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Estuarine, Coastal and Shelf Science 92 (2011) 534e545

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Estuarine, Coastal and Shelf Science

journal homepage: www.elsevier .com/locate/ecss

Otolith reading and multi-model inference for improved estimation of ageand growth in the gilthead seabream Sparus aurata (L.)

Lény Mercier a, Jacques Panfili a,b, Christelle Paillon a, Awa N’diaye a,b, David Mouillot a,Audrey M. Darnaude a,*

aUMR 5119 UM2-CNRS-IRD-IFREMER-UM1 ECOSYM, Place Eugène Bataillon, 34095 Montpellier Cedex 5, FrancebUMR 5119 UM2-CNRS-IRD-IFREMER-UM1 ECOSYM, IRD B.P. 1386, 18524 Dakar, Senegal

a r t i c l e i n f o

Article history:Received 5 July 2010Accepted 13 February 2011Available online 18 February 2011

Keywords:gilthead seabreamVon Bertalanffy growth functionmulti-model inferenceAIC weightsMediterranean SeaGulf of Lions

* Corresponding author.E-mail address: audrey.darnaude@univ-montp2.fr

0272-7714/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.ecss.2011.02.001

a b s t r a c t

Accurate knowledge of fish age and growth is crucial for species conservation and management ofexploited marine stocks. In exploited species, age estimation based on otolith reading is routinely usedfor building growth curves that are used to implement fishery management models. However, theuniversal fit of the von Bertalanffy growth function (VBGF) on data from commercial landings can lead touncertainty in growth parameter inference, preventing accurate comparison of growth-based historytraits between fish populations. In the present paper, we used a comprehensive annual sample of wildgilthead seabream (Sparus aurata L.) in the Gulf of Lions (France, NW Mediterranean) to test a method-ology improving growth modelling for exploited fish populations. After validating the timing for otolithannual increment formation for all life stages, a comprehensive set of growth models (including VBGF)were fitted to the obtained ageelength data, used as a whole or sub-divided between group 0 individualsand those coming from commercial landings (ages 1e6). Comparisons in growth model accuracy basedon Akaike Information Criterion allowed assessment of the best model for each dataset and, when nomodel correctly fitted the data, a multi-model inference (MMI) based on model averaging was carriedout. The results provided evidence that growth parameters inferred with VBGF must be used with highcaution. Hence, VBGF turned to be among the less accurate for growth prediction irrespective of thedataset and its fit to the whole population, the juvenile or the adult datasets provided different growthparameters. The best models for growth prediction were the Tanaka model, for group 0 juveniles, and theMMI, for the older fish, confirming that growth differs substantially between juveniles and adults. Allasymptotic models failed to correctly describe the growth of adult S. aurata, probably because of the poorrepresentation of old individuals in the dataset. Multi-model inference associated with separate analysisof juveniles and adult fish is then advised to obtain objective estimations of growth parameters whensampling cannot be corrected towards older fish.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Accurate knowledge of fish growth parameters is extremelyimportant for population management since it allows prediction ofgrowth rate evolution, identification of cohorts and evaluation ofpopulation dynamics (Rochet and Trenkel, 2003). As overfishingmodifies life history traits linked to individual growth, such as ageat first maturity (Ali et al., 2003), assessing growth parameters isalso vital for the definition of strategies for sustainable fisheries(Rochet and Trenkel, 2003). During the last century, otolithometry

(A.M. Darnaude).

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has emerged as the most useful tool in fish stock and age assess-ment (Panfili et al., 2002). As otoliths continuously growthroughout fish life, with no evidence of resorption (Campana,1999), the daily and seasonal (annual) increments recorded intheir structure allow retrospective assessment of fish growth withunparalleled accuracy (Campana et al., 2000).

Many published works therefore successfully used otoliths toassess growth in exploited fish species (e.g. Reibish, 1899; Campanaand Neilson, 1982; Gordoa and Moli, 1997; Tomas and Panfili, 2000;Pajuelo et al., 2006). However, in most cases, population samplingwhen assessing age and growth is based on commercial catches andonly the growth function of Von Bertalanffy (VBGF) is fitted to theageelengthdata to infer growthparameters. This generates biases inthe estimation of population growth parameters, mainly because

L. Mercier et al. / Estuarine, Coastal and Shelf Science 92 (2011) 534e545 535

juveniles are often included in the sample although VBGF badlydescribes young fish growth (Gamito, 1998; Charnov, 2008).Improved fish growth modelling is thus urgently needed to produceaccurate growth curves that encompass the shape for growth at alllife stages. In particular, confident assessment of early fish growth,based on appropriate models for young stages, is of primaryimportance, not only for fisheries management strategies(Katsanevakis, 2006) but also in an ecological perspective (Dioufet al., 2009). Fish lifetime migrations between habitats, forexample, can be assessed by combining growth measurements andmicrochemical analysis on the otoliths (Babaluk et al., 1997;Campana et al., 1999; Fodrie and Herzka, 2008). However, thisnecessitates precise timetables of otolith growth, both at the annualand seasonal scale, in order to correlate the position of the areaanalysed in theotolith to a given calendardate and its environmentalcharacteristics (Campana, 1999; Campana and Thorrold, 2001).

