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Not to be cited without permission from the authors.

International Council for theExploration of the Sea

ICES C.M. 1990/B:l4Fish Capture Cttee

Ref. Statistics

•ANALYSIS OF TRAWL SELECTIVITY STUDIES

WITHANAPPLICATION TO TROUSER TRAWLS

by

R. B. Millar and S. J. Walsh

Department of Fisheries and Oceans,Science Branch,P.O. Box 5667,

St John's, Newfoundland, AlC 5Xl.

ABSTRACT

Data gathered from trouser trawl (or twin trawl or alternate haul) surveys doesnot conform to the assumptions required by conventional statistical methods foranalysing count data. Consequently, the application of conventional statistical meth­ods leads to incorrect interpretations. We derived a statistical model that is appro­priate for this type of data and applied it to trouser trawl studies. This model wasused to fit logistic seleetivity ogives to American Plaice data obtained from studiesusing both diamond and square mesh. We tested the assumption that the split offish into the two codends (large mesh and small mesh) is 50:50.

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INTRODUCTION

The statistical methodology presented below was developed because of the needfor proper statistical analysis of data obtained from trouser trawl stüdies. Theapproach is eqtiälly applicable to data obtained from twin' trawl or alternate haulstudies. Since mir surveys üse trouser trawls we concentrate on that gear type only.Whereby we refer to the large arid small mesh codends of the trouser trawl, in atwin trawl or alternate haul survey this would be the large mesh haul and associatcdsmall mesh hau!. ". .

The trouser tra~l method has been used especially in Canada \vhere experimentalwork has shifted away from. the covered codend and thc alternate haul methods(Cooper and Hickey 1989jWalsh et al. 1989). The trouser trawl us~d in Canadianexperiments has a vertical separator panel which divides the trawl mouth into twoseparate seetions (Chopin 1988).' Nicolajsen (1988) used a vertically split Nephropstrawl to estimate seleetivity in Nephrops norvegicus. In this trawl the vertical paneldivides the mouth,as weIl aS the rest of the trawl, into t\VO sections.

An inherent assumption in a tI·ouser trawl study is that a flsh encountering thegear enters one side or the other with equal probability. (For alternate hauls thiscorresponds to assuming that the expeeted number of flsh encountering both trawlsis the same.) A major concern of the trouser trawl method is that sometimes thecatch of flsh above the selection range may be greater in the large mesh codend thanin the small mesh (control) codend (Pope et al. 1975j Nicolajsen 1988; and Walshet al. 1989). Pope et al. (1975) suggested that this may be a result of differences ofwater flow and sampling area through the. two codends caused by the two differentmeshes used. The use of a vertical panel extending the fuIllength of the trawl shouldrectify the problem of water flow influencing flsh to enter one codend over tb..e other.Nevertheless the unequal catches of large flsh in the two codends still occur. Fishmay be herded more to one side of the tra\vl than the other and if the numbersare small there is no impetus to spread across the mouth of the trawl and thereforethe 50:50 probability assumption may not be satisfied. Alternatively, it may simplybe that the unequal catches of large fish in the two codends are chance occurenceswithin the bounds of sampling variation. Our model tests whether this is the case.

Many techniques to describe the shape of the selectivity curve have been inves­tigated (see Holden 1971; and Pope et al. 1975 for excellent reviews); No\vadaysresearchers generally draw their selectivity curves by eye or use conventional sta­tistical methods such as logit Of probit models. Using the former method one canignore the unequal catches of large fish but no estimate of the error of fitting thecurve can be derived. The conventional statistical models are invalidatcd by unequalcatches of large fish in the two codends and the fitted selectivity curve and associ­ated estimates of error eire thererore also invalid. Our statistical model permits thcassumption of a 50:50 split of fish into each codend to be tested and provides properestimates of the reliability of the fitted curve and associated seleetion parametersL2S , L75 and Lso• .

The model was fit ted to data on American plaice, Hipplogossoides platessoides,

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collectedin 1988 using a trouser trawl off the coast of Newfoundland (Fig. 1) inNorthwest Atlantic Fisheries Organization Divisioris 3L and 3N (see Walsh et al.1989 for details). The trawl used in theexperirnent was a Nordsea Nova 642 ground­flshtrawl alternate!)r eqtiipped with 155 inIn diainond or square rnesh codends, anda 38 nim small mesh control codend (Fig. 2). The seleetion trials were based on13 hauls using ci. kriotless diamond mesh codend aiid 16 hauls using a squäre meshcoderid.

