Stock–environment–recruitment models for North Atlantic … · Stock–environment–recruitment models for North Atlantic albacore (Thunnus alalunga) IGOR ARREGUI,1,* HARITZ

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Stock–environment–recruitment models for North Atlantic albacore

(Thunnus alalunga)

Article in Fisheries Oceanography · June 2006

DOI: 10.1111/j.1365-2419.2005.00399.x

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Stock–environment–recruitment models for North Atlanticalbacore (Thunnus alalunga)

IGOR ARREGUI,1,* HARITZARRIZABALAGA,1 DAVID S. KIRBY2 ANDJUAN MANUEL MARTÍN-GONZÁLEZ3

1AZTI Tecnalia, Herrera Kaia Portualdea z/g, 20110 Pasaia,Gipuzkoa, Spain2Oceanic Fisheries Programme, Secretariat of the Pacific

Community, BPDS 98848 Noumea, New Caledonia3Departamento de Fı́sica, ULPGC, 35017, Las Palmas G.C.,Spain

ABSTRACT

Different stock–recruitment models were fitted toNorth Atlantic albacore (Thunnus alalunga) recruit-ment and spawning stock biomass data. A classicaldensity dependence hypothesis, a recent environ-mental-dependence hypothesis and a combination ofboth were considered. For the latter case, four stock–environment–recruitment models were used: Ricker,Beverton-Holt, Deriso’s General Model (modified totake into account environmental effects) and condi-tioned Neural Networks. Cross-validation analysisshowed that the modified Deriso model had the bestpredictive capability. It detected an inverse effect ofthe North Atlantic Oscillation (NAO) on recruit-ment, a Ricker-type behaviour with density dependentovercompensation when environmental conditions areunfavourable and a Beverton–Holt-type behaviourtowards an asymptotic recruitment carrying capacitywith favourable environmental conditions. TheNeural Network model also detected that underfavourable environmental conditions high spawningstock biomass does not necessarily have a depensatoryeffect on recruitment. Moreover, they suggest thatunder extremely favourable environmental conditions,albacore recruitment could increase well above theasymptotic carrying capacity predicted by Beverton–Holt-type models. However, the general decrease inspawning stock biomass in recent years and increasingNAO trends suggest that there is low probability of

exceptionally large recruitment in the future andinstead there is a danger of recruitment overfishing.

Key words: albacore, environment, neural-network,prediction, stock–recruitment, Thunnus alalunga.

INTRODUCTION

Recruitment is a key process in fish populationdynamics. However, the mechanisms that lead to highlevels of egg and larval mortality during the criticalperiod are still largely unquantified, making predictionof stock biomass difficult.

Environmental dependence

There are many examples of cases where environ-mental variability has had a demonstrable effect onthe dynamics of fish populations (Cushing, 1982;Beamish, 1995), including tuna (Anonymous, 1989;Lehodey et al., 1997; Fromentin and Restrepo, 2001).However, despite this general recognition, environ-mental information is rarely taken into account intuna stock assessment and management (Maunder andWatters, 2001; Watters and Maunder, 2001; Maunderand Watters, 2003). All tunas and tuna-like speciesneed warm waters for reproduction and larval growth(Nishikawa et al., 1985). This implies that the tem-poral spawning window is larger for tropical tunas thanfor temperate tunas. The physiology of tropical tunasallows them to spawn more or less continuously assoon as favourable conditions are encountered (Hun-ter et al., 1986; Itano, 2000). The temperate tunassuch as albacore, Thunnus alalunga, cannot follow thisstrategy because of their physiological adaptations tothe seasonal availability of spawning habitat, thereforethe probability of stable recruitment is much higher fortropical tunas than for temperate tunas (Fromentinand Restrepo, 2001).

In the case of North Atlantic albacore, spawningareas are located in low productivity zones in thetropical central and western North Atlantic (Bard,1981) where the environmental conditions required bythe early life stages are met. Santiago (1998) found aninverse correlation between North Atlantic albacorerecruitment and the winter pattern of the North

*Correspondence. e-mail: [email protected]

Received 6 August 2002

Revised version accepted 26 June 2005

FISHERIES OCEANOGRAPHY Fish. Oceanogr. 15:5, 402–412, 2006

402 doi:10.1111/j.1365-2419.2005.00399.x � 2006 Blackwell Publishing Ltd.