In the present work, we compared the accuracy in ageelengthprediction of various growth models (including the traditionalVBGF) for different life stages of fish, using comprehensive annualdata gathered from juveniles and adults of one of the most valuableMediterranean fish species, the gilthead seabream Sparus aurata (L.,1758). Despite the high commercial value of S. aurata, manyfundamental aspects of its biology are still poorly known. Previouswork on the species mainly focused on aquaculture production (e.g.Gordin and Zohar, 1978; Kentouri et al., 1994; Bruslé-Sicard andFourcault, 1997), and studies on wild populations are still scarce(Arias, 1980; Kraljevic et al., 1998; Chaoui et al., 2006; Mehanna,2007). As for most exploited fish, most growth studies in thespecies were based on data from commercial landings (e.g.Lasserre, 1974; Arias, 1976; Kraljevic and Dulcic, 1997), and oftenincluded age class 0 fish (Bentuvia, 1979; Emre et al., 2009) for

Fig. 1. Map of the sampling area for Sparus aurata. All the adults were caught within the fishcollected within the Mauguio lagoon.

which the application of VBGF was shown to be inadequate(Gamito,1998). In the present study, a comprehensive set of growthmodels was tested in addition to VBGF and the best model choicewas made objectively for each life stage using an informationtheory approach (Burnham and Anderson, 2002). This modernapproach, based on the likelihood theory and widely used acrossbiological fields of research (Johnson and Omland, 2004), is anemerging tool for mathematical expression of the mean populationgrowth in fish (Katsanevakis and Maravelias, 2008). When the datasupport more than a single model, it allows inference of robustgrowth curves by averaging inside the confident set of models(Diouf et al., 2009). This should allow re-assessment of growthparameters for both S. aurata juveniles and adults with adequatemodels and accurate estimations of the growth potential of thespecies in aquaculture and in the wild. This is especially needed,both at the local scale and over the whole repartition area of thespecies (Lasserre and Labourg, 1974), especially in the context ofglobal change, now that it has been reported as potentially invasivein places where it is exotic (Balart et al., 2009).

2. Materials and methods

2.1. Fish sampling

The 315 juveniles and adults of Sparus aurata used in the presentstudy were collected on amonthly basis between January 2008 andJanuary 2009, in the Gulf of Lions (France, NW Mediterranean Sea,Fig. 1). In the area, S. aurata spawns at sea in the winter (Audouin,1962) but colonizes coastal lagoons, mainly from March to October(Lasserre and Labourg, 1974). This lagoon use is facultative for theadults but seems to be the rule for the juveniles, at least during

ing area of the fish auction market of Sète (dotted line) while age class 0 juveniles were

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their first year of life. The legal minimum catch size is 20 cm TL inthe area (Crespi, 2002). Therefore, while all the S. aurata individualsabove 20 cm were collected all year round from the fish auctionmarket in Sète (Fig. 1), smaller fish were caught only between Apriland December 2008 in the Mauguio lagoon, one of their mainnursery sites in the area (Quignard et al., 1983). Fish captureinvolved demersal trawls and fishing lines at sea, and capéchades(traditional Mediterranean fishing nets) and beach seines in thelagoons. All the fish collected were measured (total length TL, inmm), weighted (W in g) and sexed on the day of capture, as“juvenile”, when no gonad was detectable from visual observation,and as “male”, “female”, “intersexual” or “undetermined” other-wise. They were then stored in the freezer until otolith extraction.

2.2. Otolith reading

For each fish, both sagittal otoliths were removed, but only theleft sagitta was used for age estimation. As annual growth markswere poorly visible on the whole otolith, all sagittae wereembedded in Epoxy resin (Araldite, 2020) and transverse thinsections (500 mm) including the otolith core were made usinga precision low speed saw (Buehler, Isomet 1000). Sections weremounted on microscope slides using epoxy resin and polished toexpose the nucleus. Following current protocols (Panfili et al.,2002), all sections were etched with EDTA 5% during 2 mn 30 sand subsequently stained with Toluidine Blue during 2 mn in orderto increase the contrast between translucent and opaque growthbands and improve otolith reading. Each otolith section wasexamined under a stereomicroscope (Olympus SZX12) at 10e30�magnifications with reflected light and photographed andmeasured with a Computer-Assisted Age and Growth Estimation(CAAGE) system, consisting in a stereomicroscope (OlympusSZX12) linked to a camera (C5 Jenoptik) connected to a PC imageanalysis system (ProgRes� CapturePro 2.5, Jenoptik). For age esti-mation, annual growth bands were identified and counted twice bytwo different readers. If there was any discrepancy, a third obser-vation was carried out to reach a final decision. When the threereadings differed, the otolith was rejected from the analyses.

For each fish, individual agewas calculated by adding the annualfraction between the capture date and the theoretical birth date tothe number of complete annual growth bands identified in theotolith, following Gordoa and Moli (1997). As S. aurata spawns inNovembereFebruary in the Gulf of Lions (Lasserre, 1974), January1st was used as the theoretical date of birth for all fish. In order toprecisely assess the timing for annual mark (opaque growth band)formation in all age classes, monthly percentages of otoliths withopaque and translucent margins were calculated based on allotolith readings. To ascertain this measure, average marginalincrement widths were also assessed monthly for all age classesabove 1 year. For this, the marginal increment was defined as thedistance from the last opaque zone to the otolith edge and it wasmeasured to the nearest mm on the dorsal radius of each otolithsection (Fig. 2). Measurements of the distances (in mm) from thecore to each opaque zone on the dorsal radius also allowed esti-mation of growth for each age class.