THE MODEL

Let Nil denote the number of flsh of length I (Le., in the daSs Gf flsh of lengthI) that are caught in the large mesh coderid. Similarly, N'2 denotes the number offlsh of lerigth I caught in thc small mesh (control) codend. The large mesh retentionprobability of a length I flsh will be denoted by r(l). The retention probabilities area funetion of I, and we have considerable choice in the type of function (seleetion

. ogive) that we choose. It could be based on logit or probit funetions, or could beailything else the user wishes to specify. The model we describe will handle anypossible choice of funetion and therefore can be üsed to indicate which funetion fltsthe data best. . . . . " . " . ,

Given Nil arid N'2 äs deflned above, the total ca.tch of flsh oflerigtli I is denoted byN,+ = Nil +N,2. For ease Gf presentation, let us asstime that a flsh approaching thegear has a 50:50 chance of entering either codend. This assumption is not necessaryand it is shown later how the model can be used to estimate the split into the t\VOcodends. Consequently, the model can also do' a. statistical test of the assumptioncf a 50:50 split. ,

The probability that a flsh enters either codend is assumed for no\v to be 0.5.It is presumed that all flsh of any size are retairied by the small mesh codend; thusthe probability that a fish entering the gear is caught in the sinall mesh codend is0.5. In contrast, r(l) is the probability that a. fish entering thC;; large mesh codendis retained. Thus, tliC probability that a flsh enters the large mesh codend ä.lld iscaught is 0.5 X r(/). ~Ioreover, thc pfobabilitythat a flsh is caught (in either codend)is simply the stim of these two probabilities, 0.5 x(1 + r(/».

For a flsh of leugth I that eriters the gear we now have the following probabilities:

P[caught in small mesh] =0.5

P[caught in large mesh] = 0.5 x r(l)

P[caught] = P[caught in small mesh]+P[caught in large mesh] = 0.5 x (l+r(/». . .. ..-

Conditional proba.bilities (from introductory statistics) tell us tha~:• • j ' •

For a. flsh of length I that' enters the gear:' The probability that it is caught in thesmall mesh, given that it is caught is

P[caught in small mesh] 0.5 1- - ----:'':'':'"P[caught] 0.5 x (1 + r(/» 1 + r(/)

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(1)

(2)

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for a fish of length I that enters the gear: The probability that it is caught in thelarge mesh, given th~t it is ~aught is'

P[caught in large mesh] _ 0.5 x r(/) _ r(l)P[caught] - 0.5 x (1 + r(l)) - 1+ r(l)'

The model can now be stated. Given that a total of Nl+ fish of length I werecaught, the number,of fish caught in the large mesh codend is a binomial randomvariable with probability l;Vll) (from above). The observed val~e of this binomial

random variable is Nil. That is, Nil is distributed as a Binomial(N,+, l;Wl») randomvariable. We can write the likelihood (see below) fOf the observed data and maximizeit to estimate the parameters of the selectivity ogive r(/). Fitting of the model isdescribed in the next section. '. .

To test the' assumption of a 50:50 split into the two codends we can make alogical modification to the model. Let p denote the probability that a fish enteringthe gear will go into the large mesh codend. The probability of entering the smallmesh codend is therefore 1 - p. Then:

For a fish of length I that enters the gear: The probability that it is caught in thelarge mesh, given that it is caught is

P[caught in large mesh] _ p x r(l)P[caught] - (1 - p) +Px r(l)'

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The model simply uses formula (2) instead of (1) and the maximization of thelikelihood now involves also niaximizing over all possible values of p to determinethe value best describing the data. Note that (2) reduces ~o (1) when p= !.

