307 (rl .,: Rapp. P.-v. R€ u& CoE, int, A\plor. MdJ 177:307-313. 1980. RECRU]TMENT IN THE PERUVIAN ANCHO\,'Y AND ITS DEPENDENCE ON THE ADULT ?OPI]LATI O N JORCE CSRKEI hstituto del Ma. del Per4 Chu€ uito, Oallao, Pmi INTRODUCTION T}e tusr. and mos c$FnrivFly uscd. equarion for rhr \pdwnfl recJ.tl;r rrla oBhip $as propo.ed by Ricker (1954, 1958) and is conmonly exprcsscd by: R:aPe\p(-bP) (1) where.R: r€ cluitmcnt; 1: spawning srock; a - a constant that includes the density-iDdcpddent mor- tality rate; and , : a constant that includes the density-dependent mortality coealicieDt. In this model Ricker differentiatcs between two causes of mortality: 6rst, those rhat are independent of the population size, ad de assumed to be constant, and.'cond. rhoce rhar incrcase ar highcr pnpularion dnnsirie, dd gcnerarc a.ompenrarory moflal;,y, or an over-comperoatory mortality, as defined by Chap- nan (1973), which produces a sharp decline of the righi-hand limb of the sto.k-rccruitment cuffe. An" otncr lormulation extcmively used is that proposed by Beverton and Holt (1957), vhich is cxpr€ ssed by: R- tl(c + dlP) (2) where recruitment md spawning sto.k a.e rep.e- sented by fi dd P respectively; d: a constant that includcs the density-independe4t motaliry coeftcient ; aDd , - a constant tbat includes borh rhe densiay- independent and the density-dependent mortality coefficient. Two possiblc causs lor monality de atso considered in this model, but the conccpt oI the densjty-dcpcndenr mortality is quite diff€ r€ nt. In thc Beverton and Holt model the compcnsatory mortality is supposcd to be relared to the density of cAgs, lame, and juveniles, sugges.in€ that the com- pensation mechanism h due to competitiotr in the early stages, while in Rickeas model this mortaliry is supposed to be related to the density of spawners I Pr$ox addr6s: Fishel1' Rdoucd md Environment Divi- sion, Departmcnt of F!hdi6, FAO, Vja d€ lle T€ rme di Cara- calla, 00100-Romej Ilary. or adult fish, suggcsting a compeNadon mechanjsm Some altenatives, principles, ard ap?lications of these two models de widely discussed by, amongsr othus, Bcvcrton and Holt (1957), Ricker (19541 19s8, 1973b, l97s), Chapnan (1973), Cushin8 (1973), Culhins and Hdris (1973), Muryhy (1966), Paulik (1973), and Paulik et ai. (1967). The importance of det€ rmining the proper stock-rccruitment relationship and the implicatioN of relying on one or the orher of these tvo genoal cur.r'es for thc puposes of fish- eries managemert are discussed by culland (1968, l97t). wirh spr'ial rFteren e ro rh. Pnrulicn d- A Rickernype curwe was fftted by rhe author to the Peruvian anchovy data during the thi.d se$ion of the Panel of Expcrts on the Population Dynamics of the Pemvian Anchovy, arld some mdagement measures wde recomended based or this crre (IMARPE, t973a., t974a). However, the lailures of recmitnent ir 1972 and in some other yerus were very difficult to explain and even moE difficuh to prcdict with the existing mod€ lsr one reason beins that none of these models accounts lor the etrects of the envimnment on the spawners or their progeny. Very drastic fluctua- lions in the areas of distdbution of the adult siock were obslse d in addition to these rccruitment failues. These fluctuations were closely related to the oceano- graphic abnormalities repo4ed for th€ same yeaN by zuta and Guillen (t9?0), z*a and urquizo (1972), wooster and Guillen (197a), and zuta et al. (1976). The obsewed fluctuations in behaviour, alrd speci- fically the diferent distribution pau€ ms of the an- chory yhools, which dFnni,iv.ly "tr ( red rh. spawnins success during recent yean, create the necessity oI develo?ing a nbdel allowing for possible reductions or enlargemeqts of the habirat. DEVELOPMEN'T OF THE MODEL Statring wiih Equation (l), where recruitment is expressed as a fuction ol the spaMing stock as a
RECRU]TMENT IN THE PERUVIAN ANCHO\,'Y AND ITS DEPENDENCE ONTHE ADULT ?OPI]LATI O N
JORCE CSRKEIhstituto del Ma. del Per4 Chu€uito, Oallao, Pmi
INTRODUCTIONT}e tusr. and mos c$FnrivFly uscd. equarion for
rhr \pdwnfl recJ.tl;r rrla oBhip $as propo.ed byRicker (1954, 1958) and is conmonly exprcsscd by:
R:aPe\p(-bP) (1)
where.R: r€cluitmcnt; 1: spawning srock; a - aconstant that includes the density-iDdcpddent mor-tality rate; and , : a constant that includes thedensity-dependent mortality coealicieDt.
