"~ ..... ,'- ..... -"""*', ',.

,'." .

;' .

. '.

. '

, ".

, "",'-:'=...I::,::":__.-:;.:..;;,,...,;:__.-::;;,;;.o;..,;:;':';;';';=--~';;';':;';:;":;:~J:.::,..:=.:;.;:-.;.;:r;,.;:c':.:·t.e..rence; 'to,,':'the 'E-u..th~,' '

~by : ,

,,' iR., Borrmann 'and Berner

, Institutefor Deep'SeaPisheries ondFlah Proc:essingRostock, ,

, German Democratic Republik

:'·Anattempttoestimatethe optimum" "/ fishing mortality rate' for~Baltic 'cod

" . ." . . 1 . ,

"." .

,'Abä.t~~c t '...:

Com'oining thc spawil1ßg stock - recru1 t \Vi ththe yield-por,;.recrui t • 'relationsh1p in a fishing mor,tality-yield curve [lnd taking in'~o'cOllsideratlonsthe point where ,the stock sizeby weight would be "two-thirds ofthevirgin one a·range of an optimum fishing mor- '"tality,was estimated for the throe management unitn. Following:rßsults .:w~re obtained for: the agegroups where partial rocruit­,ment ii,\~O: For'Sub-divioion 22 from F = 0~8. to F = 1.6,SorSub-divlsion'24 from F ~ 0.5 toF = O~8 '[lnd for Sub-divisiond25-,32'froDl"F·= 0.9: to P =,1.4 where in ench case thc secondvuluo ,ie Fma of' the yield curve. ~ut the, first value can be rccommondcd'for est1mating TAC.For cod l.n Sub-division 22' production CU1'VOS "

.. werealso constructed arid comparcd with thcfiohing mortality~yield curve. ' '

•

...

,

Ir.troduction-Up tc now sciehtific ad~iccs fdr.reguluting thc cod oto6ks intheBnltic VJere givcn by lising VPA, considcring tho resül tDofY/R-clll'v,eE,Jfor }'mnx, r;nd' me~h aize .regu~ntionu, anU comporing ,

'thc npawn'J.ng stock 8J.ZCO ('1 thc preCedl.llg ycursQ' " . ,This paper intendo to find an OI> Limum fishillg rnol'tnlit:; rateby combining the, yield-pe]'-recrui t . curvo wi th tbc npuwning ntack-··

. recruit relR tionohip.' But. ono must oay thot thc OSY-concept. (ICES; 1976) ,will not bc dlOlly realizcd bocau:Jc fishing pattornwill not bc, optimiscd, ßnJ 0100 clH:Jngc~1 in grQ\'Jth and spnvmingputtern ~ccordinc to chnI1['.cs in otoclc.nizc will bc dinrcgnrded ll

. ,

2 - ,

It will be eonsid~r~d the fislitlg mort~lity rate wherc the stockaize by weight would be two-thlrds of the virgin one o Instead cfone:half of the 'virgin:biomaoo this level of otoek oize,wouldproduee a i'cduetion in eateh varianee vJithout great loss in' y1eldand an inerease of eateh oer unit effort ,if Sehaefer's model i8applieable (DoulJleday,1976).; aüd it wao also the' area o:t" an "optimal trade~offbctweenvarianee ofeateh and eateh when anothermodel was used (Lett und Kohler~ 1976). A reduetion of'one-thirdof Fmax ' whieh eorresponus to a stock size of two-thirds of. thcvirgin one in Sehaefer'o model eun be seen, too,following thcanalysis of Lett and Doubledoy (1976) for Gulr of St o Lawrencceod beeause Fmax'was 0 0 6 und the recommended F'=0.4.

,Material und Methods.In order to construet the fishing mortalit:t"';yleld eurve 'following .steps were ncecssary: e'10 Spawning stock .per reeruit' (SiR) and yield per 'recruit (Y/R)

were euleulatcd by means of the stock and eateh equationstaking into consideration partial rceruitment and proportionof Bpawncrs per age group:

.sw/ R

Y/R\'ihcre

1" :::

N1 -

p.r. _..

