SCTB15 Working Pper MWG-2 Recen Enhncemen o he MULTIFAN-CL Sofwre John Hmpon 1 nd Dvid Fournier 2 1 Ocenic Fiherie Progrmme Secreri of he Pcific Communiy Noume, New Cledoni 2 Oer Reerch Ld. PO Box 2040 Sidney, BC, Cnd V81 3
1 Inroducion The lengh-bed, ge-rucured ock emen known MULTIFAN-CL i currenly ued for un nd oher pelgic ock emen by he SPC Ocenic Fiherie Progrmme (kipjck, yellowfin, bigeye nd Souh Pcific lbcore un in he weern nd cenr l Pcific), he Nionl Mrine Fiherie Service (NMFS) Honolulu Lborory (blue hrk, blue mrlin nd wordfih), he NMFS L Joll Lborory (Norh Pcific lbcore) nd he Jpn Nionl Reerch Iniue of Fr Se Fiherie (wh). Technicl documenion of mo of he model feure i provided in Hmpon nd Fournier (2001). Some ddiionl informion on recen developmen o he ofwre were provided he MWG eion SCTB14 (Hmpon nd Fournier 2001b). Thi pper briefly ouline developmen o he ofwre ince SCTB14. 2 MULTIFAN-CL developmen ince SCTB14 2.1 Reference poin nlyi A reference poin nlyi h been dded o he yield nlyi ecion of he model. The reference poin h hve been choen re he ol equilibrium biom ( B ), he dul dul equilibrium biom ( B ) nd he ggrege fihing morliy ( F ). To ummrie, he erie of ep involved i follow: 1. Eime populion model prmeer, including he prmeer of Beveron nd Hol ockrecruimen relionhip (SRR). Aume h he eimed prmeer of he SRR (α nd β) cn be ued o decribe he relionhip beween equilibrium recruimen (R ) nd equilibrium pwning biom ( B ): αb R = (1) β + B 2. Compue be ge-pecific fihing morliy vecor, F, vriou muliple of which re umed o be minined ino he fuure; normlly, he be i compued he verge over ome recen period of ime. 3. For vriou muliplier (x) of F compue he equilibrium ol biom ( B ) nd equilibrium pwning biom. Le = R( x) (2) where 1 exp ( M + xf ) = wm, (3) = 1 ' = 1 M i he nurl morliy re ge, w i men weigh ge nd m i he proporion pwning ge. Wih ll oher prmeer fixed, vlue of φ (x) cn be deermined for ny vlue of x. From ubiuion of (2) ino (1), we cn hen obin = α β (4) which pecifie he equilibrium pwning biom ocied wih ny fihing morliy muliplier x. R ( x ) my hen be deermined from rerrngemen of erm in (2). Similrly, he ol 2
ol equilibrium biom ocied wih he fihing morliy muliplier x my hen be deermined by: = R ( x) (5) where 1 exp ( M + xf ) = w. (6) = 1 ' = 1 4. Compue he equilibrium yield, Y ( x ) funcion of he fihing morliy muliplier x: Y ( x) = R ( x) = 1 xf xf + M 1 xf M ( 1 e ) exp ( M + xf ) ' = 1 w (7) Le z be he vlue of x h mximize Y ( x ). The i hen given by Y ( z). 5. The reference poin of inere re: B dul B ( z ) B F = ol = = B ( z ) Y ( z ) B ( z) 6. Compre he cul eimed biom nd fihing morliy level ime wih hee reference ol ol dul dul poin. Thi i done by compuing he rio B B, B B, F F nd heir 95% confidence inervl nd compring hem wih 1.0. Vlue of F F ignificnly greer hn 1.0 would indice overfihing, while vlue of would indice n overfihed e. 2.2 Incorporion of weigh-frequency d B B nd/or ol ol B B of le hn 1.0 A SCTB14, weigh-frequency d from he longline fihery unloding in Gum were preened by Kikkw nd Cuhing (2001). Thee d ppered o be exremely informive wih repec o ge rucure nd growh. A erch of OFP dbe nd conulion wih vriou nionl gencie reveled h here re ubnil weigh-frequency d vilble for longline fiherie for yellowfin nd bigeye un. Thee d ppered o be imilrly informive he Gum d nd in mny ce he mple ize repreened very lrge proporion of he ol cch (pproching 100% in he ce of he Aurlin e-co longline fihery). I w herefore decided o incorpore weigh-frequency d ino MULTIFAN -CL o ke dvnge of he vilbiliy of hee d. Thi required he following chnge/ddiion o he ofwre: 1. The inpu d file ( frq file) rucure w chnged o llow he pecificion of he rucure of he weigh-frequency d nd o include weigh-frequency d record, if vilble, for ech fihery record. 2. The MULTIFAN-CL model i ge-rucured he compuionl level bu he probbiliy diribuion of lengh for ech ge cl i lo compued o llow he model o be fi o he lengh-frequency d. We oped o pecify he probbiliy diribuion of weigh--ge deerminiic funcion of he lengh--ge. The ddiion of weigh-frequency d o he model herefore did no involve he eimion of ddiionl prmeer. The inegrion of he weigh dul dul 3