2.3. Growth modelling

All statistical analyses were carried out using R software (RDevelopment Core Team, 2009). The growth of Sparus aurata wasassessed based on the age-at-length data derived from otolithobservation and fishmeasurement. All the individual data gatheredwere used to generate 3 datasets: the “whole population” dataset(N ¼ 315), the “group 0 juveniles” dataset (including the 173juveniles of the year collected in the lagoon, with TL � 21 cm) and

the “commercial landings” dataset (including the 142 remainingindividuals, between 1 and 6 years of age, mainly collected from theauction market, and with TL between 15 and 50 cm). Six differentgrowth models were fitted to these 3 datasets (Table 1). Amongthem, the traditional Von Bertalanffy growth function (VBGF) is themost studied and commonly applied model among all the growthmodels. However, the Gompertz model (GM) has been shown tobetter describe absolute growth for many aquatic species(Katsanevakis, 2006). These two models both assume asymptoticgrowth. However, many fish and other aquatic organisms seem notto grow asymptotically (e.g. Rafail, 1971), and non-asymptoticmodels such as the Power function (PF) and the Tanaka model (TM)(Tanaka, 1982) have been proposed in these cases. The Persistencemodel (PM) and the Extended Power model (EPM) are non-asymptotic quasi-sigmoid models recently developed for the studyof species area-relationships (Tjorve, 2009). They both tendtowards the power function (PF) when age becomes large, whilethe TM is a quasi-sigmoid function with non-asymptotic limits(Tanaka, 1982). Their inclusion within the set of models testedtherefore allowed encompassing most of the likely shapes for fishgrowth.

All models were fitted using the Gauss-Newton algorithm fornon-linear regression, with residual sum of squares (RSS) as a crite-rion. Under the assumptions of residual normality and homosce-dasticity (previously verified with Lilliefors test), RSS was directlylinked to the likelihood (Burnham and Anderson, 2002). Forcomparison with past studies, the growth parameters associated tothe VBGF (LN, K and t0) were calculated for all datasets and overallgrowth performance V0 was estimated in each case following theformula (Munro and Pauly, 1983; Pauly and Munro, 1984):

F0 ¼ logðKÞ þ 2logðLNÞ:The comparison of the models was performed within an infor-

mation theory approach based on the likelihood theory (Burnhamand Anderson, 2002). For each dataset, R2 was calculated toassess the percentage of variance in fish length explained by age.However, because R2 is generally not consistent for model selectionwithin the non-linear regression context, Akaike InformationCriterions (AIC) were computed, following:

AIC ¼ n�log

�RSSn

��þ 2k

where RSS is the residual sum of squares, n the number of obser-vations and k the number of estimable parameters.

Differences between the AIC for each model and the minimumAIC obtained over the k models tested (DAIC) were calculated tocompare between models, with only DAIC variations superior to 2being considered significant following Burnham and Anderson(2002). The AIC is a very efficient tool for selection betweencompeting models (Katsanevakis, 2006) that takes into account notonly the statistical goodness-of-fit of each model, but also thenumber of parameters that have to be estimated to achieve thisparticular degree of fit. Because AIC imposes a penalty forincreasing the number of parameters, the lowest value of the indexindicates the preferred model, that is, the one with the fewestparameters that still provides an adequate fit to the data. However,AIC is a relative measure and it would be arbitrary to assign a limitAIC value, above which a given model has to be “rejected”. Toovercome this problem, AIC weights were calculated for eachmodel, following the formula (Burnham and Anderson, 2002):

wi ¼expð�0:5DiÞX5

k¼1ðexpð�0:5DkÞÞ

Table 1Characteristics of the 6 models used for ageelength relationship determination.

Model Number of parameters Shape Asymptotic?

Power function (PF)f ðxÞ ¼ a� xb

2 Convex upward No

Von Bertalanffy growth function (VBGF)f ðxÞ ¼ LNð1� expð�Kðx� t0ÞÞÞ

3 Convex upward Yes

Gompertz model (GM)f ðxÞ ¼ a� expð�bcxÞ

3 Sigmoidal Yes

Extended power model (EPM)

f ðxÞ ¼ a� xb�

cx

3 Quasi-sigmoidal No (tends towards PF)

Persistence model (PM)

f ðxÞ ¼ a� xb�expð

�cx

Þ

3 Quasi-sigmoidal No (tends towards PF)

Tanaka model (TM)

f ðxÞ ¼ 1ffiffif

p ln ð2fðx� cÞ þ 2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifaþ f2ðx� cÞ2

qÞ þ d

4 Quasi-sigmoidal No

Fig. 2. Dorsal face of the stained otolith transversal sections in 2 S. aurata individuals caught in (a) February (age 2, opaque margin) and (b) August (age 2, translucent margin). Ineach case, the black arrows indicate the opaque zones present in the otolith. The radius used for growth mark measurement is shown in white.

L. Mercier et al. / Estuarine, Coastal and Shelf Science 92 (2011) 534e545 537

Table 2Ageelength key for the gilthead seabream in the Gulf of Lions based on otolithreading.

Size TL (cm) Age class

0 1 2 3 4 5 6 Total

012 31 313 9 94 19 195 14 146 8 87 7 78 4 4

L. Mercier et al. / Estuarine, Coastal and Shelf Science 92 (2011) 534e545538

where ΔAICi ¼ AICi � AICmin, i.e. the difference between the AIC ofeach model i and the minimum AIC obtained over the k modelstested.