!). [11) ::::

Sw :::

--VI

maximum f:Lf3hing .mortnlity rate at age (this eorreo­ponds to F where p.r. ::: 1.0),

1 recruit,

p2rtial rccruitment,

proportion' of ~pawncrs,

Dp[w:ninc stock oizc by weight t

lllenn \'Je ir;h t c t nge.

2. 'file otoek-recruitment· r(;J~lLion \;J~w,e~Jtimnt'cd by thc Riekcrequntioll ,Hic.}:('1.', 1 ~rtJ), tlw '·iü1.cly usou formuln to fit adomo-nlH.llWd recl'ul t.elünt em'vc:

\

,I

---------------

, '

~ -. ,. <~

, J~'The opuvinint; stocl-: size per flshing rlo'.rtu,lity ;'iQS calculated""by,theexprecsion:

f

S= in R/S -ln cx '- ß .

where 0<.. al1d ß ure. tho paraf.18t ers. e'quation und R/S thc reciprocul of" rate-9

(4)

of thc stock-recruitmentSiR per fishing mortality .

\

(6)

-.4 0 ,The correspond ing numbcr ()f 1'8C1-ui t 0 \';8El ca lcula ted by equat ion.(3)and the yicld by multipl;/ing thenumbe;t' of 1'ec1'uits by thevalue of Y/R o

,f.:.

In o~der to be able to eotimnte'the fi~hing mortulity where theotock size by weight in t~o-thirds of the virgin,one calculated

. spawning stock oizes were converted into stock sizes by theregression lines given., in 'rable 4, Gnu the corresponding fishing

.ortality.rate was der:i.ved. T.:oreover.the fishing mortolity. level

.as estimated by reducing !!max b;)' one-third. Fm<;lX ist the fishingmortali ty Wrlere thc maximum lone-term average y~eld would be

. producedo This'r~ductiori could bu done if the relationship betweenfishing mortality and ;)iiold i.s a quadratic.one as in Schae'fertsmodel and it is asoumed b,at the co.tchobility cocfficient, isconstant .·Por this 1'euoo11 i'ollov/ing regression cquation, was fitted:

Y/F ,= a - b • F

Inpl~t 'data were used i'rom tho fishing .mortnlity-yiuld curve ofthe range frorn 0.1 toP =1.2 for SD 24 nnd frOill F = 0.1 to:F' == 2 0 0 foX'·the other munagemept units.

Thc productiori curven of cod in 3D 22 ~ere constructed accordingto thc general prodLlction models of Schaefer and of Fox (1970).'

'In order to make the resul ts .of thc two methods (yield curve undproductioncurvc) comparablefishing effort had to be convertedinto fishine mortalitYG Bcdause F = q • 'X, the catchability

It0efficient"- (q) had to be estim~::tted. 'I!v/o methads were used:

1. Accordine to ~ox (1970)

~ ~Ui, q= LJ-oi .' ,

1 ( n ' -)b .n . tn U00 - Z ln Ui - L,Xi

, l=l'·l'" 1

2. Reßrcccion of total mort~lity (Z) on X

Z_.M+q.X (7)

'\

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

t - ,

'-~ "\)

Because the res'ul ting fishing mortol i tics are menn volues, thc, F-values cf the ,yield curve were"convcrtcd ulso into rr.enn vulucs.• For cach F-valuc that represents thc F-v"n1uc wllere por o = 1 stock'sizes at age per one recruit we~e calculated und used'for ca16u­lating,the weighted, mean(r1"~). -l

Following input data were used: ,u.