Atlantic Oscillation (NAO) index (Hurrell, 1995) bymeans of a second order linear regression, whichaccounted for 64% of the variance in albacorerecruitment during the period 1969–92. However, thecorrelation coefficient decreases to 27% if the studyperiod 1975–98 is selected.

Density dependence

If large natural recruitment variability occurs or if thestock is highly exploited, resilience tends to inhibitcollapse (Myers et al., 1995). Under steady stateassumptions, density dependent stock–recruitmentmodels (Eqn 1) are the classical way to explain thisresilience (Beverton and Holt, 1957; see Berg andGetz, 1988 for a detailed review). In Eqn 1, a is ameasure of maximum reproductive rate (recruitment-per-unit-biomass), St is the spawning stock biomass attime t and aSt is responsible for the resilience of thestock (Cushing, 1973; Hilborn and Walters, 1992), asit causes a quick increase in recruitment with littleincrease in biomass. The density dependent survivalterm f(St,b) acts as a simple self-regulation functionpreventing high, unsustainable stock sizes. Evidence ofthis kind of relationships between spawner stock andrecruitment is numerous (Myers and Barrowman,1996).

Rtþs ¼ a � St � fðSt; bÞ ð1Þ

Albacore tuna, just like the rest of the temperatetunas, have a relatively late age at maturity and a longlife span (Bard, 1981; Fromentin and Restrepo, 2001).The spawning stock includes numerous year classes,acting as a buffer/reserve against recruitment failure inany particular year. Estimated total mortality can beup to four times natural mortality for some year classes(Anonymous, 2001), which suggests a high a value forthis species. The relatively large recruitment duringrecent years, during which spawning stock biomass hasdecreased considerably, confirms this fact, showingthat it is a resilient stock in Cushing’s sense (Cushing,1973). By comparison with tropical tunas, this pro-ductivity reflects a more conservative life historystrategy in a colder and more variable environment(Fromentin and Restrepo, 2001).

Stock–environment–recruitment models

Few models that combine density dependence andenvironmental dependence have been described.Modifications of Beverton–Holt (Hilborn and Walt-ers, 1992) and Ricker models (RMs) (Ricker, 1975)have been proposed to include environmental data inthe stock–recruitment relationship, the latter beingthe most commonly used stock–environment–recruit-

ment relationship (Schweight and Noakes, 1990; So-low, 2000; Williams and Terrance, 2000). In thesemodels the environmental effect acts as a multiplierthat is independent of the size of the spawning stock(Brander and Mohn, 2004).

Linear regressions (Köster et al., 2001, 2003) andArtificial Neural Networks (Chen and Ware, 1999;Huse and Ottersen, 2003) have also been applied torecruitment prediction. The latter are good atsearching the solution space but are not constrained byany ecologically meaningful hypothesis such as densitydependence. An alternative semi-parametric modelhas been defined by modification of the RM whereenvironmental non-parametric smoothing functionswere added to the Ricker lognormal distributed model(Chen and Irvine, 2001).

None of these models have been applied to tunas.In this paper, we analyse the effect of environmentalvariability on the stock–recruitment relationship foralbacore. For that purpose, we compare differentmodels of recruitment that allow for density depend-ence, environmental dependence and combined den-sity-environmental dependence hypotheses. Finally, anew stock–environment–recruitment model based onDeriso (1980) is proposed as the best way to predictalbacore recruitment in terms of spawning stock bio-mass and environment.

METHODS

Data

Recruitment (R) in number of fish and spawning stockbiomass (S) in metric tonnes, estimated by VirtualPopulation Analysis calibrated with standardized catchper unit effort (CPUE) series (Anonymous, 2001),were used (Table 1). The analysis was restricted to theperiod 1975–98 because of the uncertainty of recentrecruitment estimates and because spawning stockbiomass estimates prior to 1975 were not available.

