ICES CM 2011/H"Not be cited without prior reference to the author"

Exploring larvae recruitment variability of Peruvian anchovyand sardine with modeling and data assimilation

Olga Hernandez1, Inna Senina1, Patrick Lehodey1, Patricia Ayon3,Arnaud Bertrand2,3, Vincent Echevin2,4, Ramiro Castillo3, Philippe Gaspar1

1MEMMS (Marine Ecosystems Modeling and Monitoring by Satellites), CLS, France2IRD, UMR EME IFREMER/IRD/UM2, Avenue Jean Monnet, BP 171, 34203 Sète, France3Instituto del Mar del Peru, Esquina Gamarra y Gral. Valle sn, Apartado 22, Callao, Lima4IRD, LOCEAN, Université Pierre et Marie Curie, Boite, 4 Place Jussieu, 75252 Paris, France

A Spatial Eulerian Ecosystem and Population Dynamic Model (SEAPODYM) is used in a dataassimilation study aiming to estimate model parameters that describe spawning conditions anddynamics of anchoveta and sardine larvae in the Humboldt Current system (HCS) off Peru. Ini-tially developed for large pelagic fish (e.g., tuna), SEAPODYM was adapted for this study to smallpelagic species, and configured to a regional domain using the ROMS-PISCES coupled physical-biogeochemical model as an input. Environmental variables are used to define a spawning habitat.This habitat is critical since it controls the initial recruitment of larvae in the first cohort and subse-quent spatiotemporal variability of natural mortality during their drift with currents described by asystem of Eulerian equations. We conducted a series of optimization experiments using data of an-chovy and sardine larvae to estimate the parameters of the spawning habitat of both species. Differ-ent mechanisms proposed to control the fish larvae recruitment are explored: temperature, trade-offbetween presence/absence of prey and predators of larvae, retention or dispersion by currents.

Key-words: end-to-end model, SEAPODYM, anchoveta, sardine, upwelling ecosystem, parameteroptimization, population dynamics, spawning habitat

Contact author: O. Hernandez, MEMMS (Marine Ecosystems Modeling and Monitoring by Satel-lites), CLS, Space Oceanography Division, 8-10 rue Hermes, 31520 Ramonville, Franceemail: ohernandez@cls.fr

1 Introduction

The Humboldt Current system (HCS) off Peru and Chile is one of the most productive coastal up-welling system in the world and the most productive system in terms of fish biomass (Bakun andBroad, 2003; Chavez et al., 2008). This system is submitted to climate variability at seasonal, interan-nual and decadal time scales (Chavez et al., 2008). Peruvian anchovy (Engraulis ringens) and sardine(Sardinops sagax), with relatively short life span (around 4 years and 8 years respectively), fast grow-ing and time to maturity (one and two years respectively) are well adapted to this variability anddominate the HCS waters. Within the last decades, different periods dominated either by anchoviesor sardines occurred. The sardine population disappeared from the Peruvian coast after 1999 and didnot reappear since.

The Spatial Ecosystem And Populations Dynamics Model (SEAPODYM) has been adapted for thestudy of early life stages of anchovy in the Humboldt upwelling system (Hernandez et al., submit-ted). In this paper, we present the data assimilation approach developed for optimizing the modelparameters, using anchovy and sardine eggs and larvae data collected by IMARPE. Different mech-anisms proposed to control the fish larvae recruitment are explored: temperature, trade-off betweenpresence and absence of prey and predators of larvae, retention and dispersion by currents. After avalidation of the approach, the method is tested using a climatological series.

2 SEAPODYM spawning habitat and larval recruitment

Seapodym model has been developed initially for large pelagic species (i.e. tuna and tuna-likespecies) at basin-scale [Lehodey et al., 2008, 2010a]. We have adapted the model to study early lifestages of anchovy and sardines in the Humboldt upwelling system (Hernandez et al., submitted).The general scheme of the model for early life stages is presented in Fig. 1.

Figure 1: General scheme of the model with optimization approach

The main causes proposed to explain the variability in spawning success and larvae survival in-clude the combination of stock-recruitment relationship with more or less favorable environmentalconditions. Recruitment dependence on the spawning biomass is considered to be weak except atlow levels of parental biomass (Myers et al., 1999). Thus, we can expect that environmental variabil-ity explains a very large part of the fluctuations in the survival of anchovy larvae and the subsequentrecruitment of juveniles in the adult population rather than by densitydependent processes (Brochieret al., 2008). In this study, the stock-recruitment relationship was not included. We assume that adultsare present and distributed evenly within the spawning sites and hence that recruitment is propor-tional to the spawning habitat index (Hs).

