Marine & Freshwater Resources Institute
Fisheries Research and Development Corporation
Population Dynamics Expertise (Victoria)
V. S. Troynikov
November 1997
© Marine and Freshwater Resources Institute
ISBN: 0 7311 3168 1
The information contained in this document is solely for the use of the client for the
purpose for which it has been prepared and no representation is to be made or is to be
implied as being made to any third party.
CONTENTS
FRDC Project. 93/214.03 Final Report
Marine & Freshwater Resources Institute
NON-TECHNICAL SUMMARY......................................................................3.
FINAL REPORT.................................................................................................6.
PROJECT BACKGROUND.....................................................................................6.
OBJECTIVES.........................................................................................................6.
PROJECT OVERVIEW.............................................................................................6.
METHOD...............................................................................................................9.
RESULTS.............................................................................................................10.
BENEFITS............................................................................................................15.
FURTHER DEVELOPMENTS...............................................................................16.
FINAL COST........................................................................................................16.
APPENDIX 1
Intellectual Property and Valuable Information.....................................17.
APPENDIX 2........................................................................................................19.
Manuscripts
NON-TECHNICAL SUMMARY
93/214.03
Population Dynamics Expertise (Victoria).
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Principal Investigator:
Address:
Dr V. S. Troynikov
Marine and Freshwater Resources Institute,
P.O. Box 114
Queenscliff, Victoria 3225.
Tel: (03) 5258 0111 Fax: (03) 5258 0270
Email: v.troynikov@mafri.com.au
Objectives:
To provide additional expertise in fisheries population dynamics and modelling in
Victoria. To support better management of fishery resources and provide predictions
of the outcomes of fishery management measures.
The methodologies of mathematical statistics, stochastic processes, survival analysis
and computer modelling were used for:
1. The development of an effective method to utilise the information in growth and
allometric fishery data with high heterogeneity.
2. The development of the numerical algorithm for estimation of the length-at-age
distributions with corrections for sampling bias of fishing gear (size specific fishing
mortality).
3. The adaptation of the new mathematical tools for the study of the different
problems of growth dynamics in populations of various fish species.
4. The development of menu driven software that contains several stochastic growth
models, provides the best choice to fit for the given data and calculates biologically
meaningful indices of growth dynamics.
5. The application of the new growth models and biologically meaningful indices to
improve the accuracy of stock assessments.
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Non Technical Summary
Using new mathematical tools for the analysis of population dynamics data this
project has provided support for the management of fishery resources.
For adequate fishery stock assessment, the accuracy of the estimation of the size
distribution of individuals in the population is very important. For commercial
species, the catch often depends on the minimum legal length or size-specific
selectivity of the fishing gear. Therefore, the accuracy of the prediction of the catch,
depends directly on the precision of the modelling of the population length
heterogeneity. For example, abalone is an important commercial species in Australia
that cannot be accurately aged and exhibits extremely high heterogeneity in growth.
The choice of the model structure, that accurately reflects the distribution of actual
data, becomes an important component in fishery stock assessment.
A flexible unified approach for the stochastic parametrization of the dynamics of the
population data, has been used. New stochastic models have been developed to utilise
most of the information from a variety of different fishery surveys. The empirical
distributions of these data is a major input into these models. This has resulted in the
estimation of meaningful biological indices of the relevant fishery population. These
indices include the proportions of population that are relatively slow and fast growers
and the proportion with time of any given size class in the population, in particular,
the proportion that is above or below of the legal minimum length.
These growth models are in the form of probability density functions use in fishery
population dynamic models for risk assessment. This reduces the number of
assumptions in the resultant population dynamics models and make them more
appropriate for the given data. Population length frequencies and tag-recapture data,
using non individually identifiable tags, may be used for population growth and
mortality estimation. For example experiments using abalone that are marked with
coloured paint may be undertaken instead of individually numbered tags. This enables
tag-recapture experiments to be more cost effective and the possibility of increased
sample size will provide better estimates of population parameters.
Different stochastic versions of well known growth and allometric functions were
developed. For any given data-set, the most appropriate version can then be chosen
using suitable statistical criteria. Simple informative growth indices are calculated as
the moments of distributions. This has produced a package that is flexible and
applicable to a variety of fishery stock assessment problems.