The NAO index was used to represent climatevariability because it controls, in addition to baro-clinic winds, the changes in temperature and precipi-tation patterns over the North Atlantic (Lamb andPeppeler, 1987; Hurrell, 1995, 1996). The Decemberto February mean of the Azores-based index (I) wasused instead of the December to March Lisbon-basedindex as performed in other studies (Brander andMohn, 2004). Although both Lisbon-based andAzores-based NAO indices are similar, the latter(i.e. the difference in normalized sea-level pressureanomalies between Ponta Delgada, Azores, Portugal,and Stykkisholmur, Iceland; http://www.cru.uea.ac.uk/

Stock–environment–recruitment models for albacore 403

� 2006 Blackwell Publishing Ltd, Fish. Oceanogr., 15:5, 402–412.

ftpdata/nao.dat, 23 December 2005) better illustratesthe NAO dipole characteristics in non-winter seasons(Table 1 of Hurrell and van Loon, 1997). TheDecember to February index was selected because anexploratory analysis showed highest correlation be-tween recruitment and monthly NAO in that winterperiod (Fig. 1).

Models

The following set of environment–recruitment, stock–recruitment and stock–environment–recruitmentmodels were fitted to the North Atlantic albacore data:

Environment–recruitment models:• second-order environmental linear model (ELM).

Stock–recruitment models:• Beverton and Holt model (BHM);• Ricker model (RM).

Stock–environment–recruitment models:• second-order stock–environmental linear model

(SELM);• environmental Beverton and Holt model

(EBHM);• environmental Ricker model (ERM);• environmental Deriso model (EDM);• conditioned neural network model (NNM).The second-order ELM and the SELM are given in

Eqns 2 and 3, where NAOt is the NAO index at year tand Rt+1 is the predicted recruitment at year t + 1. Allother variable and parameter definitions are given inTable 2.

Rtþ1 ¼ aþ bNAOt þ cNAOt2 þ et ð2Þ

Rtþ1 ¼ aþ bNAOt þ cNAOt2 þ dSt þ eSt2 þ et ð3Þ

Different stock–recruitment relationships havebeen proposed from the density dependent approach,but most of them are included in the Deriso (1980)model:

Rtþ1 ¼ a � St � ð1� bcStÞ1=c þ et ð4Þ

where St is the spawning stock biomass at year t; athe maximum reproductive rate; b the recruitmentoptimality parameter; and c the recruitment limita-tion parameter. The Beverton–Holt model (BHM,Eqn 5) and the RM (Eqn 6) are particular cases ofEqn 4 when c ¼ )1 and when lim c fi 0, respect-ively.

Rtþ1 ¼aSt

1þ bStþ et ð5Þ

Rtþ1 ¼ aSt exp �bStð Þ þ et ð6Þ

In the BHM model, a/b represents the asymptoticthreshold recruitment for large S values, and in theRM model 1/b is the maximum recruitment obtainedat a certain level of S, above which overcompensationwill occur.

Among stock–environment–recruitment models,the environmentally modified Beverton–Holt model(EBHM, Eqn 7; Hilborn and Walters, 1992, p. 286)and the environmentally modified Ricker

Table 1. Spawning stock biomass (S), recruitment (R) andwinter NAO data used in the present study.

Year S (106 t) R (number) Winter NAO

1975 39.73 0.1571976 58.27 9 777 611 )1.9031977 72.27 12 610 831 )0.5931978 72.99 15 994 036 )1.9731979 71.47 8 295 545 0.3231980 64.32 12 185 642 1.1971981 62.17 10 663 908 )0.2231982 60.17 7 986 243 2.071983 54.96 7 392 748 1.6971984 42.64 7 313 655 )0.531985 31.85 8 507 667 )0.9971986 22.26 12 032 260 0.3531987 16.52 9 732 968 )0.131988 18.81 7 922 782 2.9971989 22.32 8 964 260 2.1271990 31.13 8 701 964 0.731991 37.78 9 382 724 1.6871992 37.61 8 782 582 1.411993 31.87 10 274 018 1.1731994 26.29 6 587 793 2.8971995 23.21 9 407 081 )2.241996 23.12 8 039 156 )0.4631997 26.74 9 199 428 0.6531998 7 657 130

Figure 1. Correlation coefficient between North Atlanticalbacore recruitment and the monthly NAO for the 2 yrbefore the year of recruitment.

