International Council for the Exploration of the Sea
CM l999tY:06
Th~me Session Y on Cod and Haddock Recruitment Processes - Integrating Stock and Environmentai Effects
Condition and sizc composition cffects on the simulated. ielationship bet-vveen spavtrner biomass and total egg production for Northeast Arctic cod (Gadus morhua L.).
by
Merete Kvalsund and C. Tara Marshall Institute of lvf~'ine Research
P. O. Box 1870 Nordnes :N-5817 BERGE:t"~, ~~OR\V A Y
.A RSTRt\.CT
Spawner biomass (SB) is aften assumed to be proportional to total egg production (TEP) by fish stocks. Recent studies suggest that this assumption may not be valid, particularly when the physiologic:1l condition offish varies. Th-is study used Monte Carlo techniques to simulate the rclationship bctwccn SB and TEP for 1'-~orthcast Arctic cod (Gadus inorhua). In the first simulation exercise, reproductive traits reflecting condition (length-specific maturity, weight and fecundity) were varied according to food abundance (cape lin biomass) while the size composition (numbers at length) v1as held constant. !In the second exercise, the size composition, as described by the modallength of spawners, was varied and condition was heid constant. In the final exercise, condition and size composition were varied
simultaneously. The first exercise indicated that variation in TEP was not constant but increased as the SB increased. The second exercise sho\1/ed that, for a given SB, TEP increased with increasing modallength of spawners. Cornparing the results of the first and second exercise showed that food-dependent variation in condition introduced greater variability into the relationship between SB and TEP than did shifting the size composition.
When condition and size composition were varied simultaneously, as would be expected in wild stocks, TEP cxt~bitcd approximately 4-fold lcvcl of variation at any given SB.
Keywords: cod, spawner biomass, egg production, condition, size composition, Mon te Carlo
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The cause of variability in fish recruitment has been a problem for both scientists and fisheries rnanagers for several decades. Recruitmcnt is most often studied in relation to the size of the spawning stock, where biomass of sexually mature individuals is assumed lo represent the - - reproductive potential of the stock (Marteinsdottir and Thorarinsson, 1998). However, it is
substantially different le veis of total egg prod.uction (TEP) as well as different levels of egg survival. Therefote, SB rna y not be a reliable indicator of the popuiations abiiity to sustain itself (~.1acKenzie et al., 1997).
Interannual variation in condition of spawners is one source of variation in TEP (lv1arshall and Frank 1999). Condition is commonly measured by the Fulton's condition factor (K):
K= lOOxW/L'
where W is whole body weight (ing) and L is totallength (in cm). Another measure used for describing condition is the liver condition index (LCI):
LCI= lOOxLW/EW
where L\V is liver weight (ing) and BW is whole bødy weight (ing). Studies done for a variety of species have shown !hat condition, at the individual ievei, infiuences the potentiai fecundity offema!es (Hislop et al. 1978; DeMartini 1991; Koslow et al. 1995; Kjesbu et al.
1998). vraliation in condition a1so affects the realized fecundity of spa\vning fem~les through atresia (Nia et al. i 998). Ai the stock lev el, Inature fe1nale in poor condition can skip spawning seasons (Marshall et al. 1998; Schwalme and Chouinard, 1999).
Maturity in Northeast Arctic cod occurs al age 6-9, with a length of approximately 60-90cm (Torsvik et al. 1995).Larger fish are more tecund then smaiier ones (Kjesbu ei al. 1991). In the last decades the fish seem to mature earlier; perhaps because of a higher fishing pressure
Stock reproductive potential is further dinlinished if poorer gamete quality is exl'..ibited by smaller compared with larger members (Trippel et aii. 1997).
This study used data for the i"~ortheast Arctic cod stwck to test how varying the condition and size composition of spawners affect the simulated relationship between SB and TEP. The specific objectives were in the first exercise to vary condition accm·ding to capelin biomass and keep size composition (i.e., numbers at length) .constant. In the second exercise condition was held constant and the size composition was varicd. The final exercise varied condition and size composition simultaneously to see how this affected the relationship between SB and TEP.
