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Experimentalinteractive software

for choosing and fitting- surplus production models

including environmentalvariables

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Food, and

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Nations

Experimentalinteractive software

for choosing and fittingsurplus production models

variables

P. Freon, C. Mullon and G. Pichon

ORSTOM213 rue Lafayette

75480 Paris Cedex 10, France

INSTITUT FRAN9AIS DE RECHERCHE SCIENTlFIQUEPOUR LE DEVELOPPEMENT EN COOPERATION

iii

:~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

~~~~e~;int9'1eth,:o~~g~7ds~·;~~~u;~Ua~;y ~~gu~~~~~t~~~r~[o;:,e CUi~iyt~~ ~~~~o~~0: its autho::"ities, or cO:1ce::"ning the delimitation of its frontiers orboundaries.

M-43

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

All rights reserved. No part of the procedures or programs used forthe access to, or the display of, data contained in this databasemay be reproduced, altered or stored on a retrieval system ortransmitted in any form or by any means without the priorpermission of the copyright holders, except in the cases of copiesintended for security back-ups or for FAO or ORSTOM internaluses (i.e. not for distribution, with or without a fee, to third parties).Applications for such permission, explaining the purpose andextent of reproduction, should be addressed to the Director,Publications Division, Food and Agriculture Organization of theUnited Nations (FAO), Viale delle Terme di Caracalla, 00100 Rome,italy. and to Service des Editions, ORSTOM, 213 rue lafayette,75480 Paris Cedex 10, France.

Data contained in this database may however be used freelyc,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 errorsccr dei'c..and.es. or Tor any damage that may arise from them, as wella" lcr P':"9Gm maintenance and upgrading, and documentation;u:3s<rs -3t2, GO''A'ever, kindly asked to report any errors or\..i,:;:-,::,c;::,::;,nC::"'0S {hiS vc'·duct to F,A.O.

FAO.. ORSTOM 1993

:,..,:ena[ional Business Machines Corporation.

,-adam"k' o! GORLAND INTERNATIONAL. INC.

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PREPARATION OF THIS DOCUMENT

This document is part of a series on stock and fishery assessment methodsprepared under FAO auspices to promote the rational management of fisheryresources. The computer programs distributed with the manual originate primarilyfrom national fishery research agencies, and hav" been modified to comply withFAO standards to permit easier use.

This software is the result of a cooperative programme between ORSTOM (InstitutFran9ais de Recherche Scientifique pour le Developpement en Cooperation),which conceptualized the product and the Fisheries Department of FAO, whichsupported its elaboration and reviewed it. It is still an experimental version thafcould be improved through use by and comments from the scientific community.The manual was prepared by Pierre Freon, Christian Mullon and Gaston Pichon(ORSTOM). The authors are'particularly grateful to S. Garcia (FAO) who participatedin the improvement of the software and manual, and to A. laurec, E.l. Cadima andD.S. Butterworth for their comments .and improvements of earlier papers on thistopic. The programs are interactive and should be easy to use, even by fisherybiologists or managers who have no computer specialist to assist them. As far aspossible, the authors have complied with FAO's requests to make the softwareflexible and reliable. This manual contains two main parts:

a reference guide which includes a brief theoretical section on conventionalsurplus production models and their limitations when stocks are unstable,and a general presentation of CLlMPROD and its objectives, data inputs andoutputs.

a user's guide which includes the system requirements, installationinstructions, and use of the compoter keyboard to start the programs andobtain on-line HELP.

Even though the software has been tested, unexpected difficulties in using itcould appear owing to the particularities of the recently developed TURBOPROlOG language, or to remaining bugs. As a last resort, assistance may berequested directly from the authors, who take this opportunity of thanking inadvance those users who can help improve the package by sending constructivecomments.

ABSTRACT

TABLE OF CONTENTS

REFERENCE GUIDE

E. INSTALLATION 19

1. Contents of fhe CLlMPROD distribution disk 192. System requirements....... .. 203. Insfalling CLlMPROD on your PC................. .. 214. Caution.. .. 225. Automatic CLlMPROD disk(s) backup 22

A. INTRODUCTION 1B. BACKGROUND, LIMITS AND OBJECTIVE OF THE GLOBAL

APPROACH . 21. Notation. .. 22. Background of conventional models 33. Introducing an environmental variable 34. Functions B=(V) and q(V) 55. Final models 66. Limits and objectives ot CLlMPROD 7

C. PRINCIPLES GOVERNING THE CLlMPROD CONCEPT.. 10D. PRESENTATION OF CLlMPROD...... .. 11

1. General presentation 112. Data input. .. 133. Monovariate statistics and graphs of raw data.. .. 134. Examination of time-series........................ .. ..135. Bivariafe graphics of raw dafa.. .. 146. Computer-assisted choice of the model..................... ..147. User-imposed choice of the model.... ..158. Model fitting 159. Stafistical tests of robustness (validation) .. 16

10. Output 16

USER'S GUIDE

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Freon, P., Mullon, C. and Pichon, G.CLlMPROD: Experimental interactive software for choosing andfitting surplus production models including environmentalvariables.FAO Computerized Information Series (Fisheries). No. 5. Rome,FAO, 1993. 76p.

The basic input and output is summarized as follows. CLlMPROD requiresannual data~series on catch and effort of a fishery on a singJe stock, andannual (or seasonal) data-series on an environmental variabfe knov,rn IO

influence the abundance or the catcnabi!i:y of this slock. At least '12years' observation are required. The software provides a s!a;istica1andgraphical description oi the data-se: and then a:.'b\'iS an appropriate mac-2:to be chosen, fiHing rr us~ng a ncn-!in-e2f regressbr; {Cut;",e arid tDass-ess the fit with paramet6c and ncn-p_arameuic tests :;:;·efc;r-e C""20;,o'0

the t:a.bies and -;raphs of (;'-.'S results. Tnese resu'i:s may -ex:dain h<>N6nvirc-nmen: and !ishing effort gc'>'erf).sd:he yiekis e! th·-e f:ishery cu"'~--;

the ::;''':i;c---j'..H',der $UJcy, 3as-ed cnaF, es::':T:.ate d the r"':6xt tw-o

Various equations allowing for the introduction of an environmentalvariable into surplus production models were proposed by Freon (1988).CLlMPROD helps the user select the most appropriate mode! for aparticular case, according to objective criteria. It resembles a simpleexpert-system and uses artificial intelligence language (pROLOG) toconverse with the user.

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1. Models available in CLlMPROD (equilibrium state)... . 692. Transitional stafes formulae: approach adopted............. ..713. Transitional states when the environmen influences

stock abundance........... . 724. Transitional state when the environment influences

stock catchability.. . 755. Transitional state when the environment influences

c0th acundance and catchability of the stock . 76

A. INTRODUCTION

REFERENCE GUIDE

During the Vigo Symposium on Long Term Changes in Marine FishPopulations. various equations allowing the introduction of anenvironmental variable into different surplus production models werepresented (Freon. 1988). One (sometimes two) additional environmentalvariable (V) has been inserted into the conventional models in order toimprove their accuracy. These variables appear in simple formulae. affectingeither stock abundance (surplus production) or the catchability coefficient.or both.

Conventional surplus production models are not suitable for certain stocksbecause fishing effort (E) variations explain only a small part of the totalvariability of annual production and catch per unit of effort (CPUE). In such aso-called "unstable stock". the residual variability often originates from theinfluence of environmental phenomena, which affect either the abundance(surplus production) or the catch ability of a stock. Previous attempts toincorporate environmental data in these models were purely statistical, andempirical multivariate regression analysis was unsatisfactory since it did notrepresent a real modelling approach.

CLlMPROD software can be used to fit conventional surplus productionmodels (using only E to explain CPUE variations) or some empiricalregression between V and CPUE. But. its original contribution concerns thechoice and the fit of a real surplus production model where CPUE variationsare explained both by E and V.

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UTILIZATION .1. Directory organization .2. Running CLlMPROD ....3. The CLlMPROD interface

TUTORIAL . .1. Introduction. . .2. The data file example.... . .3. Characteristics of the studied fishery4. CLlMPROD: presentation screen .5. Main menu.. . .6. Help . .7. Open or select a data file . 298. Updafe a dafa file .9. Select the appropriafe model and fit if .

10. See the chain of reasoning .11. F',t a model directly .12. Plot the model .13. Validate the model .14. Use the model for prediction carefully

F.

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APPENDIX A: BIBLIOGRAPHY.APPENDIX B: MAIN FORMULAE.

APPENDICES

vi

2·CLlMPROD Reference Guide· 3

(1 )

(2)

(3)

3. Introducing an environmental variable

Expressing absolute rate of exploited stock increase as a function of environmenfalcapacity and fishing mortality rate qE leads to the convenfional equation ofSchaefer's model:

If h is defined as the slope of the relative rate of population increase (h ~ : ),equation (1) can be rewritten as: =

For this linear case, surplus-yield models are based on the logistic equationexpressed in ferms of relative rate of stock increase:

The background and method for introducing an environmental variable into fhemodel are presented for the linear model only, More defails on the other modelsare presented in another publication (Freon, 1988),

2. Background of conventional models

Various terrestrial ecologists (synthesis in MacCaIl1984), have studied the effectsof habitat modification (in time or space) on this relationship, Habitat modificationcan in principle be introduced into equation (1) in three different ways: an effect on8= only, an effect on k only, or an effect on both 8= and k, Having analysed allthese cases, MacCall (1984) concludes that the latter is the most appropriate,specifically for the case of a constant slope for equation (1). That means that h isconstant in equation (2); it musf be noted that h corresponds to k1 from Schaefer(1954), who also considered it as a constant.

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instantaneous stock biomass

mean annual biomass during year i

environmentally limited maximum biomass or"carrying capacity" (K of terrestrial ecological models)

intrinsic rate of population increase (r of terrestriaiecological models)

time, conventionally in years

fishing mortality

catchability coefficient

annual fishing effort during year i, assumed to beproportional to F: Fi ~ qi Ei

annual yield

annual catch per unit of effort (or CPUE)

correspond respectively to 8, E, Y, and U underequilibrium conditions

maximum sustainable yield (MSY)

optimal CPUE corresponding to Ymax

optimal effort corresponding to Ymax

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B. BACKGROUND, LIMITS AND OBJECTIVE OFTHE GLOBAL APPROACH

The conventional notation, mainly lrom Ricker (1975), will be used in this paper:

1. Notation

4·CLlMPROD Reference Guide·

such that:

(8)

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(8.11)

(8.111)

(8.IV)a:j: 0 ; b :j: 0; c:j: 1 or bVc

a=O;b=1; and c:j: 1 or VC

a = 0 ; b:j: 0 ; c = 1 or bV

a:j: 0 ; b:j: 0; c = 1 or a + bV

The real mathematical functions B=(V) or q(V), linking an environmental variabl·with B= or q, respectively are generally unknown. Therefore a very flexible functiohas been used such as:

4. Functions B=(V) and q(V)

Functions (8.1) and (8.11) are justified in particular cases where a constant i:fortunately not required. The last function (8W) is still very flexible: if we are jusinterested in situations where B=(V) or q(V) are positive and monotonic functions, icovers a large number of situations.

The value of parameters a, band c (or the value of global parameters obtained afferestructuring) will be estimated by fitting the model to the data using the regressio,

which will be used only as a general form providing four particular cases where:

In some cases a single environmental variable may have opposite effect:according to its value. In upwelling areas, different processes have beelinvestigated (see Lasker, 1985 for a review); some authors have observe,opposite effects of wind stress on a'single species (Lasker, 1978; Parrish et al.1983; Freon, 1984; Mendelssohn and Mendo, 1987; Wroblewski and Richman1987; Wroblewski et al., 1989) and the concept of optimal wind stress wa:successfully applied to different upwelling areas by Cury and Roy (1989). Followin!the Mendelssohn and Mendo (1987) approach, they used a sfatistical techniqu<developed by Breiman and Friedman (1985) that estimates optimal transformatiOlfor mulfiple regression. Unfortunately this powerful descriptive tool does not allovquantitative modelling. In such cases, where B=(V) is non-monotonic, we hav,used the parabola (aV + bV2), but the Ricker form (aV e-bV) could also be use'(Freon, 1986).