404 I. Arregui et al.


model (ERM, Eqn 8; Ricker, 1975) have been con-sidered.

Rtþ1 ¼ exp cþ dNAOð ÞaSt

1þ bStþ et ð7Þ

Rtþ1 ¼ aSt expð�bSt þ dNAOtÞ þ et ð8Þ

Moreover, in the present study, we propose an-other stock–environment–recruitment model thatwould arise from substituting c ¼ c + dNAO inEqn 4. The resulting environmentally modifiedDeriso model (EDM, Eqn 9) includes environmentaldependence in the recruitment limitation parameter,meaning that the shape of the stock–recruitmentrelationship and whether or not there is overcom-pensation would depend on the environmental situ-ation.

Rtþ1 ¼ aSt½1� b cþ dNAOð ÞSt�1=ðcþdNAOÞ þ et ð9ÞThe models were fit assuming a normally distri-

buted error structure et �N(0,r) and using the Gauss–Newton method (Press et al., 1992) to minimize theleast squares error function.

Conditioned Neural Network models (NNM) werealso used to model recruitment as a function ofspawning stock biomass and environment. Artificialneural networks consist of a number of highly con-nected simple units (Hertz et al., 1991). In modelsused for predictions, we can differentiate three types ofparallel units or neurons: input neurons which are theinput vectors (predictors), output neurons which givethe results of the neural network, and hidden neuronsused in internal computations. Each hidden and out-

put layer computes a value as the weighted sum of theinputs transformed by a hyperbolic tangent or linearfunction, respectively. Unlike the more commonlyused regression techniques, neural networks do notrequire a particular functional relationship or distri-bution assumption about the data. This makes neuralnetwork modelling a powerful tool for exploringcomplex and non-linear biological problems.

The multilayer feed-forward neural network with aback-propagation learning algorithm and least squareserror function is one of the most successful networkscurrently in use and has been applied in this study.Neural networks differ from one another in thearchitecture and training algorithms. Because we aretrying to model recruitment from spawning stockbiomass and NAO values, our NNM architectureconsisted of two input neurons (ninp ¼ 2) and a singleoutput neuron (nout ¼ 1). The number of neurons inthe hidden layer was varied (nhidd ¼ 1, 2, 3 or 4) inorder to find the most appropriate predictor neuralarchitecture (a schematic view of the architecturewith two hidden neurons is given in Fig. 2). Theglobal feed-forward process can be mathematicallyexpressed as,

R ¼ f0 b0 þXnhiddj¼1

w0jfj bj þXnimpi¼1

wijxi

!" #þ e ð10Þ

where R is the recruitment vector; xi the input vectors(spawning stock biomass and NAO); wij the weightsfrom input neuron i to hidden neuron j; W¢j theweights from hidden neuron j to the output neuron; bjand b¢ the biases; fj and f0 the hyperbolic tangent andlinear functions respectively; and e is the residualvector. Back-propagation training (Rumelhart et al.,1986) was used to minimize the least squares error

Table 2. Meaning and units of theparameters and variables used in themodels. The models in which parametersare first mentioned are in brackets. ELM,environmental linear model; SELM,stock environmental linear model;BHM, Beverton–Holt model; EBHM,environmentally modified Beverton-Holt model; NNM, neural networkmodel.

Symbol Meaning Units

R Recruitment nS Spawning stock biomass tNAO North Atlantic Oscillation Index –a Intercept (ELM) nb Slope for environmental term (ELM) nc Quadratic coefficient for environmental term (ELM) nd Slope for stock biomass term (SELM) n t)1

e Quadratic coefficient for stock biomass term (SELM) n t)2

a Maximum reproductive rate (BHM) n t)1

b Recruitment optimality parameter (BHM) t)1

c Recruitment limitation parameter (EBHM) –d Environment coefficient (EBHM) –wij Weight from neuron i to j (NNM) –B Bias term (NNM) –



function, with a learning rate of r ¼ 0.01 to balancethe speed and the convergence of the iteration process.Input and target variables were standardized in orderto speed up the algorithm, and weights were initiatedrandomly 150 times in order to overcome local mini-ma problems when nhidd > 2. Because neural networksdo not otherwise have any ecologically meaningfulconstraints and the fitted function is learned exclu-sively from the information contained in the data,three additional data points were incorporated to setthe constraint that there is no recruitment in the ab-sence of spawning stock, i.e. R ¼ 0 when S ¼ 0 forlow, medium and high NAO values (NAO ¼ )1.5, 0,1.5).

