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Experimental interactive software for choosing and fitting surplus production models variables P. Freon, C. Mullon and G. Pichon ORSTOM 213 rue Lafayette 75480 Paris Cedex 10, France

INSTITUT FRAN9AIS DE RECHERCHE SCIENTlFIQUE POUR LE DEVELOPPEMENT EN COOPERATION

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:~2 cesig~atic~s 2mp~cyed a~c ~he p~esentation of mate~ial i~ :~cs p~~:icatic~ do not imply the exp~ession of any op~nion whatsoeve~ on :~e

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M-43 FAO ISBN 92-5-103335-8 ORSTOM ISBN 2-7099-1124-8

All rights reserved. No part of the procedures or programs used for the access to, or the display of, data contained in this database may be reproduced, altered or stored on a retrieval system or transmitted in any form or by any means without the prior permission of the copyright holders, except in the cases of copies intended for security back-ups or for FAO or ORSTOM internal uses (i.e. not for distribution, with or without a fee, to third parties). Applications for such permission, explaining the purpose and extent of reproduction, should be addressed to the Director, Publications Division, Food and Agriculture Organization of the United Nations (FAO), Viale delle Terme di Caracalla, 00100 Rome, italy. and to Service des Editions, ORSTOM, 213 rue lafayette, 75480 Paris Cede x 10, France. Data contained in this database may however be used freely c,re,vicied that the Institut Fran9ais de Recherche Scientifique pour d';';210ppement en Cooperation (ORSTOM) and Food and ?CTu,..ye Organization of the United Nations (FAO) be cited as

FAO 2Dd ORSTOM decline all responsibility for any software errors

ccr dei'c..and.es. or Tor any damage that may arise from them, as well a" lcr P':"9Gm maintenance and upgrading, and documentation; u:3s::,::,>;:::,;:''''

TABLE OF CONTENTS

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Final models

Following the line presented above gives several equations that describe environmental influence on abundance or catch ability (Appendix B). Numerous hypothetical examples of an environmenfal influence on abundance. through recruitment and/or poputation growth, can be found in the literature, such as! influence of upwelling strength, relationships between stock production and river discharges, influence of temperature during a critical stage (spawning, iarva! development), etc. In such cases stock production will depend on both fishing effort and environmental conditions. The catch ability coefficient q may also be linked to the environmental conditions. For instance, water mass movements can be related to fish migrafions, and therefore linked to accessibility, especially for short-range fleets. Water turbidity can increase either the vulnerability of fish to some kinds of gear (gillnets, trawls) or decrease if (light fishing). In some cases, it is reasonable to postulate fhat environment influences both stocK abundance and catchability. In such cases, q and B= will be replaced by functions of V. We have examined only the simple case where both B=(V) and q(V) are described by the function (8.IV) or by a parabola, in order to timit the number of parameters. This is acceptable because these functions are flexible, but, in theory, nothing allows us to suppose that g(V) and y(V) would be identical. Moreover, the past-efiort-averaging approach used for estimating model parameters in the case of transitional states allows for the use of these models only in particular cases (see below).

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limits and objectives of CLlMPROD

The structural approach in stock assessment is supposed to give more reliable results than the global approach because the firsf uses biological information (natural mortality, growth parameters, age or length structure in fhe catches) while the second is a blind approach! a surplus production model is a "black box" with a single input variable (E) and a single output (Y or

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Therefore simple surplus

production models have been criticized because they suffer from lack of biological realism. Nevertheless, they are still widely used and accepted in many quarters, especially in tropical areas where biological parameters and/or age structure of catches are often not available, and where environmental factors are often the predominant influence on producfion of short-lived species. In such areas fish ageing is often difficult and requires expensive and intensive sampling owing to the high variability of fish lengfh within the cohorts associated with a special type of aggregation small pelagic species (Freon, 1985). In such circumstances the usual analytic methods are hardly usable. Moreover, when only a rough age-structure is available more sophisticated age-structured models, as proposed by Deriso (1980), often do not perform better owing to difficulties in estimating to additional parameters (Ludwig and Waiters, 1985). CLlMPROD uses only one additional variable and zero to three (but most often one) additionat parameters as compared with conventional surplus production models. The artificial intelligence in CLlMPROD allows the use of any additional quantitative or qualitative data which are not included in the model as variables. It thus helps the user to choose the best model equation according to the stock characteristics, and not only using the criterion of the best fit. It has been demonstrated that this criterion does not necessarily provide thJl most realistic policy prescription (Uhler, 1980). The present approach can provide better assessment and management of the stock by taking into account the user's knowledge of the stock biology or structure, and the expert's experience of other stocks. Some negative aspects of CLlMPROD should also be underlined. Although environmental production models do not need quantitative biological data, it is necessary to have some minimum knowledge of the species ecology for their proper use. This tool will be made available to fishery biologists or fishery managers, and can be used to fit any model without special knowledge of population dynamics. The program asks the user to respond to various questions regarding the basic assumptions underlying the models. The user, however, remains responsible for the answer given and for all potential subsequent errors.