In this model Ricker differentiatcs between twocauses of mortality: 6rst, those rhat are independentof the population size, ad de assumed to be constant,and.'cond. rhoce rhar incrcase ar highcr pnpulariondnnsirie, dd gcnerarc a.ompenrarory moflal;,y, oran over-comperoatory mortality, as defined by Chap-nan (1973), which produces a sharp decline of therighi-hand limb of the sto.k-rccruitment cuffe. An"otncr lormulation extcmively used is that proposedby Beverton and Holt (1957), vhich is cxpr€ssed by:
R- tl(c + dlP) (2)
where recruitment md spawning sto.k a.e rep.e-sented by fi dd P respectively; d: a constant thatincludcs the density-independe4t motaliry coeftcient ;aDd , - a constant tbat includes borh rhe densiay-independent and the density-dependent mortalitycoefficient. Two possiblc causs lor monality de atsoconsidered in this model, but the conccpt oI thedensjty-dcpcndenr mortality is quite diff€r€nt.
In thc Beverton and Holt model the compcnsatorymortality is supposcd to be relared to the density ofcAgs, lame, and juveniles, sugges.in€ that the com-pensation mechanism h due to competitiotr in theearly stages, while in Rickeas model this mortaliryis supposed to be related to the density of spawners
I Pr$ox addr6s: Fishel1' Rdoucd md Environment Divi-sion, Departmcnt of F!hdi6, FAO, Vja d€lle T€rme di Cara-calla, 00100-Romej Ilary.
or adult fish, suggcsting a compeNadon mechanjsm
Some altenatives, principles, ard ap?lications ofthese two models de widely discussed by, amongsrothus, Bcvcrton and Holt (1957), Ricker (19541 19s8,1973b, l97s), Chapnan (1973), Cushin8 (1973),Culhins and Hdris (1973), Muryhy (1966), Paulik(1973), and Paulik et ai. (1967). The importance ofdet€rmining the proper stock-rccruitment relationshipand the implicatioN of relying on one or the orherof these tvo genoal cur.r'es for thc puposes of fish-eries managemert are discussed by culland (1968,l97t). wirh spr'ial rFteren e ro rh. Pnrulicn d-
A Rickernype curwe was fftted by rhe author to thePeruvian anchovy data during the thi.d se$ion ofthe Panel of Expcrts on the Population Dynamics of thePemvian Anchovy, arld some mdagement measureswde recomended based or this crre (IMARPE,t973a., t974a). However, the lailures of recmitnentir 1972 and in some other yerus were very difficultto explain and even moE difficuh to prcdict with theexisting mod€lsr one reason beins that none of thesemodels accounts lor the etrects of the envimnment onthe spawners or their progeny. Very drastic fluctua-lions in the areas of distdbution of the adult siockwere obslse d in addition to these rccruitment failues.These fluctuations were closely related to the oceano-graphic abnormalities repo4ed for th€ same yeaN byzuta and Guillen (t9?0), z*a and urquizo (1972),wooster and Guillen (197a), and zuta et al. (1976).The obsewed fluctuations in behaviour, alrd speci-fically the diferent distribution pau€ms of the an-chory yhools, which dFnni,iv.ly "tr ( red rh. spawninssuccess during recent yean, create the necessity oIdevelo?ing a nbdel allowing for possible reductionsor enlargemeqts of the habirat.
