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HOW TO REDUCE THE IMPACT OF MODEL UNCERTAINTY
ON ASSESSMENTS AND ADVICE
by
lake Rice
Department of Fisheries & Oceans
Pacific Biologica1 Station
Nanaimo, B.C.
Canada V9R 5K6
ABSTRACT
Assessments and projections can have uncertainty because data are noisy or unrepresentative,
and because model formulations do not capture the biological processes correctly. When
scientists quantify risk, they lose none of the uncertainty due to data sources. Moreover, they
may add further model uncertainty because they must specify the error structure of the models,
as weIl as the biological processes.
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Non-parametric density estimation methods estimate the probability density function (pdt) of
attributes from data, without specifying a particular functional relationship or error distribution.
Non-parametric density estimation, methods can forecast the pdf of features like recruitment or
weight-at-age from biological and/or physica1 influences. They can also capture environmental
vanability in tuning indices without having to specify the relationship between the index arid the
environmental factor (say, survey estimates and water temperatures). The quantitative results
can be displayed as probability distributions or ogives.
When models ,are well motivated, or model parameters are of direct interest, model-based
methods should be used to quantify uncertainty. When there are~reasons to question any
particular model formulation, non-parametric methods are useful for representing the true
uncertainty in the advice and the range possible outcomes of management actions. From my
, experiences using distributions and ogives to present iesults to managers, I will draw some
generalizations about the effectiveness of each type of display, and how each can influence
decisions.
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INTRODUCTION
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Both the models we use to represent fish populations and fisheries and the data we use to
parameü~rize the models determirie thequantltiltive advice we give on the status arid management
of fish stockS. Both the models arid the daci are impenect. The imperfections are major
comporierits of thc unceriairity in adviee arid the nsk iri management options.
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Data can be made less imperfed through impr6ved 'suivey cind sampÜng designs,: through
collection of more data; arid through better tools ror making measurements. Nonetheless data
will riever be perfect. Wheri scientists estlmate risk or 'uncertainty, the error or variarice in the
daci will coritribute to the estimates.
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The models which use the data eire inlerided to represerit actuaI biologicaI processes. At best the
models simplify and may misspecify the.i-eaI pröcesses.!Moreover, the quarititative models must
not only specify the furictional relationship between entities (say, stock arid recruitment), but the
models must speeify, the form of the vanability around thai furietion'aI relationship (the error
term). Models can be improved throiJgh research ori!biological and fisherit~s proeesses; and
througn approaches to inodel selectiori which render paor models implausible iri compärlson to
good models.
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The first strategy, is limited beeause good flsheries research takes time. The secorid 'strategy is
limited by. the ,quality arid quantity of datei avmlable to~ diserimiriate, among alternative models.
Everi good data are often incorichisive or contradidorY (e.g. Walters 1985; Richaids 1991)~
Theiefore, everi many widely used models have been chosen for mathematical convenience
rather thari for any strorig theoretical or empirical justification (e.g. Ricker 1954). Now, the
computing power available routinely to most fisheries scientists has deereased our rieed for t h e "
mathematical "convenieriee" of simple functioriaI relationships in fisheries models.
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Estirriating model parameters from pooi data ean mcikel everi good models go bad
arid
Ludwig 1981, Schriute & Hilborn in press). Conversely, why put good data irito a model which
misspecifies functional relationships or error distributions?, We would be adding additional
inäccuracyto the level ofüriceI'tainty aIready present in thc data themselves.' lri those cases we
can apply quantitative tools whieh use the data directly; ~ithout iriterposing beiweeri the data and
tne advice functional relatioriships or error terms in whieh we have little faith. Nonparametric
density estimatiöri methöds eire one class of such tools '(Silverman 1986).