The AIC weight (w) of a model represents its relative likelihoodto be the best of a defined set of alternative models to reflect thedata (Burnham and Anderson, 2002). Therefore, for a given dataset,only when a model had a w above 0.9 it was judged the onlyaccurate indication for growth estimation in this particular dataset.When the data supported more than a single model (i.e. all wi wereunder 0.9), Multi-Model-Inference through model averaging (MMI)was used to infer growth curves robust to the underlying growthprocesses. For this a linear combination of all the confident modelsweighted by their w was constructed following the formula:

TLsðAÞ ¼X6k¼1

wi � TLiðAÞ

where TLs(A) is the synthetic function giving the total length of thefish from age, k is the number of confident model(s) included in theMMI and TLi(A) the total length of the fish function of the agecalculated according to a single model.

For each dataset, the growth rate in length, averaged across thederivatives of the final selected model with respect to time(Campana and Jones, 1992), was then investigated across the agerange to emphasize the possible differences in growth estimationlinked to spurious arbitrary model choice.

9 4 410 5 511 5 512 5 513 9 914 11 1115 3 1 416 6 617 7 718 8 4 1219 12 9 2120 5 7 1221 1 122 1 123 6 2 824 8 4 1225 13 12 2526 3 5 827 1 8 1 1028 1 8 1 1029 2 6 4 1230 6 4 1031 3 1 432 2 2 1 533 1 3 1 5

3. Results

The 315 individuals of Sparus aurata used for the present workwere between 0 and 6 years old (Table 2). Their lengths andweightsranged from 23 to 508mm and 0.15 to 2000.00 g, respectively, witha positive allometry between these two growth parameters(W ¼ 0.0105 � TL3.081, R2 ¼ 0.99; b ¼ 3.081, 95% confidence interval[3.039, 3.123]). Most of the individuals were smaller than 20 cm(57.2%) and younger than 3 years (90.7%), with 54.9% individualsbelonging to age classes 0 (Table 2). Sex could not be determined for51 individuals, mainly due to conservation conditions. Out of the264 remaining fish, 73.1% were juveniles, 12.5% males, 8.0% inter-sexual and 6.4% females (Fig. 3). Maximum total length (TL) was252 mm for the juveniles but males measured between 235 and332 mm. Similarly, although the smallest female measured291 mm, both gonad types (male and female) were found in indi-viduals between 273 and 430 mm TL. These results suggested that50% (male) maturity in the Gulf of Lions is reached at 240 mm TL(Fig. 3).

34 1 135 1 1 236 1 2 33738 1 139 1 1404142 1 143444546 1 147484950 1 151Total 173 56 57 20 3 4 2 315Percent 54.92 17.78 18.1 6.35 0.95 1.27 0.63Mean size 9.9 23.2 28.0 31.5 33.7 39.2 46.8s.d. 6.1 3.1 2.9 2.4 1.4 6.0

3.1. Otolith growth patterns

Three otoliths were discarded because of unreadable growthmarks. Analysis of the 312 remaining otoliths allowed assessmentof the timing for seasonal growth mark formation, age reading andmeasurement of the width of annual increments. Staining revealedotolith annual increments to be composed of a narrow chromo-philic opaque zone, and a wider translucent zone punctuated witha few thin chromophilic marks, irrespective of fish age (Fig. 2).

Opaque margins were observed for more than 75% of the indi-viduals analysed from November to March, with a maximum of100% in February (Fig. 4). Translucent margins were mainlyobserved from April to October, with a maximum occurrence(100%) in July and August. Opaque (chromophilic) bands weretherefore considered to be deposited once a year, fromNovember toMarch. Monthly means of marginal increment widths for ageclasses 1 and 2 confirmed this result. For both age classes, the

sinusoidal pattern obtained exhibited a period of 1 year witha mode in DecembereJanuary (Fig. 4). Although sample size forolder fish did not allow measurement of marginal increment widththroughout the year, observations for these age classesmatched thepattern observed for younger fish.

Annual increment width decreased in as the fish grew, from1559 mm � 134 mm to 135 mm � 12 mm on average for age class0 and age class 6, respectively (Fig. 5). The highest annual decrease(74%) was observed between the first and the second year of life.Following annual decreases were less pronounced, around 30e35%,between year 2 and 5, and negligible between year 5 and 6.

Fig. 3. Length frequency distribution in the S. aurata individuals sampled in the Gulf of Lions.

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3.2. Growth modelling

Although all the R2 calculated were above 0.79, reflectinga reasonable fit to data for all the models, accuracy in ageelengthprediction varied highly according to the model and the dataset(Table 3). For the “whole population” dataset, R2 values werebetween 0.86 and 0.96 irrespective of the model. VBGF (R2 ¼ 0.93)provided estimations of 32.54 cm and 1.279 yr�1 for LN and K,respectively (Table 4). The calculated growth performance indexwas V0 ¼ 7.211. However, model comparisons showed that the TM(parameters: a ¼ 6.57 $ 10�4, c ¼ 0.448, f ¼ 0.0191, d ¼ 4.314;AIC ¼ 499.9; w > 0.99) can clearly be considered as best for growthprediction with this dataset. All other models had w inferior to1 �10�3, with worst accuracies in growth prediction for the Power(DAIC ¼ 353) and the Gompertz (DAIC ¼ 213) models.

Similarly, although R2 were high for all models (0.79e0.96), onlythe TM (parameters: a ¼ 4.035 $ 10�4, c ¼ 0.518, f ¼ 0.0513,d ¼ 3.053; w > 0.99; AIC ¼ 208.9) was considered best for growthprediction with the “group 0 juveniles” dataset. All other modelshad w < 1 � 10�3. Poorer accuracies in growth prediction werefound for the Power model (DAIC ¼ 393) and VBGF (DAIC ¼ 57), thelater providing to estimates of 26.05 cm, 2.115 yr�1, and 7.269 forLN, K and V0, respectively, based on this dataset (Table 4).