Reference Guide· 9

8·CLlMPROD

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The introduction of an environmental variable into global production modeis increases the number of parameters in the final formulation, and consequenHy there are tour main ditflcultles: Although the quality of the fit is improved, the confidence limits of the parameters are often high and the titting procedures may be unstabie.

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It Is sometimes difficult to estimate the real contribution of each variable (E and V) separately in the models, owing to their Interaction and/or co-linearity.

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The problem of transitional states becomes more difficult to solve, especially when the environmental influence is described by a complex function (in such a case CUM PROD does not provide a satisfactory solution).

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By Increasing the number of explanatory variables one also increases the probability of obtaining good correlations by chance, Independent of any real biological phenomena (Gulland, 1952: Belt and Pruter, 1958; Ricker, 1975, p. 227-279). The literature provides many examples of good hlsforical fits which break down as soon as the model is used for forecasting. These ditficulties, common to any multi-parameter regression, can be overcome by an objective choice of variables (supported by biological observations as tar as possible). As underlined by Bakun and Parrlsh (1980), selection of the environmental variable to be introduced Into the model must, as far as possible, be a priori and not only empirical (they present a list of likely variables). Objective choice of the environmental variable is often the key to avoiding spurious correlations. In addition, these models still have the usual limitations of conventional surplus production models, linked to their basic assumptions, as discussed by Fox (1974). Even after modification, they remain empirical procedures for assessing fish stock responses - in terms of biomass and yield - to changes In the rate of fishing and environmental conditions. Therefore they represent a blind approach for investigating recruitment variability. The utiiization of these models for predictions is not devoid of risks. It requires a rorecast of fishing eHort and in some cases a forecast of one environmental factor ('lInen there is not enough jag between this factor and its effect on the fishery). This !aner forecast is often Imprecise, as pointed out by Waiters (1987). Moreover, the confidence limits of the parameters are sometimes so high that predictions within the observed ranQe of the variables would be hazardous, and of course it would be even worse to forecast using input values outside the observed range. V.,then causal environmenta1 factors and/or processes cannot be forecast and have a short-term effect, the propGsed approach can only serve to assess the range of

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environmentally-induced fluctuations and compare It with that due to fishing. This would, however, be useful because it could Improve management sfrategles, partiCUlarly when stocks are at the upper and lower ranges of their blomass and/or catchabillty. Nevertheless, owing to fhe strong limitations of fhe global approach, CLlMPROD must be considered first of all as a training tool. From real or simulated data, It explains how the environment can confrol the yield fhrough its influence on abundance or catchability. Therefore, it will show that different MSYs can be obtained for each stafe of the environmental variable, or at least a different E max when only catch ability is modified. In other respects, it is shown fhat these models can explain how wide fluctuations in the catch (and sometimes collapses) may occur, without any increase in the nominal effort, as a result of environmental changes. However, long-term changes in population dynamics of some species (especially small pelaglcs) are often unpredictable with the present state of scientific knowledge because the whole ecological system may suddenly shift from an equilibrium relationship between the stock and the environment (in the widest sense of the word: climate, prey, competitor species, predators, etc.) to another equilibrium relationship. In such cases, two different models must be used for the two periods (see Cury, 1989, tor discussion).

Reference Guide· 11

10 • CllMPROD

'J C. PRINCIPLES CONCEPT

GOVERNING

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It is assumed that CllMPROD deals with imperfect and limited data and tries to apply imperfect models, using as much ancillary data as possible to reduce the scope tor gross errors, as previously mentioned. In respect to this last point. artificial intelligence is used to choose appropriate questions according to the case studied and to available information on the stock structure, the species biology or the fishery. CllMPROD also tries to foroe the user to look at his data-structure and interpret it himself before seeking the help of statistical tools. For instance, a simple scatter plot at CPUE versus V is shown before asking the user first if the relationship between the two variables looks monotonic or not, then linear or not. Of course. a statistical response to these questions could easily be obtained, but when outlier point(s) structure the data-set, the answer given by the user could be ditferent. In order to limit the use at CllMPROD as a predictive tool, only two years can be forecast.