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The new stochastic parametrization has adopted to study several particular problems:
1. Establishing legal minimum lengths for blacklip abalone (Haliotis Rubra) based on
stochastic growth models using length-increment data.
2. Estimation of seasonal growth parameters of abalone using the stochastic
Gompertz models for tagging data.
3 Modelling of growth increment heterogeneity in abalone harvested
off South Eastern Australia.
4. Models of vertebral growth at age heterogeneity in gummy shark (Mustelus
Antarcticus) harvested off South Eastern Australia.
5. Estimates of length-at-age distribution with correction for gillnet sampling bias in
gummy shark (Mustelus Antarcticus) from Bass Strait.
The software is written using FORTRAN with a simple, user interface. The package
contains twelve stochastic models for length-at-age and tagging data and the
numerical algorithm for estimation of length-at-age distribution with correction for
sampling bias of fishing gear.
These models have been a major input into the population dynamics model for the
quota-management of abalone fisheries of Victoria. This abalone model is now being
used for the risk assessment of management options for the fishery.
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FINAL REPORT
93/214.03
Population Dynamics Expertise Project (Victoria)
Project background
This project is the Victorian component of the national research program to provide
additional expertise in fish population dynamics.
Objectives
Specific objectives of the Victorian component are:
To provide additional expertise in fisheries population dynamics and modelling in
Victoria. To support better management of fishery resources and provide predictions
of the outcomes of fishery management measures.
The methodologies of mathematical statistics, stochastic processes, survival analysis
and computer modelling were used for:
1. The development of an effective method to utilise the information in growth and
allometric fishery data with high heterogeneity.
2. The development of the numerical algorithm for estimation of the length-at-age
distributions with corrections for sampling bias of fishing gear (size specific fishing
mortality).
3. The adaptation of the new mathematical tools for the study of the different
problems of growth dynamics in populations of various fish species.
4. The development of menu driven software that contains several stochastic growth
models, provides the best choice to fit for the given data and calculates biologically
meaningful indices of growth dynamics.
5. The application of the new growth models and biologically meaningful indices to
improve the accuracy of stock assessments.
Project overview
The modern approach to numerical analysis and predictive modelling of fishery
stocks uses integrated information about fish population. This information is
represented in the form of population dynamics models that enable comprehensive
numerical analysis. Therefore, the choice of the model structure, that reflect the
assumptions about the actual data, becomes an important component in any
procedure of stock assessment.
For adequate fishery stock assessment, the accuracy of the estimation of the size
distribution of individuals in the population is very important. For commercial
species, the catch often depend on the minimum legal length or size-specific
selectivity of the fishing gear. Therefore, the accuracy of the prediction of the catch,
depends directly on the precision of the modelling of the population length
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heterogeneity. For example, abalone is an important commercial species in Australia
that cannot be accurately aged and exhibits extremely high heterogeneity in growth.
In the framework of the random coefficient methodology, different distribution
functions can be used to approximate growth data. However, the properties of growth
models and the interpretation of the results of modeling depend not only on
distribution functions of growth parameters, but also on assumptions which are used
for construction of estimating functions. One widely used assumption is that, although
the growth of individuals differ, they can all be described by the same functional form
and the differences between individuals are contained in the coefficients. In other
words, an individual ‘knows’ all about it own growth history at the start of life. Once
the assumption about deterministic growth for an individual is established there are
implied assumptions about the distribution of residuals of individual growth data from
the deterministic growth functions (models) adopted for individuals; see, for instance,
Paler et al. (1991), James (1991) and Xiao (1994). The residuals based individual
models can adequately approximate the growth histories of individuals if residuals are
essentially smaller then the deterministic part of the length increment. However, for
some species, the growth of individuals shows that the residuals from the individual
models are large and therefore the estimated variance of residuals is large. This is one
reason why such models can predict negative size of animals. In a more general
context this assumption is equally inadequate biologically, because growth
characteristics of individuals (that are described by individual parameters) can be
randomly modified by many external factors. The main reason that the concept of
constant individual parameters is widely used, is its convenience in graphical growth
representation.