Maximum recruitment (Rm) and the associatedspawning stock biomass (Sm) for each model werecomputed taking derivatives with respect to S. For theneural network model, Rm and Sm were computednumerically, finding the maximum of the fitted surfacein the neighbourhood of the input data.

Model performance

When using small data sets, over-fitting may occur ifmodels have too many parameters or neural networkshave too many neurons, limiting predictive capability(Goutte, 1997). For that reason, K-fold cross-valid-ation (Efron and Tibshirani, 1993) was used to com-pute generalization errors and to compare thepredictive capability of NNM, EBHM, ERM andEDM. The data series were divided into six homo-geneous groups (K ¼ 6), and each of these 4-yr-longgroups (except the last one, which was 3-yr long) waspredicted with the model fitted to the rest of the timeseries. The sum of squared errors (SSE ¼ Ret2) wastaken as a measure of precision, the mean error[ME ¼ (Ret)/n; n ¼ number of observations] as ameasure of accuracy and the mean squared error[MSE ¼ R(et2)/n + (Ret)2/n2] as a measure of both,with the lower MSE representing the best predictivecapability (following Maravelias et al., 1996).

RESULTS

Different models detected different relationshipsbetween recruitment and stock and/or environment(Table 3). The ELM and SELM models showed inverserelationships between the NAO and recruitment (asfound by Santiago, 1998), with minimum recruitmentoccurring at NAO values of 2.12 and 1.70, respect-ively. Higher values of NAO did not seem to producea negative effect on recruitment (Fig. 3), which couldbe interpreted as a region of environmental inde-pendence. The SELM also detected some densitydependent behaviour with maximum recruitment atSm ¼ 65.37 · 106 tonnes and low overcompensation(Fig. 3).

Figure 2. Example of a two hiddenneuron neural network architecture.

Figure 3. Second order stock–environment linear model(SELM) fit to North Atlantic albacore recruitment (R, innumber of fish), spawning stock biomass (S, in milliontonnes) and NAO data. The dotted line indicates minimumrecruitment for every spawning stock biomass value, and thecontinuous line indicates maximum recruitment for everyNAO value. Horizontal arrows indicate the environmentallyindependent region and the downward vertical arrows indi-cate the overcompensation region.



Among the density dependent models, BH fitted anasymptotic threshold value of Rm ¼ 1.142 · 107recruits (Fig. 4) and for EBHM the asymptotic maxi-mum recruitment varied from 9.8 · 106 recruits underunfavourable conditions (NAO ¼ 2) to 1.3 · 107recruits in favourable conditions (NAO ¼ )2, Fig. 5).Conversely, overcompensation is implicit in Ricker-type models. RM fitted a maximum recruitment ofRm ¼ 1.06 · 107 recruits generated by a spawning

stock biomass of Sm ¼ 52.3 · 106 t (Fig. 4). In theERM, overcompensation occurred for stock sizes aboveSm ¼ 47.61 · 106 t independently of environmentalvalues, but the number of recruits still depended onenvironmental conditions (Fig. 6). Slightly strongerovercompensation was predicted in the ERM than inthe RM (b ¼ 0.021 vs. 0.019, Table 3).

The environmentally modified Deriso model andNNM with nhidd ‡ 3 predicted strong overcompensa-tion for unfavourable environmental conditions (highNAO) but asymptotic threshold recruitment forfavourable environmental conditions (low NAO). Inthe NNM, overcompensation disappeared in favour of

Table 3. Parameter estimates for the fitted models (see parameter meanings in Table 2).