METHODS
The goal of the first exercise-'.Vas to simulate ho'.~' varying the condition of cod \V bile keeping the size composition constant affected the relationsh.ip between TEP and SB. Field data from combined acousticitrawl surveys ofBarents Sea and Lofoten region were used to describe the size composition (numbers at length or n1) and sex ratio (s1) of Northeast Arctic cod (Marshall et al. 1998). Values of ni and Si \Vere both estimated tfor 5 cm length classes for the period 1985 to 1996. The s1 generally increases with length, but a large degree of interannual
variability occurs (Marshall et al. l 999). To remove the effect of this source of variability on the anal y sis the mean value of s1 for each length el ass from the twelve years ( s 1) \Vas u sed to partttlon the stock into rnales and fen1ales. Length-specific weight (w1), fecundity (li) and maturity (m1) were predicted using the statisticai mo.dels described in Marshall et al. (1999).
Tbese models were developed using potential fecundity data coilected from the Lofoten area (Kjesbu et al. 1998) and data from 1'-Jonvegian surve-:js of the Barents Sea region (~y1arshall et al.l998). Estin1ates of capelin stock bion1ass fro1n acoustic surveys (Gjøsæter 1999) were used as the independent variable. From these data sources, the foilowing statistical models were developed.
lv1ultiple regress1on n1odel was used to estHnate w1for a g1ven capelln bio1T1ass (w1,cb):
ln(Wtcb) = -9.5 + 4.07 (lnlength) + 0.32(lnCapBio)- 0.07(lnlength x JnCapBio) (i)
1v1ultiple regression rnodel was also used for estimating
ft
for a given capelin biornass (fi,ch):Jn(f!.cb)
= -
15.64 + 6.36(lnlength) + l.ll(lnCaj'lBio)- 0.21(lnlength x lnCapBio) (2)iogit(rnl,cb) = - 11.93 + O.lS(length) + 1.23 X 10-7 (CapBio)
The value of m1,cb was then estimated from:
e
lcg:i(ml ;:b)Predicted values of w1,ch. ti,ch and ffil,cb were assumed to have errors that were normally distributed \Vith a mean of Zero a.11d a sta.11dard deviation of CJ, For f1,cb and w!,cb cr was
(~\
VJ
estimated to be 0.32 and 0.17, respectively. For IIII,cb o was assutned to be non-constant with length, with a maximum at m1,cb =0.5 and decreasing linearly to zero at 50 and l OOcm
For each simulation in exercise l, TEP for a given capeiin biomass (TEP,b) was estimated as:
140
)'
"-'
!=50
nl X S 1 X ffiJ,cb X f1,cb
Similarlv, SB for a given capelin biomass (SB,b) was estimated as: - - -
'"'
SBcb
= L
n1 X m!,cb X W!,cb!-=50
(5)
(6)
In each simulation TEPcb and SBcb were estimated for seven levels of capelin bion1ass ranging from a minimum of 100 OOOt to a maximum of 8 million t Monte Carlo sampiing was used to estimate the rneans and standard deviation (s.d.) for!both SBcb and TEPcb· Convergence (less than 1.5% change in both the mean and s.d.) was always achieved v.rithin 1500 iterations. 95%
confidence intervals were approximated as the mean
±
2 s.d. Tweive separate simulations vvere performed using n1 values for 1985 through to !1996.In the second exercise, the size composition of spawners (nl,sc) was deterrrJned using numerical optimization techniques (Solver in Microsoft Excel for Windows, Version 7.0).
Values of ni,sc \Vere dete-f!!1ined by salving the equation:
(7)
1=50
for pre-specified values of both SB (SBsc) and the modallength. The values of ull and ·w1 used wcrc hcld constant and the observed values for 1991 were arbitrarily chosen as the constants.