11 = 0'.3 was usedas the valu6' cf naturnl mortal)ty for nIlmanagement units:and age groups. ,Proportion of spO\~/ners (p.s. ),ojao calculated from material'of the,

"G.D.R. t an~ represents the proportion of adult femnleo to the",''total stock size by num~er.~herefore theproportions take alsointo considerationthe proportion of females to the stock., They" eare given in .Table 1.' . "

, Pa;ti al. recruitment (p.r.)' was con'sidercd to bc constant for ., all F-va1ues, though it i6 obvious that it will changewhen stocksize changes to a greatcr extent. The mean velues slightlysmcothed (Table 2) were dor1ved from meen F-values calculatcd byVPA. Thc valuc cf th~ ,last pge gro~p6 was, also used for, the 'following ones.Mean weights per age grcup were taken from the v6nBcrtalanffy .growth curves, which were fitted from mean weighto per agegroupof diffürent 6ources: Fcr SD 22 'and SD 24 from Berner andBorrmarul (1977) and for 3D 25-32 from,Berner (unpublished).Among 6(lveral p06sibilities for SB 25-32 the da ta preseritod inTable 3 were the beot ones'when used for recalculating thc cutch \(t) fron: ca tch by number for the period 1966-1977

(y = 40909 + 0.762 x Yrcc., r =0.95)0 In Table 3 thc maun weißhtoat aga are only shcwn up to the, age group where input.datu for ~

calculating ~he growth curve were takeno, , , •,Stock sizesby weight were calculated uning the ~ tock. bynumber ',da ta fron Berner and Borrmuiln (1977) fol' SD 22 und from leES (1978)for the ::>ther management unito und the name menn vJeights atngeshcwn in Table 3.'The opaYJping stock sizes by weight were cotimntedfrom oto~k sizes by weight per agc group und proportion' 01' spuwncx'u(Table 1).Thin will not bewhollycorrect, for p.sQ are rclat~d tonumbers3.nd growth J of malen [jnd' femo leo io different., According tothe est~nation ofp.so,the opnwning stock Dize reprcDento th~ stocksize cf ;~dult femalen. S~ocl: sizen earo given in Tuble 4.-For calcalating the rrr_oq.uction c..YJ·V(~ for SD 22 following input. datewere usell: Uean annunl catoh per lUÜtoffort us publiohed by Bernerund BOrriJann, (1977) far I';;ecklenburg Boy und the nnnuul fi,shingeffort~ Thone datu and the ,total mortulity rateD dcrivud-from P1~{Borner und Borrmnnn, 1977) plu.8 r~1:::: 0.3 for c~1tir.lutlng Cl lJypred1cti ve rc:grc:sG ion are sLot,'H1 in Tu ble 5.

RCQultn

.\

. ,'''-

~-.. -...

1 '_

. !

.• • I" <

;..•.. '

t· .'

".

.-;'

,"

,,~,.

~: '.{.

~'- ' .'

j :

. f

..:. 5

Sub-divioion 22

Yicld-pnr-r';crui t and'spovming stock-per-rccruit curvcf:l can be­ne~n,in~Pig. 1 (A).·Tho yield-per-recruit curve in adome-shaped

. oneyJithFr.lDX =,0.40 At thia :i~-value the spawning stock: sizeper" recrui t deoreancs by 81 pürcent0. '. ", -

}'ig. 1· (B) shows theyield and spovißinß stock' curves vJh.ere thespawning ntock-rccrlftmcnt rela tionship wos taken into consid:e­:catiol1 o Tl1üyleld curve husits mrlximum ut F = .1.6with a yieldof 30 514 t. Atthis fishing rr.ortality tho spav-ming stocksize·.

. is 9 659 t o This ~erlns 0 dccreosoof 77 per cent compared with .the unfished,one. A decre~se 01' one-third \'Jould be at abou\1'\ = O.~ 0 Aone-third dccrerlse 1'01." thc stock size by weightcan

,not be' ßiven· becoueethere Vlere no dependence between stoc~ size.and· spuwninß stock size. Sec fl'ablc 4. Thc.~,rcduction of Fmax 'Qyonc-third rCGults in F = 1.1~ .