DEVELOPMEN'T OF THE MODELStatring wiih Equation (l), where recruitment is
expressed as a fuction ol the spaMing stock as a
Jorge Csirke
Jorge Csirke
Csirke, J. 1980. Recruitment in the Peruvian anchovy and its dependance on the adult population. In Saville, A. (editor). 1980. The assessment and management of pelagic fish stocks - A symposium held in Aberdeen, 3-7 July 1978. Rapp. P-v. Réun. Cons. int. Explor. Mer, (177): 307-313
'hai Ricker eavc to ea.h Paramer.r of his equ'io(whcre a is rclated to the numbd ol eggs produced,and , is rcIated to the dmsity of the eggs, or of thespa\rne$. We can then leilrite Equation (l) asfollows:
R : 4,8 exp (- ,' S) (3)
wheft B reoresens rhr bjonass ofspawD'rs $hi"h isascumed ro bc proporrional ro rhe
^umbcr of egqs
prcduccd, and S represents the denritv of thse' WiLh lhjs formularion sc have a three-dimcdonal
.oua{ion rhar r.laLcs lhe spa\vni1g slock and lhe
'e.'t,i,'e '..r"it-e'r. The ?oPulation dcnrity S isi"rroduied as a tun.'ion of rwo var;ablFs: rhc roralbiomass B and the disPersion or conccntration of thisbiomass. This new relationship caa be exprcssed loreach particurar year (t) bY:
&-PqBt (4)
where, is a.onslaDr lhaL represrnrs lhe avera8erelado;sh;e ed{irs udcr a\FrasF .ondiLions b-rwe.n rh" popul"tion deairy S d irq roral biom,sa, and Qls in index ol.onc.nrra ion. or d;sper'ion'of rhis toral biom. io relarion ro thF c\pFcred valufunder av€rase condirions.
Thh conrinrr"tion.o"r6"icnr q wil be equal tol0 when average conditions exi3t, asuming thatund.r such condi oN rhe di'rriburion parr.tn i'normal. OtheNise the coefficient will take valueseitler above, or below, 10, dependin8 on wheth$the poputation is more, or less, concentrar.d than
"or-"L Wtl' this new concept we can rewriteEquation (3) as follo$:
&: aB' lcrp (-b B'4 o-t-i (5)
wherc for each yeax (t):R : recruitment,I - iotal biorrhqs ofspawncn,O- concenration coefficient olsPawners,, - ^.onsianr Lhat indude, Ihe ssival rar" ro Lhe
stage of non-compelsatory mortality', - a cod$tant that includes the compensatory mor-
tahy coemcient.
APPLIqATION OF TIiE MODELThi! modcl is applied to thc Peruvian anchovv
Ensm li: in!e6, with sPecial r€lercnce to the sub-oo;uhrion $ar inhabn, rh" nor$ern and (enrrali.j;o" "r rr'. Peruvian coarr bcLseen b" and 16"S
(Jordan, 1976), for whicl rccmitm€nt, populationdensity, and total bioma-ss estimatcs are availablelTable l).' The li)hl to l97J re(ruirmenr vdluer R are
'hos.from IMARPE (t973419742) dd are er?ressed asan hdex of the number of tuh caught pe. unit ofeg'olt (Satersdat and Valdivia, 1964! and Boeremact at., 1967). Equivalent values have becn computedtor 1974, 1975, and 1976 when recruitments wercestimated a3 0 50 and 0 45 times the avemse of 1961-1971 and l 3 times thc avemge of 1966 1975 re-
The 1960 to l97l population density valu$ S arealso computcd from the commercial catch stalistics,tating the averagc of the tlvo highd values of themolrthly weight of adult fish caught per unit ol efi'ortdu ns July-Decembe.. Equivalent value, Ior 1972to 1975, vhen the commercial ncct activity uas re-siricted by official resulatio , were computed ftomthe data collectcd dudng thc flshery sulwe}3 carriedout by the Inslituio dcl Mar del Perrt (IMARPE,r972b, 1972c, 1972d, t972e, 1973d, 1973e, 1974c,1974d, and 1976).