In a concurrent approach, growth is considered as a random process. Cohen and
Fishman (1980) and Deriso and Parma (1988) give examples of growth models
where stochasticity is incorporated into a deterministic growth function with
assumption about independence of random growth increments. However this
assumption is the essential limitation in the models of the biology of growth (Deriso
and Parma 1988, p.1064). Another method reformulates deterministic growth models
as stochastic differential equations. The growth is described as a modification of a
Wiener or Gaussian stationary process by a differential operator. As noted by Garcia
(1983, p.1064) some of these models can predict negative growth. In other cases the
properties of estimators require multiple observation of an individuals with equal
intervals between observation (Sandland and McGilchrist 1979, p.268).
The method used in this project does not imply deterministic growth of individuals.
Parameters of the models are the random processes. The individual history of growth
is considered as the realization of a random process X(t) that has the one dimensional
distribution F(x,t). For the modeling of a random process with a given one
dimensional distribution F(x,t) we can use random realisations with very different
properties (Troynikov 1984). It follows that different models of individual growth can
give the same model (distribution of length) for a population. This means that most
population growth data do not provide enough information for testing hypotheses
about individual growth history. In the present approach, growth data X(t) are
considered to have been sampled from a distribution F(x,t) where time is a parameter.
This method emphasizes the study of growth at the population level. The
heterogeneity in growth increment x within time t is treated as conditional on
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length l1 distribution F(x, t  l1) for positive x (this is an important distinction
from residual based models). Any additional hypotheses about individual growth are
acceptable, but must not be inconsistent with the properties of F(x,t) and F(x, t  l1).
Data with a single observation or a single recapture per individual do not provide
information for testing the assumption about deterministic or stochastic version of
individual growth. However, the stochastic versions of individual growth is more
flexible for the development of population dynamics models which include size
dependent biological properties of the population.
To approximate distributions F(x,t) and F(x, t  l1), growth models in the form of
probability density functions which include time as a parameter were used. The
method is applied for the development of models with one or more random
parameters for length-at-age, tag length-increment and allometry data. This method
uniformly applies different combinations of the deterministic growth functions and
different one dimensional density functions of random processes of growth
parameters. This enables the best choice between these models to be made for
approximating the data with different statistical properties. An approximation to
Kullback’s information integral is used for discrimination between models with
respect to fit to the data.
For development of these models, there are no additional assumptions made about the
independence of growth parameter distributions or the independence of the length
increment x. To avoid the biological inconsistencies of the models such as the
prediction of negative growth, growth parameters are represented by positive random
processes. In distinction from some stochastic growth models the variance V[X(t)] of
the random growth process is not specified as function of mathematical expectation
E[X(t)]. A likelihood is constructed without using deterministic growth models of
individuals with residuals. These features allow the treatment of biological data
without the additional restrictions or assumptions on the data, such as long time at
liberty and/or small variance of length increment.
Stochastic growth models currently in use, which are residual- based models, do not
adequately represent growth data with high heterogeneity. This leads to considerable
inaccuracy in the estimates of growth indices and consequently the incorrect
prediction and assessment of stock. In particular, the abalone stock assessment faces
this problem, due to high heterogeneity in abalone growth. Therefore it is important to
develop more flexible range of models for growth data parametrization. The following
illustrates a fundamental problem in the parametrization of growth and allometry data
by stochastic models.
Suppose that process (t) 0 with probability density function (p.d.f.) f(y, t)
represents the size of individuals, then for any time t the following equality should be
valid,
f(y, t)dy = 1.
(1)
The biological meaning of this equality is ‘there are no animals with negative length
in a population’. Note that for residual based models, or the models which use normal
distribution for growth parameters, this integral is less then one. If the value is close
to ‘one’ , then for some practical reasons, the model can be applied for data
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approximation. However, if the estimated coefficient of variation of the growth
parameter is large, then the negative tail of the distribution can be large and the
integral is significantly smaller then one. This means that the model does not
represent the distribution of size in a population, or in other words, the model is
biologically invalid (Xiao 1994). In practice, this means that the estimates of
important growth characteristics such as mean size E[, t] and variance V[, t] at age
t are biased.
Similar requirements are valid for the parametrization of size-increment data. Let 1
and 2 be the sizes at time t1 t2, and  = 2 -1 be the random size-increment, with
p.d.f. f(y, t2x, t1). If growth is monotonous then
f(y, t2x, t1)dy =1, otherwise f(y, t2x, t1)dy =1.