Model a (d) b (e) c (a) d1 (b) d2 (c) SSE Classification

BHM 1.578e6 0.1381 – – – 8.795e13 9RM 5.520e5 0.0191 – – – 1.054e14 11ELM – – 9.401e6 )8.163e5 1.925e5 7.269e13 8SELM 1.022e5 )781.7 6.675e6 )7.973e5 2.335e5 6.431e13 5ERM 6.237e5 0.02100 )0.0923 – 7.236e13 7EBHM 1.335e6 0.1728 0.3858 0.0706 – 6.692e13 6EDM 7.256e5 0.0284 )0.2175 0.1582 – 5.401e13 4NNM Rw’j Rw1j R|w1j| Rw2j R|w2j|nhidd ¼ 1 )0.7211 )1.3295 2.4456 )1.3277 1.3277 9.252e13 10nhidd ¼ 2 )1.6249 0.1436 3.3953 )0.0263 2.5234 5.367e13 3nhidd ¼ 3 2.3332 )1.5844 4.4878 )1.5450 4.1870 4.907e13 2nhidd ¼ 4 )5.6700 )1.2144 5.9683 )0.5232 4.9790 4.582e13 1

For the Neural Network Models the sum of weights is indicated (following Aoki and Komatsu, 1997).In each model, the sum of squared error (SSE) and the classification from best (in bold) to worst is indicated.

Figure 4. Beverton–Holt (BHM) and Ricker (RM) modelfits to North Atlantic albacore recruitment (R) and spawn-ing stock biomass (S) data. Upward and downward arrowsindicate asymptotic threshold recruitment (in the case ofBHM) and overcompensation (in the case of RM), respect-ively.

Figure 5. Environmental Beverton–Holt Model (EBHM) fitto North Atlantic albacore recruitment (R, in number offish), spawning stock biomass (S, in million tonnes) andNAO data. Upward vertical arrows indicate asymptoticthreshold recruitment for high S values.



asymptotic threshold recruitment for most of thenegative NAO values (Fig. 7), while in the EDM thisonly happened for very negative NAO values (Fig. 8).If we analyse NNM for extremely favourable condi-tions, the NNM with nhidd ‡ 2 fitted a quasi linear

stock–recruitment relationship, similar to densityindependence with f(S,b) ¼ 0 in Eqn 1. This wouldbe a dynamically unexpected situation where infinitelyincreasing recruitment would occur due to lack ofintraspecific competition under those environmentalconditions. In Deriso’s (1980) model, this situationcould theoretically happen only if c < )1 (Schnute,1985), which, in the EDM, would correspond to animprobable NAO value of )5.59.

The multiple non-linearity of neural networksprovides the ability to detect all possible behaviour fordifferent spawning stock biomass and environmentalsituations (Conan, 1994). The evolution of the NNMas the number of hidden neurons increased is shown inFig. 9. The NNM fit with nhidd ¼ 1 was similar to BH,showing environmental independence. The secondhidden neuron detected the same behaviour identifiedby the environmental linear regressions (ELM andSELM) and the simple density dependent models(BHM and RM), namely an inverse relationship be-tween NAO and R, overcompensation for high S andunfavourable environmental conditions, asymptoticthreshold recruitment for high S and favourableenvironmental conditions, and environmental inde-pendence for unfavourable environmental conditionsand medium S values. This environmentallyindependent region reduced as the number of nhidd

Figure 6. Environmental Ricker model (ERM) fit to NorthAtlantic albacore recruitment (R, in number of fish),spawning stock biomass (S, in million tonnes) and NAOdata. Downward vertical arrows indicate overcompensationat high S values.

Figure 7. Conditioned neural network model with threehidden neurons (NNM3) fit to North Atlantic albacorerecruitment (R, in number of fish), spawning stock biomass(S, in million tonnes) and NAO data. The continuous lineindicates the maximum recruitment for each environmentalvalue. For high S values, downward and upward verticalarrows indicate overcompensation and asymptotic thresholdrecruitment occurring at high (unfavourable) and low(favourable) NAO values, respectively. The horizontal arrowindicates the environmentally independent region.