The bio]nass of spawne$ -B from 1963 to 1970 iscompuied lrom the virtual Population estimatcs pre-D^.ed for rhe *cond and third r-ion" of the Panplof E\pcfl sonrhe Popular;on Dynmi.rolrbc Peruvia^Anchovy by Burd and Valdivia (IMARPE, 1972a,1973a). The biomass i.s estimaied lor each year, lromthe avemge bionass of adul! fish rcpoftcd duringAugust October, when thc strongest spawning occus(Jordan and Vildoso, 1965; IMARPE, 1973e;Jordan,1 976) . Equivalenr biomass values are obtained for rhefollowias years from I\4-A.RPn's populatior estimatesmade through ycar-class analysis, and fishery as wellas acoustic aurveys (IMARPtr, 1972a, 1s72b, t972c,t972d,, 1972e, 1973d, t97 3c, 1974t, l9 74d, I 974e, 1976 ;Iohamesson and Robles, 1977).- Th" @n..n!ra,ion.oefncie^r qfor./ch pani ubrlear is compured f.om [qua,ion (4,. The av"rasepropoflionaliry coeln.ienr 1. pre\iously .sr;marcdl.om the linear finctional rcsressior (Cieasy, 1956;Ricker, 1973a, 1975) is applied to the obsemcd valuesof biomars a and populalion dcBiry S. m"Liq:
tsr,B (6)
RESULTSA functional r€glessioa lire was litted to thc 1963
to 1975 biomss and delNity valu€s (!'ig l), and thc,lope coefficien! 1 of 30.2182 was ther applied toesti@te thc concen[ation coeflicient I for theseyears. It jr ale used to estinaie theoretical values of
R".rui,mrnr in ,hr PrruvizD dchow dd iG dep ndFn,e on 'he adulr popularion
Table l. Yearly estimates ofpopulation density, population bioM$, and iecruitment lor the Peruvian anchovy
biomds for 1960 to 1963, when no observed valu€sare available. The a$sumption is made that in ihcseyears q is equal to 1 0.
Equation (5) is then rcduccd to its losadthmic formand fitted by least squar€s to the 1961-1976 se es.Fmm this thc lolloving paramcters are estimated:
a : 96 3654, - 0101591.
Thus, thc recruitment to the Peruvian anchorl' canbe malhenatically expressed by:
-R = 96.36s4 .8r l exp (-0 101591 Bi-r). Q)This €quation i, then used to cofttruci thc isopleth
diagram of f.i$re 2 where the axpected A - 4- Rrelationship i! Feserted, together with the plot oltheobserved rccruitment !-alues.
The expcctcd recruitment values (.Rr) estimatedusins Equation (7) a.e presellted iD the last columof Table I and indicated with drows in Figue 2. Agood fit, rrith a high correlation co€mcient, (rho :0.8865), is obtained wben they are plotted againstthei. observed values.
DISCUSSIO\The axiomatic proposition that any animal popula-
tion fluctuat$ vithin certain size limits, detemined bythe carrying capacity of its habitat, was eemined byNicholson (1933), who showed that such fluctuations$'ere naturally contolled by density-dependent mor-tality. This proposal was introduced and developedby Ricke. (1954, 1958) in his ltock recruitmcnt model,which is applied in this papcr to the Pemvian ancho\y.