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2 2Ye = EUe = qB=E - q2 ~ = q(V) B=(V) E _q2 (V) ~

Emex wiil be the value of E obtained by cancelling the derivative of equation (6)such that:

Using this formulation, environmental factors may come into play at only two levels:with q if catchability is changing, or with the pair of variables k-B= (the ratio 01 mesetwo variables being constant), if natural habitat variations are considered. !n th~

latter case, for ease of presentation, we only show the formulae where B= and nappear, and allow B= to change according to the environment. It should be noted_however, that any variation of Boo corresponds to an Inverse vanatlon in. k.Moreover, in the production model mathematical formulations, B= cannot Deinterpreted simply as the carrying oapaoity for the recruited stock_ Temporal andspatial processes affecting the survival of eggs and larvae may well limit the year­class before recruitment. In such cases, adult stocks Will not necessarily reach thecarrying capacity of their environment.

Let B=(V) be the function representing fluctuations of B= due to environmentalfactors, and q(V) the function representing fluctuations of q-

Schaefer's model assumes that, under equilibrium conditions, the rate ofpopulation increase is zero, which can be obtained trom (3) if:

6·CLlMPROD

technique. After restructuring, models with more than four parameters are "0tconsidered because they could reduce the degrees ot freedom too sUiJstar;!!2ii>jsince the data-series are usually short.

5. Final models

Following the line presented above gives several equations that describeenvironmental influence on abundance or catchability (Appendix B).

Numerous hypothetical examples of an environmenfal influence on abundance.through recruitment and/or poputation growth, can be found in the literature, suchas! influence of upwelling strength, relationships between stock production andriver discharges, influence of temperature during a critical stage (spawning, iarva!development), etc. In such cases stock production will depend on both fishingeffort 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, andtherefore linked to accessibility, especially for short-range fleets. Water turbiditycan increase either the vulnerability of fish to some kinds of gear (gillnets, trawls) ordecrease if (light fishing).

In some cases, it is reasonable to postulate fhat environment influences both stocKabundance and catchability. In such cases, q and B= will be replaced by functionsof V. We have examined only the simple case where both B=(V) and q(V) aredescribed by the function (8.IV) or by a parabola, in order to timit the number ofparameters. 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, thepast-efiort-averaging approach used for estimating model parameters in the case oftransitional states allows for the use of these models only in particular cases (seebelow).

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Reference Guide· 7

6. limits and objectives of CLlMPROD

The structural approach in stock assessment is supposed to give more reliableresults than the global approach because the firsf uses biological information(natural mortality, growth parameters, age or length structure in fhe catches) whilethe 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 ~). Therefore simple surplus

production models have been criticized because they suffer from lack of biologicalrealism. Nevertheless, they are still widely used and accepted in many quarters,especially in tropical areas where biological parameters and/or age structure ofcatches are often not available, and where environmental factors are often thepredominant influence on producfion of short-lived species.

In such areas fish ageing is often difficult and requires expensive and intensivesampling owing to the high variability of fish lengfh within the cohorts associatedwith a special type of aggregation small pelagic species (Freon, 1985). In suchcircumstances the usual analytic methods are hardly usable. Moreover, when only arough age-structure is available more sophisticated age-structured models, asproposed by Deriso (1980), often do not perform better owing to difficulties inestimating to additional parameters (Ludwig and Waiters, 1985). CLlMPROD usesonly one additional variable and zero to three (but most often one) additionatparameters as compared with conventional surplus production models.

The artificial intelligence in CLlMPROD allows the use of any additional quantitativeor qualitative data which are not included in the model as variables. It thus helps theuser to choose the best model equation according to the stock characteristics, andnot only using the criterion of the best fit. It has been demonstrated that thiscriterion does not necessarily provide thJl most realistic policy prescription (Uhler,1980). The present approach can provide better assessment and management ofthe stock by taking into account the user's knowledge of the stock biology orstructure, and the expert's experience of other stocks.

Some negative aspects of CLlMPROD should also be underlined. Althoughenvironmental production models do not need quantitative biological data, it isnecessary to have some minimum knowledge of the species ecology for theirproper use. This tool will be made available to fishery biologists or fisherymanagers, and can be used to fit any model without special knowledge ofpopulation dynamics. The program asks the user to respond to various questionsregarding the basic assumptions underlying the models. The user, however,remains responsible for the answer given and for all potential subsequent errors.

8·CLlMPROD

The introduction of an environmental variable into global production modeisincreases the number of parameters in the final formulation, and consequenHythere are tour main ditflcultles:

Although the quality of the fit is improved, the confidence limits of theparameters are often high and the titting procedures may be unstabie.

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

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

By Increasing the number of explanatory variables one also increases theprobability of obtaining good correlations by chance, Independent of anyreal biological phenomena (Gulland, 1952: Belt and Pruter, 1958; Ricker,1975, p. 227-279). The literature provides many examples of good hlsforicalfits which break down as soon as the model is used for forecasting.

These ditficulties, common to any multi-parameter regression, can be overcome byan objective choice of variables (supported by biological observations as tar aspossible). As underlined by Bakun and Parrlsh (1980), selection of theenvironmental variable to be introduced Into the model must, as far as possible, bea priori and not only empirical (they present a list of likely variables). Objectivechoice of the environmental variable is often the key to avoiding spuriouscorrelations.

In addition, these models still have the usual limitations of conventional surplusproduction models, linked to their basic assumptions, as discussed by Fox (1974).Even after modification, they remain empirical procedures for assessing fish stockresponses - in terms of biomass and yield - to changes In the rate of fishing andenvironmental conditions. Therefore they represent a blind approach forinvestigating recruitment variability.

The utiiization of these models for predictions is not devoid of risks. It requires arorecast 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 predictionswithin the observed ranQe of the variables would be hazardous, and of course itwould be even worse to forecast using input values outside the observed range.

V.,then causal environmenta1 factors and/or processes cannot be forecast and havea short-term effect, the propGsed approach can only serve to assess the range of

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Reference Guide· 9

environmentally-induced fluctuations and compare It with that due to fishing. Thiswould, however, be useful because it could Improve management sfrategles,partiCUlarly when stocks are at the upper and lower ranges of their blomass and/orcatchabillty.

Nevertheless, owing to fhe strong limitations of fhe global approach, CLlMPRODmust be considered first of all as a training tool. From real or simulated data, Itexplains how the environment can confrol the yield fhrough its influence onabundance or catchability. Therefore, it will show that different MSYs can beobtained for each stafe of the environmental variable, or at least a different Emaxwhen only catch ability is modified. In other respects, it is shown fhat these modelscan explain how wide fluctuations in the catch (and sometimes collapses) mayoccur, without any increase in the nominal effort, as a result of environmentalchanges. However, long-term changes in population dynamics of some species(especially small pelaglcs) are often unpredictable with the present state ofscientific knowledge because the whole ecological system may suddenly shift froman equilibrium relationship between the stock and the environment (in the widestsense of the word: climate, prey, competitor species, predators, etc.) to anotherequilibrium relationship. In such cases, two different models must be used for thetwo periods (see Cury, 1989, tor discussion).

10 • CllMPROD

C. PRINCIPLES GOVERNING THE CLlMPROOCONCEPT

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

It is assumed that CllMPROD deals with imperfect and limited data and tries toapply imperfect models, using as much ancillary data as possible to reduce thescope tor gross errors, as previously mentioned. In respect to this last point.artificial intelligence is used to choose appropriate questions according to the casestudied and to available information on the stock structure, the species biology orthe fishery.

CllMPROD also tries to foroe the user to look at his data-structure and interpret ithimself before seeking the help of statistical tools. For instance, a simple scatterplot at CPUE versus V is shown before asking the user first if the relationshipbetween the two variables looks monotonic or not, then linear or not. Of course. astatistical response to these questions could easily be obtained, but when outlierpoint(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 beforecast.

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

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Reference Guide· 11

D. PRESENTATION OF CLlMPROD

1. General presentation

The software is written for PC/XT/AT compatible microcomputer using MS-DOSversion 3.0 (at least). It is fully interaotive and has two main objectives: first, a normaldata management function, statistical and graphical utilities that uses TURBO Clanguage; second, a guided selection of the appropriate model, showing theinformation path. This part of the model uses an inference engine, written inTURBO PROLOG. It applies about one hundred rules which are interactive withinformation provided by:

questions to the user on the stock characteristics, independent from thedata set (example: lifespan of the species?),

statistics on the data-set (example: ratio of effort range on minimum effortvalue),

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 isstructured and does not necessarily use the whole set of questions. An example oforder 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 itwith a full screen editor; to search for the most suitable model, or to choose onedirectly; to validate the model (assess"the fit); to plot the model function, thepredicted values and the residuals; to use it for prediction and finally to see thepath of the expert decisions.

It should be noted that in order to choose among 30 multivariate models (seeAppendix B), the program first performs a regression considering the CPUE as thedependent variable and the effort (or the environment in some cases) as theindependent variable. From the graphic display of residuals of this regressionagainst the environmental variable, the user may determine which kind ofrelationship will link environment and CPUE in the final'multivariate model.

This procedure provides an easy interpretation and visualization of the process ofselecting a model, and allows interactive dialogue with the user which can

Question: most im artant influence on U ?

12· ClIMPROD

IT

Reference Guide· 13

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

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 lattervariable describes any environmental factor likely to modify the fishery cafches.Common examples are temperature, saiinity, wind speed, turbidity, strength ordirection of currents, river outflow, etc.

2. Data input

3. Monovariate statistics and graphs of raw data

4. Examination of time-series

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

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Environment (V)

Model U = f(V) fitting

Questions on the relationshipbetween U and V from graph

U=f(V)

Questions on the relationshipbetween U=1 V residual and E

ITSummary of statistical results

ITEffort (E)

Questions on environmentalinfluence

Model U=f(E) fitting

IT

Questions on the relationshipbetween U-f(E residual and V

JJ

Questions related to the stockand to the species biology

Summary of expert decisions

Model U=fhE,V) litting

Questions on model validation

Questions on the relationshipbetween U and E from the graph

U=f(E)

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

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

14· CLlMPROD

5. Bivariate graphics of raw data

The following relations are plotted: Y versus E, Y versus V, U versus E, U versus Vand V versus E. These graphs reveal any oullier points which can affect thestructure of the data-set, or any strong relationship (linear or not) between the twoindependent variables E and V. It must be emphasized that at presenf the programdoes 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 andBeverton, 1963; Fox, 1975) are systematically asked, and the program stops ifthese assumptions are not met (see user's guide). The following questions are alsosystematically asked:

do you think that the the influence of eflort on CPUE is more important thanthat of the environment (if unknown, yes Is assumed)? The answer, guidedby statistical and graphical help, orients the program either to U=f(E) or toU=f(V) models;

does the environment influence abundance, catchability or both? Theprogram does not provide any help in answering this question. It issupposed that the user knows the mechanism of action of the environmenton the stock, or has already performed time-series analyses using a monthlyor weekly time-interval (Freon, 1988) to determine it the environmentpresents an unlagged or short-lagged (influence on catchability) or a laggedrelationship with CPUE (influence on abundance or both abundance andcatchability).

Between these two questions, the program will ask one or several questions inorder to determine relationship the most suitable between U and E (Schaefer'siinear model, Fox and Garrod's exponential model or Pella and Tomlinson'sgeneralized model), and between U and V (linear, exponential, general orquadratic). Formulae are presented in Appendix B and the complete set ofquestions appears in the user's guide.

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Reference Guide· 15

7. User-imposed choice of the model

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

8. Model fitting

For non-equilibrium conditions (transitional cases), the equilibrium approximationapproach is used (Fox, 1975): a weighted average of E and/or V Is computed. Incases of delayed influence of the environment on abundance, a lag is insertedbetween U and the weighted average of V (see Appendix Band Freon (1988) forfurther details).