The authors at CllMPROD have many improvements for the software in mind. especially concerning mathematical help in choosing the model, fhe transitional situation (possibility of using the integration of the ditferential equation (3) in the software). the addition of a constant in some models, automatic choice between modeis of the same family according to their number of parameters, residual analvsis, comments on the results, etc. For this version, it has been decided to wait for comments on the interest of CllMPROD for training and stock assessment before improving the product.

PRESENTATION OF CLlMPROD

1.

General presentation

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i'. .~ CllMPROD is based on an experiment in artiticial intelligence for choosing the model best adapted to each situation, and for assessing the fit. It is designed as an expert-system, but is not self-learning.

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The software is written for PC/XT/AT compatible microcomputer using MS-DOS version 3.0 (at least). It is fully interaotive and has two main objectives: first, a normal data management function, statistical and graphical utilities that uses TURBO C language; second, a guided selection of the appropriate model, showing the information path. This part of the model uses an inference engine, written in TURBO PROLOG. It applies about one hundred rules which are interactive with information provided by: questions to the user on the stock characteristics, independent from the data set (example: lifespan of the species?), statistics on the data-set (example: ratio of effort range on minimum effort value), graphical deduction by the user from the data set (examples: does this timeseries look unstable? Do you see a decreasing relationship on this plo!?). Answering "I don't know" is allowed for most of the questions. The program is structured and does not necessarily use the whole set of questions. An example of order in the application of the rules is presented in Figure 1. From the main menu, the user is allowed to open or select a data file: to update it with a full screen editor; to search for the most suitable model, or to choose one directly; to validate the model (assess"the fit); to plot the model function, the predicted values and the residuals; to use it for prediction and finally to see the path of the expert decisions. It should be noted that in order to choose among 30 multivariate models (see Appendix B), the program first performs a regression considering the CPUE as the dependent variable and the effort (or the environment in some cases) as the independent variable. From the graphic display of residuals of this regression against the environmental variable, the user may determine which kind of relationship will link environment and CPUE in the final'multivariate model. This procedure provides an easy interpretation and visualization of the process of selecting a model, and allows interactive dialogue with the user which can

12· ClIMPROD

Reference Guide· 13

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introduce additional information. Nevertheless, the recent statistical technique of optimal transformation previously mentioned (Breiman and Friedman, 1985; Mendelssohn and Mendo, 1987; Cury and Roy, 1989) could be helpful and more rigorous for choosing the model from a strictly statistical poinf of view. As this technique only uses the multivariate time series (which is often too short to be OT maximum use) it should be considered a useful complementary tool In selecting the most eppropriate model.

Question: most im artant influence on U ?

Effort (E)

Environment (V)

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Questions on the relationship between U and E from the graph

Questions on the relationship between U and V from graph

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Questions related to the stock

Model U = f(V) fitting

and to the species biology

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Questions on the relationship between U=1 V residual and E

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Questions on the relationship between U-f(E residual and V

JJ Model U=fhE,V) litting Questions on model validation

IT Summary of statistical results

IT Summary of expert decisions

Fig. 1. Partial and simplified flow diagram of CLlMPROD, where U is the catch per unit of eHort, E the fishing effort and V an environmental variable.

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Data input

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The basic set of data used by ClIMPROD includes annual fime-series ot catch (Y), fishing effort (E), CPUE (U = V/E), and one environmental variable (V). This latter variable describes any environmental factor likely to modify the fishery cafches. Common examples are temperature, saiinity, wind speed, turbidity, strength or direction of currents, river outflow, etc.

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Monovariate statistics and graphs of raw data

The following statistics are computed for each variable: sample size, average, variance, standard deviation, coefficient of variation, coefficient ot skewness and kurtosis, minimum and maximum values, range, median. The distribution of the data is shown on a frequency histogram allowing pofential outller values fo be detected. Although no fishery data could be used if normality were strictly required for modelling, these results may give an idea of the data-structure. CLlMPROD stops the analysis, and/or displays advice or warnings, according to the distribution of the values in the different variables. For instance, the program will stop if less then 12 years of observation are available, or if the range/minimum ratio of the effort values is lower than 40%.