FITTING THE MODEL

So far the retention probability of a length I fish has simply beeil denoted byr(/). For the analyses below we chose the, selection curve to be the logit function

r(l) - exp(a+ bl) (3)- 1 + exp(a + bl)

Other choices, such as the probit, are possible. Substituting the above choice of r(l)into equation (1) gives the probability of a length I fish being caught in the largemesh, given that it is caught, to be '

exp(a + bl)1 + 2exp(a + bl)

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which will be denoted by fjJ(/). , .The work of the previous section showed that the ,trouser trawl data can be

modelIed as a binomial experiment. The log-likelihood function is

E (Nil log fjJ(/) + N12 log(1 - fjJ(/»))I

(4)

Here the summation 2: is over all length classes.Maximum likelihood estimates of thc selection curve parameters (a and b) are

obtained by maximizing (4) over all possible values of a and b. This can be doneby most maximization or optimization procedures. 'Ne have implemented the max­imization using the software packages SAS, GLIM, Splus,and Mathematica. UsingGLIM it is necessary to specify a user defined "link" furiction, and this is not trivial.With SAS the inaximization was done via iteratively reweighted least-squares usingPROC NLIN (Me Cullagh arid NeIder 1989, pg 40). The maximization is straight­forward in Splus and Mathematica because they both have built in maxiIDizingroutines. .

. Thc,log-likelihood in (4) assurnes a 50:50 split, that is,p = 0.5. To fit p as aparameter one'substitutes (3) into equation (2) to get

fjJ( I) _ p exp(a + bl)- (1- p)+ exp(a + bl)

and maXiinizes the log-likelihood funetion over all possible values of a, b and p. TheSplus and Mathematica software packagcs cando the maximization. GLIM aridSAS cari not (this is because pappears in the "link" funetion and which GLIM andSAS can not maximize). . '.

The reliability (standard error) of the estimated parameters can be calculatedfrom the standard theory of maximum likelihood. GLIM and SAS output gives thestandärd error of a and b in the case where p is assumed to be 0.5.

Remarks

It was mentioned in the introduetion section thät, in the past, the data has beendifficult to interpret and analyse for lengths above the selectivity range of the largemesh. The model presented above does not encounter this problem. For example,consider fish in a length dass above the selectivity range of the large mesh aridsuppose that 4 flsh are caught in the large mesh codend and only 2 are caught .in the small mesh codend. Since die length is above the seleetivity range, theprobability of ci. fish entering the gear being caught in either codend is 0.5. Our

. model formulates this as analagous to someorie tossing a coin six times. We couldsay that the 'coin coming up heads corresponds, to a flsh entering the large mesh andthat the coin coming up tails corresponds to ci. fish entering the small mesh. Anyonewho has tossed a coin knows that out of six tosses, getting 4 heads and 2 tails is notunusual. Thus, observing 4 flsh in the large mesh codend and 2 in the small mesh

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codend should not be considered unusual.. (Note: Getting a 4 and 2 split is aetuallymore likely than getting a 3-3 split! .A 3-3. split hcis probability 0.3125 while thcprobability of 4 heads arid, 2 tails is 0.234375. SiIDilarly, a 2 head aiid..4 taU splitalso has probability 0.234375. Thus thc probability of a 4-2 split is.0.46875.)

Previous analyses of trouser trawl data generally condition on the number of fishcaught in the small mesh. Thcit is, if 10 fish (of length I) are caught in the srriallmesh then it is assumed that 10 fish also entered the large mesh. Of·course, thisargument breaks down in the above example where 2 fish are catight' in the smallmesh arid 4 are caught in ,the large mesh. Iri contrast, our model conditions on thetotal number of fish catight (of length 1). That is, giveri that N,+,fish are caught;our model uses the canditianal probability given by (1) (or (2) if ä 50:50 split is not •asstimed).

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The length distribution of the catches (Table 1) shows that in the larger sizecategories beyond 42 cm more fish eire commonly found in the large mesh codendwith percentage retained (large niesh/small mesh x 100) exceedirig 100 percent. Thisis espedally the ca.se far the diarnond mesh (Fig. 3).