The Marquardt algorithm is used for least-square estimation of non-linearparameters. Depending on the model, the initial parameter values are 1, 0 orcomputed from the original data set in linearizing the equation before running thealgorithm. 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 R2<40%, the program stops orinvites the user to give new answers to the previously unansweredquestions. If R2>90%, a validation of the blvariate model can be tried. If40<R2<90%, the program will try to find a multivariate U=f(E,V) modelproviding a better correlation than the bivariate one;

after a multlvariate model has been chosen, validation intent is possible if2

R >70%.

it must be noted that the R2 boundaries mentioned above are completely arbitraryand do not take into account the degrees of freedom of the model.

16· CLlMPROD

9. Statistical tests of robustness (validation)

The fit assessment is mainly based on a jackknife esfimafion of the paramefers andof R2 (Duncan, 1978; Elron and Gong, 1983), and on the confidence limits of theregression coefficients. It also takes into account the residual analysis and data setcharacteristics. Predicted values of the model and of its residuals are presentedgraphically, and the user's opinion of these graphs is sought.

10. Output

a. Description of the data-set

As already mentioned, ClIMPROD provides a description of the data-set fhrough astatistical table, histograms of frequency distribution, time-series and bivariategraphs concerning the four variables.

b. Mathematical results of the model fitting

For each trial at model filting, the program displays the formulae of the equation,the value of each coefficient of regression and R2. If R2 > 70%, the followingresuits of the jackknife are displayed:

table of R2 and regression coefficients estimated by jackknife whenremoving the successive yearly data;

mean value of the R2 jackknife estimation;

jackknife standard deviation of the regression coefficients and t test

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Reference Guide· 17

c. Graphical results of the model filling

Graphs of the above mentioned mathematical results are displayed. When the fit isaccepted, the program first displays a time sequence plot of the observed andpredicted values of CPUE and then one of the residuals. Then the shape of theequation is presented in two graphs; in the case of simple regression, one graph isa lineplot of CPUE versus V (or E), the other of Y versus V (or E). When productionmodels take into account both V and E, the three-dimensional representation isnot retained but two lineplots are drawn on each graph: one corresponds to thehighest observed value of V, the other to the lowest one (three lineplots aredisplayed when g(V) or B=(V) are non-monotonic functions). For these models,iso-density diagrams of Y and CPUE are also presented, showing the location ofmaximum yields according to E and to V. Last, two graphs present the plot of MSYand Fmax versus V.

d. Limited predictions

The predictive capacity of the surplus models is usually very poor, especially whendata on overexploitation periods are not available. Therefore ClIMPROD onlyallows CPUE values to be predicted for the next two years (by entering estimatedvalues of E and V), mostly for training purposes.

e. Summary of expert decisions

At the end of every step of the main menu. the user may display the path tollowedby the program at each level ot decision, with the corresponding rule number. Thispath can be stored in a fite.

Main program

1. Contents of the CLlMPROD distribution disk

COPYCLlM.BATMODEL1.TXTMODEL13.TXTMODEL17.TXTMODEL20.TXTMODEL24.TXTMODEL28.TXTMODEL31.TXTMODEL7.TXTCOM47.TXTEND.HLPACCEPTAB.HLPSTOCKDIV.HLPPROLOG.HLPLlNEAR.HLPLlFESPAN.HLPDURATHLP

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CLlM.BATEXAMPLE2.CLlMODEL12.TXTMODEL16.TXTMODEL2.TXTMODEL23.TXTMODEL27.TXTMODEL30.TXTMODEL6.TXTCOM48.TXTBEGIN.HLPSAVE.HLPVALlDE.HLPINDEPEND.HLPDECREAS.HLPOBVIOUS.HLPINFLUEN.HLP

INITIAL$.$$$EXAMPLE1.CLlMODEL11.TXTMODEL15.TXTMODEL19.TXTMODEL22.TXTMODEL26.TXTMODEL3.TXTMODEL5.TXT.MODEL9.TXTCLlMPR.HLPPESSIMIS.HLPINCREASF.HLPUNDOPTHLPINFLUENC.HLPUNSTABIL.HLPAGEREC.HLP

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USER'S GUIDE

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CLlMPROD.EXE

ASCII files

System files

ATT.BGIIBM8514.BGISANS.CHR

E. INSTALLATION

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CLlMPROD requires the tollowing hardware and operating system:

an IBM or 100% compatible Personal Computer (PC,XT,AT)

at ieast 512 Kbytes RAM (random access memory)

one disk drive tor loading the program and a hard disk with at least 1.5Mbytes available

MS-DOS, Version 3.0 or higher

a standard DOS keyboard

a printer it you require hard copy an output ot the results and graphs (at themoment the soitware is not interfaced with plotters)

a mathematicai co-processor is not required but will be very useful forreducing computer time in model fitting and validating

2. System requirements

20 • CLlMPROD

SUBSTOCK.HLPLAGEFFE1.HLPPUEUNSTA.HLPOUTLlER.HLP

Executable files

MODELE.EXEINITIAL.EXECLlMLOGO.EXE

SINGLESTHLPCOLLAPSE.HLPRATIO.HLPISOSTOCK.HLP

VALlDE.EXELECPARA.EXE

LAGEFFE2.HLPABNORMAL.HLPSTANDARD.HLPFISHMORE.HLP

STATIS.EXEPREDICT.EXE

CHANGES.HLPADDITIF.HLPPROTECT-Ht?NOMFIC.HLP

GRAPHE.EXEEDITION.EXE

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User's Guide' 21

3. Installing CLlMPROD on your PC

Before you proceed to insfall CLlMPROD, first make a backup copy of the originadiskette and keep your original in a safe place.

a. automatic installation (install.bat)

To automatically install CLlMPROD on your hard disk, insert the ClIMPRO[diskette in drive A (or B), then at the DOS prompt type 'A:' and press the 'ENTERkey. Type 'INSTALL' followed by the name of the source drive, the name of thEdestination hard disk and the number of diskettes. For instance, it you want teinstall CLlMPROD on hard disk C from drive A with one high density diskette, type:

INSTALL A: C:

Then press the 'ENTER' key again and follow the instructions on the screen. ThEsottware will be installed on your hard disk in a directory called CLlMPROD. 11 yOlwish a special installation or if your drive is not named A or S, or if your hard disk i~

not named C or D or U, please install CLlMPROD manualiy.

b. manual installation

First you have to create a CLlMPROD directory on your hard disk. It must contain althe CLlMPROD files: the CLlMPROD software and the data files. For example, tecreate a directory called CLlMPROD on your hard disk C, type:

MD C:ICLlMPROD

Then choose this directory as the working directory by typing:

CD C:ICLlMPROD

Then insert the CLlMPROD diskette in drive A and copy all CLlMPROD files in thECLlMPROD directory by typing:

COPY A:'" IV

User's Guide· 22

3. The CLlMPROD interface

CUM

: questions and current known facts tiles

: executables files

: help files and text files

: interlace files

: user's data tiles

'.$$$·.EXE

·.HLP, ·.TXT

·.BGI, ·.CHR

".CLI

For reasons of portability, CLlMPROD does not use the Mouse tacilities or plotter 0

printer interfacing (you can simply use the 'print screen' key; in this case the MSDOS command 'graphics' must be included in your autoexec.bat file or from thEkeyboard before running CLlMPROD).

CLlMPROD has a user-friendly interface. It is driven by pulldown menus: the usehighlights an option with the arrow keys of the keyboard and then validates hi,choice wifh the Return key.

To choose the CLlMPROD directory as working directory type:

CD C:ICLlMPROD

Then to start the program type:

2. Running CLlMPROD

All the CLlMPROD files must be in the CLlMPROD directory, with the followin,convention name:

1. Directory organization

F. UTILIZATION

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If you wish you can easily duplicate your CLlMPROD disk(s) after installation. Type'COPYCLlM' from your CLlMPROD directory and follow the instructions on thescreen.

DEVICE=ANSI.SYS

5. Automatic CLlMPROD disk(s) backup

4. Caution

22· CLlMPROD

CLlMPROD uses the complete ASCII code. If you see strange characters on yourscreen, a possible reason is that your computer does not know the complete ASCIIcode. If this happens, with any text editor, modity the CONFIG.SYS file and insertthe instruction:

24' CLlMPROD

G. TUTORIAL

1. Introduction

For a practical introduction to the use at CLlMPROD and to become tamiliar with ailits tunctions, it is suggested that you run the CLlMPROD demonstration.

To start a demonstration at the DOS prompt type:

CLlMDEMO

Then select the data file EXAMPLE1.CLI but do not modi fy the data file. Chooseform the main menu "Select the appropriate model and fit it" and answer theCLlMPROD questions.

In order to complete the demonstration, select successively all the options in theCLlMPROD main menu and enter the suggested answers that appear inparentheses at the end of each question.

If you wish, you can repeat the process trying your own answers and noting thedifferences in CLlMPROD's results.

You must always exit the CLlMPROD program after completing a demonstrationsession started with the command CLlMDEMO.

2. The data file example

The data iiie used forthe tutorial procedure is EXAMPLE1.CLI. It contains data onsardine catches and wind intensity during the upwelling season in the Senegalesepurse-seine iishery ior the years 1969/1987.

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User's Guide· 25

3. Characteristics of the studied fishery

The exploitation concerns mainly a sUb-stock of juveniles and young spawnerswhich leave the nursery after first spawning. Owing to the particularity of fhe stock·recruitment relationship and of the moderate level of exploitation of the adult stock,this sub·stock can be considered relatively isolated.

No major change has been observed in the fishing pattern and the fishing effortunit has been standardized. It is in fact a tentative abundance index calculated frorrschool size estimation. The CPUE changes are supposed to be representative 01changes in abundance. The time·lags and deviation from the stable age·structurEhave negligible effects on the production rate. The fishing effort vanatlons arEknown to explain most of the variation in CPUE.

The upwelling index is obtained by averaging the wind speed during the upwellin(season. The inter-annual variability of upwelling is relatively strong but the dat,series presents a significative coefficient of autocorrelation with a one-year lag. A!the average CPUE for one year is supposed to be influenced mainly by thEupwelling of the same year and secondarily by the upwelling of the prevIous year, Ican be stated that the upwelling variability is not too strong, The effort time-sene'are highly autocorrelated, as are the production and CPUE.

There is no reason to expect highly unstable behaviour in this stock. It nevecollapsed in the past; the litespan of the species is around six years, and mainl~

one year-class is exploited by the Senegalese fishery.

The environment influences abundance through variations in primary an,secondary production throughout the lifespan of these plankton feeding fishesLet it be supposed that there are nofarge fluctuations in CPUE. when the stock "overexploited (this is in fact questionable). Age-at·recruitment IS one year (With"the first year). The environmental effect is from year 0 (spawning) fa year 1.

26' CUMPROD

4. CLlMPROD: presentation screen

When you start the program by typing:

CD C:ICUMPROD

CUM

the following screen is displayed:

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User's Guide' 27

5. Main menu

After fhe presentation screen. you reach the main menu of CLlMPROD.

~-------------------------------c L I M PRO D -------------------------------*i

IV,;.1N MSNUl *

*------------------------------ ? -----------------------------*loper: or selecta.data filE:

:·~~:~~-~o~a~~D;~~~iat:model and fit itI ; sce the" chii"i.n· or" reasoning - -- -'---------, fit-a model dIrectly*---------iPlot the modelI jvalidate-the mOdel: :~~~pca reIully_the_model_.foJ:_predict ion

I IstopI *----------------------------------------------------------------*._------------------------~~--------------~-~-------------------~-~------------*

Choose your option by using the arrow keys of the keyboard. Then press theReturn key fo confirm your choice.

28' CLlMPROD

6. Help

Most ot the menus allow on-line help. In some cases you will have to use the arrowkeys in order to read the complete message. This is an example of the help tile ofthe main menu.

"-------------------------------c L I M ? ROD -------------------------------"M..".IN M;';NU

iFrom this :'Hain menu you can;

1- OPC[] or select a c':'la file: this is the first step to takeI before attempting any other option.I1- Update a O<l.t<l file: allows you t.o correct or to add new data to a da~·.a flle.!I1- Select the appropriate model and fit it; an expert-system will helpIyou to choose tile appropriate model according to your case.I1- See the cha~.n of reilsoni~lq: after selecting ;:he model, you are allo,.edita loo:~ at :h8 ch.';:n of reasoning used by the expe.::-c.-system for its c~,oi(:('.