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ANALYTICAL METHODS
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Evaris and Riee (1988) deseribe one simple nonparametric density estimation in detäil; a keinel
estimator based on tne Caucny distribution. The' kenlel cari use the same data as' functi6rilli.
models; say pairs of historie ssbs arid reeruitmerits. The; kernel estimates the probability density
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function (pdf) for recruitmerit given a new ssb (forecast or estimated) by weighting each historie
recruitment by the similanty of the historie ssb which produced it to the new ssb. The weighting
furictlori is:'
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Dis a. tuning parameter estimated through crossvalidatlon (Bowman, et al. 1984). The xj'sare
the differerices between the "riew" ssb and eäch of the i historie ssbs. The Wj'S are sCaled to
sum to 1.0. The scaledweights are, themselves, the estimated pdf. NatufaIly,any pair of
variables
be sut>stltuted for stock and recruitmerit, and users can smooth the estimated pdf
further, if desirect.
can
Evans arid Rice (1988) report results of simulations which show tilat the kernel estimator
performed as well or better (smaller average error, much better worst case performance) than
traditiorial parametric approaches to stock - recruitment forecasting, except under ideal
conditions. The "ideä1" conditions were that the tnie functional form of the stock - recruit
relationship wa.s specified correct1y, AND the error tenn waS specified correct1Y"ANti the noise
(contribution of the error term to the. simulated data) was small compared ,to ,the signal
[coritrlbütion of the furictiorial relation to the simulated data]. Riceand Evans(1988) and Rice
(1993) illustcite applications of the Cauchy kernel to developing advice on rebuildirig fish stOCks
and on fish - habitat iriteractions.
APPLICATIONS TO RISK AND UNCERTAINTY
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PROBLEM 1: Seiecting a rebuilding strategy.
To forecast the effects of a management strategy, flsheries sdentists often must forecast exp~cted
recruitrrient levels. For example, in 1977 Canada adopted a management strategy to rehuild the
eod stock in NAFO Division 2J3KL. Decision makers needed projections of the trajectory the
stock would take under different F's. Although concems about natural variation in reci"uitment
were prominent in the ICNAF advice, there were no estimates of risk or uncertainty associated
with the rebuilding forecasts. The stock and reci"uit data available at that time did not allow
identificiltion of an appropriate stock reCruit function; because there was inadequäte information
on, the cUrVature and desceriding limt> of the function, if either existed (Fig 1). Therefore;
ICNAF ,assumed annual reCruitinerit would be the average of cohort estimates from 1962-1972
(ICNAF 1977).
Rice and Evans (1988) used the kernel esti'mator to investlgate six questions about rebuÜding cod
stock. Their answers included estimates of the range of outcomes possible given the data which
were available in 1977. Suppose the explicit objective had been to achieve an SSB of 1.0
million metric torines (mmt) ,within 10 years., If recruitment are chosen without consi~eration
of SSB (Le. if the kernel parameter D is riüide large rdative to the range of historiCal SSB's),
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the rlsk of faiÜng to achieve thai objective witb F=0.'16 is negligible (Fig 2a). If the kemei
parameter is turied, the pdf of recruitment does vary with SSB arid the probability of failirig to
achieve theit objectlve is 0030 (Fig 2a). Moreover, the approach allowed estimation of the full
pdf of future SSB for different. values of F, so the probability of the stock achieving vanous
targets \inder different management regimes could beevaluatoo (Fig 2b).. Interesting, ,when the
work was done in 1986 the kernel algorithm estimat~ the median value for actual average
fishingmortality bet'N.een 1977 arid 1984 to be 0.37.,This valuewas substintially higher than
VPA estimatesat ttiat time, but fairly elose to currerit VPA estimates F in those Years.. Not
only did the data-bcisoo method provide estimates of uncertainty directly; it also estimated the
central moment weIl, compared to model-based methods;
cf
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PROBLEM 2: Age Composition of PaCific Hake Catch
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Camida and the US both fish the migratory stock of Pacific Hake (Merluccius produclUs). In
a "typica1 year" the stock spawns in FebruarY off Southern California arid northerri Mexico, then
migrates noi-th~ ·older fish migrate further, so the :Cariadian harvest, taken from. June to
September, has ari older age' composition than the US harvest., In discussions concerning
allocation of catch between the couniries, it has beeri argued that tonne for the tonne the
Caileidicin fishery places the stock at higher risk, beeause it has a greater impact on spawriing
biomass, arid therefore on future recruitment.