4.

Examination of time-series

Each variable is plotted against fime (years) in order to detect any strong instability in the series which might hinder interpretation of the results. For istance, when E or V shows strong instability, if the retained model requires averaging one of these variables over several years in order to approximate an equilibrium state, the results will be of little value.

14· CLlMPROD

Reference Guide· 15

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• 5.

Bivariate graphics of raw data

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The following relations are plotted: Y versus E, Y versus V, U versus E, U versus V and V versus E. These graphs reveal any oullier points which can affect the structure of the data-set, or any strong relationship (linear or not) between the two independent variables E and V. It must be emphasized that at presenf the program does consider potentiallag-eflects between variables at this graphical stage.

6.

Computer-assisted choice of the model

Questions on basic assumptions of surplus production models (Schaefer and Beverton, 1963; Fox, 1975) are systematically asked, and the program stops if these assumptions are not met (see user's guide). The following questions are also systematically asked: do you think that the the influence of eflort on CPUE is more important than that of the environment (if unknown, yes Is assumed)? The answer, guided by statistical and graphical help, orients the program either to U=f(E) or to U=f(V) models; does the environment influence abundance, catchability or both? The program does not provide any help in answering this question. It is supposed that the user knows the mechanism of action of the environment on the stock, or has already performed time-series analyses using a monthly or weekly time-interval (Freon, 1988) to determine it the environment presents an unlagged or short-lagged (influence on catchability) or a lagged relationship with CPUE (influence on abundance or both abundance and catchability). Between these two questions, the program will ask one or several questions in order to determine relationship the most suitable between U and E (Schaefer's iinear model, Fox and Garrod's exponential model or Pella and Tomlinson's generalized model), and between U and V (linear, exponential, general or quadratic). Formulae are presented in Appendix B and the complete set of questions appears in the user's guide.

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User-imposed choice of the model

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The fishery biologist used to production modelling may decide to choose a model directly from the main menu. The list of models the user can choose from is available on line as a brief description of the model characteristics (effect of environment on abundance or catchability, shape of the function, etc.). The only questions that the user is asked in this case concern the number of exploited yearclasses. when the environmental influence occurs and its duration, in order to calculate the weighting factor for E and V.

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Model fitting

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For non-equilibrium conditions (transitional cases), the equilibrium approximation approach is used (Fox, 1975): a weighted average of E and/or V Is computed. In cases of delayed influence of the environment on abundance, a lag is inserted between U and the weighted average of V (see Appendix Band Freon (1988) for further details). The Marquardt algorithm is used for least-square estimation of non-linear parameters. Depending on the model, the initial parameter values are 1, 0 or computed from the original data set in linearizing the equation before running the algorithm. As an initial result, the percentage of variation explained by the model (R2) is given. The following steps depend on the quality of the fit, that Is: after a blvarlate model has been chosen, if R290%, a validation of the blvariate model can be tried. If 40
38' CLlMPROD

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User's Guide· ,

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g. Graphical questions (example 1)

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The first graphicai question is about changes in of the data series over time

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Then comes a question about the univariate histogram of the data. Try to detect outlier points. ~

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h. Graphical questions (example 2)

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Type "YES" or "NO" and then the Return key.

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Some questions are asked about the shape of a bivariate relationship.

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40' CLlMPROD

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j _ List of CLlMPROD questions on biology, population dynamics and environment The following questions are asked by CLlMPROD: Have there been changes in the fishing pattern during the period (effort allocation, quota, mesh-size, ...)?

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Is the fishing effort unit standardized, and is the CPUE proportional to abundance?

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Do time-lags and deviations from the stable age-structure have negligible effects on production rate?

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Does the data-set apply to a single stock?

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Does the data-set apply to a sub-stock? Is the sub-stock well isolated (with few exchanges) frorn others? Do you think thal the data-set covers periods both of overexploitation and of underexploitation Do you think that the data-set covers periods both of underexploitation and of optimal exploitation Is the influence of fishing effort (on CPUE) more important than the environmental influence? Do you have any (addilional) reason to expect highly unstable behaviour or collapse of the stock? Did the stock already collapse or exhibit drastic decrease(s) in catch? What is the life span at the species?

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Is the ratio (life span/number of exploited year-classes) lower than two?