When fitted on the “commercial landings” dataset, VBGF(AIC ¼ 234.8, w ¼ 0.16) provided estimates of 72.3 cm, 0.108 yr�1

and 6.343 for LN, K and V0 (Table 4). The TM failed to converge forthis dataset, even when using other available algorithms for

regression (e.g. that of Marquardt). Among the five remaininggrowth models, the R2 range was very narrow (0.81e0.82). Thelowest AIC (233.4) and the highest w (0.34) were obtained for thePersistence Model (Table 3). However, as now reached 0.9, a multi-model inference (MMI) was carried out, the respective weights inthe building of the synthetic model being 33.9, 23.0, 21.3,16.7 and4.8% for the Persistence, the Extended Power, the Power, the VBGFand the Gompertz models, respectively.

The best model for mean population growth expression there-fore depended on the dataset (Fig. 6). Among the six models tested,the TM clearly performed best for the “group 0 juveniles” and the“whole population” datasets, but only multi-model inference basedon the five other models gave robust growth curves for the“commercial landings” dataset.

The juvenile and adult growth rates estimated with these 3models were different (Fig. 7). For group 0 juveniles, growth rateincreased during the first six months of life, and decreased there-after irrespective of the estimation. However, maximum growthrate and the timing of the peaking growth depended on the datasetused to fit the TM. They were of 49.8 cm yr�1 at 0.52 year when theTMwas fitted on juvenile data only and of 38.9 cm yr�1 at 0.45 yearwhen using the whole dataset. As a result, estimated mean annualgrowth rates for the first year varied between 21.33 and24.68 cm yr�1 depending on the model retained. In the adults, thegrowth rate showed a continuous decrease between year 2 and 8,irrespective of the model. However, annual growth rates predic-tions were higher for the MMI fitted on the “commercial landings”

Fig. 4. Monthly percentages of otoliths with opaque margins (dark grey bars) and monthly means for marginal increment width in age class 1 (dotted line) and age class 2 (plainline) individuals of S. aurata. Light grey bars give the monthly percentages of otoliths with translucent margins. The value above each bar indicates the number of fish used eachmonth for otolith margin observation.

L. Mercier et al. / Estuarine, Coastal and Shelf Science 92 (2011) 534e545540

dataset than for the TM fitted for the “whole population” dataset,with mean annual growth rates of 2.70 and 1.03 cm yr�1 for year 8,respectively.

4. Discussion

Optimal sampling design for growth and life history descriptionin wild fish populations includes fish from all size classes, capturedin all their potential habitats. In the Gulf of Lions, lagoon use isfacultative for the adults of Sparus aurata, which mostly remain atsea, but seems necessary for the juveniles, at least during their firstyear of life (Lasserre and Labourg, 1974). In the present study, thevast majority of the individuals caught in the lagoon (> 95%) were<20 cm in LT and corresponded to the juvenile part of the pop-ulation traditionally ignored by commercial fishing (Crespi, 2002).All the others (N ¼ 8), with ages between 1 and 3 and TLs between21 and 33 cm, were included in the “commercial landings” dataset.Therefore, we are confident that the fish samples used for estima-tion of juvenile and adult growth reflected natural habitat use bythe species in the area.

However, as more than half of the individual analysed in thepresent study belonged to age class 0, the estimates of growthparameters and life history traits obtained must be taken withcaution. Similar biases towards young individuals were observed inmost of the samples used so far to describe growth and biology in

S. aurata, both in the Gulf of Lions (Lasserre, 1974) and in otherlocations (Arias, 1976; Emre et al., 2009), which underlines thedifficulty to gather evenly-distributed length frequency data in thisspecies, even through scientific sampling. In our case, this biastoward the young stages is partly explained by differences injuvenile and adult fish vulnerability to the fishing gears used in thelagoons and at sea. Hence, although the species is one of the maintargets of the local fisheries in the Gulf of Lions, its importance inthe catches at sea is low (Farrugio and Le Corre, 1986), while itsjuveniles are abundant in lagoon landings, especially in the Springand the Autumn,when they enter and exit the lagoons and aremorevulnerable to fishing (Quignard et al., 1983). The lengthefrequencydistribution obtained here is corroborated by standardized scien-tific sampling conducted on S. aurata in the area, with 70% of theindividuals of the population reported to be juveniles (Farrugio andLe Corre, 1986). Therefore, we are confident that our sample isrepresentative of the local population of the species in the area andthat the results we obtained are comparable with those from mostprevious studies estimating growth and population parameters inS. aurata (for instance Lasserre, 1974; Emre et al., 2009).

4.1. Otolith growth patterns and life history traits

The present study validates the seasonal timing for otolithgrowth increment deposit in Sparus aurata, and its use for

Fig. 5. Otolith radius (grey circles) and mean (�SD) annual increment width per age class (black squares) for the S. aurata individuals sampled in the Gulf of Lions.