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Hake year-elasses vary greatly. The mfluence of SSB on recruitment IS weal(; The data do not
h~nd themselves to parametric analyses; again neither ttie pcilk of the dome nor the shape of the
limbs can be determined with confidence (Swartzman; 'et al. 1983; Fig 3). We inc0rP0rated a
Cauchy kernet estimator of recruitment from SSB into eilsimulation model of the hake population
and fishery. We used the model to explore the effects of altering the eige composition of the
combiried Canada - US harvest on future recruitment; future SSB's, cind future yields. Scenarios
riuiged from age compositions younger than the preserit 'UScatch to age composiiions oider ihen
present Canadiari catch (Table 1; data from Dorn arid Methot 1992).
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The cyclic nature of hake reeruitment is present in results of all simulations (Fig 4a), as is the
skewoo and bimodal pattern in the frequency of occurrerice of cohort sizes (Fig 4b); Some
catch is foregone with the olderäge composition' (Fig 5a), but SSB is actually higher (Fig Sb),
arid catches aie more stable (Table 2).
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Fig\ires 4 arid 5. are averages of 200 runs, and do not reflect uncertaintyarid risk. The hake
stock is managed with a strategy. which reduces exploitatiori significantly, whenever the SSB falls
below a critica1 level. , Probability of reäching the crÜicaI level is available direct1yfrom the
simulations. Suppose we ideritify the criticallevel as 0.225 mrnt (the value used in 1992); With
an oider age composition of catch. the critical level is hit less often than with a younger age
corriposition. One can examine the unceItainty of any 'features presented as averages in earlier
figtires. For example, catches and ssb's after 20 or ~O years are highly skewed far all age
compositions (Fig 6a,b).
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PROBLl~M 3: Hydroacoustic Index of CapeÜri Abundance
Anriual hydroacoustic s~iveys of capelin abundance are conducted in the Northwest Atlantic.
Oceanographic conditions influence eapelin ,distributiori and aggregation patterns (Carscadden
et at. 1989). To use the survey results as either an absolute or relative index of abundarice iri
anassessment without accounting for oceanographic influences would include unnecessary
variance and uncertairity. However, there' is no. theoretica1 justification. for any specific
functiorial relationship between temperaiure and abundance. Inspectlon of the data suggests the
relatioriship may not be smooth and coritinuous (Fig 7).
Exploratory regression analyses produced statistically. significani fits to. the dati (Fig 7).
However, model estlrriates were consistently biased at temperatures above 2°C and below O°C.
Because of the aggregation of capelin, there also would be major probleins specifying the error
term in regression-based models.. If both the central moments and the uricertainty estimates.of
a model are unreliable, it is unlikely to estimate the risk ofvarious harvesting options accurately.
Relating hydroacoustic estimates ofbiomass to oottom temperature with the Cauchy-based kernei
accounted for over half the vanance iri the hydroacoustic estirriates (Fig 8). The ogives of
abundance at different temperatures correspond weIl with the patterns in the origirial data. For
very cold water (-0.5°C) only low capeliri densities are likely. The pdf changes little until
temperature reaches + 1.5°C. Over the next 2°C, the upper limb of the ogive changes
substiritially, however the ogives remain nearly flat between 2 arid 70 units of capelin. This
reflects the schooling nature of capelin. Everi in preferred temperatures one does not expect
"average" aburidarice of capelin. It is the likelihood of encountering high abundance which is
varyirig.
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From survey data and maps of bottoni temperatures, one can construct a grid of ogives for the
area. Algorithrris then cari estimate abimdance indict~s through resampling from the ogives or
using other strategies. , Repeatoo estimation will represerit a reatistic pdf of actual abundance.