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Is the single stock subdivided into various geographical sub-stocks (all must be exploited by the fleet) ? Are there natural protected areas for the stock, or constantly inaccessible adult biomass? Does the environment influence abundance, catch ability or both? Number of significantly exploifed year-classes?

Age at recruitment? Age at the beginning of environmental influence? Age at the end of environmental influence? k, Answers The correct answers, for the fraining example, are, in fact: NO, to the 'Have there been changes in the fishing pattern during the perio (effort allocation, quota, mesh-size, ...)?' question YES, to the 'Is the fishing effort unit standardized and is the CPUE proportion, to abundance?' question YES, to the 'Do time-lags and deviations from the stable age structure ha, negligible effects on production rate?' question NO, to the 'Does the data-set apply to a single stock?' question YES, to the 'Does the data-set apply to a sub-stock ?' question

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Is the fecundity of the species very low (sharks, mammals)?

Are there one or several non-negligible spawnings before recruitment?

User's Guide· 4

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YES, to the 'Is the sub-stock well isolated (with few exchanges) from others question NO, to the 'Do you think that the dataset covers periods both of overexploitatic and of underexploitation?' question YES, to the 'Do you think that the dataset covers periods both ' underexploitation and optimal exploitation?' question NO, to the 'Did you see any abnormal statistics in the previous table?' question NO, to the 'Is interannual variability too large?' question NO, to the 'Do you see outlier points?' questions (two questions) YES, to the 'Constantly increasing effort?' question YES, to the 'Are the two variables independent?' question YES, to the 'Is the influence of fishing effort more important than environment influence?' question YES, to the 'Does this plot appear to be decreasing?' question NO, to the 'Does this plot look obviously linear?' question NO. to the 'Do you have any (additional) reason to expect highly unstat behaviour or collapse of the stock?' question

42· CLlMPROD

User's Guide· 43

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NO, to the 'Did the stock already collapse or exhibit drastic decrease(s) in catches?' question 6, to the 'What is the life span at the species?' question

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NO, to the 'Is the tecundity of the species very low (sharks, mammals)?' question

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a. Results

NO, to the 'Is the ratio (life span/number of exploited year-classes) lower than 2?' question

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Once you have followed a supervised model selection, as above, you can review all the whole procedure: the answers you gave and the deductions of CLlMPROD.

1, to the 'Number of significantly exploited year-classes?' question

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ABUNDANCE to the 'Does the environment influence abundance, catchability or both?' question

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NO, to the 'May the stock present large fluctuations in CPUE when overexploited?' question

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NO, to the 'Does this plot look linear?' question

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YES, to the 'Does this plot look monotonic?' question 1, to the 'Age at recruitment?' question

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YES, to the 'Is this an acceptable model?' question YES, to the 'Good fit and no trend or autocorrelation in residuals?' question YES, to the 'Reasonable jackknife regression coefficient R2 (over 65% recommanded) and no extreme yearly coefficient ratio, and acceptable MSY graph?' question

I. Results At different steps of the "select the appropriate model and fit it" option, results on model fitting and validation will be dispiayed. As these results are the same as those obtained tram the options "fit a model directly", '''validate the model" and "plot the model", they are presented in the next sections.

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you want to trae", all the iP!."ocedure of r1.l1e application? ,You ,):15wered: NO, to the question: .. ... Have there beer. any changes ir: the ;fishir.g piltten~ during the period (efforr:. ill location, quota, mesh size, )

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!You answered: n;s, to the questior.:. __ .. Tirr:e lags and deviation from the !Stable ago structure have negligible effects on production rate? 1You Jnswered: YES, to the question: ••••. Does the dar.a set apply to a sir-gle lst.ock? IYo\) answered: YES, to the question: ••••• ls the influence of fishing effort Imore important than environmental influence? IYOLl answered: YES, to the question: ••••• Does this plot appear to be Idecreasinq? IYou answered: YES, to the question: ..•.. Do you think that the data cover Iperiods both of overexploitation J!1d of underexplOitation? l'fou ans'...rcred: NO, to the question

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b. Saving You may save the chain of reasoning in an ASCII file. This file is called "REASON.DOC". Then you may use it with a text editor.