The spawninc; stock-recruit curvc hup its maximum number of re~l;uit8

at 0 'spuwning stock sizoof ubout 9·000 t (Pig. 2)0 The number of'recruitu ßcncratcd in thc pcriod 1965-1974 was in th~ range of .thc dcsccnding' .port of thc curve.

The prod'~ctioncul'ves nnd dIe empiric data taken from Berner anq. Borrlllnnn (1977) nrc ohown in Fig.·3.In oddition the yield eurvehere relntcdto r.lOan fishing mortality (F,+) is presented•. Afterthut the maximum yield will bc produced at F1+ = 0.61 and the .I.':SY of 32 700 t (Fox) Dnd cf 33 700 t (Schaefc1."').at F1+' =, 0.57'.CP] 4 ~. 1.5)0 A rccuction cf Pmax by onc-third woud mean that. , ....- . ;.

P1+= 0.38 ünd PJ,4 ~ 0.8. . . ' .Effort nos ~onvci~tcd into fishinß mortality by using the catcha­bility cocfficicnt of q ::::. 0.004. The colculetedl values wereq = 0.00)87 occording to tile methodof Fox (1970) and q = 0.00409fitting thc regression line. . . f . .

. ,

Sub-diviDion 24/'

Yield-per-recrüi t and spowning s t ocl~-per-recrui t curves are 'given .inlt'ig.4 (A). 'rhe muximum yield per recruit will be obtained atF = 0.4.'At this fishing mortnlity thc spowning stock per recruitis only 19 per cent cf thc unfished one. . .

Takirig 'rllsointo consideration the spowning stock-recruitmentrelotionship, thc muximum~'ield of 16 399 twill be obtained at .F = 0 .. 8. Atth~s P-volue thc spovining, stock' size amounts to14 881' t. '1'his corrcDponds to 0 otocl:: size of obout 45,OOOt •.This mounothut tllC spn~ning otock 8izo d~creasesby 73 per centund the otock oize by'·62 per cent in comparison with thc unfished oneA one-third dccrünoe of., thc. Dtock oizc '\'Jould be ut about p= 0.4,.F = 0.5 would be thciv61ue thot resulto from 0 one-thirdreductionof F'mox. .

1'l1e Dpnwninn stocl(-l.'ccruit cnrve (Pin.5) hoo ito maximum nwnber 01"recruito ut [l opuwning otock oize 01' ubout 014 OOOt.This correopondsto D otock oizc oi'. 43 688 t! .The VQ lues of the period 1965 - 1975ure ßcuttercd around tobe uscendil1g limll ,of tl1e curve"

\' .. '. ,,". '

..... ,

" .G

, ,. "

. \'.'-',

,Sub~divisions 25-)2 . '

,,' ,,., • The yield.....p~r-recrui t curvc (l~'iß. 6 A) !lUG i t G mnxirnwn at F = 0.2.'" 'At: th1s fisti~g mortnlity the opavming otock per rc.cruit omounts,·,,'

to 27 per cel1-t of the unfished one ~

Th~ yieldcurve (Fig. 6 B) h~s i ts maXimUl:1 at P == 1."4 with a yicld"ot 193000 t. At this F-vcilue thc. apowriing stock aize i~ 63 9bo t- end' th,Q. coX'responding stock aize ubout 325000 t. 'rhi LI meano'u "

'" decrea,a~; ofthe stock by 59 per cent comparcd with the unfished' ono.":::A one-'tbird decreaoc \vould ,be at about P = 0.5, ond U onc..;.third .", retiuct ion of Fmax resul to in F = 0.9. ' .

" "~ The spawn1ng. stock-recrui t-curve (Fig'. 7) io [l dOll:c-shuped' onewith themax~mum numb~r' cf recruits at a opnwning stock aize· of

" ',' about 50 000 t. Th1s corrcopohdo to a stock oize,of294 000 t.