The mechanisms included in SEAPODYM to control the larvae recruitment include:

1 - The temperature; the response is described using a Gaussian distribution f1(T ) = N(T ∗0 , σ0)with

standard deviation σ0 and optimal mean temperature T ∗0 .

2 - The match/mismatch (Cushing, 1975) between spawning and presence of prey for larvae; it issimulated by the Holling Type 2 functional response (Reynolds et al., 1959). Primary production (PP)is used as a proxy for the prey of larvae:

f2(PP ) =aPP

1 + ahPP=

PP1a + hPP

(1)

where a is the success rate, h the predator handling time per prey time, and PP is prey density. Fornumerical simplification, the second form of the equation is used with α = 1

a the steepness parameterand h as set to 1 .

3- The prey-predator tradeoff mechanisms (Lehodey et al., 2008), expressed as the product of theprevious function with a decreasing sigmoid function:

f3(PP, Pred) = f2(PP ) ∗ 1

1 + expb∗(Pred−c) (2)

or can be also written as a functional response of Holling type II:

f4(PP, Pred) =PP

Pred+0.11a + PP

Pred+0.1

(3)

4- The redistribution of larvae by currents leading to higher or lower mortality according to theretention in favorable habitat or the drift in unfavorable habitat (Parrish et al., 1981, Bakun, 1996),and that is included in the treatment of the spatial dynamics using a system of Advection-Diffusion-Reaction equations (for details see Lehodey et al., 2008 and Senina et al., 2008). The average mortalitycoefficient for anchovy larvae was set to 0.69 year−1 based on Cubillos et al. (2002).

Larvae transport by currents with associated mortality is computed for a time step of five daysafter spawning, i.e., roughly corresponding to the estimated mean age of larvae collected in a sizerange between 3 and 6 mm, and based on a length of hatching of 2 mm and a growth function (Mar-zloff et al., 2009).

Various mechanisms or combination of mechanisms to define the spawning habitat have beenexplored (Table 1) and the results compared taking into account the number of parameters.

Experiment Mechanism Function ParametersHS1 Temperature Hs = f1(T ) σ, THS2 Match-mismatch Hs = f2(PP ) σ

HS3 Temperature and Match-Mismatch Hs = f1(T ) ∗ f2(PP ) σ , T, αHS4 Prey-predator trade-off Hs = f4(PP, Pred) α

HS5 Temperature and Prey-predator trade-off Hs = f1(T ) ∗ f4(PP, Pred) σ , T, αHS6 Prey-predator trade-off Hs = f3(PP, Pred) α, b,cHS7 Temperature and Prey-predator trade-off Hs = f1(T ) ∗ f3(PP, Pred) σ , T, α, b,c

Table 1: Description of optimization experiments

3 Input Data

3.1 Anchovy and Sardine data

Since 1961, the Instituto del Mar del Peru (IMARPE) conducted regular research cruises to sampleanchovy/sardine eggs and larvae data. In 1983, IMARPE also started to monitor the adult biomassusing regular acoustic sampling cruises. We use climatologies produced using all available databetween 1961-2008 (159 cruises) for eggs and larvae collected with the Hensen net, characterized by0.33m2 mouth area and 300 µmmesh size. The net was towed vertically from 50 meters to the surface.Anchovy and sardine eggs, larvae and adults were collected all along the Peruvian coast between 5°Sand 18°S, however they were mainly found between 6°S and 14°S.

Eggs of sardine and anchovy were found all along the coast without being located in a particularregion (Fig. 2), while larvae were found more particularly in the northern region from 6°S to 9°S.A possible enrichment by larval drift from nearby regions or better survival rates could explain thisfavorable region (Lett et al., 2007). Sardine’s adult are more dispersed offshore than anchovy.

Monthly climatology data maps were created by averaging eggs and larvae densities at the resolu-tion of the grid model (1/6°, cf. below) after removing the data collected during the most powerfulEl Niño events (between 04/1997- 08/1998 and 02/1992-06/1992). A mask with five coastal andoffshore regions is used to compare observed and predicted seasonal changes (Fig. 2).

3.2 Bio-physical environment

Physical and biological forcing fields (temperature, currents, O2, Primary Production (PP), and eu-photic depth) were predicted from the Regional Ocean Modeling System (ROMS, [Shchepetkin andMcWilliams, 2005]) coupled to a biological model (PISCES, [ Aumont and Bopp, 2006]). The modeldomain covers the Humboldt upwelling system in the region 5°N-25°S and 90°W-69.5°W, at a spatialresolution of 1/6° with 30 depth layers. Its configuration and validation has been described in (Pen-ven et al., 2005, Echevin et al., 2008, Albert et al., 2010).

