
-0.0007
-0.0008
-0.0028
-0.0005
0.0031
-0.0031
0.0068
0.0014
0.0027
0.0035
0.0024
0.0019
-0.0041
0.0033
0.0005
0.0025
0.0045
0.0021
0.0057
-0.0058
0.0060
0.0030
0.0052
0.0117
0.0032
-0.0023
0.0029
-0.0045
-0.0020
-0.0024
-0.0025
-0.0022
0.0009
-0.0005
0.0008
-0.0005
0.0011
0.0020
0.00 12
0.0014
-0.0026
0.0049
0.0000
0.0022
0.0061
0.0020
0.0011
0.0002
0.0029
0.0003
0.0007
0.0024
0.0014
0.0004
-0.0018
0.0012
-0.0002
0.0000
0.0013
0.0006
-0.0015
0.0019
-0.0020
-0.0001
-0.0016
-0.0008
-0.0007
0.0049
-0.0076
0.0028
0.0061
0.0054
0.0080
-0.0007
0.0000
0.0003
0.0011
-0.0010
-0.0004
0.0001
0.0006
0.0011
-0.0019
0.0011
-0.0002
0.0012
0.0015
0.0009
-0.0027
0.0021
-0.0033
-0.0028
-0.0011
0.0004
0.0000
0.0002
0.0008
-0.00 14
-0.0005
0.0000
0.0030
0.0006
-0.0002
0.0005
-0.0028
-0.0004
0.0002
-0.0014
-0.0002
-0.0012
-0.0002
-0.0003
-0.0012
-0.0018
-0.0015
-0.0004
0.0016
-0.0020
0.0022
0.0004
0.0013
0.0020
0.0017
0.0019
-0.0004
0.0034
0.0002
0.0017
0.0026
0.0016
-0.0009
0.0017
-0.0011
-0.0006
-0.0011
-0.0016
-0.0010
0.0002
0.00 13
0.0001
-0.000 1
0.0004
-0.0009
-0.000 1
-0.0015
0.0000
-0.0015
-0.0013
-0.0012
-0.0044
0.0002
0.0013
-0.0001
0.0022
0.0010
0.0018
0.0012
0.0010
0.0019
-0.0018
0.0017
0.0009
0.0020
0.0019
0.0013
-0.0001
-0.0005
-0.0018
0.0003
0.0002
-0.0030
0.0000
-0.0012
0.0003
-0.0003
-0.0005
-0.0018
-0.0025
-0.0001
0.0047
-0.0034
0.0030
0.0040
0.0044
0.0039
0.0011
-0.0005
-0.0005
-0.0025
0.0000
-0.0007
-0.0012
-0.0005
0.0043
-0.0010
0.0035
0.0051
-0.0003
-0.0022
0.0006
0.0004
-0.0001
-0.0008
0.0001
0.0003
0.0009
-0.0004
0.00 15
-0.002 1
0.0038
0.0003
0.0011
0.0023
0.0018
0.0001
-0.0011
-0.0006
-0.0015
-0.0001
0.0005
0.0008
-0.0012
0.0014
-0.0023
-0.0011
-0.0010
-0.0022
-0.0005
0.0003
0.0011
0.0007
-0.0003
0.0005
0.0003
0.0005
0.0001
-0.0019
0.0002
-0.0002
0.0005
0.0006
0.0002
-0.0012
0.0008
-0.0004
-0.0006
-0.0009
-0.0010
-0.0002
Bold: Coefficients with t-statistics significant at the P = 0.05 levels
108
relative variability of the estimates. The coefficients for strata coverage were all negative and
all significant, indicating that the higher strata coverage helped reduce the relative variability
of Synthesis estimates. The coefficients for fishery selectivity were positive for most of the
seven types of estimates, suggesting that dome-shaped selectivity resulted in larger relative
variability in Synthesis's estimates.
3.3.3 Effects on Relative Median Bias
The overall average relative bias of the median for all seven types of estimates in both
experiment Al and A2 were very close to zero (absolute values < 1%), indicating that
Synthesis's estimates tended to be median unbiased (Table 3.19, 3.20). This may be due to the
fact that the distributions of most estimates were skewed to the right (Figure 3.2, 3.3). From a
practical point of view, the knowledge that the median value of the estimates is relatively
unbiased itself will not give Synthesis users a better direction in how to use Synthesis more
effectively, because the median statistic by itself does not provide a complete picture of the
data. However, combined with knowledge of the variability and the bias of the mean, it does
give users richer information on the distribution of Synthesis estimates.
3.3.4 Sensitivity to Initial Parameter Values
The sensitivity experiments indicated that the effect of randomizing the initial
parameter values might depend on the quality of input data to the Stock Synthesis program.
For treatment 40 of Al and treatment 40 of A2, which in the main experiments produced
output values with little variability, the estimates from using randomized initial parameter
values was essentially the same as the estimates from using the true initial parameter values
(Fig. 3.4 - 3.5). In treatment 40 of Al, the results of running 100 replicates with and without
109
randomization produced identical results with relative variability on the estimates of ending
biomass both at 6.9% and average likelihood both at -5 1.0583. In treatment 40 of A2, the
results of running 100 replicates with and without randomization also produced identical
results with relative variability on the estimates of ending biomass both at 7.9% and average
likelihood both at -87.41 13.
ending bio.
*
*
Treatment 40 of Al,
Two sample T-Test,
P-Value: 0.998
31,000
26,000
true initial parameters
randomized initial parameters
ending bio.
400
Treatment 77 of Al,
Two sample T-Test,
P-Value: 0.138
300
*
*
*
*
*
200,000_
*
*
100, 00 0_
S
0true initial parameters
randomized initial parameters
Figure 3.4. Sensitivity to initial parameter values for treatment 40 and treatment 77 of
experiment Al. The dashed line represents the true ending biomass.
110
ending bio.
34.00QJ
Treatment
To-Sarrç
P-Value: C
24
true inial parameters
randomized intial parameters
ending bio.
6O.00O
50000_
40,000
*
30,000_
**
Treatment 89 of A2,
T
Sample T-Test,
P-Value: 0.310
*
*
*
*
20,000_
io,000
0
true initial parameters
randomized intial paramters
Figure 3.5. Sensitivity to initial parameter values for treatment 40 and treatment 89 of
experiment A2. The dashed line represents the true ending biomass.
111
For treatment 77 of Al and treatment 89 of A2, which in the main experiments
produced output values with large variability, using randomization produced outputs that had
larger variability than the corresponding output produced without randomization. This might
indicate that Synthesis sometimes stopped too early in its search for the maximum likelihood
estimates. When it started with the true values and stopped early, the estimates were closer to
the true values. In the sensitivity experiments, we specifically compared the relative
variability of the estimates of ending biomass. In treatment 77 of Al, randomization produced
slightly better average likelihood value (-176.766 versus -176.787) and moderately larger
relative variability values (89.9% versus 60.0%). Treatment 89 of A2 had similar results
(-106.029 versus -106.247 in likelihood and 74.6% versus 54.9% in variability). However,
both in treatment 77 of Al and treatment 89 of A2, Two-Sample T Tests did not show strong
evidence that randomization produced statistically significant differences (Fig. 3.4, 3.5).
3.3.5 Comparison of the Results from Experiment Al and Experiment A2
In experiment Al, the recruitment series were always constant, whereas in experiment
A2, the recruitment series were always variable. A2 also had a big CV value (0.5 versus 0.3)
for the population partitioning. In addition, the high level value of sample size in A2 was
smaller than that of Al (1600 versus 2000). The results from experiment A2 were generally
supportive of those from experiment Al, indicating a fairly good repeatability. However,
experiment A2 did on average produced slightly larger values for relative bias and relative
variability. For relative bias, the grand mean across the seven types of measurement was
3.29% for Al and 3.62% for A2. For relative variability, the total average across the seven
types was 2 1.7% for Al and 24.5% for A2 respectively. This means that variable recruitment,
together with larger population partitioning CV and smaller high level in sample size,
contributed to the larger relative bias and larger relative variability of Synthesis estimates.
112
Variable recruitment, larger CV in population partitioning and smaller sample size all
contributed to more variable input data to Synthesis. The results make intuitive sense because
the data for experiment A2 were more variable and Synthesis had more parameters to estimate
to account for the non-equilibrium initial age composition. In chapter two, we found that
variable recruitment resulted in more variable estimates. Although we couldn't isolate the
effect of variable recruitment itself here, the results from A2 at least do not contradict what we
found in chapter two. In other words, variable recruitment itself most likely contributed to the
larger relative bias and larger relative variability of Synthesis estimates forpopulations whose
age composition followed compound multinomial distributions.
3.3.6 Stratification and the Non-linearity of Effects
The results from experiments B 1, B2, Cl, and C2 indicated that the effect for the
factor of sample size was not linear and stratification increased the relative bias and relative
variability for most types of measurement (Tables 3.21- 3.22).
For conciseness, I will elaborate only on the measurement of relative bias of the
ending biomass estimates, since other measurements followed a similar pattern. Let's first
compare the results from experiment Bi and B2. Clearly, the effects of sample size and
number of years from B2 were much smaller than that from Bi. Also, the grand mean from B2
is also much smaller than those from B 1. A simple T-Test showed that these differences were
statistically significant (Table 3.23). Comparisons of results from experiment Cl and C2
showed the similar results as those ofBl and B2 (Table 3.24). In the experimental designs, the
only differences between B 1 and B2 were the values used in the low and high value of sample
size. There was no stratification in Bl or B2. Similarly, the only difference in the designs of
Cl and C2 were the values used in the low and high value of sample size, but there was
stratification. Thus, differences in the results (B I versus B2, Cl versus C2) were
113
Table 3.21. Analysis of relative bias for experiments Bi, B2, Cl, and C2.
Exp. Factor
Grand mean
numYrs
smplSize
El svyCv
numYrs*smplSize
numYrs*svyCv
smplSize*svyCv
B2
Grand mean
numYrs
smplSize
svyCv
numYrs*smplSize
numYrs*svyCv
smplSize*svyCv
Grand mean
numYrs
smplSize
Cl
C2
svyCv
numYrs*smplSize
numYrs*svyCv
smplSize*svyCv
Grand mean
numYrs
smplSize
svyCv
numYrs*smplSize
numYrs*svyCv
smplSize*svyCv
end Bio
end F
end Rec
start Bio
end exB
f35 catch
EB/SB*
0.0579
0.0334
0.0752
0.0321
0.0521
0.0678
0.0097
-0.0618
0.0236
-0.0761
-0.0301
-0.0612
-0.0720
-0.0179
-0.0343
-0.0149
-0.0416
-0.0226
0.0066
-0.0316
-0.0400
0.0181
0.0174
0.0089
0.0180
0.0226
-0.0022
0.0037
0.0458
-0.0259
0.0594
0.0205
0.0446
0.0538
0.0167
-0.0158
0.0101
-0.0160
-0.0076
-0.0164
-0.0130
-0.0062
-0.0197
-0.0165
-0.0062
-0.0122
-0.0161
-0.0036
-0.0025
0.0075
0.0186
0.0086
0.0244
0.0071
0.0012
0.0174
0.0224
-0.0099
-0.0125
-0.0072
-0.0101
-0.0115
0.0006
-0.0064
-0.0065
-0.0084
0.002
-0.0034
-0.0076
-0.00 1 1
0.0043
0.0008
0.0023
0.0025
0.0008
0.0075
0.0037
0.0003
-0.0014
-0.0023
-0.0036
-0.0021
-0.0008
-0.0053
0.0081
0.0095
-0.0004
-0.0003
0.0024
0.001
-0.0022
-0.0003
-0.0019
0.001
-0.0018
0.0009
-0.0005
0.0078
0.0906
0.0288
0.1283
0.0410
0.0808
0.1104
0.0276
-0.0819
0.0316
-0.1012
-0.0439
-0.0835
-0.0967
-0.0188
-0.0424
-0.0230
-0.0710
-0.0231
-0.0371
-0.0501
-0.0060
0.0416
0.0195
0.0591
0.0173
0.0402
0.0512
0.0096
0.0523
-0.0200
0.0707
0.0243
0.0509
0.0162
-0.0349
0.0066
0.0612
-0.0543
-0.0176
-0.0340
-0.0414
-0.0047
-0.0210
-0.0185
-0.0358
-0.0098
-0.0198
-0.0255
-0.0011
0.0350
0.0065
0.0055
-0.0018
0.0048
-0.0230
-0.0166
0.0140
0.0518
0.0147
0.0305
0.0428
0.0143
-0.0316
-0.0135
-0.0232
-0.0272
-0.0045
-0.0253
-0.0054
-0.0142
-0.0208
-0.0079
0.0201
0.0047
0.0138
0.0165
0.0060
0.0028
-0.0100
0.0013 -0.0138 -0.0056 -0.0098
-0.0117
-0.0016
-0.0111
0.005
-0.0125
-0.0049
-0.0115
-0.0137
-0.0042
Bold: Coefficients with t-statistics significant at the P = 0.05 levels.
* EB/SB: the ratio of ending biomass estimate versus starting biomass estimate, same as "endB/startB"
0.0131
-0.0041
0.0172
0.0074
0.0122
0.0161
114
Table 3.22. Analysis of relative variability for experiments Bi, B2, Cl, and C2.
Exp. Factor
Grand mean
BI
B2
nurnYrs
smplSize
svyCv
numYrs*smplSize
numYrs*svyCv
smplSize*svyCv
Grand mean
numYrs
smplSize
svyCv
numYrs*smplSize
numYrs*svyCv
smplSize*svyCv
Grand mean
numYrs
smplSize
Cl
C2
svyCv
numYrs*smplSize
numYrs*svyCv
smplSize*svyCv
Grand mean
numYrs
smplSize
svyCv
numYrs*smplSize
numYrs*svyCv
smplSize*svyCv
end Bio
end F
end Rec
start Bio
end exB
f35 catch
EB/SB*
9.2613
0.2843
0.4005
0.1266
0.2724
0.3199
0.1501
-0.0860
-0.0532
-0.1040
-0.0703
-0.0889
-0.0915
0.0021
-0.0819
-0.0672
-0.1447
-0.0457
-0.0847
-0.0931
-0.0390
0.0369
0.0331
0.0385
0.0102
0.0355
0.0457
0.0227
0.0346
0.0136
0.0421
0.0276
0.0357
0.0349
-0.0015
-0.0072
-0.0047
-0.0126
-0.0088
-0.0059
-0.0071
-0.0202
-0.0187
-0.0193
-0.0047
-0.0187
-0.0251
-0.0134
0.0919
0.0058
0.1441
0.1864
0.2029
0.0657
0.1499
0.1754
-0.0337
-0.0243
-0.0392
-0.0310
-0.0358
-0.0358
0.0059
-0.0325
-0.0260
-0.0504
-0.0138
-0.0391
-0.0194
0.0054
0.0029
-0.0345
0.0064
0.0008
0.0061
0.0059
0.0038
0.0121
0.0083
0.0136
0.0093
0.0007
-0.0011
0.0128
0.0132
-0.001
-0.0012
0.001
0.0007
0.0007
-0.0095
-0.0067
-0.0104
-0.0032
-0.0098
-0.0114
0.0019
-0.0054
0.2819
0.3102
0.4475
0.1440
0.2959
0.3293
0.1588
-0.0927
-0.0616
-0.1078
-0.0834
-0.0976
-0.0966
0.0043
-0.0805
-0.0753
-0.1496
-0.0498
-0.0846
-0.0880
-0.0359
0.0938
0.0731
0.0986
0.0360
0.0952
0.1106
0.0486
0.0373
0.0198
0.0437
0.0328
0.0384
0.0373
0.0008
-0.0342
-0.0082
-0.0465
-0.0342
-0.0345
-0.0334
0.0069
-0.0397
-0.0303
-0.0372
-0.0180
-0.0399
-0.0455
-0.0162
0.0991
0.1596
0.2008
0.2541
0.0766
0.1665
0.1912
-0.0413
-0.0302
-0.0450
-0.0374
-0.0449
-0.0442
0.0043
-0.0385
-0.0346
-0.0531
-0.0163
-0.0403
-0.0457
-0.0218
0.0405
0.0344
0.0424
0.0134
0.0416
0.0489
0.0254
0.0182
0.0130
0.0266
0.0125
0.0190
0.0202
0.0032
-0.0118
-0.0095
-0.0172
-0.0118
-0.0124
-0.0125
0.002
-0.0125
-0.0107
-0.0150
-0.0052
-0.0127
-0.0145
-0.0059
Bold: Coefficients with t-statistics significant at the P = 0.05 levels.