,~ "'"l; •

,'" .. '., '. '

" e, For all management units thc ,quadratic relationship 'betwcen fiohingmortal1ty and yield could bC,found. FoJlOwing purumoturo of ex-pression (5) wereestimatod: ' .

'..,

. " .;

:.... lt., :.

',', .... ';,'. "

".,", '..... '

sn22,24

, .25-3?

a36 42341 823

287.6

b-10802-28 026

105.9

yiold in tons

yicld in '000 tons

. ',,','

'"j" .

DiscussionI sc

Sub""!division 22,',Comparing the Fmax-valucs of the yield-pcr-rocruit curvo undyiela curvewhcre tho spuwningotock-recruitment rclotionohip 10included. one can see that the li'-valuo/(J..' :: 1 0 6)/oi'·the yield •curve 1s much highcr and porhaps too high. But cDnsidering theempirical data of the pcriod 1965- 1974 (menn fiohing mortalityof age group8 3 and 4 of ob.out F := 1.3 und tho cutch 01' nbout

·31 000 t), :one could suy that thc yield curvc eould bo, at leastfor this part ,- a rcalistic onc bocauoo thc differencoo betvJCenthe yields at F = 1.3 und P =,1.6 U1'0 sinnll und thc 1'iohing' mor-'tality rate did not vary tc u graut oxtont ,(for ugo group J ,,'V = 16 per ,cent) • At F =.1.6 thc opawning stock oizo VJould benoar to the'size wherc the maximum number of recruits will,beproduced. But it is k~lo\'m thnt thc grüntost fluctuntions 01'

'rocru1tmeht take pluco~thero. Thereforo it ~ould be oppropriatotC,fieh at a loworlevpl of fishing mo:rtultty ruto" This could

..... be betweenF ;::' 1.1 und p.:::' 0.8 wherc Fm~x was rcducod _by Dl1C-.thl~d.The letter valuo was dor1vod fram thc production ourve. • ,"

Thß general product~od cur~co corre~pond woll with tho fiohing, ,mortality-yield curve compurin~ tho mnxllnumi yioldu und F1+ -vßluus~

, There is only a difforenco of { per cont bot~eontho F1+ -value~.

, Comparing the production curvo occo!'dinr; to ,~ehnefer and tho yioldcurve one ought to keep inmind the cotimationD cf P1+.

, ..Ar. '. ."".:Sub-division 24

. '.~', .IIlcorporating the spn\"mir.G ·stcck-rccruitmcnt rclntionship into . ';'

'-~the yield~per-rec~uitcl;U've· t~c F.~nQ:~Cv:.llue 8hiftc~ 'f~om 10' ::: 0 0 4 - . .to F = 008~For the:per10d '19b5 - 1~75 themCDn f1shlng mortality of­the age groups'3:ci.nd 4 won. about P = 0.9 Dnd thc mcnn, catch wno '.'.about' 15 100.t. Thone voluCG cOl'.rcspond \"Jcll wi ththe correnponding '.point of the, J."ield. cur\;e.: cr.rr~is comp~risoIi is not \'Jholly" exuct ", " .because.the mean cutch pOl' fishing mörtality and riot pOl' meon, .,'fishing mortali ty had to ho tnlu:n.Eut durine the poriod conoiderednO.,ver~· greot v8rlotionG cif thofishing' mortality rote took plaCe(V = 25 per cent for ace group 4).) I,; early tho same mcon ca tcllcould be achieved "atF.= 0.6 whereb:ithe G'püwning stocl: size would',be on the right-hand, sideof the f,lOximum recrui trnent v:hereaci the '

, spawning stock: sizesof the' pe!~iod .1965 ':" 1975 \';01'0. on the left-hulld\side~The F-values are still 10\;:er thon P ::: 0.6 \'Illere the stock size'amounts totwo-th~r'ds'of -:he virgin o~e. and the 'P~ox-value' i8 . ,reduced by one-thlrd. They are about 1:" = '0~4,and l' =0.5" '

,respectively. ' ' ..,' .