Figure 8. Proposed environmental Deriso model (EDM) fitto North Atlantic albacore recruitment (R, in number offish), spawning stock biomass (S, in million tonnes) andNAO data. The continuous line indicates the maximumrecruitment for each environmental value. For high S values,downward and upward vertical arrows indicate overcom-pensation and asymptotic threshold recruitment occurring athigh (unfavourable) and low (favourable) NAO values,respectively.



increased, detecting the inverse influence of NAO onrecruitment, and finally the NNM with five hiddenneurons was clearly over fitted.

The best fit to the data (i.e. lowest SSE) was pro-vided by neural networks, the SSE being lower as thenumber of hidden neurons increased from two to four(Table 3). However, cross-validation analysis showedthat neural networks with a high number of hiddenneurons were over-fitted and thus were not good pre-dictive tools (Table 4). In fact, the simplest neuralnetwork architecture with a single hidden neuronshowed the best predictive capability in terms of MSEamong the neural network models considered.Although neural networks with higher number ofhidden neurons showed low ME values, suggestingaccurate predictions, MSE values were quite highsuggesting that, taking into account both accuracy andprecision, they were not as good predictors as othermodels, predictive capability being inversely propor-tional to nhidd. EDM was the model with best

predictive capability, with lowest SSE and MSE val-ues. BHM was the second best, closely followed byEBHM. ERM was better than NNM with nhidd ¼ 3,4but worse than NNM with nhidd ¼ 1,2 (Table 4).

DISCUSSION

By meta-analysis of marine fish stocks Myers andBarrowman (1996) demonstrated that recruitmentdepends on the level of spawning stock biomass.However, for certain stocks the ‘recruitment states’hypothesis also appears plausible. In this scenario,recruitment is considered to be independent of S buthas different mean values during successive regimes(Gilbert, 1997), with the environment probably hav-ing an important role in those regime shifts. Recentstudies have showed that both spawning stock biomassand the environment may be important but differentspecies are affected in different ways (Myers, 2001). Ingeneral, it is acknowledged that density dependent

Figure 9. Conditioned neural network model with 1, 2, 4 and 5 hidden neurons (NNM1, NNM2, NNM4 and NNM5) fit toNorth Atlantic albacore recruitment (R, in number of fish), spawning stock biomass (S, in million tonnes) and NAO data.



regressions should be complemented with environ-mental information and several studies have beenpublished along this line in recent years (e.g. O’Brienet al., 2000). However, Myers (1998) stated that onlya small proportion of published studies showing sta-tistical correlation between the environment andrecruitment are actually verified when retested withnew data, and thus they should be considered withscepticism, especially if the ecological mechanismsresponsible for the environmental effects are not clear.The weak correlation between North Atlantic alba-core recruitment and NAO when taking into accountrecent data could lead to scepticism of the potentialrelationship between those two variables. However,the relationship is still significant. Moreover, suchcorrelations derived for populations living at the limitof their geographical range are generally more robustto retesting (Myers, 1998). The fact that recruitmentof temperate tunas is more variable and affected by theenvironment than recruitment for tropical tunas(Fromentin and Restrepo, 2001), and that statisticallysignificant correlations between south Pacific albacorerecruitment and the Southern Oscillation Index(Fournier et al., 1998) and between North Pacific al-bacore recruitment and the Aleutian Low PressureIndex (Beamish et al., 1997) have been documented(reviewed in Santiago, 2004), suggests that the envi-ronmental effect on North Atlantic albacore recruit-ment is real. The present study has incorporatedenvironmental information into the stock–recruit-ment relationship and shown that both spawning stockbiomass and environmental effects can affect recruit-ment at the same time, with the response of recruit-ment to density effects depending on theenvironmental situation.

