A Point Estimate of Natural Mortality Coefficient of Southern Minke Whales Using JARPA data

Transcription

1 JA/J05/J6 A Poin Eime of url Morliy Coefficien of Souhern Minke Whle ing JAPA d EIJI TAAKA YOKO ZEITAI nd YOSHIHIO FJISE Tokyo niveriy of Mrine Science nd Technology Fculy of Mrine Science Konn Mino-ku Tokyo JAPA The Iniue of Cecen eerch Toyomi Shinko Buld. 5F Toyomi-cho Chuou-ku Tokyo JAPA ABSTACT Thi er how oin eime of nurl morliy coefficien of Souhern minke whle uing JAPA d by modifying he originl mehod rooed by Tnk (990). Skew ge comoiion by mure/immure egregion w correced uing muriy re ge. e re of nurl incree of ize of ock by new inerreion of ock boundry w eimed by mimum likelihood. ing he zero incree re of ock ize from he iicl model eleced by he c-aic he oin eime of nurl morliy coefficien were (er yer) for boh he Eern Indin Ocen Sock nd for Weern Souh Pcific Sock. ITODCTIO url morliy coefficien i one of mo imorn biologicl rmeer for boh oulion dynmic nd ock mngemen. The chnge in number of recrui nd crrying cciy on Souhern minke whle (Skurmoo nd Tnk ; Buerworh e l ) which rele o hoe in he ecoyem of he Anrcic hve been eimed uing he morliy coefficien. In he evied Mngemen Procedure (MP) which i curren conervive ool of he whle ock mngemen in IWC n umed coefficien of nurl morliy w ued in he Imlemen Simulion of he MP. In he reul of imulion ril uch erformnce iic relized roecion (P) level w ued for one of crieri of ock conervion nd w deending uon he een of he nurl morliy. The effec of he chnge in he crrying cciy which cue hoe of he recrui were emined in he robune imulion ril for develoing he MP. The eime of he een of chnge deend uon he morliy eime. Thu he nurl morliy coefficien h direcly nd indirecly been ued in he MP. JAPA urvey rogrm for inveiging he biologicl ec of he Souhern minke whle nd one of he objecive of he rogrm i o eime uch rmeer he nurl morliy coefficien. Term of he ned urvey i o long ieen yer in order o hve recie eime uing ock bundnce nd ge comoiion (Tnk990 Tnk e l. 99; Cooke e l 997; Tnk nd Fujie 997). Sudie on he eimion wih uch reerch ke under rndom

2 mling hve been reened (Skurmoo nd Tnk 989; de l Mre 990 kmur 99). In he JAPA review meeing in 997 however informion on ge egregion w recognized irreecive of rndom mling. A orion of young whle doe no migre ino he Anrcic urvey re where i ouh of 60 S. The oberved frequency in he young ge cl could be lower hn he rue frequency for he whole ock nd herefore he eime of he nurl morliy uing direcly he d would be bied. Mny of he young ge cle coni of immure comonen of he ock. If he frequency of hi comonen i correced we could mke unbied eime of ge comoiion. In ddiion Lui e l (005) rooed new cenrio of ock boundry h i differen from he rdiionl IWC ock diviion. In he cenrio he boundry i 65 E There were wo ock in Are III/E IV V nd VI/W nd he Eern Indin Ocen Sock (I-ock) nd he Weern Souh Pcific Sock (P-ock). Therefore new mehod i necery for hndling nd/or nlyzing he d becue he JAPA urvey w ned nd conduced by he rdiionl diviion. Thi er rooed n eimion of he nurl morliy coefficien inroducing mehod for correcion of he oberved ge comoiion nd nurl incree re wih egregion rmeer. Iue reling he eimion were dicued. MATEIALS AD METHODS D D ued for nurl morliy coefficien re he nnul bundnce eime rified by re e mure/immure nd ge nd eimed curve for muriy re ge (Bndo e l 005). Bic Model for Dynmic of Sock Size We conider whle oulion h ock ize i chnged due o nurl morliy nd recruimen nd h ock i coniing of mure nd immure comonen nd h orion of ech comonen i nnully migring ino he JAPA urvey re. We ume h nurl morliy coefficien i indeenden of yer nd h roorion of mure or immure ock i indeenden of ge. Le nd be ize of ock of e () ge in yer (3 ) in yer (35 T) mure ock ize immure one mure ock ize in Are (3 for Are IV V/W V/E) nd immure one reecively. Bic model for he dynmic re ereed by e( M ) () () (3) ( ) (4)