The pdf niay be quite skewed arid irregular, but can be used directly io estimate the unceItainties
and risks of varlous management options.
PROBLEM 4: Trawl Index of Shrimp Aoundance
Shrimp stockS in British Cohimbia are surveyed with trawls (BoutiÜier 1992).. BathometrY gives
significant spatial structure to. the shrimp populations. Physical oceanography also influences
distribution and aburidance. No furictional relationships have been develoj}ed to accourii for the
spatlal or temperature irifluences ori the trawl Samples~' The management strätegy for shnmp
stOCks inCludes ädvising dosure of fisheries when biorilass estirilates fall below a criticatlevel
set for individual groiJrids.
A miJitidiinensionalextension of the kernel estimator was used to estimate the pdf of aburidance
for a grid of simple points. When constIucting the pdf of aburidance äi a giveri C'gricl ti )
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position, irifluence of each sampie point was weighted bY. the siinihmty of each siuriple point to
the "grid" point on three factofs: temperature, depth, arid isotropie (positional) space (Evans et
aI. ms)~ CrossvaJ.idation was used to seleet Cauchy parameters simultaneously for all 3 features.
Differences inthe ratios of the wi~th of the tuning window to the range of observations for each
feature provided the differential weighting of each feature when estimating the pdf of abimdance
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The ogive mapping procedure produced a pdf of abundance ateach point on ci spatial gnd over
the areä. The anllual abundarice estimate; arid the uncerciinty' around that,estimate, were
estimatecI through repeated samplirig from the gnd of. pdfs.. That overaIl pdf of aburidance
provides a direct estim.tte of the probability that the stock lies lJelow the criticil1level. The pdfs
are estimaterl without having to develop ovenui, parameti"ic relatioriships between shrimp
abulldance arid temperature, nor detmled parametrle models of the spatial distribution of shrimp
Oll each fishing ground. Pacimetiie versions of such models, and paftlcularly parameterized
error terms and uncertainties of such models, ha.ve riot been produced.
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Corisider problems like estimating. how nsk to the stö~k vanes with age composition of hake
catches~ It may tie possible to develöp model-based representations of recruitment dyriamics and
use these to estirriate risk. It would require finding normalizing transforinations, obtmnirig stable
estImates of error diStributions, and many other steps.. The best models could only be
approximate ones. Moreover, given the data, it would be extiemely difficult to rejeet many
different representations of the functional relationships'and eITOrS of stock and recruitment, yet
cit least some representations would have to be wrang. I
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A careful cidvisor would run' forecastS with all the rilodeis arid error stIlictures which
plausible given the data (cf Richards 1991). As a result the range of possible outcomes would
increase, compared to results ofany single model. i The data already cOIltain substantial
uncertainly abotit the future dynamics of the stock. Proper use of model-based approaches cari
only' add uncertairity, and scierice advisors would assign less certainty and greater risk to any
management option.
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We can use the data direct1y tri produce the necessary forecasts and unceriainty estimates.. These
Can bei relateddirectly to the decisions managers inu~t ~ake. What additionaI pUrP0se is served
by addition of weak1y suppoited models?
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WHAT DO WE REALLY WANT TO KNOW ABOUT RISK?
As we focus ori assessing risk arid l1ncertlinty in fisheries advice änd mariagement, many
deeisioris depend more on the shape of the tails of ci distribution thari on its central moments.
Mariagers inay wish to keep unpleasarit everits rare, or enhance irifrequent opportunities.
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As the capelin example show&!; model-based estimates can be especially pOOl' away. froin the
average condition; Moreover, the mean condition may be unlikely. It can be arguect thatmore
sophisticated models, atlowing. for aggregatect targets änd complex patterns of eITors, address
concerns about entire distributions rather than just centriU moments. Again, one has only the
data to guide the proper treatment of error. If the data often. are inadequate to discriminate
among alternative functional relationships, is it likely they would be better ableto identify the
proper error structure? Data-based methods areri't a eure-all, but they ean be helpful.