The pre-specified vaiues of SB,c corresponded to the annua! VPA estimates of SB,c for the vears 1985 to 1996 !ICES 1999). These twelve valne., ran<>P. frnm a minimnm nf 11? non t tn
- '
~--
---o---~~---~~~~...
a ma.xi.mum of 882 000 t. The pre-specified mcdallengths ranged in 5-cm incrcrnents from 67.5 to 97.5 cm. This is a realistic range for the Inudal iengths of spawning I'lojA c od (see Fig. 9 in Marshaii et ai. 1998). Figure l iiiustrates seven different length compositions which gives a SB" corresponding to that observed for 1991 (679 000 t). Each simu!ation estimated the TEP for a given size composition (TEPsc) as:
L
l40 il],sc X S 1 X ffit X ft 1=50(8)
Tvve!ve different simulations v;ere performed using SBsc values from 1985 to 1996. To be consistent, the values of m1 and f1 u sed corresponded to the observed values for 1991. Because each simuiation heid both condition and the pre-specified SB,, constant variation in TEP,c was introduced solelv thromzh variation in the size comnosition. Uncertaintv in thP. ncsnltin<Y " ._. .L - - - - - - -..~ - - - - - - - - ---o
estimates of TEPsc v;as not estimated.
In the finai exercise, condition and size composition were varied simultaneously. The val u es of fl1 u sed corresnonded to the values ofn1 ... for thf'i mlnimnm nnrl • .L - - - - -.,~,_.-- - - - - - - - - - - - - -m;;~ximnm ---~ --~z:::,~~-~ mnfl::ll lPnoth~
maximum levels of capelin stock bion1ass (100 000 and 8 rrllllion t) were used to estimate
Wt,cb. fi,cb and ffiJ.cb using equations i, 2 and 4. TbPcb,sc and SBcb.sc were estimated from n,,"
and the predicted values of WJ,cb. f1,cb and ID!,cb using :equations 5 and 6. Monte Carlo simulations \Vere rem to estimate the s.d. of the TEP cb se ' and SBcb
..
,;c·These three exercises each generated a bivariate reiationship between 'TEP and SB. Error bars
(+ , -2 s.d.) were nut on hoth TEP anrl SR for exP.rri.,e< 1 anrl - - J - - - r·-- --- - - - - - - - · i
RESULTS
Results for cxercise 1 Ulustrate that variation in TEP was not constant hut increased as the SB increased (Fig. 2). To look tnore in detail at the magnitudc of variation, ene specific
simulation (1993) was chosen. The possibie range in vaiues ofTEP and SE is indicated by the lowest to the highest extremes in error bars in the y- and x-axes respectively. In 1993 SB ranged fron1 about 700 000 to 1200 OOQt and TEP ranged from about 120 x lO J2 to 480 x 1012. Thus, a fixed quantity of spawners subject to food-dependent variation in condition exhibits nearly 2-fo]d variationin SB and 4-fold vaniation in TEP.
In the seconQ exercise there was a linear relationshij_D bctvvcen TEP and SB (Fig. 3) \Vhen data for all simulations was combined. Looking at the resulis of each sirnulation separately the difference between lowest modallength (67.5cm) and highest modallength (97.5cm) increased \Vith increasing SB. In 1993 the values for TEP ranged from approx.imately 250 x
l 012 to 350 x 1012 i.e. less than 2-fold. Comparing the magnitude of variation in Fig. 2 and Fig. 3, which are plotted on the same scale, suggests that condition-dependent variation in reproductive trails introduced greater variability into the relationship betv;een SB and TEP than did shitting the size cornposition.
Varying condition and size composition simu!ta..11eo!!1sly (exercise 3) revealed how far the simulated relationship between TEP and STI deviates from simple proportionality, i.e., linearity. TEP shows approximateiy 4-foid ievel of variation for an y given level of SB (Pig.
4). For any given SB !arge spawners in good condition wil! have highest TEP while small spawners in poor condition has the lo\vest. More interestingly; TEP by small spawners -in good condition is higher than TEP for large spawners in poor condition. V ariation in this p lot can also be examined by comparing the slopes of the relationship between TEP and SB for the different combinations of condition/modallength. Figure 4 shows that the siopes of the high condition/high modallength and high condition/low mod al Jength combination are higher tha1:1 the siopes of the low condition/high modallength and lovv condition/lov•1 modallength
combinations. This indicates that variation in condition introduces more scatter into the simulated re!ationship hetween TEP and SB than do.es variation in size composition.
.
DISCUSSION
For aii three exercises, varying the condiiion and size composition affected the simulated relationship between TEP and SB, but varying the condition seemed to introduce more variation into the relationship between TEP and SB tha.n did varying the size composition of the stock.