* EB/SB: the ratio of ending biomass estimate versus starting biomass estimate, same as 'endB/startB"
115
unambiguously from the sample size. This means that the effect of sample size was not linear
and the value of sample size influenced the effects of other factors (Figure 3.6, 3.7). This is
probably at least partially because Synthesis was configured to treat sample size as being at
most 400 (following the suggestion of Fournier and Archibald, 1982.).
Table 3.23. Comparisons of coefficients for relative bias of ending biomass from experiment
Bi andB2.
B1
Term
Grand mean
numYrs
smplSize
svyCv
numYrs*smplSize
numYrs*svyCv
smplSize*svyCv
numYrs*smplSize*svyCv
Coef
SE_Coef
0.0579
0.0038
-0.0618
0.0038
-0.0343
0.0038
0.0181
0.0458
-0.0158
-0.0130
0.0148
0.0038
0.0038
0.0038
0.0038
0.0038
B2
Coef
SE_Coef
0.0186
0.0021
-0.0099
0.0021
-0.0064
0.0021
0.0020
0.0021
0.0078
0.0021
0.0003
-0.0014
-0.0015
0.0021
0.0021
0.0021
Difference
T_stat
p-value
12.6960
<0.001
16.7770
<0.001
9.0073
<0.001
5.1995
0.0010
12.2890
<0.001
5.2205
<0.001
3.7415
0.0048
5.2868
<0.001
Table 3.24. Comparisons of coefficients for relative bias of ending biomass from experiment
Cl and C2.
Term
Grand mean
numYrs
smplSize
svyCv
numYrs*smplSize
numYrs*svyCv
smplSize*svyCv
numYrs*smplSize*svyCv
Coef
Cl
0.0906
-0.0819
-0.0424
0.0416
0.0523
-0.0349
-0.0210
0.0283
SE_Coef
0.0064
0.0064
0.0064
0.0064
0.0064
0.0064
0.0064
0.0064
C2
Coef
SECoef
0.0350
0.0032
-0.0230
0.0032
-0.0166
0.0032
0.0140
0.0032
0.0131
0.0032
-0,0100
0.0032
-0.0111
0.0032
0.0078
0.0032
Difference
T_stat
p-value
10.9704
<0.001
11.6297
<0.001
5.0795
0.0011
5.4625
<0.001
7.7347 <0.001
4.9176
0.0013
1.9445
0.0499
4.0589
0.0033
116
svyCv
numYrs
smplSize
0.08
0.06
0.04
ci)
0.02
0.00
ç3c
c:Ql
,
Figure 3.6. Main effects on the relative bias of ending biomass estimates from the Stock
Synthesis program after combining the results of experiments Bi and B2.
svyCv
numYrs
smplSize
0.120
0.095
0.070
ci)
0.045
0.020
t9
,
Figure 3.7. Main effects on the relative bias of ending biomass estimates from the Stock
Synthesis program after combining the results of experiments Cl and C2
117
Table 3.25. Comparisons of coefficients for relative bias of ending biomass from experiment
Bland Cl.
Term
Grand mean
numYrs
smplSize
svyCv
numYrs*smplSize
numYrs*svyCv
smplSize*svyCv
numYrs*smplSize*svyCv
Coef
Bl
0.0579
-0.0618
-0.0343
0.0181
0.0458
-0.0158
-0.0130
0.0148
SECoef
Coef
0.0038
0.0038
0.0038
0.0038
0.0038
0.0038
0.0038
0.0038
Cl
0.0906
-0.0819
-0.0424
0.0416
0.0523
-0.0349
-0.0210
0.0283
SECoef
0.0064
0.0064
0.0064
0.0064
0.0064
0.0064
0.0064
0.0064
difference
p-value
6.1707
0.0004
3.7923
0.0045
1.5196
0.0897
4.4435
0.0022
1.2251
0.1332
3.5997
0.0057
1.5082
0.0911
2.5446
0.0219
Tstat
Table 3.26. Comparisons of coefficients for relative bias of ending biomass from experiment
B2 and C2.
Term
Grand mean
numYrs
smplSize
svyCv
numYrs*smplSize
numYrs*svyCv
smplSize*svyCv
numYrs*smplSize*svyCv
Coef
B2
0.0186
-0.0099
-0.0064
0.0020
0.0078
0.0003
-0.0014
-0.0015
SE_Coef
0.0021
0.0021
0.0021
0.0021
0.0021
0.0021
0.0021
0.0021
Coef
C2
0.0350
-0.0230
-0.0166
0.0140
0.0131
-0.0100
-0.0111
0.0078
SE_Coef
0.0032
0.0032
0.0032
0.0032
0.0032
0.0032
0.0032
0.0032
Table 3.27. Paired T test on relative variability of ending biomass.
Term
Experiments
Bi
Difference
grand mean
0.26127
0.28185
Cl
T-value
-3.72
P-value
0.034
grandmean
B2
0.14412
C2
0.1596
T-value
-3.72
P-value
0.034
difference
p-value
6.1247
0.0004
4.8852
0.0014
3.8042
0.0045
4.4664
0.0021
1.9886
0.0470
3.8517
0.0042
3.6294
0.0055
3.4650
0.0067
Tstat
118
We could make a direct comparison of the results between experiment Bi and Cl as
well as of the results between experiment B2 and C2, because the only difference between the
pairs (B 1 versus Cl, B2 versus C2) was the stratification factor. The results clearly indicated
that stratification produces more biased (Table 3.25, 3.26) and more variable estimates (Table
3.22, 3.27).
Table 3.28. Analysis of relative bias for experiment D.
Factor
Grand mean
NumYrs
svyCv
synSize
numYrs*svyCv
numYrs*synSize
svyCv*synSize
numYrs*svyCv*synSize
end Bio
0.0436
-0.0294
0.0223
0.0080
-0.0135
end F
0.0084
0.0090
-0.0012
-0.0002
0.0030
end Rec
0.0667
-0.0406
0.0289
0.0105
-0.0157
-0.0068
0.0006
-0.0081
start Bio
0.0166
-0.0171
0.0085
0.0036
-0.0086
-0.0038
0.0028
0.0009
0.0036
0.0011
0.0033
-0.0043
-0.0013
-0.0120
-0.0020
-0.0036
Bold: Coefficients with t-statistics significant at the P
= 0.05
end exB
0.0366
-0.0299
0.0220
0.0081
-0.0131
-0.0055
levels
Table 3.29. Analysis of relative variability for experiment D.
Factor
Grand mean
NumYrs
svyCv
synSize
numYrs*svyCv
numYrs*synSize
svyCv*synSize
numYrs*svyCv*synSize
end Bio
0.1888
-0.0540
0.0519
0.0093
-0.0135
end F
end Rec
0.3006
-0.0625
0.0563
-0.0056
0.2238
-0.0374
0.0427
0.0116
-0.0074
-0.0058
0.0012
-0.0032
-0.0092
start Bio
0.0892
-0.0458
0.0167
0.0036
-0.0141
-0.0041
0.0025
0.0011
0.0020
0.0014
-0.0027
-0.0055
-0.0021
-0.0036
Bold: Coefficients with t-statistics significant at the P
0.0066
-0.0215
= 0.05
end exB
0.1965
-0.0577
0.0528
0.0102
-0.0137
-0.0063
levels
3.3.7 Effects of Configured Maximum Sample Sizes in the Likelihood Specification
We have shown in section 3.3.6 that stratification resulted in greater bias and greater
variability of Synthesis estimates. In all previous experiments the sample size that Synthesis
119
used was the smaller of the actual sample size or 400, as suggested by Fournier and Archibald.
Were the greater bias and greater variability at least partially because the age composition data
had too much emphasis or too little emphasis? In other words, was the upper limit of 400 too
big or too small? The results from experiment D indicated that 400 was probably too big for
the stratified population.
In the coefficients for the relative bias from experiment D (Table 3.28), the
coefficients for the factor
synSize
were positive and statistically significant for four of the five
types of measurements. This means that increasing the maximum sample size from 200 to 400
caused bigger bias for most types of estimates, suggesting that the 400 upper limit gave too
much emphasis to the likelihood component for the age composition data.
In the coefficients for the relative variability from experiment D (Table 3.29), again,
the coefficients for the factor synSize were positive and statistically significant for four f the
five types of measurements, indicating that 200 is better than 400 in reducing the relative
variability of Synthesis estimates.
3.4 Discussion
Results from our experiments indicated that the compound multinomial distributions
for the age composition data adversely affected the performance of the Stock Synthesis
program. When the fishery age composition actually followed a compound multinomial
distribution, the estimates produced by the Stock Synthesis program, which assumed simple
multinomial distributions with maximum sample sizes of 400 fish, were moderately more
biased and more variable. Under the compound multinomial distribution, increasing the
stratum coverage helped reduced the bias and variability. This means in fishery sampling
design, it might be better to use a more diversified approach to reduce the impact of
120
stratification. Diversified sampling reduces the variability among age composition data. For
example, Crone and Sampson (1997) showed that the coefficient of variation associated with
the individual landing estimates of age composition can be reduced by increasing the number
of boat trips sampled. Many factors contribute to population stratification. In addition to
geographical area, differences in fishing methods, time of day, and season probably account
for the large variations that we typically see among the age/size compositions from different
fishing trips. A balanced sampling should give consideration to all these factors.
Synthesis users often follow the suggestion by Foumier and Archibald (1982) that age
sample sizes in the likelihood specification should be limited to 400 fish per sample, i.e., the
sample size that Synthesis uses should be the smaller of the actual sample size or 400. When
there is stratification within the population, the sampled age data tends to be more variable.
When applying Synthesis to populations whose age compositions follow compound
multinomial distributions, the results from our experiments indicated that such a configuration
probably gives the age composition data too much emphasis. In our experiments, we found
that using 200 as the upper limit was better than using 400. More experiments may be needed
to explore the results of using other values (e.g. 100, 250,300) as the upper limit in Synthesis
configurations.
In our main experiments Al and A2, the effect of sample size was smaller than the
effects of the number of years in the data series and the survey variability factors. At first this
was surprising. After further exploration with the four smaller experiments, we found the
factor for sample size was actually very important, but its effect was not linear. For example,
an increase from 100 to 400 on the value of sample size greatly reduced the measurement on
relative bias and relative variability. However, further increase from 400 to 1600 did not
produce proportional reductions for bias and variability of the estimates. It seems likely that
this is partially due to Synthesis using 400 as the maximum sample size. Also, in our
121
experiments, the generated data did not have any age-reading errors. Thus when 400 fish were
sampled, the sample age composition might already satisfactorily represent the population age
composition and further increases in sample size did not generate more precise information. In
a real application of the Stock Synthesis program, where the age determination is far from
perfect, a sample size of 400 probably is not big enough.
Stock Synthesis estimates of ending exploitable biomass and
F35%
catch form the basis
for the annual catch quotas for many groundfish stocks on the U.S. Pacific coast (PFMC 1996).
This study suggests that even with stratification, increased sample size has about the same
effect as reducing the survey variability with regard to reducing the variability of Synthesis's
estimates of ending exploitable biomass and
F35%
catch. For example, in experiment B 1, under
the treatment of low number of years (8 yr.), high survey variability (0.8 CV), and low sample
size (100 fish), the ANOVA model predicted that the relative variability for the estimates of
ending exploitable biomass and for the estimates of F35% catch was 71% and 76% respectively
(Table 3.24). If we reduce the survey CV from 0.8 to 0.2 and keep the other factors the same,
the relative variability for the estimates of ending exploitable biomass and for the estimates of
F35%
catch will be reduced to 33% and 34%. If we keep the survey CV at 0.8 and increase the
sample size from 100 to 400, the pair of values would be reduced to 33% and 38% (Table
3.30). Thus, a four-fold increase in the sample size (100 to 400) has about the same effect as a
four-fold decrease in the survey CV (0.8 to 0.2). However, it will take a sixteen-fold increase
in the number of survey stations to produce a four-fold decrease in the CV. If it were not for
the stratification in B 1, the same four-fold increase of sample size would have produced a
better effect than a four-fold decrease in survey CV. For example, in experiment Al, under the
treatment of low number of year (8 yr.), high survey variability (0.8 CV), and low sample size
(100 fish), the ANOVA model predicted that the relative variability for the estimates of ending
exploitable biomass and for the estimates of F35% catch was 54% and 60% respectively. If we
122
reduce the survey CV from 0.8 to 0.2 and keep other factors at their same values, the relative
variability for the estimates of ending exploitable biomass and for the estimates of F35% catch
will be reduced to 42% and 45%. If we keep the survey CV at 0.8 and increase the sample size
from 100 to 400, the pair of values will be reduced to 26% and 30%.
123
Chapter Four: The Rational Allocation of Sampling Effort for Assessing the Stock of
Yellowfin Sole with the Stock Synthesis Program
4.1 Introduction
The Stock Synthesis program (Methot 1990), which incorporates complex fishery and
survey data in a single framework, has been the primary age structured model used in the stock
assessment of groundfish fish resources along the U. S. west coast and in some other areas
(Dorn et al. 1991; NPFMC 2000; Porch Ct al. 1994; Sampson 1994). While the Stock
Synthesis program can simultaneously analyze data from different sources, the quality of
Synthesis estimates is also subject to the different error levels among the input data (Sampson
and Yin 1998). Input data usually include fishery catch biomass, sampled population age
compositions, fishery effort, and survey biomass indices. The quality of those diverse data
depends largely on the amount of sampling effort applied to each category. We have shown
using artificial stocks in previous chapters that Synthesis performed very well if all input data
were of high quality. However, in a real commercial fishery, it is unlikely that all categories of
input data are of high quality. In addition, there are usually not enough resources to improve
all sources of input data. One question facing fishery management agencies is how to allocate
sampling effort among the different sources of input data. Should they spend money and time
collecting better survey data, better fishery age composition data, or better catch data? At
present there are almost no tools for deciding how to balance the data collection programs,
with the result that a fishery agency may be spending tremendous amounts of time and money
collecting data that have little influence on the accuracy of their stock assessments.
In this study we applied our simulation package (Appendix B) and Synthesis to an
actual stock assessment of yellowfin sole
(Limanda Aspera)
in the Bering Sea to evaluate
124
whether more accurate assessment results could be achieved from a better balance in the
amount of sampling effort allocated to age composition data versus survey biomass estimates.
Yellowfin sole is the most abundant flatfish species in the Bering Sea and is the target of the
largest flatfish fishery in the United States (Wilderbuer and Nichol, 2000). One reason we
chose yellowfin sole as our case study was that fishermen, environmentalists, and fishery
managers have expressed concerns regarding the precision and accuracy of its assessments
with the Stock Synthesis program (Witherell and lanelli, 1997). Another reason was our
familiarity with the fishery.
4.2 Methods
We used a real stock assessment of yellowfin sole as the basis for this case study.
Wilderbuer and Nichol conducted most of the recent yellowfin sole stock assessments in 1998,
1999, and 2000 (NPMFC, 2000). While the Stock Synthesis program was directly used for
their 1998 assessment, they switched to a Synthesis-like assessment model implemented in the
AD-Model Builder software system for the 1999 and 2000 assessments. We acquired a copy
of the Synthesis data files from their 1998 assessment and used them as the starting points of
our experiments. First we reproduced their assessment results from their input data files. Then
we configured a "true" yellowfin sole fishery system based on the above assessment estimates
for yearly population-at-age, recruitment, fishing mortality, survey catchability, fishery and
survey selectivity, and biological characteristics such as weight-at-age. Lastly we applied our
simulation package to the "true" yellowfin sole fishery system and evaluated how sensitive the
results were to different combinations of random errors in the input data. The data series for
ye7flowfin sole covered the period from 1964 to 1998. In the simulations we used
approximately the same levels of data accuracy as assumed in Wilderbuer and Nichols
125
assessment for the years up to and including 1995, but then started modif'ing the levels of
data accuracy. The goal was to evaluate how the assessment results could have been improved
relative to what was actually achieved, given the available historical data.