!

--------------------------------M S S SAG E $-------------------------------"Use <1rro;,' keys (if necessary) and press <1ry key to c<:ln::.i:1>O.c

------------------------------------------------------------------------------"

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User's Guide· 29

7. Open or select a data file

You have to select a data file.

If this has not been done, and if you select anofher option, ClIMPROD will answer"Data File not opened"

a. Opening an existing file

When you choose this opiion. the following screen appears:

*-------------------------------c L I M PRO D -------------------------------~

I

1'----------------------------------------------------------,! 1;"i1e::a;1'.c (.cl!.) or !::NTr:R key to get fil'" list:i~----------------------------------------------------------,

*------------------------------------------------------------------------------,"------------------------------------------------------------------------------,

When the "Filename (.cli)" field appears, type the name of your dafa file. This filemust be in the CLlMPROD directory. If nof, the program will open a new file in theCLlMPROD directory.

b. Creating a new life

From now on, you will work with this file, called SARDINE.

When the "Filename (.cli)" field appears, type the name of a new data file.

User's Guide· 31

Envir. V<1 • 4

<1.324.7

5.635.535.765.665. "195.725.214.68'1.985.094.86

4 . 64.675.385. f, 44.92

year: 1969of years: 19Ef fort E

146.5127.6

130.34208.06243.66386.44320.22413.17430.39509.67

461. 9398.41535.44551.61720.42631.72

807.1760.06

1100.92

FLrs':.NumberProd.332. !;282.5306.753"?2599.4692.5612.9809.!;

776"764

691;. "7·;02. !;788.7

688719.7677.3

845.03958.431203.9

The data file is created with zero values. It is then edited with the CLlM PROD dataeditor which is presented in the following section.

As a short exercise, try to introduce the following data, under the name ofSARDINE, corresponding to the data of the EXAMPLE1.CLI file.

Following screen prompts, you will indicate the "First Year" and "Number of years"in the data-set.

'lea!:"1969197019711972':'9D19741975197619771978:979198019811982:. 9831984

9851986:. 98-'

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*-------------------------------c L r M ? ROD -------------------------------"II!

I1"--------------------------------------------------------.! I Filenarne (.eli) o'!: ENTER key to gee file li-st: i1'--------------------------------------------------------"~ I EXi\-,'1PL£l _eLL ,:XA'1?L";2 . Cl, I ,.;XA''1?Lj.:3 _eLl i ----------------------------.':' ---------------------------_.

11•• _-----------------------------------------------*---------------------------_.

EXAMPLE2.CLI and EXAMPLE3.CLI correspond to the Moroccan sardine fisheryand to the Ghana-Cofe d'lvoire sardine fishery respectively.

The file EXAMPLE1.CLI contains the data used as a CLlMPROD demonstration(Senegalese sardine fishery).

If you do nof know the exactly name of your data file, press the Return key: the listof CLlMPROD data flies appears in a window; select the one desired with the arrowkeys and confirm your choice with the Return key.

30· CLlMPROD

32· CLlMPROD

8. Update a data file

If you want to modity your data file, choose "update a data file" from the main menu.

The data editor screen is displayed:

*----------*------------*------------*-------------*I YEAH I PRODUCT I EFFORT El ENVIR. v I*----------*------------*------------*-------------*

19571 1936.00 30.50 22.83!1958 t 1695.00 46.30 23.56119591 1950.00 39.40 22.5011960) 1845.00 26.60 22.39119611 2098.00 26.60 21. 28119621 2068.00 30.30 22.00119631 1571.00 31.40 23.22!1964 I 2283.00 40.40 22.6711965 i 2264.00 '12. '1 0 22.06119661 2376.00 40.80 22.281196"1 I 2471. 00 48.20 22 _06119681 1971.00 47.30 21. 94119691 1927.00 38.70 23.331

*----------*---------------------------------------**--------------------------------------------------*

ESC key to cnd Ix *

You may change any vaiue by selecting with the arrow keys and then fyping thenew value. Use the arrow keys to validate this vaiue and to move to another cell(you do not need to use the Return key).

At the end of the updating process, press the Esc key and then:

if you want to add new years of data, at the beginning of the program, answer"YES" to the "Add new years to the data set?" question, and indicate thenumber of years of data you want to introduce; after this option, the dataeditor screen appears again with new values equal to O. Move the cursor tothe appropriate cell using the arrow keys and enter the new values.

if your answer is "NO" to the "Add new years to the data set?" question, youhave to choose whether or not to save your modifications. Then answer"YES" or "NO" to the "Save?" question. If you save, then you can proceed tocalcuiations on the modified file. If you do not save, the corrections arecancelled and the file is not altered.

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User's Guide' 33

9. Select the appropriate model and fit it

a. Introduction

This option is the most important feature of the CLlMPROD software. It has beendescribed in the Reference Guide of this manual.

Its purpose is to iimitthe occurrence of spuriously good fits by systematic triais of allthe availabie models. Given a time-series of environmental data and fisheries data, agood fit will often occur if differenl lags between CPUE and environment are tried(this risk increases if several environmental variables are successively used).Therefore the present CLlMPROD option allows a model to be selected not onlyaccording to the dala but also to external information on the biology of the specie,and general knowledge of the population dynamics of the stock (e.g. life spanknown historicai collapse). Nevertheless spurious correlation may occur, and thEuser must be very careful in applying such a model (see Reference Guide for,discussion of fhis point).

This part of the software is an elementary "Artificial inteltigence" program. Iprovides a "user-assisted" selection of a model from a fairly iarge number 0

options.

"------- x

"------------------------------------------------------------------------------"

If you answer "YES" to this question, you will continuously see messages such as:

ROD ------------------ *

II,

User's Guide· 3,

"--------------------------------M E S SAG E $--------------------------- ";?~ess any key to continueII,

·-------------------------------c L 1 M-iT t~y to apply the rule number: 45iA basic ass~~ption is not verified if:,----stock is not single!----there is a sub-stockI----this sub stock is not well is01",teo

These messages help the user to follow the reasoning of the expert-systemguided by the user's answers.

It is suggested that you answer "NO" if you are using CLlMPROD for the tirst tim,and if you want to have a qUick look at its facilities.

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--------------------------------------------------------------------------*

j'------------------------------

*-------------------------------c L I M ? ROD -------------------------------*ICu:::::c~t known faer,s

Fi le·-· C: \USERS\C1,lM?ROI)\CREV .eLlNb year" 26

-Max ..'; 5S. 200000

liDo you '~'an~: to trace all t.hc proccd~re of ru1",,­: I application?!"----------------------------------------------------------------*

b. Tracing

The first question asked by CLlMPROD in the Select Model Procedure is abouttracing the procedure ot rule-application.

34· CLlMPROD

36·CLlMPROD User's Guide· 37

"----------------------------------------------------------------*

"----------------------------------------------------------------~

ENV. V iC.P.U.S. I£C'FORT!PRODUCT!STATIST 1

Cases! 26.00 26.00 26.00 26.00 iMeap.! 1960.85 40.52 50.38 22.60 !

V<L'-iance! 68167.66 61.41 156.85 0.371Stana-aevl 261.09 7.84 12.52 o.6liCoe:'. Var , 13.32 19.34 24.86 2.691

Kl.lrtosisl -0.57 -0.47 -0.20 -0.43!S:':eY;ness I 0.32 -0.1 0.40 -0.011~lr:imum! 1569.00 26.60 32.17 21.28!:-':<!ximurn! 24"11.00 55.20 78.87 23.611

kT:plitudel 902.00 28.60 46.70 2.33!~edj.an! 1942.50 40.50 49.91 22.55!

O:x,;;,:'.ip.e cacefully this table and detect abnormal distributions

IM 0 N 0 V A R I ATE S TAT 1ST I C A L TAB L E

*-------------------------------c L I M PRO D -------------------------------*I I

i*~------------------------------~~-~~-~---~~---------------------,

i !Nurubec of significantly exploited year-classes?i!!*~~~--~-----------------------------~---~~~~-~-~-----------------*

I~~~---------------------------- ~-~~-~~-~--------------------.!illI : 2 I 1"j3 I----------~~*

• i 4 I-~~~~~------·

I i 5 I II·-------------------------------------------~--------------------* 1I I

II

f. Question on statistics

ClIMPROD asks you a question about the standard univariate statistics ot yourdata.

e. Questions on biology and environment (example 2)

Comments: This information is used to expose possible "non-equilibrium" problems(transitional states) in the data and to smooth the time¥series by a moving average.

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!:5 the fishir:g offort. unit stand<lJ;dizcd and ist.he C?U£ orooortional to abundance?

._--------_:__:_-------------------------------------------------*

* c L I M PRO D -------------------------------"

d. Questions on biology and environment (example 1)

"-----------------------------------------------------------------------------_.

Comments: this is a basic assumption of which the user must explicitly be aware. It looksobvious, but in practice is often neglected.

After the question on tracing, CLlMPROD asks you several questions about:

biology and environment,

elementary statistics on the data-series,

graphical evidence on diagrams of the data-series.

To understand how the program runs, answer these questions following yourintuition. See below for detailed example of CLlMPROD questions.

The screen, for questions about biology and environment of the fishery, has thefollowing appearance:

c. Different kinds of questions

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

Then comes a question about the univariate histogram of the data. Try to detectoutlier points.

38' CLlMPROD

E tiMe plot

User's Guide· ,

.1.10.1

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i. Graphical questions (example 3)

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

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

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

h. Graphical questions (example 2)

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

g. Graphical questions (example 1)

r----~ ... ,~-- ...~ .."..~-------Y distribution

40' CLlMPROD

j _ List of CLlMPROD questions on biology, population dynamicsand environment

The following questions are asked by CLlMPROD:

Have there been changes in the fishing pattern during the period (effortallocation, quota, mesh-size, ...)?

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

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

Does the data-set apply to a single stock?

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 ofunderexploitation

Do you think that the data-set covers periods both of underexploitation andof optimal exploitation

Is the influence of fishing effort (on CPUE) more important than theenvironmental influence?

Do you have any (addilional) reason to expect highly unstable behaviour orcollapse of the stock?

Did the stock already collapse or exhibit drastic decrease(s) in catch?

What is the life span at the species?

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

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

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

Is the single stock subdivided into various geographical sub-stocks (all mustbe exploited by the fleet) ?

Are there natural protected areas for the stock, or constantly inaccessibleadult biomass?

Does the environment influence abundance, catchability or both?

Number of significantly exploifed year-classes?

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User's Guide· 4

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

YES, to the 'Is the sub-stock well isolated (with few exchanges) from othersquestion

NO, to the 'Do you think that the dataset covers periods both of overexploitaticand 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 environmentinfluence?' 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 unstatbehaviour or collapse of the stock?' question

42· CLlMPROD

NO, to the 'Did the stock already collapse or exhibit drastic decrease(s) incatches?' question

6, to the 'What is the life span at the species?' question

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

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

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

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

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

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

YES, to the 'Does this plot look monotonic?' question

1, to the 'Age at recruitment?' question

0, to the 'Age at the beginning of environmental influence?' question

1 to the 'Age at the end of environmental influence?' question

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 MSYgraph?' question

I. Results

At different steps of the "select the appropriate model and fit it" option, results onmodel fitting and validation will be dispiayed. As these results are the same asthose 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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User's Guide· 43

10. See the chain of reasoning

a. Results

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

--------------------------------c L I M ? ~ 0 D -------------------------------*[You iloswered: Yf:S, to the question: .. _.. Do you want to trae", all the !iP!."ocedure of r1.l1e application? i,You ,):15wered: NO, to the question: .. ... Have there beer. any changes ir: the I;fishir.g piltten~ during the period (efforr:. ill location, quota, mesh size, ) !IYo\) answered: YES, to the question: .•• _.Is the fishing effort unitistandardized and is the CPUE orooortional to abundance?!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-glelst.ock?IYo\) answered: YES, to the question: ••••• ls the influence of fishing effortImore important than environmental influence?IYOLl answered: YES, to the question: ••••• Does this plot appear to beIdecreasinq? - - - - - -IYou answered: YES, to the question: ..•.. Do you think that the data coverIperiods both of overexploitation J!1d of underexplOitation?l'fou ans'...rcred: NO, to the question [._----------------------------------------------------------------------------_..--------------------------------~ E S SAG E $-------------------------------.i Press ESC key to end

*-----------------------------------------------------------------------------_.

