Dynamic catch-effort models for the southern African hake populations

Andrew, P A

Dynamic catch-effort models for the southern African hake populations

Thesis / Dissertation

1986

Abstract

Ur1til 1984, hake quota rec:·ottrttreridaticms made by the ICSEAF Scie·,.-1tific:· Advisory Cour1c:·il were based ors the prodtlcticn .. , 1trooe1 approach with evaluations made using a continuous eqi.ti l i br-i utrJ approx imat i ors. However, seri 01..1s di screpar1c·ies betwee't"1 mooei. predic:·tior1s arid data bec:·artre appare·nt arid this thesis examines the exter1t to whic:·h these are c:·o'f"1sequences of. the fa i 1 .t re t 0 a 11 ow f 0 .,.. oy·nartti cs i r1 fitting models to the data. The biology of the hake popttlatio·n and the history of the hake fisheries off the coast of southerl"1 . Afric:·a · a'r-e reviewed b'r-iefly ;:rnd the obJectives of fishery tttar1age11'1e·nt defined. This is followed by a presentation of the data l..tsed ir1 subseql..te't"1t calc::-l..tlations together with details of the sc:ti..lrces fr'otrJ whic:·h they were obtai't"1ed. 1'he basis for the surpl tts prodtu:·t i o·,.-, 1t1odel for the evaluation of sustai't"1able yields is discussed. It is show·f'"s that the steady-state assumptior1 will pretbably lead to positively biased sustainable yield estimates for fisheries whose history is dotr1ir1ated by a dec:·lir:ir1g CPUE t rer1d. !r1 Em attempt to c:·orrect for suc:·h biases, evaluations a're also carried ottt usir1g Gt1llal"1cFs method of averaging effort data. However it is riot c·lear to what extent this eqt1i 1 i bri um c:pprox itr1at i or1 approac:·h c::-ompemsates for Sl..tch errors. Col"1sequerrt ly, discrete dynamic- versions of the Schaefer and Fo>t models are fitted, i..tsi ng nor11 l near tt1i ni1t1i Lat i or1 procedures, to catch-effort data for the fottr ICSEAF areas commonly chosen for hake stock assessment purposes, nEUl'lely Divisiol"1S 1.3 + 1.4, 1.5, 1.6 and 2.1 + 2.2 (all of which indicate generally downward CPUE trends for the maJOT' part of their histories>. Monte Carlo simulation methods are employed to estitt1ate coefficients of variation for· the trJodel parameter and yield values assessed. The dyr1amic models aT'e show-n to p.,..ovide disti·nctly .ittrproved fits to the CPUE time series c:·ompared to those obtained ttsing the Gullcfl'"1d FunctioY1al Regression <GFR> or the steady-state approaches. MSY estifrrates obtail"1ed from dyr1atrtic:· model fits a.,..e, on average, appro>tifflately 1(>~ less than those resulting from the GFR procedu.,..e. Since the effects of 1..mcertainties (s1..tch as adverse environmental variability and the imprec::-ision of stoc~ biomass estittrates} can critically influence the outcoffle of mcmagement dec-i si ons, caution should be e>terci sed when 1t1ak i ng catch l i1rd t recomme·ndat ions. Various conservative approaches are advocated, arid the associated current catch limit recommendatior1s evaluated. These incltlde the Gulland and Boerefl'!a f 0 , 1 p"rocedl..tre, and an approac::-h where the qttota is reduced by a fraction of the standard error of the initial quota estimate. v The dynamic moaei is also employed to predict future biomass (as well as CPUE and quota} values. A historical examirratio't'"r of the ac:·c:·ttracy of suc:·h proJectiorrs· is used to c:·ott1<t1ent uporr the effic:·acy of the Schaefer and Fox ciy.,..1a111ic tt1odel s •. Dyr1att1ic model biomass estimates are co<t1pared to those provided by the Virtual Population Ar1cclysi s CVPA> p'r'oc:·edure for Division 1.6 • Large discrepancies in both recent t re·nds arid ccbsol .te val ttes cc re eviderrt, with biomass estimates bei't'"rg much lower i·n the cccse of VPA. Vs ri ous ext ensi O't'"1s to the dyl"1cc<tti c model a re i .,..,t roduc:·ed i .,.., an at t e<t1pt to red uc:·e the difference bet ween dyrrc:<tr i c <ttode 1 ;:md VPA biomass estimates ir1 Division 1.6. In general, the ir1corporatiorr iY1 the dyY1a<tdc:· <t1odel of ti111e lag effects (ir1 the r1et growth fi..mctioY1> a'!'"1d increased efficie'l'"1cy factors Hrs the catching operatiO'l"r) yield '!'"10 obvious itnprove<trer1t ir1 agreefflent betwee'!'"1 dyl'"1amic:· <t1odel aY1d VPA results. I·l"1 ac:iditio·l"1, the effect of allowir19 the ratio of the biomccss at th.e start of the given CPUE series to· the ca·r"ryiY19 capacity (y 1 /rO to assume val.tes oti"rer thccYr tmity is exattiil'"red. Results iY1dic·ate that this exter1ded model does ·not appear to have any advantages over models applied ear11er whic:·h asstt<tteo y 1 =r. The seemil'"rgly i·nsig'f"1ificant i<ttproveme·nts obtained S.tggest that the origi't'"ral dynamic model ·r1eerly fully e){ploits the i't'"1formatio't'"1 ·c·o·nteYrt of the data arrti that the i'l"1t1"oductio'f"1 of fttrther parattreters ca't'"r caltse the su<t1 of squares S.trfac·e to become very flat i'f"1 the vic:·inity of the <tiiriittrttm that is sought ir1 the fittir1g proc:-edttre. Dy·l"rami.c model fits .tsing the Shepherd surpltts prodttc:·t i o·n forttr (which incorporates a skewness para<tseter> are per·fortned 0'1"1 the c·atch-effort ciatcc. The ratio of the biotttass at MSY to the carryi'f"1g capacity (YMsY /K) is shown to be very poorly determined by the catch-effort data (the average coefficie'f"rt of variat iol"1 of estimates is 30~>. Results indicate that the Shepherd model is a suitable, though not necessal".ily S.tperior, alterr1ative to the Schaefer and Fox dynamic models. Possible extensio'l"1s and ·amendme'f"1ts to the dyna<ttic models are suggested. Thest? include the use of Clark's bioeco'l"1omic 1ttodel to review the f 0 , 1 strategy with regard to economic optimality, and the replacement of the traditional Schaefer and Fox for1tts with a n1ore 9eY1erali:i::ed • surplus growth fur1ctio·l"I. Also proposed. are an exa1ttination of the effects of changes in mesh si:i::e (on both catchabi l ity and growth parameters> and an adJ.tsted dyna<tric 1ttodel calculatio'f"1al procedure i'l"i which catches are 'discounted'. More appropriate weighting procedures for c·atc:·h-effort 1ttodel fits are sttggesteci a'f"1d lastly, an analysis of vessel power factors is advised.

Keywords

Mathematics

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