PRESENTATION OF RESULTS
In this paper I have usuatly presented results as curilUlative frequency distrltiutions (cfd) rnther
thanas pdfs. Both contain the same information. Which manner of presentation conveys the
key information more effectively?
In my experlence, effectivenes~ depends on the nature of the message. PDF's are more familiar
to most scientists, tiut with many audiences either mode. of presentation requires explanation;
. Ir the cöre message deals with the most likely event, or the average condition, pdfs seem to
focus attention better on that point.· If the core inessage is the probability of an extreme event,
ogives föeus attention on the shape of the distribution;
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The difference is clear
an. example I fudged from the hake forecasiing model. Consider
cumulative catch over 20 years. From the pdf (Fig 9b);. the mode of test 2 is clearly at higher
catches thari the mode of test 1. We are used to makirig decisions basect on differences iri the
peak: of a pdf. Many would irifer fishing patterns producing test 2 are better. However, due
to the skew and spread of the distributiön of forecasted catches; such a conclusion is
unwarranted. The cfd (Fig 9a) shows that the mode. is not representative of the "average"
condition. In fact, the medians and means differ very little. Do we conclude the tests produce
the same catches? Th6 cfd shows the scenarios do differ: Test 1 has a higher likelihood of
prOducing the larger catches.. Although producing large catches is not generally viewed as a
risk, the communication issue is appropriate.. Both graphs show the same information, of
course. Norietheless, ogives cäri highlight the tails of the distributions. When managers seleet
among options to avoid risks, or to encourage unlikely events, ogives may be apfuticularly
effective communicatiori tool.·
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. LITERATURE CITED
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Boutillier, J.A., W. R. Harling and D. E. Yoimg. 1990~ W. E. RICKER Shrimp survey 88-S-1~
W~st .Co~t of Vanco~ver Island, April 28-May 8" 1988. Can. Däta Rep. Fish~ Aquat.
SCI. 808. 40 p.
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Carscadden; J.E., K.T. Frank, and D.S. Mhler. 1989. Capelin (Mai/olus villosuS) späwning
on the Southeast Shoal: influence of physicäl factors past and present: Can.. J. Fish.
Aquat. Sei. 46: 1743-1754.
•I '
Dom, M. W~ and R.D. Methot. 1992 stätus of th coastaI Pacific whiting resource in 1992. in
. Pacific Fishery Management Council, Status of the Pacific Coast groundfish fishery
through 1992 and recommended acceptable biological catches in 1993; p. AI-A58.
(Document prepared for the Council and" its advisory entiÜes) Pacific Fisheries
Management Councii, Metro Center, Suite 420J 2000 SW First Ave. Portland, OR.
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Evans, G.T and J.C. Rice. ,1988. Predicting recruitment from stock siie without the mediation
öf a functionäl' relation. J. Cons. int. Exp. Mer, 44: 1 i 1-122.
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Evans, G.T., J.C.Rice, and S.A. Akenhead. ms. The probability distribution for abundance of
fish, and its pattern in space.
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ICNAF. 1977. Redbook 1977:, Standing Committee on~Research and Statistics. Proceedings of
.
special meeting December 1976 and annual meeting,May-June 1977~ Dartmouth N.S.
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Rice, J.C., in press. Forecasting abundance from habidi Ineasures using nonparametri6 density
,estimatiori' methods. Can. J. Fish Aquat. ScL 50.xxx-xxx.
,
Rice~
,
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ic. and' G~T.
Evans. 1988. Tools for ernbracing unceItairity in the m~agement of the
cod fishery in NAFO divisions 2J+3KL. J. Cons. int. Exp. Mer 45:73-81.
I'
Richards, L.J. 1991. Use of contradictory data soJces in stock assessments.
11:225-238.,'
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Fish. Res.
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Ricker; \V.E~ 1954. Stock and recruitment. J. Fish. r~s. Bd. Can. ,11:559-623..
,
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Schnute, J.T. and R. Hilbom. iri press. Analysis of contradictory data sources in fish stock
assessrrierit. Can. ]. Fish. Aquat. Sei. xx:xxx-xxx.