(2)
-x y
0y
If growth is not monotonous, then random increment  can be negative, but must be
-1, otherwise there is non zero probability for ‘individuals’ with negative size.
The models which use the assumptions about normally distributed size-increment or
growth rate (Sainsbury 1980, Xiao 1994), have values of these integrals less then one.
In the general case, such models are inconsistent with size-increment data with small
t and large heterogeneity of increments, and produce biased estimates of mean and
variance of the size-increments.
The new range of stochastic models for parametrization of growth and allometric
data gives the ability to avoid the problem of negative tail in size distribution (the
integrals (1) and (2) are equal to one) and provide flexible mathematical tools for the
study of fish populations with high growth heterogeneity.
References
All cited literature are in the manuscripts (Appendix 2).
Method
The new approach of stochastic parametrization of growth and allometry data is
described in the manuscript (see Appendix 2.1):
Probability density functions useful for parametrization of
heterogeneity in growth and allometry data
V.S.Troynikov
Marine and Freshwater Resources Institute, PO Box 114, Queenscliff, Victoria,
Australia 3225.
The problem of modelling of heterogeneity in growth and allometry is considered. In
the framework of the random coefficient approach a unified method of stochastic
parametrization of data is presented. The method does not use deterministic
description for characteristics for each individual. The method is applied uniformly
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for size-at-age, tag size-increment and allometry data. Von Bertalanffy growth models
with Weibull, gamma and log-normally distributed growth rate k are used as
examples to show the sensitivity of the stochastic parametrizations to growth
heterogeneity in a population. Simple informative indices for analysis of population
are presented on the basis of these models.
Results
The results are presented in the form of reports papers and software:
Second World Fisheries Congress, 28 July-2 August 1996 Brisbane, Australia,
Estimation and prediction of growth heterogeneity in the
context of fish stock assessment problems.
V.S.Troynikov
Marine and Freshwater Resources Institute, PO Box 114, Queenscliff, Victoria,
Australia 3225.
For an adequate fish stock assessment the problem of accuracy of estimation of
size distribution of individuals in the population is a basic one. For commercial
species, fishery mortality is defined by minimum legal length or size-specific
selectivity of fishing. Therefore, the accuracy of prediction for catch depends
directly on the precision of modelling of the population length heterogeneity.
Heterogeneity of growth can be caused by variation in environment or genetic
differences, and obviously, that type of heterogeneity of growth in population has
a “systematic character” and can not be adequately described in terms of
precision of measurement. We consider individual histories of growth as
realisations of a random process that has one dimensional distribution F(x,t) of
length x in cohort in time t. However, different random processes can have the
same one dimensional distribution. Sequentially, different models of individual
growth can give us the same model (distribution of length) for population. This
means that in most cases population growth data do not provide enough
information for testing hypotheses about individual growth. This paper
emphasises the study of growth at the population level. All our assumptions
relate to properties of F(x,t). Any additional hypotheses about individual growth
are acceptable, and the only minimum requirement is that it should not be in
contradiction with the properties of F(x,t). Similarly, in the case of a (more
conventional) deterministic growth model, the growth function is also not a
representation of individual growth, but a model of the growth of the biomass.
For modelling of growth using ageing or tagging data, we use special
conditional and unconditional density distribution functions. For building the
models we use deterministic growth functions with random growth parameters.
The general properties of growth models in the form of density distribution
functions are described. Using examples with the Weibull, Gamma and LogNormal distributed von Bertalanffy growth rate K we show the sensitivity of the
stochastic parameterisations with respect to growth heterogeneity in the
population.
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For numerical demonstration ageing data for Gummy Shark vertebrae ring growth
(from T. Walker, MAFRI) and tagging data for Abalone (H.rubra) (from
H.Gorfine, MAFRI) were used. Using examples of these data, we explicitly show
the size of the error which is caused by using expected values of growth
parameters for the estimation and comparison of biomass growth for populations
with high growth heterogeneity. New simple, informative indices for comparison
of population in growth and the management of fish stocks are proposed.
The prime outcome of this study is the development and testing of new
mathematical tools for significant improvement of accuracy in assessment and
prediction of fish stock for populations with high level of growth heterogeneity.
III rd International Abalone Symposium ,Abalone Biology, Fisheries and Culture,
October 26-31,1997, Monterey, California.
Estimation of seasonal growth parameters using a
stochastic Gompertz model for tagging data.