Sub-divisions 25~32

.The Fmax-value iofthe yield-per:'reerui~ curve is F = 0 0 2 wtn!';'notho value~ at which the highest average yield will be obtoined,18 F ;1.40 Dufingthe period 1966 - 1975 the mean fishine mortn­lity rate of' age group 4 was F ::: 0.85 '(coeffieien't of vuriation:V =22 per cent) und the eorresponding moan eateh about 157 000 t Q

This means that, at least for these values, the curve rof1octo the"situation of thc per.iod conoidered •. But it wou1d be unnuitableto fish at F = 1~4 beeause then the spawning stock size will bein the range of. the dome of-the npnwning stoek-recruit Cll1've wherefor gadoids the confidenee limits ure graatest (C~shinß und .Harri8, 1973). Therefore i t would be mol' reliable to t:::l;:e P ::: 0.9where thespawning stock size amounts to nbout. 100 000 t. Thisfinhing mortality rate is also the one that renults from thc OIle­th~rd reduction of Fm x \i;hereun~::: 0.5 io the value that \'JOs. ' .derived from the stoe~ size being hvo-thirds' 01' the v irgin one o

V,alueing the yiold curves of nIl management unfts one 1100 to pnyattention to the fact thut the spawningstoel::-rocruit ellrvo 1100 Q

.graat influence'?n' thc. behaviour of the y~eld·cu.rve ~Ild th,atespecially reeruJ.tment curv,eo nre~cert(lJ.n becousc J.nput dotu

, were not available f9r the whole range of tho curve8 nnd onlyfor 10 years. Onehas also~to benr in mind that thc valuon 01' ~heyield curves give the long-term nve~ageyields becuuec thore ara'cycles and fluctuations in recruitment enused by a log time betweenspavming und reeruitment und by environmen'tal fluctuutionD, whiehresult in difi'~rent varia t ionD of thc yie Id in dependcnce of theotock size •. In order to reduco. the f1uetuations of' thc cateh nndto make the. otocks more reoilient to deplction by a suceoDsion 'o~ weck year-claoses~ Doubleday'o (1976) recommendation to contraloffort at a level correspanding to 'au cquilibrium biomuss of two­thirdo of thc virgin otock should 'be- fo110\'..cd. Eotirnuting thia leveltvlO mothods' were used. J.t~m x v/ao roduced by one third ond P wasderived from stock sizeo fly vlCight. Ao eould .be Deon there W01'edifferent reoults. This,eauld be duC to the method far convertinßf3pu~',rning stock size into otock size becnüoe the UDCU reßreDsionlinco are o.nly ~oDed on a omall range. of opuwninr; utock oize' Gnu

1,

-,

'r

",

'. ,~,, ~._: \'.

\,

> •

I.

- .. 1

- t!> -

besides there nhould be <m exponentio.l relationship for thewhole ränge. 'fhrit meüns tha.t valueo derived. from Fmax would bemore reliable o

Comparing the two-thirds F. -va lue wi th the .preceding mean fishingmortality rates one can ue~aihat the preceding valueswerehigherfot' sn 22 -und sn 24 und some'liha t lower for sn 25-32. ~he following .Table givesthe estimated and thc preceding mean F-v~lues for theage groups where p.r. = 1.0: .

1) from production curve2) M = 0.2

. J) according tothe period of input'data4) from leES (1978)

•/'

r 'f'-.I..References

- 9 -, .,'''

Berner, 1-.1 0

"

and H. EorrQsrtn, 1977Die fischereibedinGte EntwicklID~ der Ostseedorsch-:'beGt'inde, in: dem ICES-Untergebieten 22 (Beltsee) urid24 (A~konnoee) in den Jahren 1965-1976, dargestelltmittels VPA. .