The condition of the c od stock is influenced by food supply. The main food item for the cod is the Barents Sea capelin (Kjesbu et al., 1998). ~And as the size of t.l:le cape lin stock varies, t~is
will also affect the cod stock. In tt-tis study the capelin bioinass were varied from a low level to a high ievei (Gjøsæter, 1999) and the resuiting varialtion in TEP was approximately 4-fold.
We have not included condition effects on realised TEP and egg quality. Egg quantity are neither included, but are expected to increase the variability in TEP.
In fu ture we plan to use the simulated relationship between TEP and SB ll'ig. 2,3 and 4) as the starting point in an investigation into how variation is introduced to the relationship between recruitment and SE. T\.vo additional sources of variation \Vhich 'ovill be included in this
analysis are variation in pre-recruit ruortalily and variation between the estimated values of SB (e.g. from virtual population analysis) and the <<true>> SB.
ACKl\TO\VLEDGEl\fENTS
We would like to thank Olav Sigurd Kjesbu for comrnenting on a previous version of the mam1script.
REFERENCES
De[\1artini, E.E. 1991. l~ ... nnual variations i11 fecundity, egg size, and the gonadal and sorr1a.tic conditions of queenfish Sert.phuspolitus (Scianidae). Fish. Bull. 89: 9-18.
Giøsæter, H. 1999. Prognosis for development of the Barents Sea capelin stock .. Working - - Document prepared for the ICES _.._Asctic Fisheries \Verking Group. June 19 1999, Institute of Marine Research, Bergen, Norway.
Hislop, J.R.G., Rabb, A.P., and Gauld, J.A.l978. 0\Jservations on effects of feeding leve! on gro\vth and reproduction in haddock, ]l.felanogrammus aeglejinus (L.) in captivity. J.
ICES. 1999. Report of the Arctic Fisheries Working Group. ICES CM 1999/ACFM:3
Kjesbu, O.S., KlungsØyr, J., Kryvi, H., Witthames, P.R., and Walker, M.G. 1991. Fecundity, atresia, and egg size of captive Atlantic cod (Gadus ;nor hua) in rclation to proximate bodv comnosition. Can. J. Fish. Aauat. Sei. 48: 2333-2343. J - ~ ~
Kjesbu, O.S., Witthames, P.R., Solemdal, P., and Greer Walker, M. 1998. Tempora! changes in the fecundily of Arcto-l~orweglan cod (Gadus rnorhua) in response to natural changes in food and temperature . .J. Sea Res. 40: 303-321.
K n,lnw T A flP.ll T Virtn<". P. ancl Smith. D.C. 1 'll95. Fecunditv and its variabilitv in orane:e
~~--~-···-·--·,----,-·, - - - , - - , - - - , - - - - J .. ...
roughy: effects ofpopulatiun density, condition, egg size, and senescence. J. Fish.
BioL 47: 1063-1080.
Ma, Y., Kjesbu, O.S., and Jørgensen, T. 1998. Effeots of ration on the maturation and fecundity in captive Atlantic h~rring (Clupea harengus). Can. J. Fish. Aquat. Sei.
55: 900-908.
MorKPn7iP fl R Tnmki"wi<'z L ancl Klister. F 1997. Stock structure. random variabilitv.
~'~--~~---~~-, ~-~-··
---
··---, --, - - - · - , - . . - ""'.and annual egg production in easlern Baltic cod (Subdivisions 25-32). IC:ES Wor!dng Group on the Assessment ofBaltic Fish Stock Working Document 1997.
Mor<h"ll r T KiP.<hn OS Thor"'n. A.. and Solemdal. P. 1999. Soawner aualitv effects on
... ~~~ .... -~ ... ~·-. , ... .) _ _ _ _ , - - - - , - - - , - · , · · - - · • ' .L. .L "'
two measures of reproductive polential: have we been counting our eggs before they've hatched? ICES 1999.
Marsha!l, C.T., and Frank K.T. 1999. The effect of interannual variation in growth and condition on haddock recruitment. Can. i. FiiSh. Aquat. Sei. 56: 347-355.