The Ricker model is ba$ed on the theory of apredator-prey slstem where tbc eggs or larvae are theprey randorny encolDrtercd by the predator andwhere any hcrement of egss or la!'vae is simultane-ously lollowed by an increment of the prcdato$(Ricker, 19sB). Obviously the simplest case of a com-pensatory mechanilm of this kind wilt occur wherLpa.ents are, at the same time, the predaton of their
This rcgulatory mechanism appers to work wellin the Pemvian archovy population. Thtu ki4d ofcannibalism has been frequ€ntly obserycd (de Men-diola, 1969 ; de Mendiola and Ochoa, 19 7l ; IMARFE,1972b, 1973d, 1973e, 1974b, 1974d, 1974e), especiallyduring recent ye-al, when up to 2199 dcho\,)' eggswere reported in thc stomach content! oI one singlcanchoq, caqht in September 1973, and up to 180ancholy larvae in another single anchovy caught inSeptember 1972.
It is cled that there is a compensatory moltalitymcchanism due to the predation on their own eggsand larva€ in the Pelrlvian ancholy. However, com-petition betveen the laaal stages cannot be discddedas another possible cause for mortality unlil someobservatioDs can be made. It is impotant to pointout lhar evcn rhouqh lhi, kind of.omper;tion;s mosLlikely to produce a Beverton and Holt type of stock-recruitmcnt r€lationship, some recruitment over-com-p.nsarion can be prcdur"d under.erLain circum-stances if high lawal mortality and lowej: growth athigher spawning stock dcnsities occur, as suggestedlot Clulea harensus ^td Satdiv?s caamleaby tles (\968,1973). This mean, that even those larac that sunive
3t0
competition vould become highly vulnerable ro allother mortality causes.
A po\ril,le r.Larion"hip betwe.n popular;on densirvand popularion biomasq is con ider' d in rh. t."d;-rion.l .on.epr. wher" 'thc populatjnn d.n'iry. 'r-prcssed in term of catch per unit of efort, is propor-tional to the total biomas if the endronmental con-ditions and distribulion arcas remain constant, or ifthev are .elerred to average conditions for largeperiods of time". We accept the secord part of thisgeneral proposition in computing an avemgc prc-portionality coeffi.ient (1, in Equations (4) and (6))for the 1963 1976 pe.iod. but, as stated for the firstparr oI rhi' i on.rpr a ), ar-rolear r.lar ionrhip .annotbc csrablish"d o$ins ro rhc obs"n.d flu.ruarioru inrhe cnvironme'rt dd distdbutional areas.
It is wcl Lnown that large fluctualions in the catchrler u.i, etron .an bc ptodu.ed ilrhFre ae variarion.in rhe cat.habiI y cocffi.ienl 4. t his ,nFffi.ienr isinvenely proportional to the area inhabited (Palo-he;mo and Di.kie, 1964), and as Gulland (1977)poinr.d oul. rhe Rucrudrions in,he "n\i.otrn"nr"lcondi,iom and rhe dn,ribu,ional arFa cD 1," r.spon-sible for fluctuations in lhe catchability coefficient-
During the ?cruvian ancho\a fishcry, high values
S = 30.21358 It -0.6nU
of catch per unit effort have becn observed at lowpoputation levels when there has bccn a shrinkageof the arcas of disrdbution. According 10 this, ourcomputed corcentration coeffi.icnt qh r€Lated 1o thecatchability cocfffcient q, and its fluctuations can beintcrpleted as b€iry reprcscntative of the size of theto1al area or of the total volume inhabited by thepopulation, assuinB that there m no va ations dueto possible chang€s in the frshing shategy.