'Fischerei-Forschung' 15: 7 - 31 0

Cushing, D.H. und J.G.K. Har~is, 1973Stock ond Recruitment nnd theproblem ofdensity dependence.Rapp. P.-v. Cons. int. Explor~Mer•. 164: 142-155

\.: .. '

Doubledny"W.G.,· 1976Environmentnl fluctuations nnd fisheries management.

'Int. Comm. Northwest Atl o Fish. Sel. Pap. 1:141-150.

e Fox, \"/.1'1., 1970An exponential Gurplus-yield model for optimizingexploited fishpopulations.Trolls.'amer o rish o soc. 1: 80-88.

" ,' ...-.-'

H':.b.S, 1976

ICES, 1978

" Lett ,1'.P.

Report'of the nd ho6 meeting ~n'the ~rovision ofadvice on the biological basis for fisheries .management. 'lCES C.M. 1976/ Gen: 3~

Repont cf the 00rking group on assessment ofdcmersul Gtocks in the Baltic.IC~S C.M•.1978/J: 3.

and ri'. G. Doub leday, 1976Thc influcncc of fluctuations in recruitment onfishcries mmwgcment· strategy, with specialreference to_Southcrn Gulf of St. Lawrence cod.Int. Comm. HorthVJcst Atlant. Fish. SeI. Pap. 1:171-193.

Lett, P.P. nnd l\.C. Kohler, 1976.Recruitmcnt: n problem cf ~ultispecies interactionend cnvironmentnl perturbations, with specialreference to Gulf of S t ~ wwrence A tlnn tic herring(Clupen harengus harengus).J. FiGh o ReG. Board Can.33: 1353-1371~

Ricker, W.E o ; 1975Computntion and interpietation cf 'biological statisticsoi' f lnh pofHlln t ions.Bull. Finh. HCf;. Ed o Cnn. 191: JU2 pp~t~

SD 25-3'2

O~OO,.'" ',;

, 0.05, "

" ,0 0 24

O~42

'0.56 .,

".0.64

0 •.78

SD24

0.00, 0.04

0.33

0.52,

0.79, 0074

'" 0.85

, Prop6rtiori"6fndultf~mulcs t6~hsi~ta11citockofcod (p~s.) bysge and manugemcllt' u.riit

" ...'-, , ",' ,~,

" Tabie1"

',Age

1:2

3..4''"'' .

" 5

6

>6

, ....'-, ",', -:

.' ',. ',~ . "

, ' ; ~

Table 2. Pa~t~alrecruit~ent otri6dbY.ageandmanagement·unit

Age1

2

3"4

56

SD22

. .0.050.69'1.00

·,1000

.0.730 0 73

,.' .. SD 24

,01>027

.: 0.682

",1.000 .-1.000 .

" .

' .. 0.545

0.545'

0~10

O.5~ .'. 0.80 '.

, '1.00

.1.00.... O~95

, "',... " '

... '

.,' lCES,' 1978. . ",' .'

•'source of Berneranddata '. Borrmann

. (1977) .

period1970-75 " 1977-79 1966-75

" <.'

'. '.

Meanweight (g) ut age derivcdfrom vonBertalanffy growth curves by. management units

, '

('

; iI'

~

Age ,"

, .1­

2

3'45

SD 22 "

, 100

407920

1585'2340

3129'39114656

SD24

100

377862

1545'

23943370

'4435-, 5552"

. sn 25-32

99'253 '

, 513,909-

1465. 2208

31644356

5809 '

'.' .',...' ,.'.'., .J ...•.. ,

. ~ .'

7545

"

.~.. ;

Tcible 4 (continued) .

• sn 25-32Year P1+ S\'J N·1....

( '000 t) ( 10-6)(' OOOt)

1-966 430.1 '98.7 ~)4809.. .