!
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Swartzman, G.L., W.M. Geti, R.C~ Frands, R.T~ Haar, and K. Rose. 1983. A management
analysis of the Pacific whiting (Merluccitis productus) fishery usirig an age-structurecI
stochastic recruitment model. Can. J~ Fish. Aquat. ScL 40:524-539~
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Walters, C.J. 1985. Bias in the estimation of functional relationships form time series data. Can.
J. Fish. Aquat. Sci. 42:147-149.
Walters, C.J. and D.L. Ludwig. 1981. Effects of measurement errors on the assessment of
stock-recruitment relationships. Can. J. Fish. Aquat. Sci. 38:704-710.
FIGURE LEGENDS
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Fig. 1.
Scatter plot of recruits (#'s at age 4) vS. ssb for eod in NAFO Div. 2J3KL from
1962 - 1977 (see Rice and Evans 1988).
Fig 2.
Ogives of SSB estimated from 200 independent simulations, starting with 1977
conditions and proceeding 10 years: a) F= 0.16, using a very large value for
"0" (no stock-recruit relationship) or "0" tuned with data in Fig. 1; b) tuned "0"
and F increasing from 0.16 to 0.52 in steps of 0.03.
Fig 3.
Scatter plot of recruits (#'s at age 2) vs ssb for Pacifie hake, using data from
Dorn and Methot 1992.
Fig 4.
Recruitments of Pacific Hake stock and fishery over 100 years; population
parameters from table 1. a) Time series of recruits averaged over 200 independent
simulations. b) Ln frequency of occurrence (y-axis) of cohorts of various sizes
(x-axis); from 200 siniulations, each of 100 years.
Fig 5.
As in Fig 4a, but for a) catch, and b) SSB.
Fig 6.
Ogive of a) catches and b) SSb, after 20 years, from 200 simulations of Pacific
hake stock and fishery (Fig 4),
Fig. 7.
Scatter plot of capelin density (arbitrary hydroacoustie units) vs bottom
temperature, from survey of NAFO Div. 3LNO in 1987 with linear and
polynomial regression lines.
Fig 8.
Ogives of density of capelin for 4 trial values of bottom temperature; data from
Fig. 7, and tuned Cauchy algorithm.
Fig 9.
Forc:~cast
cumulative catches of hake over 20 years, for two test fishing scenarios
(details are artificial; to produce desired pattern of frequencies for example). a)
Results displayed as ogive (efd), b) results displayed as pdf.
TABLE 1. population parameters input to hake simulation model.
AGE
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o.ta from the 11192 .. llllment
POPAC' 0.678'
0.528
NMORT
0.237
0.237
POPWT0.278
0.371
4
5
8
7
0.042'
0.237
0.448
0.476
0.2370.531
0.475
0.237
0.575
0.064
0.2370.628
- 0.97
MATURE
0.19
0.&4'
o.n'
0.82
0.D3
USSLCT
CANSLCT
0.04
0'
0.15
0.51 '
0.<42
0.56
0.73
0.81
0.92
0.67
IPROPFEM
0.48 -
0.512
0.52
0.524~
O.~
0.878
0.763-0.654
0.828
0.860
0.801
0.GG4:
0.678.
0.875 ;
0.501
Exper'rm«lUII cetch Ill-oe veotore (MIeetIvItIM),
0.037
0.150
0.417
Vounger
0.053
0.213 :
0.514
0.145
0Ider
0.036
0.403
Aeeeaament
POPAC
NMORT
POPW'T,
MATURE
USSLCT
CANSLCT
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0.98:
0.74-
8
0
0.237:
0.666
10·
0.454
0.237
0.678
1
1
1
0.8
0.99
0.88
0.529
0.538
0.818
_0.887
0.886
0.828
0.878
0.801;
0.008
0.237
0.694
12-
11
0.002 _
0.2370.75
14
13
0.158;
0.237:
0.88'
0.002
0.237,
0.n8
0.005:
0_237
0.967'
15-
0.067.