4.2.1 Configuration of Yellowfin Sole Fishery System
The yellowfin sole system in our simulation approximately followed the configuration
used in Wilderbuer and NichoPs assessment. However, we did not adopt one unusual setting
from Wilderbuer and Nichol's original assessment. In their original configuration, Synthesis
was instructed to estimate the initial age composition for the first year of the simulated period,
1954, but, there were no age composition data until 1964. Under this configuration, Synthesis
appeared to have difficulty converging and took a considerable amount of time to complete
one run. We modified the configuration so that the simulated period started with 1964 and
found that Synthesis produced similar estimates as with Wilderbuer and Nichol's original
configuration but took only about one tenth of the time to converge to the solution. Because
our study needed large numbers of simulations, we decided to use the new configuration in our
study to improve the convergence properties and reduce the total simulation time.
The parameters that defined the system were directly from the reproduced results of
Wilderbuer and Nichols assessment. The fishery system consisted of a yellowfin sole stock, a
single fishery that exploited the stock, and a single survey that monitored the status of the
population. Within the yellowfin sole population, male and female fish were not treated
separately. They were subject to the same instantaneous rate of natural mortality (0.12/yr),
followed the same weight-at-age (Figure 4.1), shared the same maturity-at-age (Figure 4.2),
and the assumed sex ratio was 50:50. The yellowfin sole stock had a variable recruitment
series from 1964 to 1998 (Table 4.1) and the initial population-at-age in 1964 was not at
equilibrium (Figure 4.3). The fishing intensities varied considerably from 1964 to 1998 (Table
126
4.1) and the annual survey was conducted from 1982. The fishery selectivity and the survey
selectivity both had asymptotic shapes (Figure 4.4) and were constant for the simulated period,
1964 to 1998.
5W
4W
400
3E
3O0
2J0
150
100
50
0
0
5
10
15
Age.)
Figure 4.1. Weight-at-age of yellowfin sole, with maximum age at 20 years.
ZJ
127
Table 4.1. Yearly recruitment and fishing mortality values estimated in the 1998 assessment.
Year
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
Recruitment (in million fish)
858.5
831.3
1177.6
1449.6
2513.0
2757.1
2746.7
3792.5
4458.5
3985.7
2857.6
3788.8
4299.4
2990.6
3599.3
2429.2
1484.3
2933.1
2118.0
6154.8
702.1
5230.7
1324.7
1190.0
1817.6
2928.7
3086.4
1461.1
1613.7
5584.4
4135.2
5848.5
2654.8
2653.7
2652.3
Fishing Mortality
0.529
0.213
0.331
0.518
0.275
0.590
0.566
0.883
0.288
0.398
0.164
0.179
0.114
0.088
0.165
0.098
0.072
0.070
0.061
0.063
0.088
0.124
0.116
0.104
0.132
0.092
0.046
0.052
0.085
0.057
0.079
0.070
0.074
0.106
0.038
128
0.8
- 0.6
0.4
0.2
0
3
5
7
9
11
13
15
17
19
Age ( yr.)
Figure 4.2. Maturity-at-age curve, with inflect age at 10 years.
Numbers
0.0
2
4
6
8
10
12
14
16
18
500.0
1000.0
1500.0
2000.0
37
Age
Numbers
858.5
4
720.0
5
1066.0
6
931.6
7
1056.1
8
1184.1
9
238.9
10
220.0
11
225.4
12
151.3
13
. 54.5
14
14.5
15
1.8
16
0.1
17
1.0
18
1.0
19
1.0
20
1.0
20
Figure 4.3. The initial non-equilibrium age composition at the start of 1964. The fish numbers
are in millions and the ages are in years.
129
I
0.8
0.6
Suy
0.2
-- mn
01
3
5
7
9
11
13
15
17
19
Age
Figure 4.4. Fishery selectivity and survey selectivity. For fishery selection curve the inflection
age = 8.8 years and the slope = 1.0 / yr. For survey selection curve the inflection age = 5.4
years and the slope = 1.4 / yr.
4.2.2 Configurations for the Simulation and Stock Synthesis
We configured our simulation and Synthesis following the same assumptions used in
Wilderbuer and Nichol's original assessment. Both deterministic and non-deterministic
(stochastic) methods were used by the Data Simulator to mimic the characteristics of the
yellowfin sole fishery system (as listed in 4.2.1). The deterministic method simulates the
dynamics of the yellowfin sole population using the same deterministic equations that underlie
Methot's Stock Synthesis program. The stochastic method takes the true demographic data
produced by the deterministic method and generates random data sets that can be analyzed
directly by the Stock Synthesis program. Data for total catch and survey biomass were
assumed to follow lognormal distributions and all random data were generated in a manner
that they would be unbiased. Observed age composition data were generated following simple
multinomial distributions with unbiased aging error. Because the recruitment series were
130
Table 4.2. Initial values for the parameters of the non-equilibrium age composition at the start
of 1964 and yearly recruitments from 1964 to 1998. Both "number of fish" and "recruit" were
in millions of fish.
Initial Age Composition
age
number of fish
Yearly Recruitment
year
recruit
20
1.060
64
19
1.088
65
818.092
18
1.015
66
1170.669
17
1.073
67
1443.954
16
0.270
68
2513.285
15
0.211
69
2760.229
14
0.163
70
2750.221
13
0.152
71
3802.927
12
0.160
72
4471.759
11
1.735
73
3997.424
10
128.937
74
2863.532
9
182.375
75
3793.270
8
286.437
76
4307.600
7
271.995
77
2990.203
6
667.584
78
3601.616
5
2427.163
79
2427.382
4
4680.076
80
1475.718
3
6146.323
81
2932.184
82
2112.493
83
6155.517
845.944
84
684.220
85
5228.259
86
1312.085
87
1174.320
88
1806.145
89
2924.356
90
3089.952
91
1436.893
92
1587.107
93
5681.410
94
4280.349
95
6608.023
96
2564.971
97
2563.932
98
2562.590
131
highly variable and the yellowfin sole fishery was not at equilibrium, the Stock Synthesis
program was configured to estimate the initial non-equilibrium age composition. Note that all
the simulated data series used the same set of true values for the recruitment series and we did
not change the dynamics of the stock by estimating new random recruitment series. The aging
error was assumed to be normally distributed and Synthesis was configured to use unbiased
aging errors. The value of the survey catchability coefficient in the simulation was 1.0 and
Synthesis was given the same value for survey catchability parameter. In addition, Synthesis
was not allowed to estimate this parameter, meaning Synthesis was forced to treat the survey
biomass data as absolute measurements of the biomass, as Wilderbuer and Nichol had done in
their original assessment.
The Stock Synthesis program used in this study was the version released in 1999 for
the Windows 95 platform. The program's author, Richard Methot, provided it to us in August
1999. The Stock Synthesis program needs initial parameter values with which to start its
iterative search for the set of maximum likelihood parameter estimates. In this study, we gave
the Synthesis program the same set of values used in Wilderbuer and Nichol's assessment as
the initial values (Table 4.2). Note that these starting values were not the true values (Table 4.1
and Figure 4.3) used in our simulation. The reason we did not use the true values was mainly
because we did not want our configuration diverging too far from Wilderbuer and Nichol's
original assessment.
In configuring the likelihood specification, Synthesis users often follow the suggestion
by Fournier and Archibald (1982) that age sample sizes in the likelihood specification should
be limited to 400 fish per sample, i.e., the sample size that Synthesis uses should be the
smaller of the actual sample size or 400. In the 1999 original assessment, Wilderbuer and
Nichol reduced the upper limit to 200 fish per sample. In other words, the sample size that
Synthesis used was the smaller of the actual sample size or 200. In this study we followed the
132
same practice and let Synthesis treat sample size as the smaller of the actual sample size or
200.
The configuration of likelihood components was also the same as in Wilderbuer and
Nichol's original assessment. The total likelihood was composed of components for fishery
catch, fishery age composition, survey biomass, survey age composition, the spawner-recruit
relationship, and the likelihood for the moment of the spawner-recruit relationship. Note that
the fishery catch likelihood value is always zero because Synthesis exactly fits the observed
catch biomass data by modifying the estimates of fishing mortality. Among the likelihood
components, an emphasis of 1 was given to fishery catch, fishery age composition, survey
biomass, and survey age composition. Likelihood components for the spawner-recruit received
much less emphasis: 0.5 for the spawner-recruit relationship and 0.1 for the moment of
spawner-recruit relationship.
zL2.3 Experimental Design
The main objective of this study was to evaluate how the yellowfin sole assessment
results could have been improved relative to what was actually achieved, if a different
allocation of sampling effort had been used for the last three years. Sampling effort can be
partitioned into different "sampling" categories, including effort for collecting observed
fishery catch biomass, effort for conducting the survey to measure biomass status information,
effort for collecting fish samples, and effort for aging the individual fish in the samples. The
quality of the data collected from each of the category is proportional to the amount of effort
spent on -the category. For example, if a larger proportion of resources is allocated to the
biomass survey, the survey data are expected to have less variability. Thus, instead of
experimenting directly on the different allocations of sampling effort, we can evaluate
different combinations of errors in the input data categories. Error levels in the observed
133
fishery catch biomass, survey biomass, age determination, as well as sample size constituted
the four explanatory variables in the experiment.
Error levels for fishery catch, survey biomass, and aging precision all can be measured
in terms of a coefficient of variation (CV). In the actual yellowfin sole assessment, the CVs for
survey data were listed in the data file as being between 0.06 and 0.18 but these values were
ignored and replaced by the relative root mean squared error (RMSE) of the fit to the observed
biomass estimates. Calculation from Synthesis indicated this relative RMSE should be around
0.17, suggesting that survey data were much less precise than the survey estimates of sample
precision. The original assessment also assumed a value of 200 for the sample size used in
collecting yearly age composition information for both the fishery and survey. In our
experiment, for the data series up to and including 1995 we used the following fixed error
levels: survey biomass CV at 17%, sample size at 200, fishery catch CV at 10%, and aging
precision CV at 10%. For data series from 1996 to 1998, we tried three different error levels
for each of the four categories of input data: the same as the historical level, reduced by 50%,
and increased by 50%. For example, the three values of the survey biomass CV for data from
1995 to 1998 were 17%, 25.5%, and 8.5%. Because we wanted to exhaust all possible
combinations of the four factors, we ended up with a
34
full factorial design, which had a total
of 81 treatments (Table 4.3). Note that the error values listed in Table 4.3 applied only to data
series between 1996 and 1998.
For each of the 81 experimental treatments, we applied the Data Simulator four times,
each time generating 100 replicate data sets that were analyzed with Stock Synthesis. We used
the term "batch' to describe each of the four 100 data sets. Actually, all 400 data sets within
the four batches were replicates because they were based on the same true values and
generated with same degree of random errors. For example, the observed catch data for each
year were all based on the same true catch data and randomly generated with same CV
134
Table 4.3. Design of experiment on the combination of input data errors in last three years.
Treatment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
SmplSize
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
200
SurvCV
25.5%
25.5%
25.5%
25.5%
25.5%
25.5%
25.5%
25.5%
25.5%
17.0%
17.0%
17.0%
17.0%
17.0%
17.0%
17.0%
17.0%
17.0%
8.5%
8.5%
8.5%
8.5%
8.5%
8.5%
8.5%
8.5%
8.5%
25.5%
25.5%
25.5%
25.5%
25.5%
25,5%
25.5%
25.5%
25.5%
17.0%
17.0%
17.0%
17.0%
17.0%
17.0%
17.0%
17.0%
17.0%
8.5%
CatchCV
15.0%
15.0%
15.0%
10.0%
10.0%
10.0%
5.0%
5.0%
5.0%
15.0%
15.0%
15.0%
10.0%
10.0%
10.0%
5.0%
5.0%
5.0%
15.0%
15.0%
15.0%
10.0%
10.0%
10.0%
5.0%
5.0%
5.0%
15.0%
15.0%
15.0%
10.0%
10.0%
10.0%
5.0%
5.0%
5.0%
15.0%
15.0%
15.0%
10.0%
10.0%
10.0%
5.0%
5.0%
5.0%
15.0%
AgeingCV
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
135
Table 4.3 (continued)
Treatment
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
SmplSize
200
200
200
200
200
200
200
200
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
SurvCV
8.5%
8.5%
8.5%
8.5%
8.5%
8.5%
8.5%
8.5%
25.5%
25.5%
25.5%
25.5%
25.5%
25.5%
25.5%
25.5%
25.5%
17.0%
17.0%
17.0%
17.0%
17.0%
17.0%
17.0%
17.0%
17.0%
8.5%
8.5%
8.5%
8.5%
8.5%
8.5%
8.5%
8.5%
8.5%
CatchCV
15.0%
15.0%
10.0%
10.0%
10.0%
5.0%
5.0%
5.0%
15.0%
15.0%
15.0%
10.0%
10.0%
10.0%
5.0%
5.0%
5.0%
15.0%
15.0%
15.0%
10.0%
10.0%
10.0%
5.0%
5.0%
5.0%
15.0%
15.0%
15.0%
10.0%
10.0%
10.0%
5.0%
5.0%
5.0%
AgeingCV
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
15.0%
10.0%
5.0%
following lognormal distributions; the fishery age composition data were all generated as
simple multinomial random variables based on the true catch-at.age proportions and the same
sample size as defined by each treatment. We used four batches to get "replicates" for sample
summary statistics and to make our analysis better conform to the ANOVA assumptions. For
136
example, the average values of the 100 replicates should be fairly normally distributed even
though the individual replicate values are not.
The Stock Synthesis program routinely produces a wide variety of estimates, e.g.,
estimates for the annual series of biomass, fishing mortality, catch, and recruitment In this
study we focused on two categories of Synthesis outputs, the estimate for the last year for total
biomass (ending biomass) and the estimate for the last year for total exploitable biomass
(ending exploitable biomass). For each experimental treatment and output type, we calculated
the relative mean squared error (MSE) for each of the four batches (each batch contained 100
data sets). We used MSE as one of our summary statistics mainly because it combines bias and
variability into one statistic. For reference purpose, we also calculated the relative bias and
relative variability within each of the four batches. The relative root mean squared error was
simply the square root of the MSE divided by the true value,
RMSE
true value
J(sampie mean true value)2
+
(estimated value
sample mean)2
true value
where the sample mean is the average value of the 100 estimates within a batch.
The relative bias was defined as
1
100
estimated value)
true value )
1
The measurement of relative variability was simply the coefficient of variation (CV).
We summarized the results for each experimental treatment by calculating the mean relative
RIVISE, the mean relative bias, and mean coefficient of variation across the four batches. We
conducted the statistical analyses using the Minitab statistics program (Release 13.1 for
Windows).
137
Table 4.4. Relative bias, variability, and RMSE of the 81 experimental treatments. The values
shown are averages of four batches, each with 100 random replicates.