L. Mercier et al. / Estuarine, Coastal and Shelf Science 92 (2011) 534e545 541

accurate age estimation in the Gulf of Lions. Otolith edge obser-vation and marginal increments measure both indicated thatopaque zone formation in this area occurs yearly betweenNovember and March, i.e. in the winter, the translucent zonebeing deposited between April and October. S. aurata is known tobe very sensitive to low temperatures (Ibarz et al., 2007). Winteris a period of gametogenesis for specimens above 2 years (Arias,1976, 1980) and the species is thought to stop feeding in thewinter, which results in physiological changes and an importantweight loss during this period (Audouin, 1962). Growth patterns

Table 3Comparison of the 6 models fitted on different parts of the ageelength dataset in S. auraAkaike criterion (AIC) and AIC weight (w) are given, with, in bold, the values obtained foreach model and the minimum AIC obtained over the k models tested.

Dataset Model

Power VBGF

Juveniles R2 0.799 0.952RSS 2966.52 703.30AIC 601.86 265.61DAIC 392.96 56.71w <1e-3 <1e-3

Commercial catches R2 0.813 0.815RSS 715.25 707.54AIC 234.34 234.82DAIC 0.93 1.41w 0.213 0.167

Total R2 0.864 0.931RSS 4631.10 2337.96AIC 852.71 639.40DAIC 352.79 139.48w <1e-3 <1e-3

on S. aurata scales from the Gulf of Lions suggested that winter isa period of low growth for all age classes (Lasserre and Labourg,1974; Arias, 1976, 1980). The intra-annual variations of growthrate we observed in the group 0 juveniles (Fig. 7) confirm thisresult. Opaque zone formation in S. aurata thus seems to corre-spond to slow growth in the winter, as already shown for otherMediterranean sparids (Goncalves et al., 2003; Pallaoro et al.,2008; Abecasis et al., 2008).

Our derivation of mean annual growth rate for the first yearsuggests particularly favourable growth conditions for group

ta from the Gulf of Lions. For each dataset, model R2, Residual sum of squares (RSS),models with w > 0.9. DAIC in each case stands for the difference between the AIC for

Gompertz Tanaka EPM PM

0.960 0.963 0.959 0.959594.40 547.84 596.52 604.10226.07 208.90 226.91 229.8717.17 0 18.01 20.97<1e-3 >0.999 <1e-3 <1e-3

0.812 e 0.820 0.817720.26 e 704.21 700.44237.32 e 234.16 233.413.91 e 0.75 00.048 e 0.230 0.339

0.913 0.956 0.952 0.9432952.89 1492.00 1626.70 1937.79712.96 499.92 525.15 580.27213.04 0 25.23 80.35<1e-3 >0.999 <1e-3 <1e-3

Table 4Von Bertalanffy growth parameters (LN, K, t0), overall growth performance F0 and parameter of the weightelength relationship (a,b) obtained for Sparus aurata in differentlocalities adapted from Chaoui et al., 2006.

Locality Area Age N a b Linfinity K t0 F’ Study

Gulf of Lions (France) Gulf of Lions 1e6 142 0.0093 3.113 72.30 0.108 �2.208 6.343 This studyGulf of Lions (France) Gulf of Lions 0e6 315 0.0105 3.081 32.54 1.279 0.233 7.211 This studyThau lagoon (France) Gulf of Lions 1e4 713 0.0226 2.886 62.02 0.221 �0.774 6.745 Lasserre and Labourg, 1974Thau lagoon (France) Gulf of Lions 1e4 383 0.0121 3.064 57.66 0.272 �0.541 6.807 Lasserre, 1976Mar Menor (Spain) W Mediterranean 2e6 135 0.0289 2.907 53.00 0.315 e 6.785 Arnal et al., 1976Ebro estuary (Spain) NW Mediterranean 1e7 611 0.0112 3.055 62.19 0.171 �0.531 6.494 Suau and Lopez, 1976Mirna estuary (Croatia) N Mediterranean 1e12 314 0.0112 3.052 59.76 0.153 �1.711 6.303 Kraljevic and Dulcic, 1997Eastern Adriatic N Mediterranean 1e22 462 0.0101 3.087 84.98 0.073 �2.823 6.268 Kraljevic et al., 1998Mellah lagoon (Algeria) SW Mediterranean 1e7 370 0.0129 3.067 55.33 0.513 �0.282 7.359 Chaoui et al., 2006Beymelek lagoon (Turkey) E Mediterranean 0e4 1881 0.0174 2.977 44.60 0.394 �1.331 6.664 Emre et al., 2009Port Said coast (Egypt) SE Mediterranean 0e4 1714 0.0123 3.028 37.98 0.500 �0.600 2.860 Mehanna, 2007Arcachon Bay (France) NE Atlantic 1e4 126 0.0144 3.075 42.29 0.456 �0.451 6.704 Lasserre and Labourg, 1974Arcachon Bay (France) NE Atlantic 2e5 94 0.0541 2.618 53.48 0.264 �1.340 6.627 Lasserre, 1976Bay of Biscay (France) NE Atlantic 2e5 79 0.0575 2.590 56.17 0.265 �0.409 6.729 Lasserre, 1976Cadiz estuaries (Spain) NE Atlantic 1e7 1775 0.0071 3.120 84.55 0.130 �1.586 6.834 Arias, 1980

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0 juveniles in the Mauguio lagoon, with a predicted size of 24.7 cmat the end of the first year of life, comparable to that for SWMediterranean lagoons (25.5 cm, Chaoui et al., 2006). Because thisvalue is slightly higher than the average size observed for age 1 fishin our population sample (TL ¼ 23.2 cm), it is likely that lessfavourable growth conditions are encountered in other lagoonnursery areas or at sea, as already suggested by Audouin (1962) andLasserre (1974). The positive allometry found between the lengthand the weight of S. aurata in the present work contrasts with someof the previous findings for the species, including in the Gulf ofLions (Lasserre and Labourg, 1974; Lasserre, 1976) (Table 4).However, this result is expected since the value of the growthexponent (b) and, therefore, the nature of the isometric relation-ship change with respect to environmental conditions, food avail-ability, and many physiological factors such as sex, length, age andgonad maturity state (Ricker, 1975). Differences in the habitatssampled and in the proportion of juveniles or spent adults in thelandings can be responsible for the higher value of b obtained in ourcase, when compared to previous studies from the same area(Lasserre and Labourg, 1974; Lasserre, 1976).