0.237
1.047
,1.'
, 1
0.97 "
0.95
0.88
1
0.58
0.94
0.24
0.68
0.06 .
0.32 _
0.01
0.1
0.539
0.544 -
0.l553
0.M1
0.!568
0.575
0.880"
0.860
0.919
0.810
0.763
0.967
0.701'
0.514
0.410
0.213
O.9OQ'·
o.~
0.163'
0.053,
0.310'
0.047.
0.009
0.097
ln/tIaI populelon vector (blUionI)
Naua! mortaUtv rate
•. PopulatIon -'ght IllIlQ8 (Kg) ,
•
Propor1Ion of eexuaIIV ma1ure tem.Iee
U.S.l\ehery eeIectMty et age.
• Canadlen fIeh«y eeIec1IvIty 1ll1lQ8.
• Total flehety eeIec1Mty et 1lQ8.
.- .·--.-Vounger·---.· F1ehingeelec1lvltytoryoungerlleh _ _ •
0Ider •
F1ehing aeIec1Ivity for oIder fleh
"'_"
.
.
~
•__.
.'
._
II
-. - I
I,
TABLE'2.
Years
.
0
0
25
26
28
21
21
25
50
100
125
150
175
200
•
Younger.
Catch;
0
75
Over 200 simulations of hake moder, tabulation
of.tl:t e number,of years thatthe SSB;was;below.the
cr~tl.cal value used by.managers to indicate need to
apply' conservative-exploitaiton rates.
Control;
Catch,
22.
22
15
45.
Older
Catch
1
25
22
29
27
19
16
21
19
51
23
15
18
26
23
39
900
800
....fit
C
0
FIG 1
.--
700
-E 600
.
'-" 500
3
'(J
CD
cx
400
300
200
1913
100
o
•
.25
.5
.75
SSB (mmt)
1
1.25
Projected SSB of Cod After 10 Years
F-0.16
200~-----------------------'
....., Larp "Ir
•••• 'I'uDed "D"
-
.
150
,.o.
.•.•.
..• .•
.-
..•
,:
,
,,
"
100
:
..
.
.. .
..,,.
•. -
FIG 2A
•
,.'
,'
50
'
.
..
."
.
. ..
'
'
o +-----""""""'i~~--...r.;....-..+-.•-••-.'- - - - - 1 - - - - - - - 1
2.0
1.5
1.0
0.5
0.0
SSB (mmt)
~oo .-------~--':":_:_::::;_.~-=:i:I_---=
.
!.
I'
__
FIG
100
E
:J
(..)
OL.--"raa~u.&:::;"c.::.._::;;o.a.-I.
o
.25
.5
__J~
.75
SSB (mmt)
.1_
1
....J
1.25
2a
Recruits vs Spawning Biomass
Pacific Whiting 1979 - 1991
10
•
a."....
I'J
-......=
CI
•
0
6
,0
FIG 3
C
+J
E
4
CJ
"
•
~
•
2
0
0.0
I
I
0.5
.
•
•
..a.
~
'W'
1.0
SSB (mmt)
.....
,.,
I
1.5
2.0
\
1
-
.
.... ......
~_
..
I
I
I
j
j,
.
Number Recruita va Time (averaged over 200 runs)
Paci1ic Whiting - fram' model farecasts
!
2.0 ~-.-;...---.-;....-;...;...-.----------------,
l
FIG 4A
J
II
t
1.5
1.0
•
.Ale Compoll1Ucm
0.5
Assessment
- - Yo1ui&er
Older
-T-----+-----------f-----.-;...-~
0.0 -+-
o
100 I
I
Year;,
50
200
150
I
1
I
I
I
I
•I
Frequency Distribution of Recruits
Pacific Whlting - from model forecaats
!
•
10
FIG 4B
-
8
~
()
d
CD
&
...