The proposed NNM nhidd ‡ 3 fitted to albacoredata suggested that the shape of the stock–recruitmentrelationship could change depending on environ-mental conditions. This observation lead to the EDMproposed in this paper, which also predicts similarenvironmental effects that are ecologically plausible.The advantages of EDM are that it is based on well-discussed stock–recruitment theory (Beverton andHolt, 1957) and it shows higher predictive capabilitythan the neural networks. The idea that favourableenvironmental conditions would cause an increase inrecruitment carrying capacity and with no overcom-pensation is ecologically sensible. Santiago (2004)suggests that high NAO values would reduce larvalsurvivorship because of wind-induced turbulent diffu-sion. This could explain the enhancement of thecarrying capacity under favourable NAO conditions.An underlying mechanism to explain the disappear-ance of overcompensation would be that the negativeeffect of intraspecific competition and/or cannibalismon survival of early life stages would decrease underfavourable environmental conditions. This wouldimply bottom-up control of recruitment. In addition tothis, the high increase of recruitment detectedby NNM (nhidd ‡ 2) when both favourableenvironmental conditions and high spawning stockbiomass occur suggests the existence of a loophole(sensu Bakun and Broad, 2003). Although favourableconditions of both environment and spawning stockbiomass may have a low probability of occurrence, thesuggested loophole could represent an adaptivestrategy in a variable environment and competitiveecosystem.

The present study suggests that environmentaleffects are more important when spawning stock

Table 4. Results of the sixfold-cross-validation analysis, showing the sum of squared error (SSE), mean error (ME) and meansquared error (MSE) for each model.

Model

Precision Accuracy Precision and Accuracy

SSE Classification ME Classification MSE Classification

BHM 7.346e13 2 )5.456e5 7 3.326e12 2RM 9.909e13 5 )4.700e5 2 4.494e12 7EBHM 7.468e14 8 )5.353e5 6 3.381e12 3ERM 9.388e14 9 )5.598e5 8 4.252e12 6EDM 7.132e12 1 )6.016e5 9 3.225e12 1NNM n ¼ 1 8.075e13 3 )4.984e5 4 3.659e12 4NNM n ¼ 2 8.896e13 4 )4.883e5 3 4.033e12 5NNM n ¼ 3 1.216e14 6 )5.043e5 5 5.518e12 8NNM n ¼ 4 1.387e14 7 )1.649e5 1 6.307e12 9

Models are classified according to the lower error function criteria.



biomass is high. This could explain the lower corre-lation between the recruitment and NAO when con-sidering recent data, given the downward trend ofspawning stock biomass. However, it should be notedthat, in this paper, we have assumed that recruitmentand spawning stock biomass values, which are VPAoutputs, are correct. Some authors have suggested thatenvironmental variability could affect catchability bytraditional fleets rather than recruitment itself (Ortizde Zárate et al., 1997; Bard, 2001). Because catch ratesfrom these fleets are used for VPA calibration andabundance estimation, further research would benecessary to determine the respective role of theenvironment in determining both catchability andrecruitment.

In general, the present analysis stresses theimportance of taking into account environmentalvariables in stock assessment and management(Brander, 2005), at least in stocks where recruitment isdemonstrably affected both by spawning stock biomassand environmental variability. In the case of NorthAtlantic albacore, the EDM suggests that even if thespawning stock biomass was in very good condition,unfavourable environmental conditions could stilllead to very poor recruitment. Information aboutenvironmental variability could be used in yearly re-vised short-term projections because the winter NAOof a given year affects the recruitment of the next year.In the long term, if the NAO continues with thegenerally increasing trend of recent years, according tothe EDM the relationship between spawning stockbiomass and recruitment would be Ricker type, withovercompensation at high SSB values. However, thegeneral decreasing trend of the spawning stock in re-cent years because of fishing activities suggests thatovercompensation is unlikely to occur. In fact,decreasing biomass and increasing NAO trends suggestthat there is low probability for loopholes to produceexceptionally large recruitment of albacore in the fu-ture and instead there is a danger of recruitmentoverfishing.

ACKNOWLEDGEMENTS

Part of this research was carried out thanks to a traininggrant from University of Las Palmas de Gran Canaria,Physics Department, and the project RP2004 Templa-dos funded by the Basque Government to AZTI Tec-nalia, Marine Research Unit. David Kirby was fundedby the European Commission through the Pacific Re-gional Ocean and Coastal Fisheries (PROCFish) Pro-ject. This paper is a contribution to the GLOBECCLIOTOP (Climate Impacts on Oceanic Top Preda-

tors) Project. The authors sincerely thank XabierIrigoien for his constructive suggestions and commentsfor this paper and Victor Martinez for his estimablehelp. The authors also wish to thank two anonymousreviewers and the Editor for their helpful comments.

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