Treatment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
Relative Bias
end Bio
end exB
-0.0024
0.0435
-0.0047
0.0510
-0.0293
0.0406
0.0035
0.0452
-0.0248
0.0332
-0.0367
0.0300
-0.0078
0.0392
-0.0198
0.0380
-0.0387
0.0329
-0.0143
0.0300
-0.0208
0.0329
-0.0372
0.03 14
-0.0008
0.0366
-0.0177
0.0383
-0.0377
0.0300
-0.0053
0.0378
-0.0258
0.0309
-0.0462
0.0219
-0.0050
0.0328
-0.0186
0.0294
-0.0296
0.0282
-0.0028
0.0325
-0.0152
0.0304
-0.0308
0.0276
-0.0012
0.0348
-0.0158
0.0340
-0.0305
0.0271
0.0064
0.0458
-0.0013
0.0512
-0.0365
0.0317
0.0206
0.0568
-0.0154
0.0427
-0.0263
0.0399
0.0208
0.0600
-0.0025
0.0550
-0.0334
0.0343
0.0015
0.0408
-0.0114
0.0417
-0.0328
0.03 12
0.0059
0.0444
-0.0173
0.0398
-0.0399
0.0275
-0.0063
0.0366
-0.0207
0.0376
Relative Variability
end Bio
end exB
0.1243
0.0959
0.1257
0.0949
0.1161
0.0872
0.1222
0.0938
0.1283
0.1016
0.1169
0.0867
0.1174
0.0933
0.1212
0.0931
0.1195
0.0914
0.0961
0.0716
0.0941
0.0686
0.0906
0.0654
0.0891
0.0673
0.0948
0.0670
0.0895
0.0679
0.0901
0.0696
0.0922
0.0651
0.0942
0.0692
0.0694
0.0527
0.0690
0.0539
0.0682
0.0524
0.0641
0.0504
0.0620
0.0494
0.0609
0.0524
0.0668
0.0530
0.0708
0.0530
0.0658
0.0510
0.1072
0.0860
0.1155
0.0935
0.1119
0.0867
0.1094
0.0897
0.1230
0.0966
0.1172
0.0937
0.1117
0.0881
0.1184
0.0918
0.1148
0.0918
0.0843
0.0637
0.0821
0.0638
0.0854
0.0655
0.0892
0.0695
0.0852
0.0631
0.0816
0.0629
0.0891
0.0698
0.0852
0.0688
Relative RMSE
end Bio
end exB
0.1246
0.1097
0.1259
0.1122
0.1166
0.0998
0.1232
0.1083
0.1278
0.1103
0.1188
0.0944
0.1174
0.1053
0.1213
0.1046
0.1213
0.1000
0.0959
0.0797
0.0951
0.0783
0.0950
0.0746
0.0891
0.0788
0.0950
0.0796
0.0941
0.0763
0.0903
0.0819
0.0937
0.0743
0.1014
0.0743
0.0695
0.0636
0.0704
0.0631
0.0726
0.0609
0.0643
0.0615
0.0631
0.0594
0.0670
0.0606
0.0669
0.0650
0.0716
0.0645
0.0711
0.0592
0.1084
0.1012
0.1160
0.1110
0.1140
0.0951
0.1141
0.1109
0.1225
0.1096
0.1173
0.1056
0.1161
0.1111
0.1183
0.1115
0.1165
0.1017
0.0846
0.0778
0.0823
0.0786
0.0900
0.0747
0.0903
0.0853
0.0865
0.0769
0.0884
0.0706
0.0891
0.0813
0.0861
0.0807
138
Table 4.4 (continued)
Treatment
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
max
mm
average
Relative Bias
end Bio
end exB
-0.0324
0.0301
0.0047
0.0361
-0.0170
0.0298
-0.0251
0.0301
-0.0015
0.0314
-0.0191
0.0299
-0.0325
0.0251
0.0044
0.0385
-0.0107
0.0338
-0.0265
0.0284
0.0123
0.0530
0.0055
0.0562
-0.0156
0.0480
0.0132
0.0525
-0.0080
0.0478
-0.0353
0.0328
0.0200
0.0571
-0.0119
0.0448
-0.0202
0.0462
0.0028
0.0412
-0.0180
0.0356
-0.0375
0.0283
-0.0013
0.0382
-0.0141
0.0403
-0.0295
0.0373
-0.0002
0.0381
-0.0117
0.0409
-0.0346
0.0330
-0.0039
0.0319
-0.0185
0.0284
-0.0316
0.0279
-0.0039
0.0322
-0.0165
0.0342
-0.0306
0.025 1
0.0037
0.0363
-0.0127
0.0360
-0.0292
0.0246
Relative Variability
end Bio
end exB
0.0854
0.0660
0.0604
0.0526
0.0641
0.0521
0.0618
0.0493
0.0606
0.0511
0.0624
0.0509
0.0637
0.0499
0.0669
0.0519
0.0668
0.0551
0.0586
0.0473
0.1150
0.0924
0.1111
0.0897
0.1055
0.0848
0.1059
0.0846
0.1088
0.0862
0.1064
0.0837
0.1150
0.0932
0.1142
0.0915
0.1050
0.0837
0.0819
0.0636
0.0874
0.0696
0.0873
0.0660
0.0871
0.0682
0.0841
0.0663
0.0847
0.0672
0.0879
0.0693
0.0853
0.0673
0.0822
0.0642
0.0611
0.0508
0.0620
0.0508
0.0618
0.0512
0.0626
0.0524
0.0625
0.0530
0.0625
0.05 13
0.0584
0.0464
0.0571
0.0502
0.0617
0.0505
0.0208
-0.0462
-0.0147
0.1283
0.0571
0.0887
0.0600
0.0219
0.0370
0.1016
0.0464
0.0696
Relative RMSE
end Bio
end exB
0.0891
0.0747
0.0609
0.0655
0.0653
0.0614
0.0653
0.0590
0.0609
0.0615
0.0642
0.0604
0.0698
0.0571
0.0674
0.0665
0.0671
0.0664
0.0632
0.0566
0.1173
0.1109
0.1120
0.1102
0.1055
0.1012
0.1084
0.1036
0.1093
0.1029
0.1089
0.0926
0.1193
0.1140
0.1144
0.1065
0.1053
0.0992
0.0830
0.0784
0.0880
0.0805
0.0920
0.0736
0.0874
0.0807
0.0842
0.0800
0.0881
0.0794
0.0881
0.0815
0.0854
0.0813
0.0871
0.0745
0.0611
0.0614
0.0639
0.0596
0.0679
0.0596
0.0630
0.0633
0.0637
0.0647
0.0683
0.0585
0.0589
0.0603
0.0578
0.0634
0.0669
0.0574
0.1278
0.0578
0.0905
0.1140
0.0566
0.0816
139
Ending Biomass
60
45
C)
V
30
I)
15
0
2.5
1.5
3.5
4.5
Ending Exploitable Biomass
40
30
C)
V
V
20
IC
C
I.,.#
1.1.)
c.I
Figure 4.5. Example histograms (from experimental treatment 1) of variables output by the
Stock Synthesis program and used as response experimental variables. The dashed lines
indicate the true values. The units for the biomass variable are in million tons.
140
4
response is relative MSE of ending biomass
S
S
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ci,
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2
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Figure 4.6. Diagnostic plots of the residual versus fitted values for the two response variables.
The three clumps correspond to the three levels of the survey CV factor, with the high CV
producing less accurate estimates.
141
4.3 Results
The yeflowfin sole fishery we studied had a long data series, totaling 35 years from
1964 to 1998. The results of our experiment showed that changing the error levels in last three
years of the data series directly affected the Synthesis estimates. Among the 81 experimental
treatments, Synthesis estimates for ending biomass and ending exploitable biomass varied
moderately in relative bias, relative variability, and relative mean squared error (Table 4.4).
For the estimates of ending biomass, the relative RMSE ranged from a low of 0.0578 for
treatment 80, where SmplSize was 300, SurvC V was 0.085, CatchCVwas 0.05, and AgeingCV
was 0.10, to a high of 0.1278 for treatment 5, where SmplSize was 100, SurvC V was 0.255,
Catch CV was 0.10, and A geingC V was 0.10. For the estimates of exploitable ending biomass,
the relative RMSE spread from a minimum of 0.0566 for treatment 54, where SmplSize was
200, SurvCVwas 0.085, CatchC V was 0.05, and AgeingC V was 0.05, to the maximum of
0.1140 for treatment 61, where SmplSize was 300, SurvCVwas 0.255, CatchCVwas 0.05, and
AgeingCVwas 0.15.
For each of the 81 experimental treatments, the distributions of ending biomass
estimates and the distribution of ending exploitable biomass estimates were both fairly
symmetric (e.g., Figure. 4.5). For the two response variables, the relative RMSE of ending
biomass estimates and the relative RMSE of ending exploitable biomass estimates, diagnostic
plots of the residual versus fitted values indicated little evidence of heterogeneous variability,
although there seems to be slightly more variability in the clumps with higher predicted values
(Figure 4.6). The residuals in Figure 4.6 are clumped into three groups, which correspond to
the three levels for the survey CV.
142
4.3.1 Effects of Error Combination on Synthesis Estimates
In general, treatments that had a combination of low error levels produced better
Synthesis estimates than treatments that had a combination of high error levels. We used
treatment 41 as our baseline for comparisons because it had the same error levels for data in
the last three years as occurred in the previous 32 years. Treatment 41 thus represented status
quo levels of sampling. Averaged across the four batches for this particular treatment, the
relative RMSE for the estimates of ending biomass was 0.0865 (standard error: 0.0027) and
the relative RMSE for the estimates of ending exploitable biomass was 0.0769 (standard error:
0.0030). Using the relative RMSE as our measurement, we statistically compared the results of
other treatments with this baseline treatment. Among the other 80 experimental treatments, 27
of them produced statistically better results (P < 0.05, two sample T-Tests) in terms of the
relative RMSE values for the ending biomass estimates and the relative RMSE values for the
ending exploitable biomass estimates. In addition, the treatments that produced better relative
RMSE values primarily were ones where the survey CV was at the low level, 0.085 (Table 4.3
and Table 4.4).
Statistical analysis indicated that the four factors (survey CV, age composition sample
size, catch CV, and aging error CV) had different degrees of importance. Analysis of variance
of the relative RMSE of ending biomass (Table 4.5) indicated that the survey CV and age
sample size main effects were statistically significant (P value < 0.05). In addition, the survey
CV main effect was of dominant importance, as its MS (Mean Square) value was 40 times
larger than the MS value of the age sample size main effect. The ANOVA of the relative
RMSE of ending exploitable biomass (Table 4.6) showed that the statistically significant main
effects were the survey CV and aging error CV effects. The MS value for the survey CV main
effect was about 37 times larger than that of the aging error CV effect, suggesting the
uttermost importance of the survey CV. Note that the catch CV main effects were not
143
statistically significant either for the relative RIMSE of ending biomass or for the relative
RMSE of ending exploitable biomass.
Three-dimensional plots of the experimental results also visually show the relative
importance of the survey CV, the age composition sample size, and aging error CV. Using the
relative RMSE of ending biomass as the response variable, we created nine 3-D surface maps
with survey CV and age composition sample size as the two explanatory variables. Each of the
nine 3-D plots corresponded to a combination of the catch CV and aging CV values. All nine
graphs showed similar pattern as the one illustrated in Figure 4.7, where the lower survey CV
greatly reduced the relative RMSE of ending biomass. Using the relative RMSE of ending
exploitable biomass as the response variable, we also made nine similar 3-D plots, but with
survey CV and aging error CV as the two explanatory variables. Again, all nine graphs
showed similar dominance of survey CV (e.g., Figure 4.8).
4.3.2 Optimal Balances of Error Levels
The experimental results indicated that yellowfin sole assessment results could have
been improved relative to what was actually achieved, if a different allocation of sampling
effort had been used for the last three years. A fishery management agency normally does not
have the resources to improve data collected in all categories, thus the experimental treatments
that produced the best relative RMSE of ending biomass and the best relative RMSE of ending
exploitable biomass were not necessary the best treatments in terms of the optimal allocation
of sampling effort. For example, treatment 80 produced the minimum relative RMSE (0.05 78)
of ending biomass estimates on average across the four batches. However, to achieve this
required a 50% decrease in the survey CV, a 50% decrease in the catch CV, and a 50%
increase in the age composition sample size. Given the importance of having a low value for
the survey CV, a reasonable combination would be to allocate more effort on the survey at the
144
Table 4.5. Analysis of variance for relative RMSE of ending biomass estimates.
Source
SmplSize
SvyCV
CatchCV
AgeingCV
SmplSize*SvyCV
SmplSize*CatchCV
SmplSize*AgeingCV
SvyCV*CatchCV
SvyCV*AgeingCV
CatchCV*AgeingCV
SmplSize*SvyCV*CatchCV
SmplSize* SvyCV*AgeingCV
SmplSize*CatchCV*AgeingCV
SvyCV*CatchCV*AgeingCV
DF
2
2
2
2
4
4
4
4
4
4
8
8
8
8
Seq SS
0.00340
0.13878
0.00001
0.00014
0.00040
0.00034
0.00013
0.00006
0.00087
0.00003
0.00043
0.00054
0.00041
0.00015
F
P
55.97000
2287.700
0.22000
2.36000
3.29000
2.79000
1.03000
0.52000
7.15000
0.23000
1.76000
2.24000
1.71000
0.63000
0.00000
0.00000
0.80300
0.09600
0.0 1200
0.02700
0.39100
0.7 1800
0.00000
0.92100
0.08400
0.02500
0.09700
0.75200
Table 4.6. Analysis of variance for relative RMSE of ending exploitable biomass estimates.
Source
SmplSize
SvyCV
CatchCV
AgeingCV
SmplSize*SvyCV
SmplSize*CatchCV
SmplSize*AgeingCV
SvyCV*CatchCV
SvyCV*AgeingCV
CatchCV*AgeingCV
SmplSize* SvyCV*CatchCV
SmplSize*SvyCV*AgeingCV
SmplSize*CatchCV*AgeingCV
SvyCV*CatchCV*AgeingCV
DF
2
2
2
2
4
4
4
4
4
4
8
8
8
8
Seq SS
0.00002
0.10578
0.00005
0.00286
0.00011
0.00019
0.00003
0.00008
0.00048
0.00007
0.00072
0.00025
0.00014
0.00023
F
P
0.27000
1757.89
0.77000
47.450
0.91000
1.59000
0.24000
0.67000
3.97000
0.56000
2.97000
1.05000
0.57000
0.96000
0.76700
0.00000
0.46300
0.00000
0.45800
0.17800
0.91400
0.6 1400
0.00400
0.69500
0.00300
0.39600
0.80500
0.46900
145
CatchCV = 0.05, AgeingCV =1.0
0.12
0.11
MSE(EB)
0.08
0.07
125
0.06
1
SmplSize
300
ryCV
Figure 4.7 Example surface plot of relative RMSE of ending biomass.
SmpleSize = 300, CatchCV=0.05
MSE(EEB)
0.115
0.105
0.095
0.085
0.075
0.065
0.25
0.055
0.
SvyCV
AgeingCV
0.15
Figure 4.8 Example surface plot of relative RMSE of ending exploitable biomass.
146
expense of reduced effort on collecting better fishery catch data and population age
composition data. For example, in treatment 19, where the survey CV was reduced by 50%
and the age composition sample size was decreased by 50%, but the catch CV and aging CV
were both increased by 50%, the relative RMSE of ending biomass was still reduced from
0.0865 to 0.0707 and the relative RMSE of ending exploitable biomass was decreased from
0.0764 to 0.0646.
4.4 Discussion
Results from our experiments were not totally in accord with what we anticipated. We
expected that increased sampling during the last three years would improve the yellowfin sole
assessment results relative to what was actually achieved. However, we did not anticipate the
dominant importance of high quality survey data. In previous chapters, where we conducted
experiments on artificial stocks, we found the factor of age composition sample size was as
important as the factor of survey CV in reducing the relative variability and relative bias of
Synthesis estimates for the artificial stocks.
Some major differences in Synthesis configurations between the experiments in
previous chapters and the experiment in this chapter might explain the differences in the
relative importance of sample size and survey CV. In all previous experiments, the survey
catchability coefficient (Q) was given an initial value of 0.1 and was treated as a rarameter to
be estimated by Synthesis, which implied that the survey biomass data were treated as a
relative index of the real biomass. In the experiment here the value of survey catchability in
the simulation was 1.0 and Synthesis was given this same value as a fixed parameter, meaning
Synthesis was forced to treat the survey biomass data as absolute measurements of the biomass.
The configuration of fixed survey Q in the yellowfin sole assessment might have forced
Synthesis to depend more heavily on the survey data.