......,
6
CD
$.4'
e::t
4
iie ComposlttoD
-
Aatl10811m8Dt
- - YO\1Dl8r
Older
2
.....
0
0
1
2
3
4-
5
6
II
Recruits (bi;llions)
I
7
B
9
~
Catch Over Time (averaged over 200 runs)
Pacific Whiting - from model forecasts
0.225
Ale ComposlUon
FIG 5A
- klsessment
- -Youna er
.... Older
0.200
'Z'
-~
.d
0.175
Q
~.
«S
tJ
.e
0.150
0.125 +----+---+---I----t---+---+---t---;
200
175
125
150
75
100
25
50
o
Year
SSB over Time (averaged over 200 runs)
Pacüic Whiting - from model forecasts
•
0.45~---------------~-----,
Ale CompoelUon
- Aaseument.
- -Youna er
...• Older
FIG SB
0.40
0.35
0.30
0.25
0.20 -+-----.;.-----.------+-------1
o
50
100
150
200
Year
CDF of Catch After 20 Years
Pacific Whiting - from forecasting model
200 -r-------"::::::J"I-----,
>.
g 160
Q,)
50
~ 120
FIG 6A
lil:.
.-...>
Q,)
«'
'3
80
S
§ 40
u
-
Seleclivity
Assessment
•
.••. Younger
-
Older
O-l--l.--+--+-----t---+----I
1.0
0.2
0.4
0.6
0.8
0.0
Catch (millions tons)
Spawning Biomass after 20 years
Pacific Whiting - trom torecasting model
200
•
-r---------=_--,
>.
()
t:::
160
Q,)
;:3
0-
~ 120
~
.-....
FIG 6a
Q,)
>
«l
;;
8
e
;:3
u
80
Seleclivity
40
- Assessment
.••• Younger
-
Older
0+.L.--1--+---+--~_+--+--+-_I
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
SSB (millions tons)
1987
Cape1in Density vs. Bottom Temperature ,
(/)
125
.+J
R-square
R-square
c
:J
= 0.361
= 0.28 I
u
0
.+J
r.n
::J
0
FIG 7
a
u
0
0
0
0
~
'1J
I
0
0
~
...
.-
8
0
a
..'
.... 0
.' -erc]"
2.0
~
.0
~
.
..
.. ..
0
~
«
...
0
-2.0
0.0
a
6.0
4.0
Degree (C)
1.0 ~--===~_~_:""':_~_~-"="'-'='"._~_::-:_:-:_:"""ll_~-r----~":",:,,". . ~,,,~,'~;o:-:-:-"-I
I
,,
c
o
--toJ
I
0.8
,
,
~
•
FIG
a
,
o
a.
o 0.6
I
I
I
~
CL
.+J
....
I
",
-
.... .. _..I
I
I.····
..
0.4
o
:1
"
'
_
:, ,. ...r
::J
E
..... " ,
....
.... .... ....
I
Cl)
.>
I
..
I
I
0.2
='
()
0.0
.
o'
_0 .-0'
_.,-"
,._,,1
.--"~
S.S·C
3.S·C
:,"
~
~
0
.
20
40
60
, .S·C
-O.S·C
80
Capelin Density (Hydroacoustic Units)
100
Cummulalive Catch
from model forecasts
500 - r - - - - - - - - - - - - - - -.,...:"...:"" ,. .- =-------,
.-..~
...' ......'..'..'
..'
Fig. 9a
........
400
....
..
.'
~
u 500
=
."
.'"
Ai. Compol1t1on
-
Test 1
.. .. rest 2
... ....
'
'
'
Q)
&
r: 200
Q)
100
0
0.0
2.0
4.0
6.0
10.0
8.0
Cummulative Catcb (mmt)
Cnmmulative Catch
from model forecasts
Fig. 9b
_. Compoaticm
15
-
Teilt 1
.... Test 2
~
(J
s:=
10
.:
Q)
&
Q)
~
ö
····
·
·
0
0.0
2.0
4.0
6.0
Cummulative Catch (mmt)
8.0
10.0