diribuion w done uing he me inervl pecified in he weigh-frequency d. A weighlengh relionhip ( W = L b ) w ued o compue he weigh diribuio n from he lengh diribuion. The weigh-lengh prmeer nd b mu be pecified. 3. The likelihood funcion for he weigh d i idenicl o h for he lengh d. However, we dded ome flexibiliy in pecifying he effecive mple ize for boh he lengh nd weigh d. Previouly, he effecive mple ize (which influence he vrince erm in he likelihood funcion) w he cul mple ize up o mximum of 1,000 divided by 10. Thi w done o cknowledge he likelihood h rel ize mple re unlikely o be ruly rndom umed by he iicl model. However, ome of he weigh mple repreen very high proporion of he ol cch, reuling in n increed likelihood of he mple being rndom (or repreenive). In hee ce, i would be pproprie for he cul mple ize o more ccurely reflec he effecive mple ize. We hve herefore dded more flexibiliy o boh he weigh nd lengh likelihood funcion by llowing he relionhip beween cul nd effecive mple ize o be pecified on fihery by fihery bi. 4. The Jv-bed MULTIFAN-CL viewer w upded o genere oberved nd prediced weigh frequencie. A cpbiliy o red he d file (o diply he oberved lengh nd weigh d only) w lo dded o he viewer. 2.3 Cobb-Dougl cchbiliy model A pr of bioeconomic modelling projec, we were ked o e he hypohee h: () cchbiliy i independen of he level of effor, gin he lernive h he level of effor impc cchbiliy hrough, for exmple, informion hring (poiive impc) or crowding (negive impc) (b) cchbiliy i independen of ock ize, gin he lernive h ock ize impc cchbiliy (he noion of n underlyin g populion h feed urfce chool which would enble pure eine CPUE o remin relively conn he ol populion declined) Thi w done follow: () ln( F ) = ln( ) + ln( q) + α ln( e), where F i fihing morliy, i eleciviy, q i cch biliy, e i fihing effor nd α i he prmeer. Thi effec cn be grouped cro fiherie, in which ce n index of relive grouped effor i ued. Eime of α ignificnly differen o 1 would provide evidence for he lernive hypohei over he null hypohei. (b) ln( F ) = ln( ) + ln( q) + ln( e) + β ln( B), where B i he biom index nd β i he prmeer. Thi effec cn lo be grouped cro fiherie if deired. Eime of β ignificnly differen o 0 would provide evidence for he lernive hypohei over he null hypohei. 2.4 Seonl nd ime -erie movemen Currenly, movemen coefficien re conn over ime. We re currenly ( he ime of wriing) incorporing rucure o llow eonl vriion in movemen for ech e of coefficien. There i ome indicion in he d for Souh Pcific lbcore h uch eonliy could be imporn. Vriou nlye hve uggeed h lrge-cle ENSO-ype ocenogrphic vriion influence he diribuion nd movemen of un. We herefore pln o inroduce rucure ino he model o llow movemen coefficien o vry over ime ccording o n environmenl correle. 4
3 Reference Hmpon, J., nd Fournier, D.A. 2001. A pilly-diggreged, lengh-bed, ge-rucured populion model of yellowfin un (Thunnu lbcre) in he weern nd cenrl Pcific Ocen. Mr. Frehw. Re. 52:937 963. Hmpon, J., nd Fournier, D.A. 2001b. Recen enhncemen o he MULTIFAN-CL ofwre. Working Pper MWG-1, SCTB 14, 9 16 Augu 2001, Noume, New Cledoni. Kikkw, B., nd Cuhing, J. 2001. Vriion in growh nd morliy of bigeye un (Thunnu obeu) in he equoril weern Pcific Ocen. Working Pper BET-2, SCTB 14, 9 16 Augu 2001, Noume, New Cledoni. 5