To each mesh type (square and diarnond) we fitted two selectivity cu!ves, oneassuming a 50:50 split (p -: 0.5) and the other where p was estimated. The 50:50split model resulted in the diamond mesh 50% i'etention length (35 cin) being 2 cmhigher than square mesh (33 cm) with a selection range of 6 eIn fo! diamond meshand 4 cm for square mesh aiid selection factors of 2.3 and 2.1 respectively (Table 2;Fig. 4). , ' ,

The p estimated model (Le. no 50:50 split cissumed) showed that for. diamondmesh the split was, .59 for large inesh and .41 for the small mesh. The likelihoodratio test showed that these catches weresignificantly different from,a 50:50 split.For the square mesh experiment the split was .46 for the large mesh and .54 farthe small mesh, arid here the split was also found to be significantly different from50:50. Using this model the 50% retention length in the diamond inesh (38 cin)was 6 cm higher than thc square mesh (32 cm); with a selection range of 8 cm forthe diamond mesh arid 3 cin for the square mesh arid selection factors of 2.5 and2.1 respectively (Table 2; Fig. 4). Both models indicate that square mesh codendsretain more smaller American plaice than diamond mesh codends.

DISCUSSION

The theory of the trouser trawl method suggests that the cateh should be splitroughly 50:50 with regard to xlUmbers and length composition of the populationbeing studied. The use of a vertical separator panel should enhance the probabilityof attaining a 50:50 split by negatiiig the problems of \vater flow documented intwin/split codends (Pope et al. 1975). The ratio of the large mesh to the smallmesh catch; for each length dass, should produce a sigmoid selection curve with

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asymptote at unity. This large rriesh (test mesh) to smaU mesh ratio in the data.from the 155 nim experiments showed high sampling. variation in the larger sizes ofAmcrican plaice. In the square mesh experiment ihe scatter ,vas mainly belo\v unity .with the number of fish above the 75% retention length (using either model) higherin the small mesll codend~ However, in the diamond mesh experiment the scattcr ofsarnpling varia.tion was above unity with the number of fish above the 75% retentionlength higlier in the test mesh in both models. Similar results were found in 140mm diamond and square mesh selectivity experiments of Americäll plaice (Walsh eta!. 1989). .

, In fitting a fixed 50:50 split model or the p estimated model, the sampling vari­ation is conditioned on the total number of fish caught at each length elass and noton the ratio ofthe large mesh to the smaU mesh at each length dass. The largesampling variation, whether above (diamond) or below, (square) unity is minirruzedin the model. Walsh et al. (1989) used a probit model in their maximum likelihoodanalysis on the same, data base and their reslllts foz. the diamond mesh were eloseto the results of the fixed 50:50 split model. However; their results for square rriesh'showed a 20 cm seleetion ränge due to the probit model being llilableto deal withthe large sampling variation below unity found in higher size elasses. In this stlldybotli models resulted in almost identical retention lengths; selection factors, andselection ranges in the square mesh analyses with the, estimated p \ralue showinga 46:54 split elose to the expeeted 50:50 theoretical split. ,The p .estimated modelresults forthe diainondriiesh exPeriment shows a significantdeparture from a 50:50splii ,caused by higher nllmber of larger fish caught in the large mesh than in thesmall mesh codends. .

CONCLUSION

,A fuU iength vertical separator panel divides the sampling ar~ä. into two equalhalves and reduces the influence of unequal water flow or sampling area in theentrance of the two cod ends. Ho\vever,as Pope et al. (1975) criticized; there \verestill differences in catches of fish above the selection range whiCh callses problems inusing regular logistic or probit models. The 50:50 fixed split model presented hen~

can handle' these sampling Variations effectively by not conditioning on the largemesh/sinall mesh ratio which causes problems with other models. We can also testwhether the 50:50 split assumption is valid by using the p estimated model so thatwe are aware how mush deviation there is from the 50:50 assumption.

Beverton and Holt. (1957) reported that in their selectivity work on plaice thelarge mesh trawl caught more fish in the larger size classes than the srriall mesh andthis seems to be a common problem in seleetivity studies of trouser trawl, alternatehauls and twin trawl experiments. Previolls workers in this area have suggested thatincreasing the number of hauls or the haul duration to reduce the sampling variation,but we fcel that the problem will still exist, probablyon a larger scale. Providedthat the sampling gear is warking efficiently, it may oe that unequal catches of largefish in the two codends are due to either low numbers or chance occurrences withinthe bounds of sampling variation associated with uneqii~ sampie siies.