44' CLlMPROD

User's Guide· 45

f: ···fI c. An example of .REASON.DOC file:

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You answered: NO, to the Do you want to trace all the procedure of rule application? question

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You answered: YES, to the Does the data-set apply to a single stock? question

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You answered: NO, to the Changes in fishing pattern, due or not to management decision (effort allocation, quota, mesh-size, etc)? question

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You answered: YES, to the Is the fishing effort unit standardized and is the CPUE proportional to abundance? question

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You answered: YES, to the Time lags and deviation from the stable age structure have negligible effects on production rate? question

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You answered: YES, to the Is the influence of fishing effort more important than environmental influence? question You answered: YES, to the Does this plot appear to be decreasing? question You answered: NO, to the Did you see any abnormal statistics in the previous table? question You answered: NO, to the Do you see strong instability in any of these plots? question You answered: NO, to the Do you see outlier points? question

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From rule number 17 I infer that the relationship between CPUE and effort is perhaps governed by equation CPUE~a+b.E You answered: 1, to the Number of significantly exploited year-classes? question

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CPUE~a+b.E

and find a coeff of determination: #77

From rule number 30 I infer, knowing the relation between CPUE and E is CPUE=a+b.E, and the environmental effect is on abundance, that the global model is perhaps CPUE~a.V+b.E, and the relation RES V: CPUE=a+b.V is to be studied

From rule number 30 I infer, knowing the relation between CPUE and E is CPUE~a+b.E, and the environmental effect is on abundance, that the global model is perhaps CPUE=a.V'b+c.E, and the relation RES V: CPUE=a.V'b is to be studied You answered: NO, to the Does this plot look monotonic? question From rule number 30 I infer, knowing the relation between CPUE and E is CPUE=a+b.E, and the environmental effect is on abundance, that the global model is perhaps CPUE~a.V+b.V'2+c.E, and the relation RES V: CPUE~a.V+b.v'2 is to be studied From rule number 29 I inter the relationship between residuals and environmental variable is perhaps governed by equation CPUE=a.v+b.V'2 You answered: 1, to the age ot recruitment? question You answered: 0, to the age at the begining of envirormental influence? question You answered: 0, to the age at the end of environmental influence? question I fit the model CPUE=a.V+b.V'2+c.E and find a coeff of determination: 78 From rule number 4 I infer that the selected model is governed by equation CPUE~a.V+b.V'2+c.E

~.~

You answered: YES, to the Is this an acceptable model? question

~.t!

You answered: YES, to the Reas«nable jackknife regression coefficient R2 (over 65% recommended) no extreme yearly coefficient, and acceptable MSY graph? question

~.~

You answered: YES, to the Good fit and no trend in residuals? question

You answered: abundance, to the environmental influence? question You answered: NO, to the May the stock present large fluctuations in CPUE when overexploited? question

From rule number 30 I infer, knowing the relation between CPUE and E is CPUE~a+b.E, and the environmental effect is on abundance, that the global model is perhaps CPUE=a+b.V+c.E, and the relation RES V: CPUE=a+b.V is to be studied

~

.. t!

From rule number 1 I infer that m 4 is validated

~.~

Normal end ot this sub-program. You can try to use the model for predictions, but note that this possibility is mainly proposed for training. Predictions over two years are not reasonable.

~.~

The most suitable model is

~., ~

You answered: NO, to the Does this plot look linear? question ~.~

CPUE~a.v+b.V'2+c.E

46' CLlMPROD

User's Guide· 47

I!-~

11.