Marshall, C.T., Kjesbu, O.S., Yaragina, N.A., Solemdal, P., and Ulltang,
Ø.
1998. Is spavvner biomass a sensitive measure of the reproductiive and .recmitment potential of Northeast Arctic cod? Can. j, Fish. Aquat. Sei. 55: 1766-1783.Marteinsdottir, G .• and Tnorarinsson, K. 1998. I1npr,eving the stock-recruitment relationship in Icelandic cod (Gadus morhua L) by including age diversity of spawners. Can. J.
Fish. Aquai. Sei. 55: 1372-1377.
Schwalme, K., and Chouinard, G.A. 1999. Seasonal dynan1ics in feeding, organ weights, and reproductive maturation of Atlantic cod (Garias mor hua) in the southern Gulf of St Lawrence. ICES j.lviar. Sei. 56: 303-319.
Torsvik, N., Mortensen, S., og t~edreaas, K.H. 1995. Fiskeribiologi. Landbruksforlaget 1995.
Trippei, E.A., Kjesbu, O.S., and Solerndal, P. 1997 .. Effects of adult age ruJ.d size structure on '""nrnrlnrtiv" nntnnt in marine fisbes. In Earlv life historv and recruitment in fish
~-r~---·- --·-r-·---·-··-·· ·· · _, ...
popuiations. Edited by R.C. Cha.mbers and E.A. Trippel. Chapman atJ.d Hall, }~evv
·York. Pp. 31-62.
350
r---,
e.s
m.-
50 60 70 80 90 100 110 120 i30 14{)
Length (cm)
~~-Mode67,51
1 _ " . _ . Mode 72,5 1
I--Mode77,5 l
1~;:~. Mrvlø !I'J <:: l l ' ·~~~ ·-.. l
~~Mode87,5 1
l-+-Mode 92,5 l l-+-Mo de 97,5 l
Figure 1: Seven different size compositions giving modallengths lli""ld constant SB.
6E+i4
5E+i4
4E+l4
e:
,_, 3E+i42E+l4
lE+i4
o
o 200000 400000 600000 800000 1000000 1200000 1400000
SB (i)
Figure 2: The simulated relationship between SB and TEP when varying the condition of the spawners wP-ile holding the size- composition (numbers at length) of the stock constant. Rcsults for 12 sirnulations using observ·ed size cornposition for 1985 to
1996 are shown.
"'
~
6E+l4
l l
5E+!4
t
l 4E+14
+
l l
3E+14
t
l
2E+i4
+
l l
lE+l4
+-
ltlf' -"'
l
l
o l
o 200000 400000 600000 800000
SG (t)
•
+i
IIJIiOOOOOO 1200000 'Annnnn l.'tVVVVV
1.
Mode 67 .sl t..:. .. ' " ' l .l UilVJUUC: IL.,_l
l
l ÅMode77,5
l
>~ Mode82,51
1 ÆMode 87,51
[e Mode 92,5 [
l +Mode 97,51
Figure 3: The simulated relationship between SB and TEP when varying size
composition/modallength of t..he stock and holding condition of the spawners constant.
Results for 12 siHIUlations using observed SB for 1985 to 1996 are shown_
6E-ri4 ~----~
~Mt l T
l
.,.1 .,.It·r
tiT
~~ 67,5-l~~-1@+1411 11
l -11 l l
* .
o. l
~ T ild l i'
T!:l
3E+r4 t1
+
;[i!.j. ~ 1!1~
'
l-l Ill V .t:."1<: l ,_,-lllj5-ll !";~'-l l
l
&97,5-lowl
l
X97,5-high )11 . : ;_
"j1ifDrl
1 \ ]1
1 2
E+l
4
+ I.,.
11•ollHTBH 1 jf 1
/ 1
~~
r 'i1fi1'f±lj' ·ll _~.,. '...IT_' Tl l li ~ -
lE+l4 l =""'-' 11
-"'~ 1 ,
æ 11
'i , 1 _,_l ~'" !111
:Jf .l' . . . 0~~~-+---~----~----~----~o 200000 400000 600000 800000 1000000 1200000 1400000 SB (t)
Figure 4: The simulated relationship between SE and TEP when varying size