We used a climatological run with a 5-day time step, forced by COADS heat fluxes and Quikscatwind stress, as in Albert et al. (2010). At the open boundaries the model is forced by the dynamicalfields and biogeochemical tracers from a monthly climatology of the ORCA2 OGCM simulation at 2°resolution over 1992-2000. Ten years of spinup were produced to reach a statistical equilibrium.

To drive the anchovy and sardine model, temperature and currents fields were averaged over themixed-layer depth where eggs and larvae are believed to concentrate (Mathiesen, 1989). Total pri-mary production was integrated over all the vertical layers. Each simulation had the same resolution

in time and space as the input fields.

To test the mechanisms of predation on larvae by the micronekton, the mid-trophic level model ofSEAPODYM (Lehodey et al., 2010) has been used with this ROMS-PISCES physical-biogeochemicalenvironmental forcing. This model includes 6 functional groups from surface to 1000 m with verti-cally migrant and non-migrant components (Lehodey et al., 2010). The biomass of larvae predatorsis calculated as the sum of biomass of the epipelagic group and the migrant groups coming intothe surface at night weighted by an estimated fraction of the day where predation is maximum, i.e.,day-time and one hour at sun-set and one hour at sun-rise.

Figure 2: Composite distribution maps for eggs (a), larvae (b)and adult(c) of anchovy (top) and sardine (bottom) collectedby the Instituto del Mar del Peru over the period 1961-2008(a and b) and 1983-2009 (c). Circles radius are proportionalto density values with the higher biggest circle correspond-ing to (a) 107 376 (anchovy) and 63 840 (sardine) eggs.m−2,(b) 84 939 (anchovy) and 36 120 (sardine) larvae.m−2 and (c)sA=438 333 (anchovy) and sA=23 304 (sardine) nm.m−2. Alldata were provided by IMARPE.

4 Data Assimilation approach

The optimization method in SEAPODYM has been developed by Senina et al. (2008) using fishingdata. The authors used the maximum likelihood method with fishing data to estimate the set ofparameters that minimizes the differences between predictions and observations. Here we adapt themethod to with a data assimilation procedure using eggs and larvae data.

4.1 Choosing the likelihood function

The choice of a distribution function is critical in the likelihood approach. Normal, Log-normal,Poisson, Negative Binomial and Zero Inflated Negative Binomial distributions were explored usingQuantile-Quantile (QQ) plots (Fig. 3). If data distribution and tested theoretical distribution are iden-tical, the Q-Q plot follows the 45 line y = x. Negative binomial and ZI negative binomial were foundto be the best distribution fitting the data. We chose the Zero Inflated negative binomial because itallows to estimate the probability of zeros in the data, thus providing more information.

Figure 3: A Q-Q plot of a sample of eggs (left) and larvae (rigth) climatology versus a Zero Inflatednegative binomial distribution ("Negative binomial distribution fitted with only positive values").The 95 and 98 quantile are shown in red, n corresponds to the number of observations used and r isthe correlation coefficient.

4.2 Likelihood function

Larvae and eggs data are aggregated at the 5-day time step resolution of the model. Density of eggsand larvae data, da,n,t,i,j , at time t, in a cell i, j, for a type of net n is given in number per square meter.To take into account differences between net sizes, this density is multiplied by the sampling effort,ea,n,t,i,j in square meters. Thus the abundance in observed samples of eggs or larvae Sobsn,t,i,j are givenby the equation (4):

Sobsn,t,i,j =

k∑a

da,n,t,i,j • ea,n,t,i,j (4)

and associated to a total cell sampling effort En,t,i,j :

En,t,i,j =

k∑a

ea,n,t,i,j (5)

with k the number of samples in the cell i, j during time step t.

Using this sampling effort En,t,i,j , the predicted abundance of eggs or larvae Spredn,t,i,j (in numbers) attime t, for the net n, and in cell i,j is given by equation (6):

Spredn,t,i,j = En,t,i,j • qn •Nt,i,j (6)

with Nt,i,j the predicted density of larvae or eggs per square meter and qn the catchability coefficientcharacterizing the net which will be estimated during the optimization process.