Fit a model directly

a. Choice of the model

~~~

b. List of CLlMPROD models

~." ~

See Appendix B for details

~

CLlMPROD allows the user to choose and fit a model directly withouf assisfance from the expert sysfem. To employ this option, simply select the desired model and press the "Enter" key. This option may be useful in three instances:

for training purposes.

.._~

~,~ ~

, U = f(E) models

.~

when an expert in global modelling wishes to fit directly one or several models of his or her choice. (Keep in mind, however, that the best fit is not the only criterion for choosing a model. The main objective of CLlMPROD is to avoid an arbitrary choice which might lead to spurious correlations.)

-------------------------------c

L I M PRO D -------------------------------

,---------------------------------------------------------------_. iWhLch OOl:' ?

I

U=a.exp(b.E)

(exponential)

U=a+b.E

~.~

Af the end of the "Select the appropriate model and fit it" menu, CLlMPROD may suggesf directly fitting another model of the same family rather than the one already selected by the software. The choice of another model should be based on the preliminary results and on the user's background knowledge of the stock behaviour.

I (linear)

U=(a+b.E)A(1/(c-1 ))

~

~

~

~

~

(linear)

U=a.VAb.

(exponential)

~

U=a+bVAc

L

~

['

~

~---------------------------------------------------------------_.

,------------------------------ ? -----------------------------" Conventional rr.cdels C;'UE'"'f (Sl !

I

~

~

[

= f(V) models U=a+b.V

£ £

I

!U

~

l

i C?U~> (iHb. f:)" Of (c-l) )

Simple regressions

CPUS~f(V}

! iC?U'>a+O.V

i.

iC?US'"'(a.V+b.V 2) .exp(c.E) (Jackknife Method) 1 A

a. The jaCkknife method

J!~~

This consists of titting the model, once for each year, on the data-set which contains all the years except the current one.

J!-~ ~

In this way, you obtain a succession of coefficients ot determination and ot estimated coefficients. By observing the variations in these values, you can draw conclusions about the stability ot your model.

~-~

See Duncan(1978) for a theoretical presentation of the jackknife method.

I[ .•... ~

~.~ ~

I[ '" ~ b. Validating

._-----------------------------------------------------------------------------, IMODEL VALIDATING: CPUi:>(a.V+D.V"2).exp(c.E) (JacHnife Metr.od) I *------------------------------------------------------------------------------" Observ Sstim Jackn

ICPU!:::

"

b

"

29.516 29.490 29.351 29.534

-1.047

-0.024

-1.049

-0.024 -0.024

30.039

-1.06S

;

j"t£AR: all

i

1957 1958 1959 1%0

I

63.5

36.6

61. 2 37.2

49. :; 69.4

51. 6 71. e'iod 01 environmental inltvence

(cf;l,cal stage)

L.

E.

4.

Transitional state when the environment influences stock catchability

When the environment inlluences catchability (or abundance and catchabi[ity) the models must be reformulated, first replacing qE by a mean fishing mortality coeificient F taking into account the various fishing effort Ei and catchability coefticient qi estimates for the different years, Using Fox's (1975) weighted average, we obtain:

F,

!

nqiEi+ (n-1) qi-1 E i _1+ '" + qi-n+1 E i _n + 1 n+(n-1)+(11-2)+ +1

to generalize the formulae to any case and then to avoid reformulation of mJCSLS, this equation is approximated by:

D,rC.','2f

Fig. 2. Graphical solutions of the estimated weighted average Vi involving

the number of years during which the environment influences the CPUE of year i, according to different temporal locations (Fig, a, b, .. , e) of the critical stage (see text),

(U i)

nq+(n-1)q, 1+' ,+q, 1 nE,+(n-1)E, 1+ '" + E, 1 I JI-n+ I I~ I-n+ - -n~+-;(-n--1;-;)-+";(~n--2"):--+-,~,~, "'+"'17 -~n+--;-(n-_-017) +-'-:'(n'-_""27) +-,-,,"'+-";1~ ? se:::cuj scep, the remaining values of q in the models (corresponding to the

= q!Bi ) receive the index i. Finally, all instances of q can be '02 corresponding q(V) function, where V receives the same index

76· CLlMPROD

~.~.

,.

~~-. ~_.-.

as q. It must be remembered that the objective is not to determine the q value, but only to take into account its variability in the model.

. .• -'.•. ..

~~. ~'"

~,~.

5.

Transitional state when the environment influences both abundance and catchability of the stock

~'.

~_

Owing to the transition prediction approach and the simplifications retained in the formulae, the only acceptable cases are obtained when the weighting factors are the same for environmental influence on abundance and catchability. This condition is respected when the environmental influence on abundance concerns

all exploited year-classes. When using CLlMPROD in such cases with n exploited year classes and recruitment at age tr, the answers given to the questions "Age at the beginning of environmental influence?" and "Age at the end of environmental influence?" must be tr and tr+n-1 respectively.

~-.

~". ~ ~

~

~.

~-. ""' r.·.'vw

Ill;;

..

~'. ~

~

po.

p. p

,.

~".

~,,,

Notes

..." ...__ r ....... _ ... _ • • __ .........

"

,

.

_

.

.

_

~

.

-

-

.

"

.

,

_

.

.

,

_

,

___________

..- - - - , - - - .

"--~~~~====="'---'''~~~::~~~~~~~~?.~''~_~~.~'''C"A770'''S

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