Use the arrow keys to see the complete text.

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

c. An example of .REASON.DOC file:

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

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

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

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

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

You answered: YES, to the Is the influence of fishing effort more important thanenvironmental 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 previoustable? 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

You answered: YES, to the Are the two distributions independent? question

You answered: YES, to the Does this plot looks obviously linear? question

From rule number 17 I infer that the relationship between CPUE and effort isperhaps governed by equation CPUE~a+b.E

You answered: 1, to the Number of significantly exploited year-classes?question

I fit the model CPUE~a+b.E and find a coeff of determination: #77

You answered: abundance, to the environmental influence? question

You answered: NO, to the May the stock present large fluctuations in CPUEwhen overexploited? question

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

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

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User's Guide· 45

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

From rule number 30 I infer, knowing the relation between CPUE and E isCPUE~a+b.E, and the environmental effect is on abundance, that the globalmodel is perhaps CPUE=a.V'b+c.E, and the relation RES V: CPUE=a.V'b isto 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 isCPUE=a+b.E, and the environmental effect is on abundance, that the globalmodel 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 andenvironmental 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 equationCPUE~a.V+b.V'2+c.E

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

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

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

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 overtwo years are not reasonable.

The most suitable model is CPUE~a.v+b.V'2+c.E

46' CLlMPROD User's Guide· 47

b. List of CLlMPROD models

(exponential)

(linear)

(generalized)

(linear)

(exponential)

(general)

(quadratic)

I

(linear-linear)

(linear-linear)

(linear-exponential)

(linear-quadratic)

(exponential-linear)

(exponential-linear)

(exponential-linear)

(exponential-exponential)

(exponential·exponential)

(exponential-quadratic)

(generalized-exponential)

(generalized-quadratic)

U=a+b.V+C. E

U=a.VAb+c.E

U=a+b.V+c.VA2+d.E

U=a.V.exp(b.E)

U=(a+b.V).exp(cE)

U=a.exp(b.E)+c.V+d

U=a.VAb.exp(c.E)

U=aVAb.exp(c.VAd.E) without constraints

U=(a.V+bVA2).exp(c.E)

U=((aVAb)+c.E)A(1 /(d-1))

U=((a+bVA2Y(d-1 )+C.E)A(1 /(d-1))

U = f(E,V) models; influence of V on abundance

U=a.V+b.E

See Appendix B for details

, U = f(E) models IU=a.exp(b.E)

U=a+b.E

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

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

U=a.VAb.

U=a+bVAc

U=a.V+bVA2+c

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

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for training purposes.

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iWhLch OOl:' ?I

when an expert in global modelling wishes to fit directly one or severalmodels of his or her choice. (Keep in mind, however, that the best fit is notthe only criterion for choosing a model. The main objective of CLlMPROD isto avoid an arbitrary choice which might lead to spurious correlations.)

Af the end of the "Select the appropriate model and fit it" menu, CLlMPRODmay suggesf directly fitting another model of the same family rather than theone already selected by the software. The choice of another model shouldbe based on the preliminary results and on the user's backgroundknowledge of the stock behaviour.

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

i C?lj~>a .exp (b. Eli CPU~>il +0. Ei C?U~> (iHb. f:)" Of (c-l) )

Simple regressions CPUS~f(V}

! iC?U'>a+O.ViC?US'"'<l.V"b·CP"';:.>a+O. V"cjC?US~a_V+b.V"2+c

Mixed models C?U£~f(S,V)

·C?:J;;>a.V+b.£

a. Choice of the model

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

11. Fit a model directly

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

48· CLlMPROD

[MOD,:L FlTTl:XG: 0 CPUE>a+b.E (Marqu<lrdt Method)iNuTr.Ocr of years l)>>ea for fiu:.~ng: 26"-----------------------------------------------------------------------------_.

!Number of iterations: 0 it 0 it 7. it!Co,\'''ergi~g [Zletor (R2); 73.0803 73.0803 73.0803._-----------------------------------------------------------------------------

Total trials: it is the total number of evaluations 01 least squares.

lambda, alpha: technical parameters of the Marquardt Method.

Converging Factor: the criterion value of the algorithm; it corresponds to thlDetermination Coefficient, reached at different steps of the algorithm. It i,given by the formula:

2R = 1-

Residual varianceTotal variance

Initial Coeff, Previous Coeff, Variation. Actual Coeff: values of the parameterof the fitted model at different steps of fitting.

User's Guide· 49

Marquardt's Method is one of the most efficient optimization algorithms of the lamil)of NeW1on's algorithms. It is an iterative method. In CLlMPROD, a lirst step is techoose initial values 01 the parameters in linearizing the equation of the litteemodel.

On the screen, the lollowing data are displayed:

The number and the formula of the selected model.

The number of years used lor litting: total number of years minus lags irfishing effort and/or environmental influence.

Iteration: the number of iterations presently done.

Trials: at each iteration, the algorithm chooses a direction in which it willlincthe next point; then it selects the next point by a certain number of trialseach of which is an evaluation by least squares. If this number is positive. ihas increased the initial direction; if it is negative, it has reduced the initiadirection.

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Actual Coeff

105.742963-1.366240

(linear-linear)

(linear-linear)

(linear-exponential)

(exponential-linear)

(exponential-linear)

(exponential-exponential)

(linear-quadratic)

(exponential-quadratic)

0.000.00

(Iinear-exponential-exponential)

(Iinear-quadratic-exponential)

(exponential-exp.-exp.)

(exponential-quadratic-exp.)

Variation (%)

105.712963-1.366240

?revioU5 Cocti

105.71,2963-1.36621,0

I.'1itial Cocti

,b

ilter,1tio" nO 7. TrL:<ls -1 Total trials 2:lam.oca: 36.000000 alpha: 2.000000

U=a.V'(b+c)+d.V'(2.b).E

U=a.V'(1+b)+c.V'(2+b)+d.V'(2.b).E

U=a.V'b.exp(E.cV'd} with sign constraint

U=(a.V'(1 +b)+c.V'(2+b)) .exp(d.V'b.E)

c. Filling algorithm

IU = I(E,V) models; influence 01 V on catchability

U=a.V+b.V'2.E

U=a+b.V-c.(a+b.V)A2.E

U=a.V'b+c.V'(2.b). E

U=a.V.exp(b.V.E)

U=(a+bV) .exp(-c.(a+b.V) .E)

U=aV'b.exp(c. E.V'b)

U=a.V.(b-c.V)-d.V'2. (b-c.V) '2.E

U=a.V. (1 +b.V) .exp(c.V.(1 +b.V) .E)

IU = I(E,V) models; inlluence 01 V on both abundance and catchability

d. Results: model coefficients and coefficient Of determination

50' CLlMPROD

This graph allows you to estimate the goodness of fit.

This screen displays

above: the observed and fitted data plotted during the years of observation

below: the residuals of the model (differences between observed and littevalues) plotted during the years of observation. With this graph, you cadetect any situation of autocorrelation or trend in residuals, which woulinvalidate your model.

a. Predicted and observed values

User's Guide' 5'

12. Plot the model

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Mln E = 26.600000Nb years = 26

Kgerec = 1Begin'" 0

Variance = 150.819320RZ '~ 85

b ~ -1.0469308293

Model ~ CeUE~(a.V+b.VA2}_exp(c.E)

File ~ C:\USERS\CLIMPROD\CRSV.CLIMax E ~ 55.200000

Nb exploIt ~ 1Climatic infl ~ abundance

-';:;nd~O

Var.rcsidus ~ 23.002836a ~ 29.5161272893c ~ -0.0242460309

*--------------------------------M E S SAG E $--------------------------------IPrcss any key to continue II II II II I"------------------------------------------------------------------------------~

I I*-----------------------------------------------------------------------------_.

*-------------------------------c L I M r ROD -------------------------------"ICurrent known facts

On this screen, the results ot fitting are displayed:

Model is the name of the fitted model

File is the name of the DATA file

Min E and Max E are the extreme values of the effort

No. years is the number of data values

Agerec is the age at recruitment

Climatic_infl is abundance, catchability, or both and corresponds to the kindof environmental effect

Begin and End are ages at the first and fhe last year of environment effect

Variance is the variance of the CPUE

Var.residus is the part of this variance which is not included in the model

R2 is the conventional coefficient of determination

a, b, c are the values of the coefficients of the fitted model

52· CLlMPROD

This screen displays:

on the left: the curves of Y~production (here, between 0 and 1800) vsE~effort (here, between 0 and 1001) for extreme values of observedenvironment (here, 4 and 6). It contains a broken line joining the successivepoints of observation (Y,E). The point corresponding to the last year ofobservation is indicated with a solid square.

on the right, the same graphs for CPUE insyead of Y.

Note that from these pseudo three-dimensional plots, it is not possible to estimatethe goodness of the fit, especially when the relationship between CPUE and V isnon-monotonic and when there is a non-equilibrium situation (look at the help filefor more details). In this last case most of the points appear above (increasing effort)or under (decreasing effort) the equilibrium curves of production on the left graph,because the abscissa corresponds to average past effort (see Appendix B fordetails).

PRODUCTION (Y) ISOlJ;ILUES

User's Guide· 5~

On the graph of iso-values, you may visualize the conjugate effect of environmenand effort on production as estimated with the filted model. The first curve whictappears on the screen corresponds to the minimal values of production and i1marked Ymln. The last one corresponds to the maximum value and is marked Ymax.

c. Production iso-values

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b. Three-variate graphs

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54· CLlMPROD

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

"bCoefficient:

Let Yi equal the observed CPUE and Ym the mean of all observed CPUEs.

,

[ Value: 0.7470 -0.316 -0.0013 ii Jackk'li[c Standard deviat Ion: G.0626 0.0170 0.0001 i

Jackknife t-ratio: 11.9257 -1.8622 -9.3088 I*------------------------------------------------------------------------------*

),"JODEI. VALIDATING: C?UE>(a.V+b.V A 2) .exp(c.E) (Jackknife Method) 1~------------------------------------------------------------------------------*

User's Guide' 5,

The conventional coefficient ot determination is the ratio ot variance of CPUexplained by the model, fitted on all years, on the total variance of CPUE. Itgiven by the formula:

~------------------------------------------------------------------------------~

"------------------------------------------------------------------------------~

Let yei equal the estimated CPUE when fitting the model on all years and yi! thestimated CPUE when fitting the model on all years except year 1.

I Conventional coefficient of determination: 92.54I Jackknife coefficient of determination: 89.74

~------------------------------------------------------------------------------~

c. Results

~------------------------------------------------------------------------------~

In the same way, the jackknife coefficient of determination is given by:

I(~i -Yi/2 -'.i _

Rik~1-" 2L., (Yi - Ym)

i

The jackknife t-ratio is a Hest on the regression coefficient. Empirically the limit2.0 has been retained without taking into account the degrees ot freedom.