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Further work

We are in the proeess of applying this model to other seleetivity data on plaiee,eod, nephrops,and herring (the latter from data supplied by other researehers).Work on methods to derive estirriates of the reliability of the estimated parame­ters and goodness of fit of the model is ilearing eompletion. This will also. allowealeulation of estimates of the reliability of L2S , Lso and L7S •

REFERENCES

Beverton, R. J. H. and S. J. Holt. 1957. On the dynaInies of exploited fish popu- •lations. Fishery Investigation, Series 2 (19): 533 p. HMSO London.

Chopin, F. 1988. Design of a vertieal separator panel trouser trawl for eodendmesh selectivity experiments. ICES Fish Capture Working Group, Ostend:. 6p.

Cooper, C. G. and W. M. Hickey. 1989. Seleetivity experiments with square mesh .eodends of 135, 140 and 155 mm.. Fisheries Development and Fisherman'sServices Division Projeet Report 154: 29 p.

Holden, M. J. (editor). 1971. Report of the ICES/ICNAF working groups onseleetivityanalysis. ICES Coop. Res. Rept.· 25:, 144p.

Me Cullagh, P. and J. A. NeIder. 1989. Generalized Linear Models, 2nd edition.Chapman and Hall. 511 p.

Nicolojsen, A. 1988. Estimation of seleetivity by means of a vertieally split Nephropstrawl. ICES C.M. 1988/B:9: 12 p.

Pope, J. A., A. R. Margetts, J. M. Hamley and E. F. Akyuz. ·1975 Manual ofmethods for fish stock assessment, Part IH. Seleetivity of fishing gear. FAOFish. Teeh. Pap. 41: 65 p.

Walsh, S. J., C. Cooper and W. Hickey. 1989 Size seleetion of plaiee by square anddiamond mesh eodends. ICES C.M. 1989/B:22. 13 p.

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Table 1. Length frequency distribution of American plaice from the 155 mmNordsea 642 trouser trawl.

Small Diamond Small SquareLength Diamond mesh % Square mesh %group codend codend retained codend codend retained

8 0 0 0 0 1 010 0 1 0 0 1 012 0 0 0 0 1 014 0 1 0 0 4 0

e 16 0 3 0 0 5 018 0 4 0 0 19 020 0 6 0 0 18 022 0 5 0 0 19 024 1 11 9 0 21 026 0 17 0 0 33 028 1 26 4 2 37 530 5 39 13 8 56 1432 18 57 32 37 88 4234 20 69 29 65 114 5736 39 74 53 82 104 7938 56 69 81 76 90 8440 58 64 91 71 68 10042 52 62 84 81 88 9244 60 53 113 71 94 7646 55 48 115 85 80 10648 39 41 95 51 80 . 6450 28 23 122 37 67 5552 22 15 147 35 36 9754 15 5 300 22 24 9256 11 10 110 17 16 10658 10 5 200 9 10 9060 11 4 275 4 4 10062 10 3 333 5 12 4264 8 3 267 3 3 10066 2 2 100 5 1 50068 0 1 0 1 2 5070 3 1 300 0 2 072 0 0 0 0 0 074 1 0 0 0 0 0

Total 525 722 767 1208

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Table 2. Seleetivity parameters fitted to 155 mm diamond and square mesh. For each

mesh type the selectivity parameters were fit ted with and without the assumption

of a fixed 50:50 split of fish (p=0.5) into the large and small mesh.

diamond diamond square squarep=0.5 p estimated p=0.5 p estimated

a -12.88 -9.97 -18.34 -22.01b 0.3653 0.2608 0.5534 0.6819p 0.5 0.59 0.5 0.46

10.25 32.25 34.00 31.14 30.6710.5 35.26 38.21 33.13 32.2810•75 38.27 42.42 35.12 33.89

Seleetionfactor 2.3 2.5 2.1 2.1

Seleetionrange 6.0 8.4 4.0 3.2

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Fig. 2. A 3-D diagram of a trouser trawl with a vertical separator

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rig. 3. Plot of proportion retain (Large mesh/small mesh x 100') of,

catches of American plaice using 155 mm diamond (0) and square mesh. ..(0) trouser ~WlS. •

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Selectivity ogives tor American Plaice

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Fig. 4. Selectivity ogives of 155 mm diamond and square mesh experiments

. usinq the two models: a) 50:50 split model (p-0.5) and

b) p-estimated model.

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