147
To check the effect of having a different configuration for the survey catchability, we
re-ran Treatment 41 but with survey Q estimated. We took parameter files from the original
Treatment 41, which was essentially equivalent to Wilderbuer and Nichols original
assessment, and batch edited the parameter files so that the survey Q would be estimated rather
than fixed. Averaged across the four batches in the new Treatment 41, the relative RMSE of
the ending biomass estimates was 0.3885 (standard error: 0.0057) versus 0.0865 in the original
treatment, and the relative RMSE of the ending exploitable biomass estimates was 0.43 53
(standard error: 0.0079) versus 0.0769 in the original treatment. Thus, treating the survey
biomass data as relative estimates of biomass rather than as absolute estimates produced much
less accurate estimates of ending biomass.
In most of our previous experiments, we followed the suggestion by Fournier and
Archibald (1982) that age sample sizes in the likelihood specification should be limited to 400
fish per sample, i.e., the sample size that Synthesis uses should be the smaller of the actual
sample size or 400. In the original yellowfin sole assessment, age sample sizes in the
likelihood specification were limited to 200 fish per sample, meaning the sample size that
Synthesis used was the smaller of the actual sample size or 200. This reduced emphasis on
sample size might also help explain the decreased relative importance for the age sample size
factor.
Lastly, aging error and the length of the data series might also have played some roles.
In all our previous experiments, there were no aging errors and the configuration within a
specific experimental treatment was applied to the entire simulation periods. In the yellowfin
sole experiment, aging errors were applied to all the age sampling data and the configuration
of data errors within a specific treatment only applied to the data in the last three years.
In this study, the historical data between 1964 and 1995 were assumed to have fairly
good quality (survey CV: 0.17, sample size: 200, catch CV: 0.10, aging CV: 0.10). If we keep
148
the same error levels in the last three years, the ANOVA model from our experiment predicted
a value of 0.0865 for relative RMSE of ending biomass estimates and a value of 0.0764 for
relative RMSE of ending exploitable biomass. These values were already fairly low. However,
the model predicted that those low values could be further reduced if in last three years we
could improve the survey data, even at the cost of degrading other kinds of input data. For
example, if we use the combination of survey CV at 0.085, sample size at 100, catch CV at
0.15, and aging CV at 0.15, the model predicted a value of 0.0707 for relative RMSE of
ending biomass and a value 0.0646 for relative RMSE of ending exploitable biomass. It is
possible that the actual error levels in the historical data were much higher than those we
assumed. In such a case, the improvement in the survey data for the last three years might have
an even greater effect on improving the accuracy (RMSE) of the Synthesis estimates. However,
only more experiments can verify those speculations.
149
Chapter Five: Summary
This work evaluated the sensitivity of Synthesis and showed how the accuracy of
Synthesis estimates could be improved through an optimal balance of sampling effort.
As the first step of the work I developed a simulation package consisting of three of
C++ programs: the Stock Definer, the Data Simulator, and the Statistical Analyzer. A fishery
system of interest can be specified with the Stock Definer program. The Data Simulator
simulates the dynamics of a fishery system and produces input data used by the Stock
Synthesis program. The Statistical Analyzer summarizes the output data producedby the
Stock Synthesis program. Although this simulation package was developed primarily for the
purpose of this study, the package is generic enough to be applied in testing the performance
of Synthesis in the assessment of other commercial fisheries.
In the first chapter, I briefly described the evolution of stock assessment methods and
introduced the Stock Synthesis Assessment Model. After mathematically depicting its
maximum likelihood methodology, I illustrated some potential issues related to the robustness
of the model.
In the second chapter, I evaluated the sensitivity of the Stock Synthesis program on
populations with simple multinomial age compositions. More specifically, I evaluated the
impacts of input data errors and stock characteristics on the accuracy and precision of
Synthesis estimates. Factors examined included the length of the time series of data, the
natural mortality coefficient, the shape of the fishery and survey selectivity curves, the trend in
fishing mortality, variability in the recruitment pattern, and errors in observed annual catch,
fishing effort, fishery and survey age composition, and survey biomass indices. Simple
multinomial distribution is the statistical structure assumed by Synthesis for age composition
samples. Under the simple multinomial distribution, the experiment in Chapter two suggests
that increasing the number of years in the data series and increasing the age composition
sample size are very crucial for obtaining less variable results in Synthesis estimates.
In the third chapter, I extended the study to populations with compound multinomial
age composition, which constituted a violation to one of Synthesis's assumptions. I conducted
Monte Carlo experiments with factors similar to those used in Chapter two. Resilts from those
experiments indicated that the compound multinomial distributions for the age composition
data adversely affected the performance of the Stock Synthesis program. When the fishery age
composition actually followed a compound multinomial distribution, the estimates produced
by the Stock Synthesis program, which assumed simple multinomial distributions with
maximum sample sizes of 400 fish, were moderately more biased and more variable. Under
the compound multinomial distribution, I also found that increasing the stratum coverage
helped reduced the bias and variability. This implied that in fishery sampling design, it might
be better to use a more diversified approach to reduce the impact of stratification.
Synthesis users often follow the suggestion by Fournier and Archibald (1982) that age
sample sizes in the likelihood specification should be limited to 400 fish per sample, i.e., the
sample size that Synthesis uses should be the smaller of the actual sample size or 400. When
there is stratification within the population, the sampled age composition data tend to be more
variable. When applying Synthesis to populations whose age compositions follow compound
multinomial distribution, the results from our experiments in chapter three indicated that such
a configuration probably has given age composition data too much emphasis. In our
experiments, we found that using 200 as the upper limit was better than using 400.
In the fourth chapter, I took the actual stock assessment of yellowfin sole (Limanda
Aspera)
in the Bering Sea as a case study. I used simulation to evaluate whether more accurate
assessment results could be achieved from a better balance in the amount of sampling effort
151
allocated to age composition data versus survey biomass estimates. Ifound that the yellowfin
sole assessment results could have been improved relative to what was actually achieved, if
more effort were spent on improving the survey biomass estimates at the cost of less effort on
age sampling even for only the last three years. The quality of the survey data appeared to be
extremely important in the yeliowfin sole case study. I found the reason was probably because
the special configuration that Synthesis was not allowed to estimate the survey catchability
parameter, meaning Synthesis was forced to treat the survey biomass data as absolute
measurements of the biomass.
The findings of this study have important implications for stock assessment with the
Stock Synthesis Program and for future sampling design by fishery management agencies.
Although Synthesis has been the primary tool for many west coast and Alaska groundfish
stock assessments since 1988, the performance of Synthesis has not been fully tested (Methot
2000). Given the uncertain nature of the stock assessment model, the lack of comprehensive
testing may pose a risk if there is widespread adoption of the model by fishery scientists,
because Synthesis users often have no knowledge on the robustness of the program. This study
evaluated the performance of the program and identified factors (e.g., the length of the time
series and age composition sample size) that Synthesis is most sensitive to. This study also
found that Synthesis was not particularly robust for populations with compound multinomial
age composition data and that reducing the sample size emphasis (from 400 down to 200)
improved the robustness. With this knowledge, fisheries management agencies and Synthesis
users will have better ideas on where to improve data quality and thus improve their stock
assessment. For example, fisheries management agencies might allocate more resources for
age composition sampling and collecting a longer data series; A Synthesis user might want to
reduce the maximum sample size used from 400 to a smaller value if he suspects his age
composition samples are quite variable. Furthermore, the simulation package of this study can
52
be adapted to accommodate a commercial fisheries. Thus a Synthesis user can use the author's
simulation package for his assessment needs. For example, just as we did in Chapter four, a
Synthesis user can run Monte Carlo simulation with our package and identify the optimal
allocation of sampling effort for his specific fisheries.
Although this study has done a fairly comprehensive evaluation on the Stock
Synthesis program, there still are issues worthy of further investigation.
1.) Although actual landings data are reasonably accurate for many fisheries, the data for the
discarded portion of the total catch are usually a rough guess. For some fisheries, the discarded
portion can be substantial (Pikitch et al.1988), with the result that the errors in estimates of
total catch data can be considerable. How does discarding affect the performance of Synthesis?
2.) Data could also be collected from different sources and at different time intervals. For
example, there were different practices (annual, biennial, and triennial) in the fishery sampling
and surveys of the groundfish resources in eastern Bering Sea (NPMFC 2000). In the practice
of fishery age composition sampling, we can either conduct sampling every year with smaller
sample size or conduct sampling every other year with bigger sample size. Similarly for the
strategy in the survey of biomass indices, the survey can either be carried biennially with
smaller errors or conducted annually with less preciseness. Between the options, which
strategy is better?
3.) In the application of the Stock Synthesis program, fishery scientists often placed different
emphasis for different likelihood components based on their perception on the quality of
different input data source. How does this practice influence the quality of estimates from
Synthesis? What if larger emphasis was incorrectly given to data with higher errors?
The three issues above can be investigated by directly applying our simulation
package because the package has built-in supports for addressing these issues. In addition, the
153
package needs to be further updated to accommodate systems with multiple fisheries, multiple
survey, and sexual dimorphism.
154
References
Bence, J.R., A. Gordoa, and J.E. Hightower. 1993. Influence of age-selective surveys on the
reliability of stock synthesis assessments. Can. J. Fish. Aquat. Sci. 50:827-840.
Beverton, R.J.H, and S.J.Holt, 1957. On the dynamics of exploited fish populations. Fishery
Investigation Series II, Marine Fisheries, Great Britain Ministry of Agriculture, Fisheries
and Food 19.
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APPENDICES
158
Appendix A: Terminology
tsiomass
The total weight of a fish stock.
Ending biomass
The biomass of a stock at the start of the last year of the data series.
Ending fishing mortality
The instantaneous rate of fishing mortality applied to a stock during the last year of the
data series.
Ending recruitment
The recruitment to the stock at the start of the last year of the data series.
Ending exploitable biomass
The exploitable biomass at the start of the last year of the data series.
Exploitable biomass
Not all fish in a stock can be exploited by a fishery. For example, some age groups of a
stock might have a geographic distribution that does not completely overlap with that of
fishery. Exploitable biomass is the portion of total biomass that is directly exploitable by
the fishery and is calculated as the sum across all age classes of the selection at age
times the biomass at age.
159
F35%
and F35% catch
F35%
is defined as the value of fishing mortality that would reduce the spawning stock
biomass per recruit to 35% of the level that would exist with no fishing. The F35% catch
is the predicted catch biomass when F35% is applied to a stock.
Moment of the spawner-recruit relationship
The degree to which the estimated stock-recruitment curve and recruitment variability
parameter fit the observed mean and variability of the individual year recruitment
parameters respectively. Methot (2000) includes a more detailed description.
Recruit or recruitment
New fish that join the fish stock when they attain the age of recruitment.
Selectivity and selectivity function
The probability that a fish being caught partly depends on the biological characteristics
of the fish and the physical nature of the fishing gear being applied. Selectivity reflects
the relative possibility of being caught for fish of specific age or size when they are
subject to the fishing gear. The selectivity function is the relationship between
selectivity and age (size).
Spawner-recruit relationship
The relationship between spawning biomass and the amount of recruitment it generates.
160
Starting biomass
The biomass of a stock at the start of the first year of the data series.
Yield per recruit
The total yield in weight harvested from a year-class of fish over its lifetime, divided
by the number of fish in the year-class at the age of recruitment.
161
Appendix B: Creating a Generic Fisheries Simulation Package for a Monte Carlo Evaluation
of the Stock Synthesis program
B. I The Stock Synthesis Program
Stock Synthesis uses maximum likelihood as its approach in stock assessment.
Maximum likelihood is a statistical method for estimating true parameters based on observed
values. For a given set of observed data and a predefined statistical model, the maximum
likelihood method tries to find the parameter values that most probably generated the set of
observed data. The input to Stock Synthesis consists of a series of data, including annual
landings, observed age composition, estimates of discarded harvest, biological characteristics
of the fish, intensity of the fisheries, information acquired through scientific fishery surveys,
and initial target parameter values. The output from Stock Synthesis is the set of estimated
parameters, contained within a file known as the output file. All input data must be stored
within three files, categorized as biological file, observed data file, and initial parameter file.
Fig. B. 1 illustrated this scenario.
biological data file
initial parameter file
The Stock Synthesis Program
output file
(estimated parameters)
Figure B.1. Illustration of the Stock Synthesis Program.
observed data file
162
The actual estimating process of Stock Synthesis is mainly numerical and CPU extensive.
Starting with the given initial target parameter values and using a set of mathematical and
statistical models, the Stock Synthesis program calculates the total likelihood of the
observation data. It then recursively modifies the values of target parameters until the value of
total likelihood reaches its maximum. See Chapter one for a detailed presentation of the
statistical theory that Stock Synthesis based upon.
B.2 Organization of the Fish Stock Simulation Package
In this section, we describe the organization of the fish stock simulation package and
the architectures of the component programs. The entire simulation process is composed of
four inter-related tasks. Basic parameters of a fishery system need to be specified first. With
the Monte Carlo method we generate a series of simulated data sets through a simulation
method. The simulation method also produces additional true parameters such as ending
biomass and ending fishing mortality. Next the simulated data sets are analyzed using the
Stock Synthesis program. Finally we compare estimates from Stock Synthesis with the true
parameter values. This scenario is illustrated in Figure B.2.
B.2. 1 Selecting a Fishery System
A typical fishery system is composed of a fish stock, a fishery harvesting the stock, a
survey monitoring the status of the stock, and a series of sampling conducted by fisheries
scientists. The selection of a fish stock involves the specification of parameters that define the
biological nature of the fish stock. For example, average body weight at a particular age
(weight-at-age) defines the growth rate of the fish selected; number of offspring produced
yearly by a stock (recruitment) determines the group reproduction capability of the stock. A
163
fishery can be defined by fishing intensity (Fishing Mortality), duration of the fishery (year
started and year ended), fishing power (catchability), and gear-fish relationship (selectivity).
A survey is described by survey selectivity and the proportion of the stock covered by the
survey. A sampling event is usually controlled by the number of fish to be sampled (sample
size).
Specify
a stock
and
its fishery
(Stock.exe)
I Basic
parame ter
Simulate
dynamics
I
I Simul ate
of
a fishery
system
data
files
The Stock
Synthesis
program
(Sim.exe)
Estimates
produced
by the
Stock
Synthesis
program
Comparison of true and estimated
parameters
(Stat.exe)
Evaluation of the performance of the
Stock Synthesis program
Figure B.2. Flowchart of the Evaluation Process.
To increase the validity of the simulation, we need to specify a fishery system in a way
such that it closely mimics the real world situation. Because many of the parameters that
define the characteristics of a stock are heavily interrelated, setting correct values for
parameters of a fishery with predefined behavior is not an easy job. For example, the
164
selectivity curve, which can take any shape ranging from a flat line to domed or asymptotic
curvature, is defined by four parameters. Mapping a curvature with values of the four
parameters is a process of trial and error. Thus we need a way to visualize the curvature with
given parameters and vice versa. To simplify the process of specifying the parameters for an
artificial stock and its fishery, we developed a graphical application that could be used
interactively to achieve the objectives. The program is a MFC (Microsoft Foundation Classes)
application based on the so-called document-view architecture.
B.2.1.1 Document-View Architecture
The Document-View architecture is the core of the Microsoft Foundation Classes
(MFC) application framework. In simple terms, the document-view architecture separates
data from the user's view of the data, thus there can be multiple views of the same data.
Consider a document that consists of statistical data for a series of experiments and suppose a
table view and a chart view of the data are available. When new data are available, the user
updates values through the table view window, and the chart view window changes because
both windows display the same information (Figure B.3). Notice that a view does not
necessary reflect all the data contained within the document that the view is attached to.
In a MFC library application, documents and views are represented by instances of
C++ classes. MFC provides several classes that implement the document-view architecture
(Figure B.4):
CwinApp
The CWinApp class is the base class from which we derive a Windows application object.
The application object provides member functions for initializing and running the
application. Each application that uses MFC can only contain one object derived from
CWinApp.
165
CdocTemplate
The document template is the glue that holds together a document and its views. It is the
liaison between documents, views, and fame windows. CDocTemplate has two subclasses:
CSingleDocTemplate and CMultiDocTemplate. A CSingleDocTemplate supports one
document at a time, whereas a CMultiDocTemplate supports multiple documents
simultaneously.