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100.00%Difference:591. 3

Observ Sstim Jackn " b " R2

29.516 -1.047 -0.02463.5 61. 2 60.9 29.490 -1.049 -0.024 84.236.6 37.2 37.3 29.351 -1.040 -0.024 84.049. :; 51. 6 51. "I 29.534 -1.048 -0.024 84.969.4 71. <1 71. 9 30.039 -1.06S -0.025 83.3

iIter: 4 Trials: -1 Residuals:

ICPU!:::;j"t£AR: alli 1957

195819591%0

I 1961 I._-----------------------------------------------------------------------------"

The values appearing on this screen have the following meaning:

observ is the observed CPUE

estim is the estimated CPUE when titting the model on all years ot the data­set

jackn is the estimated CPUE when fitting the model on all years except thepresent one

a b c are the coefficient of the model and R2 is the current determinationc~efiicient when titting for all years except the present one.

Note that the first line of data displays the resulls of the initial fitting, using all years.

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

*------------------------------------------------------------------------------"

b. Validating

a b c31.468 -1.127 -0.025

~------------------------------------------------------------------------------~

a. The jaCkknife method

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

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

13. Validate the model

User's Guide· 5

hS-E VE'I'$US UrtSY verSuS U

e. Graphs of MSY and MS-E

The abscissa corresponds to the environmental variable.

These graphs show how MSY and the corresponding effort E depend on thenvironmental variable,

The curves on the graphs are:

a continuous line, the mean of the set of MSY values estimated during t~

jackknife procedure (one value for each year of observation)

dashed lines, this mean plus or minus two standard deviations.

The ordinate corresponds to the CPUE value, which gives the maximum value ofin the fitted model at the corresponding environment value.

Nofe thaf when the relationship between Y and F is monotonic no graph can tdrawn (example: CPUE = a.exp(b.F)+c.V+d)

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12 c n plot

For each coefficient of fhe fitfed model, a, b, c, R2, fhese graphs confain, for everyyear of fhe data set (here, between 0 and 22), the following ratio:

coefficient of fitting model on all years,except the present one100 coefficient of fitting model on all years

56' CLlMPROD

d. Graphs of R2 and regression coefficient stability

The horizontal line indicates the 100% value.

The closer to the 100% value the different yearly values are, the betler the modelfitting is. Empirically, it can be assumed that yearly ratios greater than 140% or lowerthan 60% will invalidate the model fitting.

Negative values can be observed when coefficient signs become inverted duringthe jackknife compulation.

58· CLlMPROD

14. Use the model for prediction carefully

Once a model has been fitted on your data, after a guided choice or not, you mayuse this model for prediction. For different reasons, which are explained in thereference guide, CLlMPROD permits you to make predictions on only for the twofollowing years.

a. Initial vatues

The first step consists in giving for these two years the values of etfort andenvironment which seem the most reasonable to you.

x * * * -------------*I YEAR I EF20RT i ENV. I I* * * * -------------1i 19831 51.90 23.22! iI 19841 51.90 23.221*----------*--------------------------*----------------------------~x x

lYou can change these values (last year values) before prediction I* x

~-~;~-k~;-;;-;~;---------------------------------------------------~x ~ ~ ~ ~ ~ -------------~

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User's Guide· 59

b. Resutts: model predicted CPUE for the next two years

~----------*------------*------------*------------*------------*----~----------*1 YEARI PRODUCT 1 E.fORTI ENV.I OBS CPOE EST CPUE I*~---------*-----~------*------------*------------*~-------=---*--------=------*

19731 2333.00 38.60 22.22 60.44 54.5019741 1642.00 40.60 23.00 40.44 46.7319751 1688.00 34.50 22.72 48.93 56.4019761 2103.00 46.40 21.83 45.32 ~7.21

19771 1851.00 47.00 23.00 39.38 40.0119781 1776.00 55.20 22.28 32.17 36.1719791 1569.00 46.20 23.50 33.96 37.67 119801 1724.00 44.90 22.11 38.40 47.41 119811 191\9.00 51.80 23.17 37.63 34.70 119821 1670.00 51.90 23.22 32.18 34.35 119831 0.00 54.00 24.00 0.00 28.45 I19841 0.00 56.00 24.00 0.00 27.10 i

*----------*-----------------------~-----------------~-------------------~-----*

I BSC key t.o end I*-------------------------------------~----------------------------------------*

This screen contains the result of the prediction:

Effort is the value of average effort according to the number of exploited yearclasses; for explanations, see Appendix B.

Env is the value of average environmental variable as used in the model; forexplanations, see Appendix B.

Est·CPUE is the value of CPUE estimated with the model.

As the model fitting is done using CPUE and not the production, note that noproduction estimates (catches) are made, although this could have been donesimply by multiplying the estimated CPUE by effort.

BELL, F., and A. PRUTER, 1958.- Climatic temperature changes and commerciayields of some marine fisheries. J. Fish:Res. Bd. Canada, 15 (4): 625-683.

BiNET. D., 1982.- Influence des variations climatiques sur la pecherie de'S:::;r0inelia aurita ivoiro-ghaneennes: relation secheresse surpeche. Oceanol. Acta5 {4';:: 443~452.

BIBLIOGRAPHYAPPENDIX A:

This bibliography deals with four topics:

the theory of surplus production models (rather extensively),

the influence of environmental factors on abundance or catchability (fewexamples),

the mathematical tools used by CLlMPROD,

the examples from Morocco, C6te d'lvoire and Senegal that are presented.

BELVEZE, H., 1984.- Biologie et dynamique des populations de sardine fulrQllliQilchardus Walbaum peuplant les c6les atlantiques rnarocaines et proposition pouun amenagement des pecheries. These Universite Bretagne Occidentale, BrestFrance: 532 p.

AUSTIN, H.M. and M.C. INGHAM, 1978.- Use of environmental data in theprediction of marine fisheries abundance. ill Climate and Fisheries. Proceedingsfrom a Workshop held March 29-30, 1978. Ed. by Center for Ocean ManagementStudies: pp. 93-106.

BAKUN, A. and R.H. PARRISH, 1980.- Environmental inputs to fishery populatiormodels for eastern boundary current regions. ill Workshop on the effects 01environmental variation on the survival of larval pelagic fishes. pp. 67-104. Ed. b)G.D. SHARP. Inter Governmental Oceanographic Commission Rep., 28: 323.

i!" ~

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62· CLlMPROD

BRAVO DE LAGUNA, J., MAR. FERNANDEZ, et J. ARIZ, 1980.- Determinacilonde una medida de esfuerzo pesquero de una flota de cerco espatiola que faena enAfrica Occidenfal. ill Rapport de la deuxieme reunion du groupe de travail sur lasardine, Sardina pilchardus Walb. 58-70. Rome, FAO, COPACE/PACE.Series/79/15 : 108 p.

BREIMAN, L. and J.H. FRIEDMAN, 1985.- Estimafing optimal fransformation formultiple regression and correlation. J. Am. Stat. Assoc. 80: 580-619.

CECAF, 1982.- Report of the ill!...!:lQ.(; working group on Sardinella off the coast ofIvory CoastlGhanalTogo. CECAFITECH/82/40: 57 p.

CECAF, 1989.- Report of the technical consultation on small pelagic species of thestatistical division Western Gulf of Guinea. CECAF/ECAF/89/47.

COPACE, 1980a.- Rapport de la deuxieme reunion du groupe de travail sur lessardines (Sardine pilchardus Walb.). COPACE/PACE Series 79/15: 40 p.

COPACE, 1980b.- Rapport du groupe de travail~ sur les sardinelles descotes de Cote d'lvoire-Ghana-Togo. FAO, COPACE/PACE Series 80/81,73 p.

CSIRKE, J. and G.D. SHARP, 1983.- Reports of the expert consultation toexamine changes in abundance and species composition of neritlc fish resources.FAO. Fish. Rep. 291(1): 102 p.

CURY, Ph. and C. ROY, 1987.- Upwelling et peche des especes pelagiquesc6tieres de C6te-d'lvoire: une approche globale. Oceanol. Acta, 10 (3): 347-357.

CURY, Ph. and C. ROY, 1989.- Optimal environmental window and pelagic fishrecruitment success in upwelling areas. Can. J. Fish. Aquat. Sci., 46 (4): 670-680.

DERISO, R.B., 1980.- Harvesting strategies and parameter esfimation for an age­structured model. Can. J. Fish. Aquat. Sc!., 37:268-282.

DICKIE, L.M., 1973.- Interaction between fishery management and environmentalprotection. J. Fish. Res. Board Can., 30: 2496-2506.

DIXON, W.J. and M.B. BROWN, 1979.- BMDP-79: biomedical computer programs.P. series. University of California press, Berkeley, CA.: 880 p.

DOUBLEDAY, W.G., 1976.- Environmental fluctuations and fisheriesmanagement. ICNAF selected papers, 1, 1976: 141-150.

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APPENDIX A: Bibliography· 63

DUNCAN, G.T., 1978.- An empirical study of jackknife-consfructed confidenceregions in nonlinear regression. Technometrics, 20 (2): 123-129.

EFRON, B. and G. GONG, 1983.- A leisurely look at the Bootstrap, the Jackknifeand Cross-validation. The American Statistician, 37 (1): 36-48.

FLETCHER, R.I., 1978.- On the restructuring of the Pella Tomlinson system. Fish.BuB., 76 (3): 515-521.

FOX, W.W" 1970.- An exponential surplus-yield model for optimizing exploited fishp8pulations. Trans. Am. Fish, Soc., 99 (1): 80-88.

FOX, W,W., 1971.- Random variability and parameters estimation for thegeneralized producfion model. Fish. Bull. (u.s.), 69 (3): 569-580.

FOX, W.W., 1974:- An overview of production modelling. ICCAT workshop on tunaoopulatlon dynamics, Nantes, France 1974, Rec. Doc. Scient. CICTA, 3: 142-156.

FOX, W:W., 1975.- Fitting the generalized stock production model by least squaresand eqUllibnum approximation. Fish. Bull. (U.s.), 73 (1): 23-36.

FREON, P., 1983:- Production models as applied to sub-stocks depending onupwellmg fluctuations. ill Proceedmgs of the expert consultation to examinechanges in abundance and species composition of neritic fish resources. Ed.byG.D. SHARP and J. CSIRKE, FAO Fish. Rep., 291 (3): 1047-1064,

FREON, P., 1984.- Des modeles de production appliques it des fractions destocks dependantes des vents d'upwelling (peche sardiniere au Senegal),Oceanogr. Trop., 19 (1): 67-94.

FREON, P., 1985.- La variabilite des tailles individuelles it I'interieur des cohortes etdes banes de poissons ; 11: application a la biologie des peches. Oceanol. Acta, 8(1): 87 H 99.

FREON. P., 1986.- Reponses et adaptations des stocks de cfupeides d'Afrique de~OueSt it la variabilite du milieu et de I'exploitation: Analyse et reflexion it partir dei exemp!e du Senegal. These de doctorat d'etat. Universite Aix-MarseilleC>RSTO\1 Etudes et Theses: 287 p. .

64· CLlMPROD

FREON, P., 1988.- Introduction of environmental variables into global productionmodels. !n: Int. Symp. Long Term Changes Mar. Fish Pop., Vigo, (Spain) (T.WYATT and M.G. LARRANETA, Eds.), pp. 481-528. Consejo Superior deInvestlgaclones Clentltlcas.

FREON, P., 1991.- Seasonal and interannuat variations of the mean school weightIn the Senegalese sardine ftshenes: effect of the behavior of fish or fishermen? InLong-term Variability of Pelagic Fish Populations and their Environment Ed by TKAWASAKI, S. TANAKA, Y. TOBA and A TANIGUCHI Pergamon Pre;s OXford:pp. 135-145. " .

FREON, P., C. MULLON, and G. PICHON, 1991.- CLlMPROD: a fUlly interactiveexpert-system software for choosing and adjusting a global production modelwhich accounts for changes in environmental factors. !n Long-term Variability ofPelaglc Fish Populatlons and their Environment. Ed. by T. KAWASAKI STANAKA, Y. TOBA and A TANIGUCHI, Pergamon Press, Oxford: pp. 347-357.' .

FREON, P., et J.. WEBER, 1983.- Djifere au Senegal: La peche artisanale dans uncontexte Industnel. Rev. Trav. Inst. Peches marit., 47 (3-4): 261-304.