As in most fishes, growth in S. aurata is maximal during the firstyear of life and decreases steadily with age, although otolith incre-ment widths provide evidence of occasional sharp declines ingrowth. Drastic reductions in otolith growth are associated tomajorphysiological changes in fish and can be used to infer life historytraits such as age atmaturity (Panfili et al., 2002). In theGulf of Lions,initial sexual maturity as a male is known to occur at the end of thesecond year of life for S. aurata, the sex inversion occurring after 1 or2 years as a male (Bruslé-Sicard and Fourcault, 1997). However, sexchange in the species cannot be related only to individual deter-minism and depends on the environment and social conditions(Happe and Zohar, 1988). The development of the female zone(secondary sex) is thus progressive and occurs each year during thepost-spawning period, females being increasingly numerous in thelarger size classes (Chaoui et al., 2006). The decrease in annualincrement widths observed in the present study, maximumbetween years 1 and 2, and nearly constant between years 4 and 5,agrees with the statement of the onset of male maturity during thesecondyear of life in the area, and suggests that sex change to femaleprogressively occurs during the third to fifth year of life. This isconsistent with the TL50 observed for sexual maturity (24 cm) in thepopulation sampled, although this size is slightly lower than thatpreviously reported for the area (27 cm, Crespi, 2002). Differences ingrowth rates explain the smaller size for sexualmaturity observed inthe present study when compared to the SW Mediterranean(32.6 cm, Chaoui et al., 2006) as both sizes correspond to the second

half of the second year of life. Similarly, all S. aurata specimens werefemales when above 43 cm in our sample, against 56 cm in the SWMediterranean (Chaoui et al., 2006), which corresponds in bothcases to an age of minimum 6 years. Interestingly, otolith incrementsizes were very similar for the fifth (124 mm) and the sixth year(135 mm), suggesting a slow but steady growth for old fish. As stip-ulated by the Big Old Fat Fecund Female Fish hypothesis (BOFFFFhypothesis, Morita et al., 1999), this might greatly contribute to themaintenance of local populations of S. aurata, as large femalesproduce more eggs with higher survival rates (Longhurst, 2002).

4.2. Growth models

Most of the previous attempts in growth modelling for wildSparus aurata used length frequency datasets from commerciallandings and VBGF to infer population growth parameters (Table 4).Among them, some included group 0 juveniles into the dataset. Asalready suggested by Gamito (1998), this may lead to spuriousparameter determination because the shapes of juvenile and adultgrowths differ in the species, mainly because the energy invest-ment in body growth is lowered during gametogenesis. This isconfirmed by our results. Among the 6 models tested, the Tanakamodel best fitted the data for the whole population. However,although its overall accuracy in growth prediction was acceptablefor this 0e6 years dataset (w > 0.9), residuals heteroscedasticity(p ¼ 0.02, Pearson’s correlation test) indicated that the high valuesof R2 and w for this model were driven by the young individuals,with an important lack of fit for the oldest fish (Fig. 6). Therefore, allthe models tested failed to accurately describe the growth ofS. aurata over all its life stages. Even if expected, this result confirmsthat no single equation could correctly describe the whole growthof a fish, and it is advisable to separate juveniles and adults whenassessing growth parameters (Quince et al., 2008a,b; Alos et al.,2010). In our case, it consists in separating group 0 juveniles fromolder fish since gonad development in S. aurata occurs during thesecond year of life (Kraljevic and Dulcic, 1997). Our procedure is lesssubtle than previous ones used on similar species (Alos et al., 2010)because the separation between the two groups is arbitrary.However, the accurate description of growth in this species withthe approach chosen by Alos et al. (2010) would have necessitatedthe creation of another model with at least 6 more parameters thanthe original VBGF, which would have been inadequate for AICestimation. By inferring between several models with a diversity ofshapes likely to cover all the patterns to be expected for growth,this study was able to provide an accurate method for inferringlength-at-age in juvenile and adult S. aurata in the Gulf of Lions, and

Fig. 6. Best models for growth prediction of S. aurata in the Gulf of Lions. Grey circles: individual ageelength data used for model fit. Dotted line: Tanaka model fitted on the “wholepopulation” dataset, plain lines: Tanaka model fitted on the “age 0 juveniles” dataset, multi-model inference (MMI) for the “commercial landings” dataset. The shaded areacorresponds to age class 0.

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to identify the shape in juvenile growth for this fish, which is verydifferent of a VBGF curve.

Juvenile growth was best described by the Tanaka model (TM,Fig. 6), probably because the quasi-sigmoid shape with no asymp-totic limits of this function allows it to precisely mimic the varia-tions of growth rate observed during this period of life in S. aurata(Bilgin et al., 2004). Hence, the high water temperature and foodavailability in the lagoons in the late spring and the summer(Audouin, 1962) result in a very fast growth (>2.5 cm per month,Fig. 7) from June to August. The monthly gain in size slows at thebeginning of the autumn (<1.6 cm per month, Fig. 7), probablybecause feeding is more dedicated to the accumulation of reservesbefore the fasting winter period (Lasserre and Labourg,1974), whengrowth rate is minimum (0.6e0.8 cm per month, Fig. 7).