Cdocument
The CDocument contains the raw data within our application. It represents the unit of data
that the user typically opens with the File Open command and saves with the File Save
command. A CDocument object reveals its internal data to the outside world through
CView objects that attache to it.
Cview
A CView represents the actual window a user sees on the screen. It is attached to a
document and acts as an intermediary between the document and the user. The view
renders an image of the document on the screen or printer and interprets user input as
operations upon the document.
CframeWnd
A CFrameWnd is the window used by MFC to contain views. It has two major
components: the frame and the contents that it frames. The frame, which is around a view,
consists of a caption bar and standard window controls. The "contents" consist of the
window's client area, which is fully occupied by a child windowthe view.
Fig. B.4 illustrates the class relationship for a typical Single Document Interfa (SDI)
application.
166
Experimental Data Summary
groupi group2 group3 group4
testl
6
4.2
test2
average
5.1
6
5.5
5.75
4
4.8
4.4
7
6.5
6.75
Experimental Data Summary
ftfIf
'flft
groupi
group2
group3
oavJagI
group4
groups
Document
__I
U.
Purl ol documart
currertly ioite
Figure B.3. Document-view architecture illustration. Note that a view may be a partial picture
of a document.
167
r CWinAppfl
L
object
j
Figure B.4. Objects and classes used by the SD! application.
168
B.2.2 Simulation of a Fishery System
Both deterministic and non-deterministic (stochastic) methods are used in the
simulation of a fishery system. The deterministic method simulates the dynamics of an
age-structured fish population using the same deterministic equations (described in Chapter
one) that underlie Methot's Stock Synthesis program. The stochastic method takes the true
demographic data produced by the deterministic method and genelates random data sets that
can be analyzed directly by the Stock Synthesis program. The Stock Synthesis program uses
the so-called "age-structured population" model as its theoretical foundation. Our
deterministic method should use the same model, otherwise there is no basis to make valid
statistical comparison.
Figure B.5 illustrates our simulation mechanism. The total number of fish in a stock
at the beginning of year y comes from two sources, survivors from year y-1 and recruitment
(new fish) entering the stock at the start of year y. A survey may be conducted on the fish
stock at this time. The result of the survey is survey abundance and survey size composition.
During year y, some fish die of natural causes, while some others get harvested by fishing
fleets. The remaining fish in the stock survive to year y-l. The fishing activities in year y
generate a total catch. Based on the total catch, a random data generator produces the
observational data for total landings and total discarding. Sampling is then conducted on the
fish landed and the observed age composition data are generated.
The simulation process takes the file produced by the GUI (Graphical User Interface)
program as input and generates observational data sets by simulating the random sampling
process. In the observational data sets, the values for the annual catches and the survey
estimates of biomass are unbiased and their enors follow either normal or lognormal
distributions. Values for average weight-at-age also are unbiased with normally distributed
enors. The discarded portions of the annual catch are divided from the total catch and the
division follows a uniform distribution. The fisheries age composition data are generated by
simulating a multistage sampling process. The simulated population first is partitioned into
several subpopulations, each of which has a different age composition. Then random samples
are drawn from a subpopulation. Size composition data in the survey process are converted
from the age compositions by a growth equation that incorporates normally distributed error.
Survivor
into
year y+
Survivors
from year
y-1
Natural
death
Population
at year y
Total
removal
in year y
Recruits at
year y
Discarding
Fishery
catch
Landings
Sampling:
Survey:
survey abundance
survey size composition
Figure B.5. A Schematic Illustration of a Fishery System.
'V
fishery catch-at-age data
170
By repeating this random sampling process a large number of times, replicate data sets
are generated for each particular set of stock, fishery, and survey. The large number of data
sets, which are replicates of a given set of experimental conditions, are then applied, one at a
time, to the Stock Synthesis program as input data in order to generate a large number of sets
of estimated results.
B.3 Design and Implementation
In this section, we describe the design and implementation of the three programs
within the package. While all three programs were implemented with C++ on the Windows 95
platform, the first one, the graphical interactive application, has been developed using the
Document-View architecture and the Microsoft Foundation Classes framework.
B.3.l The Graphical Interface Program
The interactive MFC application can be used to specify the parameters for an artificial
fish stock and its associated fishery. As mentioned earlier, the major objective of the design is
to create a GUI environment under which users can easily specify, visualize, and modify all
the parameters in a convenient way. To achieve the goal, we create several different view
classes that are all attached to the same document class (Figure B.6). Users can easily switch
among different view window, viewing and modifying parameters from different angles.
Multi-Document Interface (MDI) and Single Document Interface (SDI) are the two
options within the MFC application. We chose SDI for our GUI application mainly to avoid
possible confusion resulting from MDI. You can open or create multiple documents
simultaneously in a MDI application, thus sometimes it is not very clear which view belongs
to which document. To reflect the fact that this application is to be used for the creation of an
artificial stock and its associated fishery, we gave it the name of stock" (Figure B.7).
171
CStockApp
Figure B.6. Class Organizations.
Ele
dit
View
Li_L!i
I
Fish
mullion
UsIp
SelecvilyPeremeters
SetectMty Curves
-
Sel.(%)
istslope
2ndslope
- 05
10
//
60
2
ntIe:
2nd inflec
J
151 slope
-10
5
2nd nlIc
-
20I
_J
j
:J
2nd slope
- 02
J
rAge (yr.)
1
lslinllcc
Cornmd
Grid off
6
ii
NUM
Figure B.7. Screen Shot of Stock Program.
172
B.3.1.1 Class CStockApp
The class definition of CStockApp is shown in Figure B.8. CStockApp represents our
window application. By deriving it directly from CWinApp, we make sure the stock
application inherits most of the common functionality from the MFC framework. The only
essential method of the class is the Initlnstance ()
virtual function, where we put our
specific initialization code to make our application unique. The initial binding of document,
view, and frame window also happens here (Fig. B.9).
class CStockApp
public CWinApp
:
public:
CStockApp
// ClassWizard generated virtual function overrides
;
//{{AFXVIRTUAL(CStockApp)
public:
virtual BOOL InitInstance;
//} }AFX VIRTUAL
Figure B.8. Class Declaration of CStockApp.
BOOL CStockApp: :Initlnstance()
AfxEnableControlContainer
// more regular initialization here
;
//initial binding of document, view, and frame
CSingleDocTemplate* pDocTemplate;
pDocTemplate = new CSingleDocTemplate(
I DR MAINFRAME,
RUNTIME CLASS (CStockDoc),
RUNTIMECLASS(CMainFrame),
//RUNTIME CLASS (CStockView) );
RUNTIME CLASS (CSlctViewfl;
AddDocTemplate (pDocTemplate);
Figure B.9. Partial Listing of Method Initlnstance ()
// main SDI frame window
173
B.3.1.2 Class CStockDoc
The class definition for class CStockDoc is shown in Figure B.lO. CStockDoc is
the data container for the stock application. Its member variables represent parameters that
specify the characteristics of a stock and its fishery. Since the framework handles the
instantiation of a CStockDoc, the constructor for CStockDoc is not public. CStockDoc
supplies several methods for data exchange between the document, view, and dialog box.
Method Serialize () is for serializing the member data to/from disk The command
.
handlers for 'File Open" and "File Save" invoke this method internally.
174
class CStockDoc
public CDocument
:
protected: // create from serialization only
CStockDoc
;
// Attributes
public:
CStringList*
GetLineList()
CStringList mlineList;
{
return &mlineList;
CArray<float, float> m_nRecruitArray;
BOOL mblnitEquil;
mnNumSubstock;
float mnSurveylstlnflecAge;
PINT
// more member variables
// Operations
public:
// Overrides
virtual BOOL OnNewDocument;
virtual void Serialize(CArchive& ar);
/1 Implementation, data exchange methods
public:
void setDlgData( Clnfo & dlg);
void setDlgData( CRecruitDlg & dlg);
void updateLineList ()
void getRecruitFromDlg( CRecruitDlg & dig);
void getDataFromolg( Clnfo& dlg);
virtual -CStockDoc
#ifdef DEBUG
virtual void AssertValid() const;
virtual void Dump (CDumpContext& dc) const;
#endif
;
Figure B.1O. Class Declaration ofCStockDoc.
175
B.3.I.3 Class Clnfo
class Clnfo
:
public CDialog
// Construction
public:
Clnfo(CWnd* pParent = NULL);
void setDefault ()
/1 standard constructor
// Dialog Data
//{ {AFXDATA(Clnfo)
enum { IDD = IDDDIALOGG INFO };
BOOL mblnitEquil;
float mcoef a;
float mcoefb;
1/ more dialog data
//}}AFX DATA
// Overrides
/1 ClassWizard generated virtual function overrides
//{{AFXVIRTUAL(Clnfo)
protected:
// DDX/DDV support
virtual void DoDataExchange(CDataExchange* pDX);
//} }AFX VIRTUAL
// Implementation
protected:
1/ Generated message map functions
//{{AFXMSG(Clnfo)
virtual void OnOK;
virtual void OnCancel ()
virtual BOOL OnInitDialog;
//} }AFXMSG
DECLARE MESSAGE MAP ()
private:
Figure B.1l. Class Declaration of Clnfo.
A partial listing of class Clnfo is shown in Figure B.l1. Clnfo is a dialog box with
which users can specify general parameters. As a regular dialog class, C Info uses member
variables to store parameters temporarily. Method DoDataExchange ()is used to map data
176
between controls and member variables. Any update of parameter data will be sent to the
CStockDoc object through the document's data exchange routines. To create a Clnfo dialog
box, simply call the Clnfo constructor, and then invoke its DoModal () method:
Clnfo infoDig;
infoDig. DoModal
Figure B.12 is a screen dump of a
C Info
;
dialog box and its creating process. This dialog box
was invoked by a command handler under menu "Edit".
2ndrn#ec
Minge jl
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stan
Cetchalsility
lb
ManAge
2
b
emr
Bnne
OK
Trend
Cancel
I
Fi5her3eleceiry
ndYeaz
Natur&M
Vh Patametems
RecrudOphons
w Wnt()))
nstani
SPeYenri
r Random
2nd intlec
Inital at Equilibrium
102
Fish Modal
Sane
10
Trend
r-
islinfic age
Sus Sampling
2
surveyO
lslslope
sample size
00
Age lyn3
2nd infic age 5
2nd slope
Ii
SueySelecti
Num Subslock
Istinfic age
1
1 nt
Fishe
sample size
lnpe
2
11
Sampling
400
#snmpiepetvr 50
2nd info age ji 0
2nd slope
Reac
stedl gMicmnnoft Word -mae.
101
Ii
1
NUM
ntock-MictosoftDev jiUnbfled - stock
CaptureEze97 Previe.
I
Figure B.12. A Clnfo Dialog Box Invoked Inside a Graphical View.
8 4J 841 Ptl
177
B.3.1.4 Class CRecruitDlg
class CRecruitDlg
:
public CDialog
/1 Construction
public:
CEont * mpFont;
CRecruitDlg(UINT nStartYear, UINT nNumEditCtrl, CWnd* pParent = NULL);
// standard constructor
// Dialog Data
//{ {AFXDATA(CRecruitDlg)
enum
IDD = IDD DIALOG RECRUIT };
// NOTE: the ClassNizard will add data members here
//}}AFX DATA
{
/1 Overrides
// ClassWizard generated virtual function overrides
// { {AE'X VIRTUAL (CRecruitDlg)
public:
virtual void OnSetFont(CFont* pEont);
protected:
virtual void DoDataExchange (CDataExchange* pDX)
//} }AFX VIRTUAL
// DDX/DDV support
public:
// for dynamic creation of controls
UINT mcEditCtrl;
UINT
mnStartYear;
CArray<float, float>
mnRecruitArray;
CArray<CEdit, CEdit&>
mctrlEditArray;
CArray<CStatic, CStatic&>
mctrlStaticArray;
// Implementation
protected:
// Generated message map functions
// { {AFX MSG (CRecruitDlg)
virtual BOOL OnInitDialog;
//} }AFXMSG
DECLARE MESSAGE MAP ()
Figure B.13. Class Declaration of CRecruitDlg.
The class declaration of CRecruitDlg is shown in Fig. B.13. CRecruitDlg is a
dialog box for specifying the yearly recruitment. Since recruitment numbers are only available
during run time, we can not statically pre-create all the edit control box at compile time. To
178
create edit control and label control at run time, we need to save the font of the dialog box into
a member variable (Fig. B.14), creating a specified number of control objects in a constructor
(Fig .B.15), and displaying control windows associated with these control objects during
dialog initialization (Fig. B.16). Since the number of controls can vary considerably, we
should arrange them evenly at run time. Figure B.l7 shows two CRecruitDig dialog boxes
with different numbers of controls. The instantiation of a CrecruitDlg is similar to that of
Clnfo, the only difference being that the constructor of ORe cruitDig takes 2-3
arguments.
void CRecruitDig: :OnSetFont (Cpont* pFont)
mpFont = pFont;
Figure B. 14. Font Saving Method Called by Windows.
CRecruitDig: :CRecruitDlg(
UINT nStartYear,
UINT nNumEditCtrl,
CWnd* pParent /*=NULL*/)
CDialog(CRecruitDlg: :IDD, pParent),
mnStartYear (nStartYear),
mcEditCtrl (nNumEditCtr1
mnRecruitArray. SetSi ze (mcEditCtri);
for (mt i=0; i<mcEditCtrl; i++
mnRecruitArray [i] =0;
mctrlEditArray. SetSize (m oEditCtri)
mctrlStaticArray. SetSize (m oEditCtrl)
Figure B.15. Dynamic Creation of Control Objects.
179
BOOL CRecruitDlg: :OnlnitDialog()
//dynamically create all the static and edit controls
CRect rectClient;
GetClientRect ( &rectClient);
// more initialization and position calculation here
// dynamic creation of controls window
for (mt i=0; i<mcEditCtri; i++
nthColumn = i/numRows;
xStatic = nthColumn*columnWidth +
(coiumnWidth - 2*ctrlwidth_4)/2;
xEdit = xStatic + ctrlWidth +4;
yStatic = yEdit = (i%numRows)*rowHeight;
itoa
m_nStartYear +i, bufYear, 10);
(
mctrlStaticArray[i] .Create(
CStringY'Year ") +CString(bufYear),
WSVISIBLE ISS RIGHT,
CRect
CPoint(xStatic, yStatic), sizeCtri),
(CWnd*) this
WSCHILD
(
m_ctrlStaticArray[i] .SetFont (mpFont);
mctriEditArray[i] CreateEx
WSEXCLIENTEDGE,
"EDIT",
"EDIT",
WSCHILD
CRect
(
WSVISIBLE WSTABSTOP ES LEFT,
CPoint(xEdit, yEdit), sizeCtrl),
this,
IDC RECRUIT BASE+i
);
mctriEditArray[i] .SetFont(mpFont);
CDialog: :OnlnitDialog()
GetDigltem ( IDC RECRUIT BASE) ->SetFocus
return FALSE;
Figure B.16. Dynamic Creation of Control Windows.
;
I 80
Year 77
OK
Year 7811800
Cancel
Year 7913000
Year 8012000
Year 81 11600
Year 82
Year 8313000
Year 8413200
Year 85 Jzeoo
Year 86 127001
Year 5013000
Year 63
Year 7611200
Year 89 Jo
Year 5112000
Year 6413200
Year7ljlloo
Year 90 Jii
Year 52 14000
Year 6512300
Year 78 11000
Year 9110
Year 5312000
Year 6612400
Year 7911200
Year 9210
Year 54
Year 6711600
Year 80 11200
Year 93 Jo
Year 5515000
Year 6811400
Year 8112300
Year 94 Jo
Year 5613000
Year 6913400
Year 82110001
Year 9510
Year 5712000
Year 7012300
Year 8310
Year 96 Jo
Year 56 Jizoo
Year 7111500
Year 84 Jo
Year 97 Jo
Year 5915000
Year 7213400
Year 85 Jo
Year 6012300
Year 7313400
Year8G 0
Year 6111700
Year 7414500
Year87 0
Year 6212500
Year 7511000
Year88 0
________
OK
Cancel
Figure B.17. Screen Shots of CRecruitDlg Windows with Dynamic Control Creation.