In general tcrms 1re can say that there is a goodcorrespordence bctwcen the computcd values of Qfor each year (Table l) and the obsea-ed oceano-graphi. condirions. $hi,h may "ff.' tir-h r'tr"cr rh.arFds normdlty inhdbi'cd by rh" an' hovy. High con-ceDtration valu$ are shom for the last part of thefollowiDs years: 1964 (q : l sl), 1e7l (q - 2 01),1e72 (q- r.76), re73 (q - r23), nd tsTa (Q: 1 47),corr€spondins to the initial or the dwelopmentphasc of abnormal warm-vater Periods, ideniined asthe "El Nino" phenomena. Valucs of 4 close to l 0conespond to both normal and cold-ifatcr Periods,with thc lowest valuer lor thc last part ot 1969 (Q:0 55), defincd as a normal year, and for 1975 (q:0 47) and 1966 (O: 0 62), defred as cold yean
Thc plot ofthe stock-.ccruitment cu e for succeesive conccntration levels (Fig.2) sho$'s that the an-chovy population appears as a eturaied Population
800
7N
600
500
3m
200
t00
5 t0 15 20 25 30
n DDla iol b:o-qs " on1",\ -O )
lisure l. Rebnon,hip betweeo thc potul"tioq density J and the PoPulation bioma$, in the Pe'uwian an'hovv du'ing th€ spring;pawoins sealor 1963-1975
Rccruitment in the Peruvian an.ho!-y and its derEaclence on the a.tulr poputarion 3rl
i?I
900.0
800,0
7AA.Q
600.0
500.0
!o0.0
300.0
200.0
100.0
R. - 96.3654 o..)
O=0-4
Q-0.6
Q=0.8= 1.0= \.2
20.o 25.0 30.0 J5.0 14.0
ticna.. .i tr e .du t !ornlat: or ni_r (,".nes r: rO_,)Figure 2.rgRectuitnmt ,rr in rle ptruwian anchqv and irs depd.lence on rh€ adult popurarion , for di,l*nr .oncentration q
wh.n ir i' h;gbly co'l,-n rar.d. produ,;n8 puur r.-.ruim.nrq juds.d b) a rnw sru.L re..ui,;Fn! r.]a_rior ship. as o", urr.d in I ,6i, lq/2. t974, and 1975.
Thc oppo\i,F casF would o!, ur ar tow, on.c,rdrionlevels, where rhe adutt stock has a lmatlcr chan.e ofindx,inS d) .6mposar^r] monali,v and ,h.reforca b;qh.r rF.ru;rm.n, ;, oLsenFd, s n;, un.d in rq70aDd 1976.
. -fh. pafli, ipa,ion b\ somF orher ,pcri,s in .ff".ring
rh. r""rui,menr b) mcans ofcompetition o. prcda,ionon spdwDer. Fs8,J ldrvde, or iuvFnit.s app;dq ro bean imporranl tu.ro. ru 1,. in.l rded in furui" d.v{op-ment oathe model Foposed here.
An eff".r of rhis lnnd fot Soldinop\ raouha i, "ug-geqled by Vurphy \lr6b . who firrd't$o r.produ.rioncunps: rhr frr,, one for 19 12 ,9+8, MhFn (ddinF waslhe domindt rp..h"; and rh","cond one for 19471957, whe'r this population sutrered a drasric reduc-tion and has almosr r"pla.ed hy Enptuuti no a^(Ahlqlron. I966; MalT. lq60; Cu'hing. tqb8).