3 c e (5) (6) (7) γ (8) Here γ : re of ize of immure ock in urvey re o ol immure ock(>0) : re of ize of mure ock in urvey re o ol mure ock(>0) : ock ize in ol : muriy re ge M : nurl morliy coefficien (er yer). Eimion Procedure for Averge url Morliy Coefficien From equion () we hve z r M (9) r (0) z () () i j j i i i (3) Here r(er yer) i he ne re of incree of ock ize. When ge comoiion i firly ble he verge nurl morliy coefficien i ereed by z r M ~ (4) 3

4 ~ z (5) Therefore hoe eime re ereed by r z M (6) T k k T z 3 ) ( (7) Correcion of Age Comoiion Age comoiion in he urvey re w correced by bundnce by chool ize nd ge comoiion by chool ize (Fujie e l 99). However if he vlue of γ i differen from h of he ge comoiion i bied nd herefore hould be correced. Auming h in ome ge cle re cloe o ech oher nd uing equion (3) (4) (7) nd (8) n eime λ i roimely ereed by λ γ γ (8) ing equion (8) we reduce he following equion: λ λ λ λ (9) 4

5 Eimion of r Suoe h (0) hen he ock ize in Are IV or V/W i ereed by ( λ ) ( ) () The men of roorion of ock ize in Are IV o h in Are IVV/W i denoed by.for he I-ock r i eimed by mimizing he following log-likelihood: LL W LL LL () { ( ) ( ) ( ) r ( ) } LL { ( )} π σ υ (3) σ υ { ( ) ( ) ( ) r ( ) } { } LL π σ υ (4) σ υ For he P-ock uming r i eimed by mimizing he following log-likelihood: { ( ) ( ) r ( ) } { } LL 3 E π σ 3 υ3 (5) σ 3 υ3 where υ : ddiionl vrince by ock σ : meuremen error of bundnce eime. eul Tble -3 ummrize he reul of eimion nd Figure nd illure he verge of he correced ge comoiion. Comring he comoiion before nd fer he correcion in Figure he correcion eemed o be effecive in he Are V bu no in Are IV. From he c-aic vlue in Tble he model uing r0 were eleced nd he oin eime of nurl morliy coefficien were (er yer) for boh he Eern Indin Ocen Sock nd for Weern Souh Pcific Sock. Dicuion The correced ge comoiion will be ueful for eiming he eleciviy of reerch ke by he JAPA comring he correced bundnce ge nd he cch ge. Alo he comoiion will be vilble for monioring chnge in number of recrui which rele o ock dynmic. The erformnce of he reened mehod for correcing ge comoiion deend uon reciion of he ge comoiion nd muriy re ge. The ge comoiion in urvey re w 5

6 eimed by ) bundnce eimion by ub-re nd chool ize nd ) ge comoiion by ub-re nd chool ize (Ko e l 99 Kihino e l. 99). The bundnce eime ued in he er w comued uing he only d from mling nd couing veel (SSV) becue he boor mle for CV comuion re mde by ir of he bundnce nd ge comoiion from SSV nd he d ize for couing veel (SV) i oo mll o eime bundnce by ub-re nd chool ize. However bundnce eime doed in he JAPA urvey w mde from he combined d becue he eime i eeced o modify by uing he SV d. The ge comoiion will be modified inroducing he SV d. The muriy re ge (Bndo e l 005) w eimed by he rw d nd migh hve unceriny due o egregion. However he eime w much revied hn h from he commercil cch d nd will be relible. In he eimed vlue of r we noe h he r eime my reflec chnge in. The dicriminion in riculr for he P-ock w difficul becue he only d in Are V/E w vilble nd uch comrion of he rend for he me ock rend in Are IV nd V/W w imoible. In h ene iicl crierion i no licble nd he comrble d re necery for he dicriminion. The eime of M i cloe o h by he ADAPT VPA (Buerworh e l 00) nd h for Are V (Kikdo e l. 005). The CV w no ye eimed bu h cn be comued uing boor mle (Efron 979). Thi i n iue in he ner fuure. eference Bndo T. Zenini. Fujie Y. nd Ko H Biologicl rmeer of he Anrcic minke whle bed on meril colleced by he JAPA urvey in 987/88 o 003/04. Per JA/J05/PJ5 reened o hi meeing. Buerworh D.S. Pun A.E. Geromon H.F. Ko H. nd Miyhi T An ADAPT roch o he nlyi of cch--ge d informion for Souhern Hemihere minke whle. e. in. Whl. Commn 46: Buerworh D.S. Pun A.E. Geromon H.F. Ko H. nd Fujie Y Furher ADAPT nlyi of cch--ge informion for Souhern Hemihere minke whle in Are Ⅳ nd Ⅴ. Per SC/M97/6 reened o he IWC Scienific Commiee. Cooke J. Fujie Y. Leer. Ohumi S. nd Tnk S A elorory nlyi of he ge diribuion of minke whle colleced during JAPA eediion 987/88 hrough 995/96. Per SC/M97/ reened o he IWC Scienific Commiee. de l Mre W.K A fureher noe on he imueou eimion of nurl morliy re nd oulion rend from cch -ge d. e. in. Whl. Commn 40: Efron B Boor mehod:noher look he jckknife. Ann.S. 7:-6. Fujie Y. Ko H Zenini. nd Kihino. H. 99. Seonl nd rel chnge in ge diribuion nd egregion of he Jnee reerche. Per SC/44/SHB0 reened o 6