V.S.Troynikov1, R.W.Day2 and A.Leorke2
1. Marine and Freshwater Resources Institute, PO Box 114, Queenscliff, Victoria,
Australia 3225.
2. Zoology Department, The University of Melbourne, Parkville, Vic. 3052. Australia
Precise estimates of growth and growth heterogeneity are essential for
stock assessment, as abalone fisheries are managed in part by size limits. Yet
abalone growth is notoriously variable, and is known to vary widely between
seasons and sites. It is also well known that the growth of juvenile abalone does
not fit the commonly used von Bertalannffy model. We present a stochastic
Gomperz model for tagging data, in which asymptotic length is a random
parameter, and use it to fit tagging data for abalone of a wide range of sizes.
Every three months, over an 18 month period, abalone were collected using
SCUBA from within an area of approximately 200m by 200m on Point Cook reef,
in Port Phillip Bay. They were brought to shore, tagged, measured and returned
to the reef within 1-2 hours. Previously tagged abalone were found and measured
in situ with vernier calipers to minimise disturbance. Thus the data obtained
provide information on the growth of abalone for six consecutive seasons.
Consecutive increments over successive seasons were obtained for a subset of
animals. Sizes ranged from 15 mm to 125 mm maximum shell length. We show
that the use of this stochastic model, rather than a deterministic model, leads to a
more realistic estimation of actual growth increments, and allows an unbiased
estimation of the Gomperz parameter g, which reflects the acceleration of juvenile
growth with initial size. We estimate this parameter for a number of seasons.
The data show that juvenile growth varies more markedly with season than with
initial size, whereas in larger abalone, growth increments vary with initial length,
and are less dependent on season.
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Alternative approach for establishing legal minimum lengths
for abalone (Haliotis Rabra) based on stochastic growth
models for length increment data.
V.S.Troynikov and H.K.Gorfine
Marine and Freshwater Resources Institute, PO Box 114, Queenscliff, Victoria,
Australia 3225.
Selection of appropriate legal minimum lengths (LMLs) that conserve
proportions of abalone populations to ensure reproductive capacity is maintained
at sustainable levels is generally based on deterministic estimates of growth.
However, deterministic estimates simply provide average values of growth
parameters and give no indication of the proportion of individuals that may or
may not attain a specific LML. Consequently, deterministic estimates of growth
can be misleading and may result in setting inappropriate LMLs. Lengthincrement data from tagging for three H. rubra populations in Victoria, Australia
were analysed using a new Gompertz stochastic model for tagging data that we
present. The Gompertz growth model was chosen because although the more
commonly used von Bertalanffy model describes the growth of adult abalone, it
fails to adequately describe the earlier juvenile phases. In contrast, the Gompertz
model appears to accommodate both juvenile and adult growth. Outputs from
the stochastic Gompertz model for tagging data include quantile distributions of
L. Quantiles of L showed that 70-80% of the abalone in each study population
were likely to attain the LML and enter the stock. Alternatively, 20-30% of
each population could be regarded as conserved by existing LMLs. It is
presently unknown whether this level of protection will ensure the long-term
sustainability of these populations. If the proportion of abalone required to
provide sufficient egg production for sustaining a particular population is known,
then the stochastic Gompertz model for tagging data can be applied to select the
appropriate LML.
Workshop, South East Fisheries Committee Shark Research Group, Hobart
Tasmania, 21-23 April 1997,
Estimates of length-at-age distribution with corrections for
gill- net sampling bias in school shark (Galeorhinus galeus),
(Ed) T. I. Walker.
The following manuscripts contain the results according with the
Objectives (Appendix 2).
Objective 1. The development of an effective method to utilise the information in
growth and allometric fishery data with high heterogeneity.
.
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Probability density functions useful for parametrization of
heterogeneity in growth and allometry data
Vladimir S. Troynikov
Marine and Freshwater Resources Institute, PO Box 114, Queenscliff, Victoria,
Australia 3225.
In press: Bulletin of Mathematical Biology, Journal of the Society for Mathematical
Biology. (Appendix 2.1)
Objective 2. The development of the numerical algorithm for estimation of the lengthat-age distributions with corrections for sampling bias of fishing gear (size specific
fishing mortality).
