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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.
� 2006 Blackwell Publishing Ltd, Fish. Oceanogr., 15:5,
402–412.
-
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) –
Stock–environment–recruitment models for albacore 405
� 2006 Blackwell Publishing Ltd, Fish. Oceanogr., 15:5,
402–412.
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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.
406 I. Arregui et al.
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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.
Stock–environment–recruitment models for albacore 407
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402–412.
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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.
408 I. Arregui et al.
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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.
Stock–environment–recruitment models for albacore 409
� 2006 Blackwell Publishing Ltd, Fish. Oceanogr., 15:5,
402–412.
-
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.
410 I. Arregui et al.
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402–412.
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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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