Although similar seasonal feeding patterns have been reportedin the adults (Chaoui et al., 2005), intra-annual variations in growthrate are less marked for this life stage (Figs. 6 and 7), probablybecause of energy allocation to gametogenesis reduces the gain insize in the summer. For this dataset, the TM never converged andonly multi-model inference, mainly based (34%) on the Persistencemodel, allowed producing a robust curve for growth description.The persistence model is a derivative of the Power Functiondesigned to predict variations of growth according to the scale ofobservation (Tjorve, 2009). As age increases, this model asymp-totically approaches the Power Function, as does the ExtendedPower Model. This explains the non-negligible weights (>20%) ofthese two last models in the MMI. Since there is no horizontalasymptote for these 3 models, their importance in the MMIsuggests that the plateau in growth expected for old fish is notreached in our sample. Increasing the number of old fish and

including specimens over 6 years in the dataset could constrain thegrowth model and ameliorate inference of growth parameters forS. aurata in the area. Hence, the estimate for LN (72 cm) obtainedwith VBGF on the “commercial landings” dataset in the presentwork is larger than those found in many other studies (Table 4),especially those from the same area (Lasserre, 1974; Lasserre andLabourg, 1974). Yet, it is inferior to the maximum size recordedfor the species in the Gulf of Lions (TL ¼ 77 cm, A. M. Darnaude andL. Mercier, in prep.) or elsewhere in the Mediterranean (Bauchotand Hureau, 1986; Kraljevic et al., 1998), suggesting that VBGFinferences failed to accurately describe adult growth in manyS. aurata populations, including this one. This might be due to thelack of old fish in the data since the only estimate of LN for thespecies above 77 cm TL was obtained with a comprehensive sampleof fish older than 12 years (Kraljevic et al., 1998). However, it is alsolikely that, for many studies, it resulted from the inclusion of group0 juveniles in the data. The inappropriateness of VBGF for growthdescription in the youngest fish, suggested by various authors (e.g.Charnov, 2008; Alos et al., 2010), is confirmed by our results. WhenVBGF is fitted to the “whole population” dataset, including thegroup 0 juveniles, the parameters obtained are irrelevant, witha higher K and a far lower LN than those predicted based on theadult dataset only (Table 4). This trend could partly explain thelarge discrepancies in growth parameters estimates observedamong areas for S. aurata, raising doubts of the relevance of growthparameters comparisons between areas when the age range of thesample differs among them, as suggested in other fish species byKatsanevakis and Maravelias (2008).

These results clearly demonstrate that VBGF is not the mostadequate model for growth description in Sparus aurata and may

Fig. 7. Growth rate calculated from models with the lowest RSS. Dotted line: Tanaka model for the whole dataset, plain lines: Tanaka model for age class 0 individuals, multi-modelinference (MMI) for individuals from commercial catches. The shaded area corresponds to age class 0.

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lead to wrong evaluations of growth parameters, potentially preju-dicial to the sustainable management of its fisheries. Hence, K andLN, both commonly derived from the fit of VBGF to the age-lengthdata, are used to definefishery strategies, as theyare directly used toinfer the sustainable yield of a fish stock (Beddington and Kirkwood,2005). If K has been overestimated and LN underestimated in thepast for some populations, including that of the Gulf of Lions, thenthe sustainable yield is lower than previously thought. This mightexplain the recent decrease in the landings of S. aurata in theMediterranean (FAO, 2010), by a recurrent overexploitation of thestock due to spurious estimations of growth parameters in the past.If this hypothesis is confirmed, then a retrospective analysis of thedata with appropriate growth models providing accurate estimatesof K and LN is urgently needed to take management strategies andensure the sustainability of S. aurata fisheries.

5. Conclusions

The results obtained here for Sparus aurata improve ourknowledge on the biology and the life history traits of this speciesand contribute to a better growth modelling for both fishery andecological science based on otolith interpretation. Exhaustivemonthly sampling of the juveniles and adults of the species allowedaccurate description of its otolith growth patterns in the Gulf ofLions. Comparison of the fits for various models on the lengtheagekeys derived from these data allowed improvement of growthdescription for both juveniles and adults. The results provideevidence that growth analysis based on non-exhaustive samplingand VBGF must be taken carefully since the use of different partsof the population dataset provides different values for growthparameters.

Growth model comparison reveals that the sampling and thechoice of the growth model are especially important in theassessment of growth parameters of a fish stock, and thus itsviability. Juvenile removal from the dataset is essential for accurateestimates of LN and K. Nevertheless, when the proportion of oldindividuals in the sample is limited, asymptotic models fail tocorrectly describe adult growth. When sampling towards older fishcannot be achieved, multi-model inference based on a compre-hensive set of models that encompass various shapes for growth isto be preferred to correctly describe growth in wild populations.This robust methodology allows for an objective re-assessment ofthe spatio-temporal variations of growth in S. aurata both at thelocal scale and over its whole distribution area, which shouldimprove management strategies for this highly valuable species.

Acknowledgements

This work was funded by the French National Research Agency(ANR) through the young scientist research program LAGUNEX (07-JCJC-0135). Authors would like to thank local fishermen for theirhelp with sampling and François Guilhaumon (UMR 5119 ECOLAG,Université Montpellier 2) for advice on the multi-model inference.

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