Estimats of length-at-age distribution with correction for
gillnet sampling bias in gummy shark (Mustelus
Antarcticus) from Bass Strait
Vladimir S. Troynikov and Terence I. Walker
Marine and Freshwater Resources Institute, PO Box 114, Queenscliff, Victoria,
Australia 3225.
Submitted: Bulletin of Mathematical Biology, Journal of the Society for Mathematical
Biology (Appendix 2.2)
Objective 3. The adaptation of the new mathematical tools for the study of the
different problems of growth dynamics in populations of various fish species
Alternative approach for establishing legal minimum lengths
for abalone based on stochastic growth models for length
increment data.
V.S.Troynikov and H.K.Gorfine
Marine and Freshwater Resources Institute, PO Box 114, Queenscliff, Victoria,
Australia 3225.
In press: Journal of Shellfish Research. (see Appendix 2.3).
Estimation of seasonal growth parameters using a
stochastic Gompertz model for tagging data.
By Vladimir S. Troynikov1, Robert W. Day2 and Anne M. Leorke2
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1. Marine and Freshwater Resources Institute, PO Box 114, Queenscliff,
Victoria, Australia 3225.
2. Zoology Department, The University of Melbourne, Parkville, Vic. 3052.
Australia.
In press: Journal of Shellfish Research (see Appendix 2.4).
Vertebral size-at-age heterogeneity in gummy shark
(Mustelus antarcticus) harvested off south-eastern Australia
Vladimir S. Troynikov and Terence I. Walker
Marine and Freshwater Resources Institute, PO Box 114, Queenscliff, Victoria,
Australia 3225.
In preparation for publication. (see Appendix 2.5).
Objective 4. The development of menu driven software that contains several
stochastic growth models, provides the best choice to fit for the given data and
calculates biologically meaningful indices of growth dynamics..
The software is written using FORTRAN with a simple, user-friendly
interface. The three packages contain twelve stochastic models for length-at-age and
tagging data and the numerical algorithm for estimation of the length-at-age
distribution with the correction for the sampling bias of the fishing gear. The NelderMead simplex method is used for the numerical approximation of the maximum loglikelihood function. For the discrimination between models, with respect to the best
fit to data, the Kullback’s information mean is used.
The first package contains six stochastic versions of the von Bertalanffy and
Fabens growth models for ageing and tagging data with Weibull, gamma and lognormal random parameter k and two deterministic growth models.
The second package contains six stochastic versions of the Gomperz growth
models for ageing and tagging data with Weibull, gamma and log-normal random
asymptotic size and two deterministic models.
The third package contains the numerical algorithm for the estimation of the
length-at-age distribution of catch with the correction for sampling bias of fishing
gear. This algorithm is developed on the basis of the stochastic growth models for
size-at-age data with using the selectivity function of fishing gear.
The results of the growth estimation include the distributions of the size of
individuals in a population for any age, the dynamics of the quantiles of the size
distribution at age, dynamics of the proportion of any given size-class in a population
with age, the dynamics of mean and variance of sizes of individuals, the distributions
of von Bertalanfy growth rate, the percentages of the population by intervals of
growth rate values, the distributions of size-increments, the distribution of the
asymptotic size. These functions give a variety of information about the behaviour of
the structure of sizes in population.
Objective 5. The application of the new growth models and biologically meaningful
indices to improve the accuracy of stock assessments.
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.
The stochastic growth models were incorporated in the abalone population dynamics
model in the form of the Markov transition probability matrices with any resolution in
size classes and time (the current model uses l = 2mm and t= 1year). The
transition probabilities were calculated as the integrals from the conditional
probability density functions of the stochastic growth models. The parameters of the
stochastic growth model were estimated using abalone tagging data from several
locations in Victoria. This model was applied to risk assessment problems in the quota
management in abalone fisheries in Victoria; 1998 “Risk Assessment and Harvest
Strategy Evaluation for the Victorian Abalone Fishery”- Confidential report to
Victorian Directory Fisheries by MAFRI Abalone Risk Assessment Team, chaired by
Dr. Tony Smith, Fisheries Division, CSIRO, Hobart.
The length-at-age distributions of school shark were estimated with correction for
gill-net sampling bias. This information was used by Dr. Terry Walker, MAFRI and
Dr. A. Punt, Fisheries Division, CSIRO, Hobart as input into shark stock assessment,
in Australia and internationally.