It is likely rhat the prosresive irvasio; bv E. m,da,of the aieas previousty occupied by S. cizrutca pro-
du.rd (omF "ge. pr"dari^n a, w"ll as a I isher mot.rdtrryol rhF cardinc laru"e, du" ro .omper;;ion wirh rh;
A11 these lactors, added to the realuced sardinepopuld,ion hv,l. and ro Jre shrinlagF of rhe hab;rar,could be_ a major reason for a higher mortaliry of theyounq. due ro an in"neare in rh" rompensdrory mor_raliry producen. in.lud;nC in rhh group bor-h rhesardina drd rhe an, hoviFs. Atong thcre li;Fs, rhF, ri,-ical situation of the sardine population can be retared,o d hiqh rtrui,mpnr over-Lompc nca rory morrdlirythar bas noL properh balan,ed by an "qunatcnt cggproducrion. ll rhis pra..* aaualty omur'., ir rnusr berenpcrFd in ar inrr"m.nr in rh. comD"n.arorv mor_rality rare erponenr. , qB;n rqua,ion s,. ih;s issbown \hFn rhe :ardinr 6"hpr' , o apced. wherF irh ob.erved rh"t rhe e\ponpn( incr"a5et 6, 6,. ,*",
A similar case occurred with fie pcruvian anchor"y.Th" whul. popularion sd\ ar a vprl low lnet aniw_"s expord r^ hpalf hshine when Lh" ..Dl Nino.,phFnomenon o..urred in I'172. A re, ruilmenr fail,,rewd obytucd dur;ne r}dr pd,i, utar year. follnwed bypoor recrurtme-nt ove. thc nexr rhree years,
3t2
While thc Peruvian archoly population was ad-veNcly aflected, there was an unusually suc€$sful$fairLe (Sddino!' l,saL) spawnins in 1972 and in thelollowing ycars. This was shown by the high numberof eggs and laryae of sardine lirund during July andnueu{ lq72 ,5d,andcr and d. Ca.rillo, 1977a\',nd b) rhe high proponion ol 'ardinc r.PnflFd a, din, idc,!rl.a'.1. duins rh" 1973 comm"r.ial dn' hovTfish.,y. Abour I j0000 ronncs uf youlq s"rdn," u"rcthen caught, a quantity that is exceptionally high whcncompaed with the haditional total landings of thissp".i.,, whi.h rag.d lrom 1000 ro 10000, in Pre-viou,\""rs. fordl\"rdinelandinqshddbF"n ii"r.a.ingsince i972, reaching a maximum of900000 t in 1977A similar gro$th had bccn obselved by Santddcrand dc Castillo (1977b) for the spawnins areas andthe spawning intcmity of sardine over this period.
All this cvid€nce prcvidcs a clear indication ihatthe sardine population was groving very {aPidly,reaching a level that was probably as hish d thatrcported lor the anchovy- This is an important point,be.ausc the sardine had abo been repoft€d to beleedins on anchovy eggs and larvae, espccially in theircommon arcas of distribution. Thtu Process ce therc-lore bc suggestcd as ar explanation of why the ob-served Ecruitment values were below thcir exPectedvalucs in 1974 and 197s (Table 1, l'ig.2).
In rhis pape! we are assming that a constantftactiotr of the adult population spawns each year.Thft is partially true lor thc pe od considercd hcrc,wiih the eaceptions of 1965, when a smaller propor-tion of sparening fish was observed in the northemregion, and of 1971, when this fraction was considcr-ably rcduced along rhe whole coat.
'l}ris rcduction in the proportion of the stock repro-ducing, duriry 1965 and 1971, provides a reasonableelplanation of thc lower recruitmeDt values obsefledduring 1966 and 1972. It also points to the possibilityof iniroduciry thii factor as an additional variable inthe model. This could be done by modifying thespawning biomass A, which is related to rhe cgg Pro-du.tion, by expressing the constant a as a functionof thc spavning fraction or ot the total f€cundity,leaving thc non-coDpcnsatory morlality, u - 96 365i4 Equation (7), as fie valid value fol average or fornorm'l .ondilions.
ACKNOWLEDCEMENTSThe author wishes to expres his indebtedDess to
R..lordan, L lsukayama, and J. Valdivia, of theInstituto del Mar del Perttr to J. -A Gulland, G. L
Kesteven, and K. Johannesson, of FAO; and to ASaville, of the Marine Laboratory in Aberdeen.
ANstrom, E. H. 1966. Di!ftibtrtion and abnndanc€ df sardincand an.hovy latuac in the Cal ifo. a current olt Calitornia andBaja California, 1951 &: A sunry. Spc.. S.icnt. R.pp.Fi! Wild. Setr U.S., 534: 71pp.
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