181
B.3.1.5 Class CSlct View
class CSlctView
:
public CFormView
public:
CSlctView()
enum { IDD = IDD FORM SELECTIVITY };
mt mnFlnflecl;
/1 more publlic data member here (parameters that define curve
// Attributes
CStockDoc* GetDocument ((;
// Operations
CBrush mbrushwhite;
void DrawSelectCurve
;
/1 Overrides
virtual void OnlnitialUpdateQ;
protected:
virtual void DoDataExchange (CDataExchange* pDX( ;
/1 DDX/DDV support
virtual void OnUpdate(CView* pSender, LPARAM lHint, CObject* pHint);
virtual void OnDraw(CDC* pDC);
// Implementation
virtual -CSlctView()
II Generated message map functions
//{ {AFXMSG(CSlctView)
afxmsg void OnHScroll (DINT nSBCode, UINT nPos, CScrollBar* pScrollBar);
afxmsg void OnVScroll(UINT nSBCode, DINT nPos, CScrollBar* pScrollBar);
afxmsg void OnComrnitO;
afxmsg HBRUSH OnCtlColor(CDC* pDC, CWnd* pwnd, UINT nCtlColor);
afxmsg void OnButtonGrid();
//} }AFXMSG
DECLARE MESSAGE MAP ((
private:
bool mbGridOn;
void UpdateDocFromControls 0;
void enableCommit( bool bEnable);
bool mbNeedComrait;
COLORREF mcolorFish;
COLORREF mcolorSurvey;
mt ConvertSlopeToPos (float slope)
void UpdateControlsFromDoc ((;
float ConvertToSlope
const mt vscrollPos)
(
Figure B.18. Class Declaration of CSlCtView.
The class listing of CSlCtView is shown in Fig. B.18. As mentioned earlier, one of
the most important characteristics of a fish stock is its selectivity curve. There are two
182
different kinds of selectivity curves, one associated with the fishery and the other with the
survey. Each selectivity curve is defined by 4 parameters that control the shape of the
curvature. Dependent upon the values of the 4 parameters, the shape of the selectivity curve
varies considerably. Since there is no intuitive mapping between the values of the parameters
and the shapes of the curve, it is necessary to create a graphical tool to ease the process. Class
CSlctView is designed to satisfy this objective. Within CSlctView window, both the
numerical values of selectivity parameters and the curvature they represent are displayed
together, thus the user can check the match between value and shape. The parameters are also
represented in "analog" forms: positions of the vertical scroll bars indicating the values of
slopes and sliders referring to the inflection ages. By dragging the slider bars or pushing the
scroll buttons with the mouse, the user can easily modify the values of the parameters and
immediately see the change in the selectivity curves. Whenever he is satisfied with the curve,
the user can click the "commit" button to make the change permanent. The idea of committing
is borrowed from database design and the use of commit here is mainly for efficiency
considerations. If we let CSlctView continuously updates CStocDoc's data for each minor
change of CSlctView itself, OStockDoc will also continuously send messages to all other
views that are attached to it, causing them to update themselves at the same rate. By
displaying both the fishery selectivity curve and the survey selectivity curve within the same
graphical window, we make the comparison easy and straightforward. When viewing curves,
some people want to have gridlines to help them determine the Y value at a given X value,
while some others don't like this feature. We supply gridline as an option. Users can turn it on
or off by clicking the "grid on/off' button. Fig. B.19 shows screen dumps displaying the
features listed above. Because the actual implementation of class CSlctView involves
detailed Windows message handling and lengthy graphical drawing manipulation, here we
choose to omit the description of the actual coding techniques.
183
DIII H ILJi
FisherySelestyPeremeters
.J
J
I
2ndslopa
slope
JJ
7
:J
2nd intlec
60
J
....
tetinflec
St slope __i
6
60
2nd slope
20
33
J
4
Selectivity Curves
Sel(%)
:J
Agetyr.)
I
2
4
tO
6
6
J
letinflec.
2nd inIlec.
J
Commit
God cft
24
Reedy
NU4
I!_fli
Fishery Selectn.ity Prwneters
OI
lotslope
0.4
:LJ
2
j
Selectivity Curves
Sal. (Y)
2ndslope
15
100
-
00-
:J
1st inIlec
-_j
2nd mIsc
J
28
60
40
-
20
slope
-16
2nd s1ope
1 SI
50
:J
12
Ondinfiec
16
24
Age (yr,
32
J
lstrnflec
J
Gndon
27
Reedy
Figure B.19. Screen Dump of CSlctView windows.
NUM
184
B. 3.1.6 Class CText View
class CTextView
public:
:
public CScrollView
CTextView ()
DECLARE DYNCREATE (CText View)
II Attributes
public:
CStockDoc*
GetDocument));
CFont* GetFontQ;
CSize
CSize
GetDocSize() const
GetCharSize() const
return mDocSize;
{
{
return m_ViewCharSize;
1/ Operations
public:
void changeFont));
1/
Overrides
public:
virtual void OnDraw(CDC* pDC, mt nFirstLn, mt nLastLn, mt nXPos=O,
mt nYPos=O)
virtual void OnDraw(CDC* pDC);
virtual void OnlnitialUpdate));
protected:
virtual void OnUpdate)CView* pSender, LPARAM lHint, CObject* pHint);
// Implementation
protected:
virtual -CTextView
;
void ComputeViewMetrics 0;
void ComputeVisibleLines(CDC* pDC, int& nFirst, int& nLast);
II
1/)
Generated message map functions
{AFX MSG (CTextView)
afx_msg void OnKeyDown(UINT nChar, UINT nRepCnt, DINT nFlags);
afxmsg void OnUpdateFileNew)CCmdUI* pCmdUI);
afxmsg void OnUpdateFileOpen(CCmdUI* pCmdUI);
//} }AFXMSG
DECLARE HESSAGE MAP ()
// member variables
CSize m_ViewCharSize; /1 Dimensions of character in device units
CSize
mDocSize; 1/ Document size in device units
CFont* m_pFont;
II
/1
Current font
using different colors for concnent text and data text
COLORREF
mcolorConsnent;
COLORREF
mcolorData;
private:
bool isCormnent )CString & str)
Figure B.20. Class Declaration of CTextView.
185
The class declaration of class CTextView is shown in Fig.B.20. A ClextView is
the textual representation of the characteristics of the stock as well as its fishery and survey.
This representation reflects the content of the ASCII file ('true parameter file" in Fig. B.1) to
be used as input for the simulation program. To facilitate the understanding of the data,
comments were inserted and displayed in a different color. Since the content of the textual
view is usually larger than a normal window area, we derive CTextView from CFormView
to support scrolling. Several member functions are supplied within CTextView to increase
the flexibility of the class. For example, method OnKeyDown () (Fig.B.21) maps regular
keyboard operation such as "page up" and "page down" with appropriate scroll movement;
The change Font
(Fig. B.22) command can be used to select any font available in the
system . A Screen dump of CTextView window is shown in Fig. B.23.
void CTextView: :OnKeyDown(UINT nChar, UINT nRepCnt, UINT nFiags)
switch (nChar)
case VKHOME:
OnVScroll(SB TOP, 0, NULL);
OnHScroll(SB LEFT, 0, NULL);
break;
case VKEND:
OnVScroli(SB BOTTOM, 0, NULL);
OnHScroil(SB RIGHT, 0, NULL);
break;
case VKUP:
OnVScroil(SB LINEUP,
break;
0, NULL);
case VKDOWN:
OnVScroll(SBLINEDOWN, 0, NULL);
break;
case VKPRIOR:
// more codes
Figure B.21. Method OnKeyDown () of Class CTextView (partial listing).
186
void CTextView: :changeFont()
CFont * pFont = GetFont;
LOGFONT
if;
pFont->GetObject(sizeof(LOGFONT), &lf);
CFontDialog dlg(&lf, CF'SCREENFONTS
CFINITTOLOGFONTSTRtJCT);
I
if(dlg.DoModal() == IDOK)
if (mpFont)
delete mpFont;
mpE'ont = new CFont;
if (mpF'ont)
mpFont->CreateFontlndirect (&lf);
1/
This will cause Onupdate() to be called ensuring
that our cached metrics and scrolling get updated
GetDocument ->UpdateAliViews (NULL);
//
Figure B.22. Method changeFont () of Class CTextView.
Ele
I
Edit
II
View
I
Help
I
multion
I?L
% Fishing Mortalities
% trend=0.000000
0.200000 0.200000 0.200000 0.200000 0.200000 0.200000 0.200000
% Catchability q
% trend=0.000000
0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000
% Fishery Selectivity.
% option is:
1
END
% specified by double logistic function:
% inflcAge(fl) : 2.000000; slope(fl) :
1.000000;
% inflecAge(f2): 5.000000; slope(f2): 1.000000;
2.000000 1.000000 5.000000 1.000000 END
0.410154 0.739675 1.000000 1.000000 0.739675 0.410154 0.183883
% Number of Subtocks:
NUM
Figure B.23. Screen Shot of CTextView Window.
187
B.3. 1.7 Class CMainFrame
class CMainFrame
public CFrameWnd
:
protected: // create from serialization only
CMainFrame
;
DECLARE DYNCREATE (CMainFrame)
// Operations
public:
// Overrides
/1 ClassWizard generated virtual function overrides
//{ {AFXVIRTUAL(CMainFrame)
virtual BOOL PreCreateWindow(CREATESTRUCT& cs);
//} }AFX VIRTUAL
// Implementation
public:
virtual -CMainFrame ()
protected:
// control bar embedded members
CStatusBar mwndStatusBar;
CToolBar
mwndToolBar;
// multiple view support
CTextView
mpCTextView;
CSlctView * mpCSlctView;
/1 Generated message map functions
protected:
// { {AFX MSG (CMainFrame)
afxmsg mt OnCreate(LPCREATESTRUCT lpCreateStruct)
afxmsg void OnViewSelectivity;
afxmsg void OnViewText;
afxmsg void OnUpdateViewText (CCmdUI* pCmdUI);
afxmsg void OnUpdateViewSelectivity(CCmdUI* pCmdUI);
afxmsg void OnViewChangeFont;
afxmsg void OnUpdateViewChangeFont (CCmdUI* pCmdUI);
afx_msg void OnSimulationStart;
afxmsg void OnSimulationTextfile
afxmsg void OnEditGeneralparameters Q;
;
afxmsg void OnEditRecruitment ()
//} }AFXMSG
DECLARE MESSAGE MAP ()
private:
enum EnumView
TEXT =1, SELECTIVITY=IDD FORM SELECTIVITY
void SwitchToView
EnumView nView);
{
(
Figure B.24. Class Declaration of CNainFrame.
};
188
The class declaration of CMainFrame is shown in Fig. B.24. The major task of class
CMainFrame is to map various menu command messages to appropriate member functions
of the active view. For example, when the user invokes the "Change Font" menu item from
"View" menu (Fig. B.25), the command is mapped toCTextView's change Font ()
member function. CMainFrame also handles updates of the user interface object. When a
user pulls down a menu, each menu item needs to know whether it should be displayed as
enabled or disabled. For example, if the current active view is CTextView, when the user
pulls down the "View" menu, while item "Text" should be disabled (grayed), item
"Selectivity" must be enabled(blacken) so that the user can easily switch to the CSlctView
window (Fig. B.26). To achieve the effect, we map UT update messages to appropriate
message handler functions (Fig.B.27).
File
FOIl
View
Help
SirosilIioo
00 00 oo!o?'o%0o0 0000 )0 0 0 0 < 0000000000 ,0 00000000 i0
00
tiuio pa*ainetei
?Ixf
o Explanation
afer 'o0 will b
e
To,rnirinl
n0es New Ronu.in
0ENI)11 ettino
'tWingdinge3
'o MAX. AGE ( ii
'!o O3tattiii
J 20
j
AaBbYyZz
10 END
MIN AGE (
C,ncel
1
14
10
10
I
I
-
1
P0,10 lnloi
'F Wnp,dine
'tWingdino2
I END
..d
'F Webdingo
0edeflL
0000 o°o° e°o° 000000 ,0 00 00 00 00 00
Ei11
ii
VeefleIn
and E
77 88 END
n Expacted Wet8.ht-At-A8e (in kg),
'Oe in Vo Bertal1anfi curve, Wint- 10.000000. k200000. t00 000000
% Kvalue
0200000 END
0.059562 0358325 0.918488 L669847 2525805 3.412475 4276437 5083673 5815579 6.464623 END
___I
Reo1y
istnrtI
Mieioeoft Word ross
J
steck- MwreooltOee
. Untitled
stock
HUM
3C.sptereEoe0? Preore
Figure B.25. Screen Shot of Font Selection Process.
ilJ 122PM
189
File
Fdit
Help
I1l
eIectivity
In,
?289
muIation
Change Font
'
Toolbar
t /'thingofthesiarIfeBr).
conz/xnctn.
IJ
-j
706482402 78 7659 11S1.286
Status Bar
NJUM.
UflTBF:
[e
Fdit
11
Help
Text
Toolbar
Status Bar
I
..lDIxI
Simulation
1
-1
NUM
Figure B.26. Disabling and Enabling of a Menu Item Command.
void CMainFrame: :OnUpdateViewSelectivity(CCmdUI* pCmdUI)
1/
Only enable the graphic view menu if the current view
is the text view.
pCmdUI->Enable
II
GetActiveView 11 ->IsKindOf (RUNTIME CLASS (CTextView)));
void CMainFrame: :OnUpdateViewText (CCmdUI* pCmdUI)
II
Only enable the text view menu if the current view
II is the graphic view.
pCmdUI->Enable
GetActiveView()->IsKindOf(RUNTIMECLASS(CSlctView)));
Figure B.27. Message Handlers for UI Update.
II,I,
CMainFrame class also takes care of the functionalities of the menu 'Simulation".
There are two menu items under "Simulation" menu, 'Text File" and "Start". If item "Start" is
clicked, the member function OnSimulationStart () (Fig.B.28) will be called. As a
result, the actual simulation program will be invoked from a separate thread. When item "Text
File" is invoked, method OnSimuiationTextfiie () (Fig. B.29) is called and then a
dialog box (CText Dig object) pops up, prompting the user to save the contents into an
ASCII file to be used later by the simulation program.
void CMainFrame: :OnSimuiationStart()
mt nChoice = AfxMessageBox( IDS SIMULATION ALERT, MBOKCANCEL);
if
(
IDOK == nChoice)
DWORD dwSimThreadlD;
HANDLE hThread= CreateThread( NULL, 0, simThread, NULL, 0,
&dwSimThreadlD);
CioseHandie ( hThread);
Figure B.28. Method OnSimuiationStart () of Class CMainFrame.
191
void CMainFrame: :OnSimulationTextfile()
CTextDlg dig;
mt nChoice=dlg. DoModal
if (IDOK != nChoice)
return;
;
CDocument* pDoc = GetActiveDocument;
CStockDoc *pstockDoc = (CStockDoc *)pDoc;
ofstream out (dlg.mstrTextFileName);
out<<"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"<<endl;
out<<"% file name: "<<dlg.mstrTextFileName<<endl;
CStringList *pLineList = pStockDoc->GetLineList;
CString
strLine;
POSITION
pos = pLineList->GetHeadPosition( );
while
NULL != pos)
(
strLine = pLineList->GetNext (pos);
out<<strLine<<endl;
out. close ()
CString str;
str += "Data Pile \" + dig.mstrTextFileName +
+
AfxMessageBox
"\" \nwas created!"
" You may use it in actual simulation.";
(
str, MBOK
I
MBICONINFORMATION
);
Figure B.29. Method OnSimulationTextfile() of Class CMainFrame.
B.3.2 The Main Simulation Program
The main simulation program is involved primarily with mathematical and statistical
manipulations. We implemented it as a console application and named it "Sim.exe". The
application can be divided into three logical blocks: input parsing, mathematical and statistical
calculation, and output data formatting.