GARCIA, S., 1985.- Reproduction, stock assessment models and populationparameters in exploited penaeid shrimp populations. Second Australian NationalPrawn Seminar, 1984: pp. 139-158.

GARROD, D.J., 1969.- Empirical assessments of catch effort relationship in theNorth Atlantic cod stocks. Res. Bull. ICNAF, 6: 26-34.

GRAHAM, M., 1935.- Modern theory of exploiting a fishery and application to NorthSea trawling. J. Cons. Explor. Mer, 10: 264-274.

GRIFFIN, WL, .R.D. LACEWELL, and J.P. NICHOLS, 1976.- Optimum effort and~~nidlstnbutlon In the Gulf of Mexico shrimp fishery. Amer. J. Agr. Econ., 2 : 644-

GULLAND, J.A., 1952.- Correlations on fisheries hYdrography. Letters to theeditor. J. Cons. Perm. Int. Explor. Mer, 18: 351-353.

GULLAND, J.A., 1969.- Manual of methods for fish stock assessment. Part I: Fishpopulation analysIs. FAO Man. Fish. Sci., 4 : 154 p.

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t!iII! .jI

t!iI

t!·iI

APPENDIX A: Bibliography· 65

KAWASAKI, T., 1983.- Why do some pelagic fish have wide f1uctuafion from theview point of evolufionary ecology. !n Proceedings of fhe expert consultation toexamine changes in abu ndance and species composition of neritic fish resources.Ed by G.D. SHARP and J. CSIRKE. FAO Fish. Rep., 291 (3): 1065-1080.

LAEVATSU, T. and H.A LARKINS, 1981.- Marine fisheries ecosysfems, itssimulation and management. Fishing News (Books) Ud., Farnham, Surrey,England: 162 p.

LALOE, F., 1989.- Un modele global avec quantite de biomasse inaccessible lieEaux conditions environnementales: application aux donnees de la peche ivoiro'ghaneenne de Sardinella 3urita. Aquat. Living Resour., 1: 289-298.

LARKIN, P.A., 1977.- An epitaph of the concept ot maximum sustained yieldTrans. Am. Fish. Soc. 106 (1): 1-11.

LASKER, R., 1978.- The relation between oceanographic conditions and larvaanchovy food in the California Current: identification of factors contributing terecruitment failure. Rapp. P.-v. Reun. Cons. int. Explor. Mer, 173: 212-230.

LASKER, R., 1985.- What limits clupeoid production? Can. J. Fish. Aquat. Sci., 4;: 31-38.

LE GUEN, J.C. et R. CHEVALIER, 1983.- Etude des pecheries; rellexions suI'environnement et la gestion mUltispecifique. Rev. Trav. Inst. Peches marit., 46 (1: 9-70.

LOUCKS, R.H., and W.H. SUTCLlFFE, 1978.- A simple fish-population modEincluding environmental influence, tor two western Atlantic shelf stocks. J. FishRes. Board Can., 35 (3): 279-285.

LUDWIG, D. and C.J. WALTERS, 1985.- Are age-structured models appropriate focatch-effort data? Can. J. Fish. Aquat. Sci., 42: 1066-1072.

MAC CALL, A, 1984.- Population models of habitat selection, with application t,the northern anchovy. Nat. Mar. Fish. Serv. Southwest Fisheries Center. AdrrRep. LJ-84-01: 98 p.

MAROUARDT, D.W., 1963.- An algorithm of least-square estimation of non line,parameters. J. Soc. Ind. Appli. Math. 11: 431-441.

66' CLlMPROD

MENDELSSOHN, R. and Ph. CURY, 1987.- Fluctuations of a fortnightlyabundance index of the Ivorlan coastal pelagic species and associatedenvironmental conditions. Can. J. Fish. Aquaf. Scl., 44: 408-421.

MENDELSSOHN, R. and J. MENDO, 1987.- Exploratory analysis of anchovetarecruitment off Peru and related environmental series. !n The Peruvian anchovetaand its upwelling ecosystem: three decades of changes. Ed. by D. Pauly and I.Tsukayama, ICLARM Studies and Reviews, 15: pp. 294-306.

NELDER, JA and R. MEAD, 1965.- A simplex method for function minimization.Compuf. J., 7: 307-313.

NELSON, W.R., M.C. INGHAM, and W.E. SHAAF, 1977.- Larval transport and year­class strength of Atlantic menhaden, BrevoQrtia tyrannIJs. Fish Bull. (U.S.), 75 (1):23-41.

ORSTOM, 1976.- Rapport du groupe de traval[ sur la sardinelle (S. aIJrita) des cotesivolro-ghaneennes. Fishery Research Unit Tema, Centre Rech. OceanQgr.Abidjan, ORSTOM: 86 p.

PARRISH, RA, A Bakun, D. M. Husby and C.S. NelsQn, 1983.- CQmparatlveclimatQ[ogy Qf selected envirQnmental processes in relation tQ eastern bQundarycurrent pelagic fish reproduction. !n Proceedings Qf the export cQnsultation tQexamine changes in abundance and species cQmpQsitiQn Qf neritic fish reSQurces.Ed. by G.D. SHARP and J. CS[RKE. FAO Fish Rep., 291 (3) : 731-777..

PARRISH, R.H. and A MAC CALL, 1978.- Climatic variation and exploitation in thePacific mackerel fishery. Ca[il. Depf. Fish. and Game, Fish Bull., 167: 110 p.

PELLA, J.J. and P.K. TOMLlNSON, 1969.- A generalized stock production model.[ATTC Bu[l., 13 (3): 419-496.

R[CKER, W.E., 1975.- Computation and InterpretatiQn of biological statistics of fishpQpu[atiQns. Bu[1. Fish. Res. BQard Can., 191: 382 p.

RIVARD, D. and L.J. BLEDSOE, 1978.- Parameter estlmatiQn fQr the Pella­TQm[inson stock productiQn mQde[ under nQn eqUilibrium conditiQns. Fish. Bull.U.S., 76 (3): 523-534.

ROFF, D.A. and D.J. FAIRBA[RN, 1980.- An evaluatiQn of Gulland's method forfitting the Schaefer mQdel. Can. J. Fish. Aquaf. Sci., 37: 1229-1235.

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APPEND[X A: Bib[iQgraphy' 6~

ROY, C., 1991.- Les upwellings: le cadre physique des pecheries cotieres cuestafricaines. In: Pecheries ouest-africaines; variabi[ite, instabilite et changemenf. Edby Ph. CURY and C. ROY. ORSTOM, Paris: pp. 38-66.

'SAVILLE, A, 1980.- The assessment and management of pelagic fish stQcks. JsympQsium held In Aberdeen 3-7/7/1978. Rapp. P.-v. Reun. Cons. Inf. ExplQrMer, 177: 517 p.

SCHAEFER, M.B., 1954.- Some aspects Qf the dynamics Qf popu[atiQns impQrtantQ the management of the commercial marine fisheries. Bull. IATTC, 1 (2): 27-56.

SCHAEFER, M.El., 1957.- A study of the dynamics of the fishery for yellQwfin tun,in the eastern tropical Pacific ocean. Bu[1. IATTC, 1 (2): 245- 285.

SCHAEFER, M.B. and J.H. BEVERTON, 1963.- Fishery dynamics: their analysi,and interpretatiQn .!n: M. N. H[LL (ed,) The sea (2): pp. 464-483.

SCHNUTE, J., 1977.- ImprQved estimates from Schaefer production modeltheoretical consideratiQns. J. Fish. Res. BQard Can" 34: 583-603.

SHARP, G., 1980.- WorkShQp Qn the effects Qf envirQnmenta[ variatiQn Qn thlsurvival Qf [arval pe[agic fishes. IOC WQrkshQP RepQrt 28: 321 p.

SHARP, G.D. and J. CS[RKE, 1983.- PrQceedings of the expert cQnsultatiQn teexamine changes in abundance and species composition of neritic fish resourcesSan JQSe, CQsta Rica, 18-29 April 1983. FAO Fish. Rep., 291 (2) and (3): 553 pand 557·1224.

SILVERT, W., 1983.- Amplificafion Qf the envirQnmenta[ fluctuations by marinlecosystems, Oceanol. Acta n° special Actes 26e Symposium Europeen dEBiQlogie Marine, Brest, 27/9-1/10/1982: 183-186.

S[LVERT, W, and W.R, SMITH, 1981.- The response of ecosystems tQ externapertubations. Math, Bioscl., 55: 279-306.

SKUD, B" 1982.- DQminance in fishes: the re[atiQn between envirQnment aneabundance. Science, 216 (9): 144-149.

SOUTAR, A, and J,D. ISAACS, 1974.- Abundance of pe[agic fish during the 19t1and 20th centuries as recQrded in anaerobic sediment Qff the Californias. Fish. BullUS, 72 (2): 257-273.

. U = f(E,V) models; influence of V on abundance IThese models have been obtained by replacing the standing stock value B= b)I,near, exponential or quadratic function of V in conventional global productimodels. For more details, see Freon (1988).

(linear)

(exponenfial)

(linear)

(exponential)

(general)

(quadratic)

(generalized)

(linear-linear)

(linear-linear)

(linear-exponential)

MAIN FORMULAE

Models available in CLlMPROD (eguilibrium state)

U=8.V+b.E

U=a~b.V+c.E

APPENDIX 8:

1.

U~(a+b.E)A(1/(c-1»

U~a.v+b.VA2+c

i~(v) models IU=a+b.V

IU = I(E) models IU~a.exp(b.E)

J!"" ~~--.~~.~

~.~. .,~ .. .,~-.,

~ ... ;j

~.~ ;j

~~;j

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l! .,.

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l!.'.

l! '.l! .;j

l!"l!. ,.,~

l!. .•

l!. ·B

l!.~

WALTER, G.G., 1973.- Delay differential equation models for fisheries. J. Fish.Res. Board Can., 30: 939-945.

WROBLEWSKI, J.S., J.G. RICHMAN and G.L. MELLOR, 1989.- Optimal windconditions for the survival of larval Northern anchovy, Enoraulis mordax: amodelling investigation. Fish. Bull., U.S., 87: 387-395.

TROADEC, J.P., 1982.- Introduction it I'amenagement des pecheries: interet,difficultes, et principales methodes. FAO Doc. Tech. Peches, 224: 64 p.

UHLER, R.S., 1980.- Least squares regression estimates of the Schaeferproduction model: some Monte Carlo simulation results. Can. J. Fish. Aqual. ScL,37: 1284-1292.

WALTER, G.G., 1986.- A robust approach to equilibrium yield curves. Can. J. Fish.Aqual. ScL, 43: 1232-1239.

WALTER, G.G., 1975.- Nonequilibrium regulation of fisheries. ICNAF Res. Doc.,75/1X/131.

WROBLEWSKI, J.S., and J.G. RICHMAN, 1987.- The non-linear response ofplankton to wind mixing events - implications for survival of larval northern anchovy.J. Plankton Res., 9: 103-123.

WALTERS, C.J., 1987.- Nonstationarity of production relationships in exploitedpopulations. Can. J. Fish. Aqu. Sci., 44 (Supp. 2): 156-165.

WALTER, G.G., 1975.- Graphical methods for estimating parameters in simplemodels oflisheries. J. Fish. Res. Board. Can., 32: 2163-2168.

STEELE, J.H. and EW. HENDERSON, 1984.- Modelling long-term fluctuations infish stocks. Science, 224: 985-987.

STEELE, J.H., 1984.- Kinds of variability and uncertainty affecting fisheries. .LoExploitation ot marine communities, Ed. by R.M. MAY. Dahlem Konterenzen,Springer-Verlag, Berlin: pp. 245-262.

68· CLlMPROD

70' CLlMPROD

U = f(E,\I).rn_()clf)I~LInlluence 01 V on calchability

These models have been obtained by replacing the catchability coefficient q, by alinear, exponential or quadratic function of V in conventional global produclionmodels. For more details, see Freon (1988).