7 he IWC Scienific Commiee June 99. Fujie Y. nd Kihino H Furher eminion of egregion ern of minke whle in Anrcic Are IV nd V reveled by logiic regreion model. Per SC/M97/3 reened o he IWC Scienific Commiee My 997. Ko H. Kihino H. nd Fujie Y Some nlye on ge comoiion nd egregion of ouhern minke whle uing mle obined by he Jnee feibiliy udy in 987/88. e. in. Whl. Commn 4: Ko H. Fujie Y. nd Kihino H. 99. Age rucure nd egregion of ouhern minke whle by he d obined during he Jnee reerch ke. e. in. Whl. Commn 4:87-9. Kihino H. Ko H. Kmu F. nd Fuijie Y. 99. Deecion of heerogeneiy nd eimion of oulion chrceriic from he field urvey d:987/88 Jnee feibiliy udy of he Souhern Hemihere minke Whle. Ann.In.Si.Mh. 43(3): kmur T. 99. A new look Byein cohor model for ime-erie d obined from reerch ke of whle. e. in. Whl. Commn 4: ihiwki S. Muok K. nd Kwki M eview of he ighing urvey in he JAPA. Per SC/M97/ reened o he IWC Scienific Commiee My 997. Pene L.A. P.Goo M. Knd. Bndo T. Zenini. Hkmd T. Oni. nd Fujie Y. A new inerreion of he ock ideniy in he Anrcic minke whle bed on nlye of geneic nd non-geneic mrker. Per JA/J05/PJ3 reened o hi meeing. Pun A. E. Cooke J. G. nd Borcher D.L Eiming he een of roce error for Souhern Hemihere minke whle from he reul of he IWC/IDC cruie. e. in. Whl. Commn 46:3. Skurmoo K.. nd Tnk S A new muli-cohor mehod for eiming for Souhern Hemihere minke whle oulion. e. in. Whl. Commn 35:6-7. Skurmoo K.. nd Tnk S Furher develomen of n emen echnique for Souhern Hemihere minke whle uing muli-cohor mehod. e. in. Whl. Commn 36:07-. Skurmoo K.. nd Tnk S On he eimion of ge-develomen nurl morliy. e. in. Whl. Commn 39: Tnk E. nd Fujie Y Inerim eimion of nurl morliy coefficien of ouhern minke whle uing JAPA d. Per SC/M97/ reened o he IWC Scienific Commiee. Tnk E. nd kmur T Preliminry eimion of verge nurl morliy coefficien of Souhern minke whle uing JAPA d. Per SC/47/SH8 reened o he IWC Scienific Commiee June 995. Tnk S Eimion of nurl morliy coefficien of whle from he eime of bundnce nd ge comoiion d obined from reerch cche. e. in. Whl. Commn 40:53-6. Tnk S. Kmu F. nd Fujie Y. 99. Likely reciion of eime of nurl morliy re from Jnee reerch d for Souhern Hemihere minke whle. e. in. Whl. Commn 4:

8 Tble. eul of eimion of λ. ) Are IV Are / Seon 989/90 99/9 993/94 995/96 997/98 999/00 00/0 003/04 IV() b) Are V/W nd V/E Are / Seon 990/9 99/93 994/95 996/97 998/99 000/0 00/03 004/05 V/W() V/E(3) Tble. eul of eimion of r ndυ nd. Sock Model c-aic LL n r υ υ υ 3 I-ock Full r P-ock Full r Tble 3. eul of oin eime of verge M Sock I-ock P-ock M

9 0. Are IV Age in yer : 0. Are V/E Age in yer : 0. Are V/W Age in yer : Figure. Comrion of uncorreced ge comoiion (oen circle) nd correced one (olid curve). 9

10 Age in yer : IV V/W V/E Figure. Comrion of he ge comoiion in hree re. 0