192
B. 3.2.1 Input Parsing
Input parsing includes parsing both the command line argument and the true input
parameter file. Although the deterministic parameters are contained in the input file, factors
that control the form and degree of randomness must be available before the simulation can
if (argc ==l)
cout << "Enter the name of file that specifies the simulation:
cin>>datafile;
cout<<"Enter output file prefix (3 characters)
:
cin>>pre fix;
cout<<" Is initial ages composition at equilibrium (y/n)?:
cin>>tempChar;
if ((tempChar !='y') && (tempChar !=
lnitialAgelsAtEquil=FALSE;
1/ more interactive input codes
";
else if (argc >1)
//parse comandline arguments
for
mt 1=1; i< argo; i++)
if (strcmpi (argv[i], "-p") ==0)
//perfect data needed
stockDivideError=O;
landingError=O;
discardError=O;
effortError=0;
bioweightError=O;
useSize =FALSE;
useTrueCatchAtAges=TRUE;
useTrueSurveyAtAges=TRUE;
surveyBiomassError =0;
copies =1;
createPerfect=TRUE;
if ((argc
6) && (argc
=7))
usage();//show how to set commandline args
(
else if (strcmpi (argv[i], "-ia") == 0)
// more commandline parsing codes
else
usage(); // display how to set comxnandline args
Figure B.30. Code Fractions of Command Line Parsing.
193
actually run. These controlling factors include the choice of random distributions (normal,
lognormal, multinomial, uniform, and etc.), values of the distribution function parameters
(mean, standard deviation, and etc.), and the number of replicate output files (50, 100, 1000).
Users can put all the controlling factors into the command line or specify these one by one
interactively. The code fraction in Fig. B.30 implements this process. Notice that putting all
factors into the command line makes batch processing much easier.
The process of parsing the true input file simply skips comments and reads the true
parameter values into variables or containers. The format of the data arrangement is strictly
checked during the serialized reading. Fig. B.3 1 is a partial listing of the relevant code section.
char* usefile = convert( datafile.cstrO);//skip off comment
ifstream in(usefile)
//////////////////////////////////////////////////////////////
//
declares variables and get their values from the data files
//////////////////////////////////////////////////////////////
//read maxAge and minAge:
in>>maxAge; checkEnd(in); //check format of data arrangement
in>>minAge; checkEnd(in);
//read startYear and endYear:
in>> startYear>>endYear; checkEnd(in);
//read k value
float kValue;
in>>kValue; checkEnd(in)
//read expected weight-at-age.
vector<float> wt (maxAge);
for ( mt i =0; i<maxAge; i+-1in>>wt [ii;
checkEnd(in)
// more input file parsing codes
Figure B.3 1. Code Fraction of Input File Parsing.
194
B.3.2.2 Numerical Simulation
The simulation block involves heavy data manipulation. To make the calculations
efficient, we implemented several container structures (e.g., 3D-matrices) to store data. Fig.
B.32 shows the declaration of a 3-dimension matrix. Since the simulation involves various
kinds of random numbers, we also implemented a series of random number generating
functions, including generators for normal, lognormal, multinomial, and uniform random
numbers. Figure B.33 shows the implementation of the random number generator for a normal
distribution using the polar method.
1/
class tritrix
three dimensional arrays
//
template <class T>
class tritrix
public:
tritrix( unsigned mt layers, unsigned mt numberOfRows,
unsigned mt numberOfColumns);
tritrix (unsigned mt layers, unsigned mt numberOfRows,
unsigned mt numberOfColumns,
T
initialValue);
-tritrix ()
matrix<T> & operator
]
(unsigned mt index) const;
mt numberLayers() const;
private:
vector<matrix<T> *>
nmatrix;
Figure B.32. Declaration of Class tritrix.
195
// random number generator for uniform distribution
float randU( float low,
float up)
assert( low <= up);
up - low)*(float)rand() / RAND MAX);
return
low +
(
(
// random number generator for normal distribution
float randN( float mu, float sigma2)
//using polar method generate 2 normal r.v. Randomly
I/choose one to return
float s=5;
float ul, u2, vl, v2,xl, x2;
s>l)
while
(
ul=randU
u2=randU
vl=2*ul_l; v2=2*u2_l;
s=vl*vl+v2*v2;
;
;
float temp = sqrt( _2*log(s)/s);
xl= temp*vl*sqrt(sigma2) + mu;
x2 =temp*v2*sqrt(sigma2) +mu;
if
random(2) ==l)
return xl;
return x2;
(
Figure B.33. Random Number Generator for a Normal Distribution.
The actual numerical simulation can be summarized in the following steps:
1.
For each year, randomly split the population into sub-population called strata;
2.
For each stratum, calculate the true target values based on deterministic equations
described in section 2 of the report. Target values include growth, survival, catch,
discarding, age composition, and etc.
3.
Integrate randomness into target values to mimic the observation and measurement
process and merge all strata's data to get yearly-observed data.
The implementation of these procedures, albeit straightforward, is very tedious and errorprone. Fig. B.34 shows a small fraction of it.
196
//divide stock randomly into "nstrata" strata
zeroVect (tmpVect)
for
i=0; i<simYrs; i++
(
for (mt j=minAge-l; j<maxAge; j++
if (stockDividelsNormalError)
randNdiv( pop[i][j], tmpVect, stockDivideError);
else //logNormalError
randLogNdiv( pop[i] [j], tmpVect, stockDivideError);
for (mt k=0; k<nstrata; k++)
strata[i] [ii [k] = tmpVect[k];
// pop( in year i) is divided into strata now.
//calculating real catches from each strata:
for
j=minAge-l; j<maxAge; j++
/1 initialize with zero.
if
< maxAge -1)
j
if
i<simYrs -1) pop[i+l] [j+l] =0;
else
endBioNum[j] =0;
(
(
(
tmpZ = M{j] + F[i]*slct[j]; //tmpZ is just Z: total mortality.
realCatchNum[i][j]= pop[i][j]*slct[j]*F[i]/tmpZ*(l_exp(_tmpZfl;
realCatchwt[i][j] = realCatchNum{i][j]*wt[j];
for (mt k =0; k<nstrata; k++)
strataCatch[i][j][k] =strata[i][j][k]* slct[j]*F[i]/tmpZ
II
/1
* (l-exp(-tmpZ)
more codes for numerical calculation
Figure B.34. Partial Listing of Codes for Numerical Simulation.
B. 3.2.3 Formatting Output Files
As mentioned earlier, the format of the output files must follow the rules set by Stock
Synthesis. A clear understanding of these rules is a prerequisite for a successful
implementation of the block. Based on these format rules, we create a template file (also
called the default file) for each type of output, and then modify the template for each replicate
file. For example, one type of output file is called the parameter file (not to be confused with
the true parameter file generated by "Stock"). We firstly create a default parameter file (Figure
B.35) based on the configuration of the simulation. When it is time to output the actual
replicate file, we modify the template based on the values of the observed random data (Figure
B .36).
197
//creat a default parameter file. Other parameter files are just
//slight modification of this default file.
mt parHandle;
assert ((parHandle=creat( "sim.par", SIREAD
I
SIWRITE))>=O);
fstream par;
par.open( "sim.par", ios: :in
ios: :out)
par.setf(ios: :showpoint);
par<<"SIM00000.DAT
\n"<<"SIMOOOOO.BIO"<<endl<<"RUNOOOOO.RUN
<<VVSIM00000 PAR
<<"run labels goes here\n";
par<<BEGDELF<<"
"<<ENDDELF<<endl
<<LAMSTART<<"
"<<LAMBDA2<<endl
<<MAXCROS S<<endl
<<"1 READ HESSIAN\n"
<<"SIMOOOOO.HES\n 1 WRITE HESSIAN\nSIM00000.HES\n"
<<
.00l\n";
"<< minAge<<"
par<<minAge<<" "<<maxAge<<"
"<<maxAge
<<"
MIN.AGE,MAX.AGE, SUMMARY AGE RANGE\n";
par<<startYear<<"
"<<endYear<<endl;
par<<"l 12 0 0 O\nl.00\nl.00\n"
<<"0.00 0.00 0.00 0.00
SEASONAL WT. FACTORS\n";
par<<"l
NEISHERY NSURVEY\n"
1
<<l<<" N SEXES\n";
// more codes for default parameter file creation
Figure B.35. Code Fraction for Creating Template Parameter files.
copyFile ("sim .par", parFile);
//modify the content of "parFileName".
alterOneLine
parFile,
1, outDataFile);
(parFile, 2, bioFile)
alterOneLine
parFile, 3, prefix +intToChar(cp) + ".run");
alterOneLine
alterOneLine
parFile, 4, newParFile);
alterOneLine (parFile, 10, prefix + intToChar(cp)+ ".hes");
// more codes for modifying template file
Figure B.36. Code Fraction for Modifying Template Parameter File into Actual Output File.
198
B.3.3 Statistical Utility
The running of Stock Synthesis generates a large number of files that contain the various
estimated parameters. The statistical program "Stat" can be used to summarize the output files
into different forms of statistics. These statistics can be pulled into a commercial statistical
software package for further analysis. The algorithm used in "Stat" can be summarized as
follows:
1.
Open Stock Synthesis's output file one at a time;
2.
For each file opened, sequentially search the entire file for the value of interest and
read it into a vector-like container. If the container get so big that memory become
low, serialize the container onto disk;
3.
After all files have been searched, calculate all the required statistics based on the
element values of the container. If the container is too big, serialize the data from
disk and compute partial statistics first.
As an example, a fraction of codes that search file for values of ty
"RECRUIT" and "SUM-
BlO" is shown in Fig. B.37.
in>>curreflt;
while (current 1= "RECRUIT:")
in>> current
±n>>current; in>>current; //skip first 2 years before fishery
for
1=0; i<simYears; i++)
(
in>>temp;
recruit<<temp<<"
";
recruit<<endl;
//sum-bio:
±n>>current;
while (current !="SUM-BIO:")
in>>current;
// more codes
.
.
Figure B.37. Code Fraction for Searching Values of Type "RECRUIT" and "SUM-BlO".
199
Appendix C: Common Simulation Methodology and Stock Synthesis Configurations
The experiments in Chapter two and Chapter three share some common features in
terms of simulation strategy and Synthesis configuration. Instead of repeating phrases in the
two chapters, we summarized their common description in this appendix.
All Monte Carlo simulations were conducted with a simulation package that we
developed for this study. The package consists of three C++ programs, namely the Stock
Definer, the Data Simulator, and the Statistical Analyzer. The attributes of a fishery system
can be specified with the Stock Definer program. The Data Simulator program simulates the
dynamics of the fishery system as defined by the Stock Definer and produces auxiliary data
used by the Stock Synthesis program. The Statistical Analyzer program summarizes the output
data produced by the Stock Synthesis program and compares them with the true values.
A typical fishery system that can be specified with the Stock Definer is composed of a
fish stock, a fishery harvesting the stock, an annual research survey monitoring the status of
the stock, and a series of age composition samplings from the fishery and the research survey
conducted by fisheries scientists. The specification of a fish stock involves the selection of
parameters that define the biological traits of the fish stock, e.g., average weight-at-age,
maturity-at-age, natural mortality, recruitment, and etc. The Stock Definer also allows you to
quantify the parameters that define the processes by which we observe the stock and its fishery,
e.g., fishing mortality, catchability, fishery selectivity, survey selectivity, sampling frequency
and sample size both for fishery and survey. The end result of the Stock Definer is a text file
used as the input to the Data Simulator program.
Both deterministic and non-deterministic (stochastic) methods were used by the Data
Simulator in the simulation of a fishery system. The deterministic method simulates the
200
dynamics of an age-structured fish population using the same deterministic equations that
underlie Methot's Stock Synthesis program. The stochastic method takes the true demographic
data produced by the deterministic method and generates random data sets that can be
analyzed directly by the Stock Synthesis program.
The Statistical Analyzer program scans the output files of Synthesis and summarizes
the Synthesis estimates into a series of statistics. It then compare these statistics with their
corresponding true values and generates comparison results that reflect the relative accuracy
and precision of Synthesis's estimates.
The fishery system simulated is composed of one fishery and one survey. The
simulated fishery generated data annually on total catch, age composition, and nominal fishing
effort. The simulated survey provided estimates of annual stock biomass and age composition.
Data for total catch, fishing effort, and survey biomass were assumed to follow lognormal
distributions and all random data were generated in a manner that they would be unbiased.
The Stock Synthesis program used in this study was the version released in 1999 for
the Windows 95 platform. The program's author, Richard Methot, provided it to us in August
1999. The Stock Synthesis program needs initial parameter values with which to start its
iterative search for the set of maximum likelihood parameter estimates. In this study, we gave
the Synthesis program the true parameter values as the initial values for the major experiments.
We also conducted two small exploratory experiments to examine the influence of using true
parameter values as the initial values. For each treatment of the simulation, we also let the
Data Simulator to generate a set of errorless data that we analyzed with Synthesis and thereby
verified an exact correspondence between the deterministic population equations of the Data
Simulator and those of Stock Synthesis.
One assumption in the Stock Synthesis model is that the data on catch biomass are
exact. Although actual landings data are reasonably accurate for many fisheries, the data for
201
the discarded portion of the total catch are usually a rough guess. For some fisheries, the
discarded portion can be substantial (Pikitch et al.1988), with the result that the errors in
estimates of total catch data can be considerable. In this study, the catch biomass data were
generated as lognormally distributed random variable with expected values equal to the true
value (Y) and with a fixed coefficient of variation for all years. The age composition data for
both fishery and survey were generated without age-reading error, but with either simple
multinomial sampling error (Chapter two) or compound-multinomial sampling error (Chapter
three). In either case, the Stock Synthesis program was then configured to treat the age
composition data as if they were generated with multinomial sampling error but without agereading error. The Stock Synthesis program was also given the true sample size used in
generating the sampling data. The fishing effort data were generated with expected value
equal to the true value (F/Q) and with a fixed coefficient of variation
(CVF)
for all years.
Synthesis was then configured to treat the fishing effort data as being lognormally distributed
and was given the true log-scale standard deviation for these data (CF). The survey estimates
of biomass were generated with expected value equal to the true value and with a fixed
coefficient of variation
(cv5) for all years. The Stock Synthesis program was then configured to
treat the survey biomass estimates as being lognormally distributed and was given the true log-
scale standard deviation for these data ().
The coefficient of variation (cv) values used in the generation of random data on catch
biomass, fishing effort, and survey biomass were on arithmetic scale. However, these data
were actually generated as lognormally distributed random variables. For these data, the mean
and standard deviation on the arithmetic scale (E[Y], V[Y]) are related to the mean and
standard deviation on the log scale (j.i, ) by the following:
E[Y]=exp(u+-a2)
(1)
202
(2)
v[y]= exp(2jt+2a2)exp(2p+2)
Given the values of E[Y] and V[Y], the values for
t
and
can be calculated from equation (1)
and (2).
In all the simulations, the instantaneous rate of natural mortality was constant with age
and through time. The Stock Synthesis program was then configured with the natural mortality
parameter fixed at its correct value. All stocks were unfinished prior to the start of the
simulated period and suffered an instantaneous rate of fishing mortality (F) of 0.07 per year
during the first year, with F increasing a fixed amount at the start of each year thereafter. The
true fishery catchability coefficient and the true survey catchability coefficient were constant
throughout each simulated period and were at the values of 0.003 and 0.1 respectively. The
selectivity coefficients for the fishery and survey were also constant throughout each simulated
period. All simulated fish stocks had no sexual dimorphism, with both female and male
sharing the identical growth rate and identical vulnerability to the fishing and survey gear. The
true weight-at-age data were generated with the following deterministic growth function,
W(a) = 10[1
exp(-0.2a)]3
(3)
where, the unit of W(a) is in kilogram.
For each simulated stock the maturity-at-age coefficients were constant throughout
each simulated period and the Stock Synthesis was given exactly the same information.
However, the long-lived stock did not share the same maturity-at-age coefficients as the shortlived stock in the simulation.