U=a.V.exp(b.E))

U=(a+b.V).exp(c.E)

U=a.exp(b.E)+c.V+d

U=a.VAb.exp(c.E)

U=aVAb.exp(c.VAd.E) without constraints

U=(aV+b.VA2).exp(c.E)

U=((aVAb)+c.E)A( 1/(d-1))

U=((a.V+b.VA2)A(d-1 )+C.E)A(1/(d-1))

U=a.V+bVA2.E

U=a+bV-c.(a+b.V)A2. E

U=aVAb+c.VA(2.b). E

U=a.V.exp(b.V.E)

U=(a+b.V). exp(-c. (a+b.V) .E)

U=a.VAb.exp(c. E. VAb)

U=a.V. (b-c.V)-d.VA2. (b-c V)A2.E

U=a.V.(1 +b.V).exp(c.V.(1 +b.V).E)

(linear-quadratic)

(exponential-linear)

(exponential-linear)

(exponential-linear)

(exponential-exponential)

(exponential-exponential)

(exponential-quadratic)

(generalized-exponential)

(generalized-quadratic)

(linear-linear)

(linear-linear)

(linear-exponential)

(exponential-linear)

(exponential-linear)

(exponential-exponential)

(linear-quadratic)

(exponential-quadrafic)

~- Ii~~. Ii

.... I:

.... 1:

...~ I:

..... 1:

...... ~

..~~.... ~... ~

~._~

~ ... ~

~'I:

~.... ~

~ -~

~~!..!...~

I:

!.. ~

~

!.~

! ~

!. 11

APPENDIX B: Main Formulae' 7

U = I(E,V) models; influence 01 V on both abundance and catchabil

U=a.VA(b+c)+d.VA(2.b).E (Iinear-exponential-exponential)

U=a.VA(1 +b)+cVA(2+b)+d.VA(2.b). E (Iinear-quadrafic-exponential)

U=a.VAb.exp(E.c.VAd) with sign constraint (exponenfial-exp.-exp.)

U=(a.VA(1 +b)+C.VA(2+b)) .exp(d.VAb.E) (exponential-quadratic-exp.)

2. Transitional states formulae: approach adopted

The transition prediction approach (past-effort-averaging or past-environmelaveraging) is used in CLlMPROD to lit data on non-equilibrium conditions. Trequilibrium approximation approach (integration of the differential equation) is n,yef available.

Gulland's (1969) method involves the relationship between the annual CPUEyear i (Ui), and the lishing effort averaged over some previous years. Fox (197.proposed a weighted average. The latter method was used for eflomeasurements.

Even though this approach is unsuitable when g(V) and/or y(V) are not monotonfunctions, the authors proposed to adapt it to environmental production models I,pragmatic reasons.

it has been recognized that the transition prediction approach can lead to sonbias or errors concerning the parameter estimations, as emphasized by Waite(1975), Schnute (1977) and Uhler (1980). However, the last mentioned authshows that the best statistical estimates of the parameters do not necessarprovide the best estimates of Ymax and Emax , which are the main Objectivesthe global production models.

72· CllMPROD APPENDIX B: Main Formuiae • 7:

U. = U.. + U.. 1 + U.. 2 + + U. . 1I I,) I,J- 1,1- I,J-n+

These four cases are not mutually exclusive, of course, and sometimes it is difficultto identily at which stage the environmental intluence is greatest.

3. Transitional states when the environmentinfluences stock abundance

If we consider that a possible effect on the stock-recruitment relationship is alreadytaken into account by the usual tormulation of global production models, it can beassumed that, in the first case, the environmental factors will act on the stock mainiyduring the months prior to spawning. The CPUE of the total fishable popUlation,assuming equal catchability of each year class j, is:

(nV. + (n-1)V' 1 + (n-2)V. 2 +....+ V. 1)V. = I 1- 1- l-n+

I n+(n-1) +...+1

The same approach can be developed for the second case, using environment,data from the spawning period.

and

U.. - B=(V. + V. 1 +...... V. t \I,l I l~ 1- r'

U. - B=(nV. + (n-1)V. 1 + (n-2)V. 2 +....+ V. 1)I 1 1- 1- I-n+

This formuia is easy to modify when the environmental effect starts d years affrecruitment, replacing n by nod in this case (Fig. 2c

The expression of V. will be given by:I

where tr is the mean age at recruitment and t the mean age of the oldest fishablyear class. When using ClIMPROD, in such cases, answer 1 and 1 to thquestions "Age at the beginning of environmental influence?" and "Age at the enof the environmental influence?". When sexual maturation occurs mainly the ye,before spawning, answer 0 and O. When it occurs during two years, answer 0 an1

The two last cases need different formulations because an environmental facfecan affect the abundance of a cohort over several years, which leads to the use (weighted averages. Following an approach similar to Fox's (1975) concerning thfishing effort, let us first consider the simple case where the environment has aeffect throughout the post-recruitment period. Then the CPUE of the incominyear class j in year i, Uiij, is related to the value of Vi during the same year; that of thprevious year class, Ui,j-1, is related to the values of Vi and to Vi-1; and so fort(Fig. 2b). This can be written as:

~- iI~ .. iI

~~ ..~m• ..

~ ...~~~

~.~

~-~

1'. - ~

~-.

t.. -'.~-.

~-.

~-.

~ .•~ .•~ -.t.. '0'"~ .~

t.. ..~ o.t.. ....

!.. .•

V. t + V. t 1 + ... + V.1- 1- + I

t -'tr +1V.

I

where Ui,j is the CPUE of the incoming year class j in year i, for n year classes in thefishable population. Therefore, Ui will be related to the average Vi at seasonalenvironmental factor during the years corresponding to the sexual maturation ofthe different parental stocks of each fishable cohort. When sexual maturation andspawning occur during the same year i, this can be written as (Fig. 2a):

Concerning the environmental variable, the use ot the transition predictionapproach assumes that the life-stage during which environment acts upon thestock is already known. Schematically four periods, or critical stages, have beenidentified:

1 Before spawning, when the fecundity of the parental stock may beinfluenced;

2 During the early life stages, when fecundation and/or natural mortality ofeggs and larvae may be influenced;

3 During the period of high growth rate (corresponding generally to the pre­recruitment stage) when the environment influences individual growthand/or natural mortality;

4 During the post-recruitment period, if natural mortality and/or the condition­factor (and secondarily the growth rate) are affected at this stage.

74· CLlMPROD APPEND[X B: Main Formu[ae • 75

when the environmentcatchability

Transitional stateinfluences stock

n(V,+V, 1+....+V' d)+(n-1)V, d 1+""+V, d 1V - _-,-I-,1---'--;c~-cI--7-;-~--":-:-",--,---;_",I-",n,,-",+,-,-i- n(d+1)+(n-1 )+(n-2)+....+1

Mean fishing effort Ei is calculated separately from Vi using Fox's (1975) weightedaverages.

!t the environmental effect starts d years betore recruitment (Fig, 2d), we obtain:

1n other cases, where for example the environmental effect on a cohort concernsboth pre-recruitment and post-recruitment phases (Fig, 2e), with a graphicalsOlution the proper formulation of Vi can be obtained (in CLlMPROD a[1 theprevious cases are also solved by a an algorithm equivalent to a graphical solution),

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

4.

.~

!'.' ~

~ .[ .[' .r.r •[.

r.r.r.L.

E.

Vi :::(Vi + 2vi_l +- 2 Vi_ 2+V'_3)/ (;I ~

S : spawll,o.g

tR year of recruitment

t), las\ !istlable year class

I 4 i 3 1-2 i-I

to yea' 01 spawning

_ ;:>e'iod 01 environmental inltvence(cf;l,cal stage)

- - -exploited slages

,l- to

I to,+ I

,1II

1! toT I

2t

'r ~~X.I Vi O(3V j + 2v i_1+v i_2}/6L-el-+----+-"M.' f---'-I--1' I

Coho'!,

F,!

nqiEi+ (n-1) qi-1 Ei_1+ '" + qi-n+1 Ei_n+1n+(n-1)+(11-2)+ +1

Fig. 2. Graphical solutions of the estimated weighted average Vi involvingthe number of years during which the environment influences the CPUE(U i) of year i, according to different temporal locations (Fig, a, b, .. , e)of the critical stage (see text),

D,rC.','2f to generalize the formulae to any case and then to avoid reformulation ofmJCSLS, this equation is approximated by:

nq+(n-1)q, 1+' ,+q, 1 nE,+(n-1)E, 1+ '" + E, 1I J- I-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, butonly to take into account its variability in the model.

5. Transitional state when the environment influencesboth abundance and catchability of the stock

Owing to the transition prediction approach and the simplifications retained in theformulae, the only acceptable cases are obtained when the weighting factors arethe same for environmental influence on abundance and catchability. Thiscondition is respected when the environmental influence on abundance concernsall exploited year-classes. When using CLlMPROD in such cases with n exploitedyear classes and recruitment at age tr, the answers given to the questions "Age atthe beginning of environmental influence?" and "Age at the end of environmentalinfluence?" must be tr and tr+n-1 respectively.

~.~. ,.~~-.

~_.-.

~~.

~'" .~,~.

~'.~_.•~-.

~".~ -'.~ .•~ ..~.

~-.

Ill;; ""'r.·.'vw

~'.~ .~ .po.p ,.p.~".~,,,

Notes

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DROIT D'AUTEUR ET AUTRES DROITS DE PROPRIErE INTELLECTUELLEOtll"'~."""__UnIH _ r_tion et I'ogriculture (FAO) 111114• LaFAO.·eltan::ecr.....l·lIXIICIiaIdedesdonrNktsmai.n·assumeaucuneresponsabilit6&IX .,... • omissions powant 18 trouver dans les donnbes fournies aux usagers ou ddocu••'.lioi. qui" accompagne.• la FAO • ,.... le droit de modifier ces donntMts. ainsi que las oodes. cIa~.... f' 7 • dcAililii..COlMtt'tS per 185 strias. Elle se reserveaussi la droit de modffierletGdes donn6es qu.... fournit ~ I'usager.

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ClIMPROD

ExperImental Interactive soltware lor choosing and Illungsurplus productIon models Including environmental variables

Various equations allowing 10( tha Introduction 01 an .nv.onmantal variabla into surplusproduction modals .Ira available In ClIMPROD sohwa/a. h h.~s the user to select IMmodel corresponding 10 his case aca:)lding 10 objectiva crit.ria. h looks like .. simplaexpel1-system and uses artificial intelligence language (PROlOG) 10 conve,.e with theus.r.

CllMPROO require. annual data-series on catch and e!fOR ol a !ishery on a single stock,and annual (or seasonal) data-series on an environmental variable known to inllu.1'laI tMabundance or Ihe catchability 01 lhis slock. Th. sohwar. provides a statistical andgraphical description 01 the data-set and then allows lor Choosing an appropriale model.lining it using a non-linear regreuion routine and trying lo aSMssthalit with param.tric andnon-parametric lUll before prilS.nting the lables and graphs ollh. results. Th.... r.sultsmay .xplain how .n... ironm.nt and ll.5hlng .Uort gO"'lIrned Ih. yields o/lhe lishery during th.hislorical period. Based on an estimale 01 the nnt two y.ars' dala on .110rt and.nvlronmantal regima, an exploratory pr.diction Is proposed lor catches per unit 01 ellon(CPUE). and a graph gives a variation of the "maximum sustalnabl. yields (MSYr and"optimal lishlng .1I0RS (Imax)" aoc:ording to dillerent environm.nlal regimes.

CllMPROD can 01110 be used lor filling th. thr•• conv.ntional IUrplus production mod.ls(linear, exponantial, generalized) without .nvironm.ntal Inltuance or, lor lining Ih.relationship between environment and production without fishing influ.nce. In both C8;sesnon~ramelric tests and graphicallacilCkls are availabl•. CllMPROD can also be used asa training tool.

1lia manual contaln.lwo main paR.:

a reler.nce guide which Wtdudes a brielthllOretical.ection, a general pres.nlalionof CllMPROO and ilS obj8CIives, data inpulS and Outpull.

a user's guide which include. Ihe system requilemenl" InslaJlation instructionl, andUSII 01 the compulllr kllyboard to lIart Ih. programs and obtain on-~ne HELP.