1967 . 496.3 128.4 453.71-968 494.5 139.3 375.41969 45902 137.1 427.4 .1970 428.3 134.9 521.5197.1 . 416.8 127.5 716.8,

816.0J ~72 477.6 138.61973 547.7 147.1 452.51974 622.4 176.3 281 08 ·

. 1975 . '657.4 224.0 123.8e. F1+ = 184.7 + 20192 Sw (r .- 0.90)

Table 5. Catch per wüt effort (U) • effort (X) und totalm01'1a. Li ty rate (z) for cod 01' 3D ~2

Year·· 0 X 21+(t/day) J(10- dnyo) .

-. '1 965 0.21 132.7 0.811966 0.28 99.5 0.G5.:1

·1967 0.26 111 • 1 .0 0 701968 0~32 102.8 0.94..

1969 103.9 O.GOe· 0.28\

1970 0.34 92.2 0.1341971 0.26 123.5. 0.82

01972 0.34 . 96.5 0.731973 0.30 127.5 1.1 J1974· .0.16 1195 0 8

1975 . 0.32 .. 99.6

300

A

~ .,'

.,"

SvJR"", ";'!J. .• 'I

{c'.....

'4000'.~ ....

3000

2000

, 1000

•

'-'---'r-~'--i-l-'-;>

1.5 F

,".'

20 .

30

18

----..' ,

, _ 10

~_ .....-

Cod, sn 22:A Yield per re.crul t end sp...nmtng ~J toc1;: i,ox- l'C.(:\"ld. t curV80B Yleld end spnwning otock curV80

I--

10

20

30

\ .

"

"-.."

1'\',.

'7J)(

..

'69x

'61~

'68)(

66x

'74x,"

'72x

;P.'

'70)(

50001000L.---,--..,---,.--,---,-----r--~-1r__r_-_r1 -··-rt--,---r----,---r,--,--..:..-..---r-

10000 \SOOO Sv/.

100000e

1000

. 'Pig. 2. Cod, SD 22: Spawning otock~recru1t ourveIJ (year = ycor cf opanning), ... ,f

• •

.' !

rI •

-., I

,'(

(Iooot)

40

·30

20

10

..

'73)(

3. Cod, ~"3D• 22t .

.- Fizhinc _n:ortI.111ty - yiold Ctu'VO

--, Goncl.':ü FJ.·ü.:'~ ii~tion curvo (Fox)

~--.- Genoral production CLtrVO (Sc1HJ.cfer)

, .

. "

4000

2000

3000

1000

,5000A

•, '

"'7"l~--r--""'l---r---r--y---r----,r--rl~.-~-'--"--""'-"Ir'-'>

, !I

l(jC~ "\

200·

f ,~

,.-~ ,

",

....

20

40.'

30

10

Sw, ('OOOJ

508

1" .u· ,

\'

, .

l."" (;od, Subdiviaion 24:

.., Y:lclc1 per rocrui t und spn~'ming stock per recrui t curves13 ;':Leld end opowning otock curves

....

R ~.

(10-3)

60000

e50000

\

40000

JOOOO'~\

'66)4

'67.)(

x' 71

'70x·

'693(

'68)(

i ...

16000 SWt ).I

10000li. ;-----

20000

2000

e\0000 -

Fig. 5 .. eDel, SD 24: Spown1ne stock - recruit ourve('lüHr ::: year of apawning). .

. ''-- "

.J" '.1'" t

r, ..

•,

1R'.(g)

300

200

100

~ '. A

Sw/R(9)

4000

3000

2000'

1000

200

Sw('Oooft

20

. 100

'B )

. '.

20

100 -

,200

yrOOOt)

per recruit curV08

t:--o""'.1---r---.--r--o.rs-r:--T--'---'-'l!O--.---r-- 1--'--l-r-~S~"

Vip. 6. Cod. 3D 25 - 32:A Yield per recruit un~ spnwning otock13 Yield und 3prmninG 0 tocl~ cu ::,voa

> ,

R(10il)

.. 1000

500

20 100

'71~

I20(

I I~

300 Sw('OOot)

Fig. 7 i Cod, sn 25 - 32s'Spnwning stocl. - rocruit curve(year = yoar of'opawning)

, .