The results from a new modelling approach were used in ‘The Port Phillip Bay
Fishery 996/97, Victorian Fisheries Assessment Report. Compiled by the Bay and
Inlet Fisheries Stock Assessment Group. Fisheries Victoria Assessment Report No.
(Ed) Coutin, P. C., 1997. (Fisheries Victoria, East Melbourne).
Benefits
The abalone, shark, scale-fish and many other fisheries, that use similar population
data can benefit by using these new models and software. The more accurate
parametrization of size distribution in a population will assist with improvement of
stock assessment.
The software contains several stochastic growth models for size-at-age and sizeincrement data and provides the ability to choose the best model, with respect to the
data. The output includes a variety of information and biologically meaningful
parameters, that enable detailed analysis of growth in a population.
The software is menu-driven and has user friendly interface. It is available from the
author with manual and sufficient consulting.
Further Development
From fisheries literature, as well as practical stock assessment, it is well known that
one limitation of the accuracy of the stock assessment is the poor estimation of an
important population characteristics such as age and size dependent natural mortality.
In many cases the numerical values of this characteristic are to be assumed, but not
estimated from the data.
The age and size dependent mortality should be reflected in the age and size
composition of fish population. This new method (that allow an accurate
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parametrization of size distribution in a population ) can be applied to extract the
effect of natural mortality on size composition.
A number of issues are being considered for further development; the estimation of
size dependent natural mortality and the calibration of the selectivity function of
fishing gear. This will provide a more accurate assessment and prediction of the
discarded catch. The determination of the minimum information that are needed for
the reliable estimation of the mortality and selectivity parameters with using the new
stochastic models. Such studies will involve large simulation processes.
Final Cost
Refer to separate statement of Receipts and Expenditure.
Conclusion
The work on the project was undertaken in collaboration with experienced fisheries
biologist and population dynamics experts from Marine and Freshwater Resources
Institute, Victoria; Zoology Department, the University of Melbourne; and Fisheries
Division, CSIRO, Hobart. This has helped the author to interpret the biological data
and to introduce some idea and methods from the stochastic modelling in
epidemiology and the modelling of the physical systems with random parameters into
the modelling of a population dynamics.
As result of such (interdisciplinary) collaboration the flexible mathematical tools were
developed, which enable the study of a wide range of the practical biological and
management problems in fisheries.
This proposed method for stochastic parametrization of growth and allometric data is
suitable for further development and can be extended beyond the set of the problems
that considered in this work.
Appendix 1.
Intellectual Property and Valuable Information
The papers has been accepted for publication:
Probability density functions useful for parametrization of
heterogeneity in growth and allometry data
Vladimir S. Troynikov
Marine and Freshwater Resources Institute, PO Box 114, Queenscliff, Victoria,
Australia 3225.
FRDC Project. 93/214.03 Final Report
16
Marine & Freshwater Resources Institute
In press: Bulletin of Mathematical Biology, Journal of the Society for Mathematical
Biology (see Appendix 2.1).
Alternative approach for establishing legal minimum lengths
for abalone based on stochastic growth models for length
increment data.
V.S.Troynikov and H.K.Gorfine
Marine and Freshwater Resources Institute, PO Box 114, Queenscliff, Victoria,
Australia 3225.
In press: Journal of Shellfish Research. (see Appendix 2.3).
Estimation of seasonal growth parameters using a
stochastic Gompertz model for tagging data.
By Vladimir S. Troynikov1, Robert W. Day2 and Anne M. Leorke2
1. Marine and Freshwater Resources Institute, PO Box 114, Queenscliff,
Victoria, Australia 3225.
2. Zoology Department, The University of Melbourne, Parkville, Vic. 3052.
Australia.
In press: Journal of Shellfish Research (see Appendix 2.4).
FRDC Project No. 93/214.03 is acknowledged in these papers.
The software and output of the modelling are currently being used by several projects
in MAFRI and other agencies in Australia and Department of Fish and Game, Marine
Resources Division, CA, USA .
FRDC and Fisheries Victoria contribution to the development of this software is
acknowledged in the user manual and initial screen of the software.
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Marine & Freshwater Resources Institute
Appendix 2. The Manuscripts
FRDC Project. 93/214.03 Final Report
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