For this particular study, since we use monthly climatological series of eggs and larvae densities aver-aged at the resolution of the grid model (1/6°) and collected with one single type of net (cf. paragraph3.1), the sampling effort En,t,i,j was set to 1 with eggs or larvae abundance equal to equation (7):

Sobsm,i,j =

k∑a

da,n,t,i,ja

(7)

and predicted eggs or larvae densities were averaged by month (eq. 8):

Spredm,i,j =L∑t

(q • Nt,i,j

nts) (8)

with nts the number of time step in the month m.

Finally, using a zero inflated negative binomial distribution, the cost function is defined by Eq. 9:

Leggs or larvae

(θ|Sobs

)=

∏tfij

(pf + (1− pf )

(βf

1+βf

)βfSpredtfij1−pf

), if Sobstfij = 0,

∏tfij

((1− pf )

Γ

(Sobstfij+

βfSpredtfij

1−pf

)

Γ

(βfS

predtfij

1−pf

)Sobstfij !

(βf

1+βf

)βfSpredtfij1−pf

(1

1+βf

)Sobstfij

), if Sobstfij > 0,

f = 1, 2. (9)

where parameter βf is the negative binomial parameter which will be estimated in the optimizationprocess and parameter pf is the probability of getting a null observation. βf is inversely related tothe variance σ2 = Spred(1+ 1

βf) and (1+ 1

βf) shows how much variance exceeds expected value. Both

parameters will be also estimated during the optimization process.

When we use both eggs and larvae data for optimization, the negative log-likelihood function to beminimized (L− = −ln(L)) is the sum of the negative log-likelihood function for eggs and for larvae:

L− = L−eggs + L−

larvae (10)

The adjoint method has been developed in SEAPODYM (Senina et al., 2008), but the new likelihoodfunction required several modifications. To verify that the changes were correctly implemented,we checked that the value of the gradient J(x) calculated with finite differences (using utilities ofautomatic code differentiation library AUTODIFF - Otter Research LTd., 1994) was identical to thegradient calculated by the adjoint code. Then we verify that equation (11) is correct, i.e., that thediscrepancy between each gradient component (obtained by analytic differentiation (adjoint code)and its finite difference approximation changes parabolically with step h (Senina et al., 2008).

L̄ (θk + h)− L̄ (θk − h)

2h−∇kL̄ = O(h2) (11)

Finally, the approach was validated with a twin experiment. Starting from larvae and eggs pseudo-observations simulated with a fixed set of parameter values, we verify that after changing the param-eter values, the model can converge and find the exact original values of the parameters. Six twinexperiments with randomly created sets of perturbed parameters were conducted and all success-fully recovered the original values with a relative error below <1%. Furthermore, we verified that thehessian was definite positive which validate the local minimum found.

5 Results

5.1 Seasonal variability in anchovy and sardine reproduction

Seasonal spatial and temporal variability of anchovy reproduction was analyzed in detail in Hernan-dez et al. (submitted). Highest abundance of anchovy eggs was observed along the coast in region3 and 4, with density starting to increase after July, decreasing in October, and increasing again fromDecember to February to peak in March. Density decreased when moving towards the south (region5). A single small peak appeared off coast in region 2 in August (Fig. 4) and almost no eggs weresampled far offshore in region 1.

Figure 4: Seasonal variability in anchovy (top) and sardine (bottom) eggs and larvae density after removing0.5 per cent of outliers (all regions) with box plots showing the median and the 25th and 75th percentiles, thegreen line indicating the mean and red bars the standard error of the mean, and blue crosses being outliers.The number of cells sampled is provided and can be compared with the total cells of 2029 over all the regions.The result of the statistical analysis is illustrated with black arrows showing non significant changes betweenmonthly samples (Mann-Withney U test; p>0.05) The significant abundance and scarce periods are illustratedwith yellow and blue shading highlighting.

The seasonal pattern for larvae was very similar to the one described for eggs, with a major peakof density in September and a secondary peak between December and March (Fig. 4). The northern

coastal region 3 had the highest observed density, followed by region 4. In the intermediate offshoreregion 2, the highest density of larvae occurred in September and March. Interestingly, in the south-ern coastal region 5 density started to increase in July before it occurs in northern regions.

For sardine, highest abundance of eggs occurred along the coast in region 3 like for anchovy. How-ever though anchovy abundance of eggs and larvae show a peak in September followed by a plateauuntil March, for sardines, one main peak and a secondary peak in February are more clearly separatedby a period of lower abundance (Fig. 4).

5.2 Optimization with climatology time series

Before running optimization experiments, we tested the sensitivity of predictions and cost functionto parameters. Since we cannot test the n-dimensional space, we computed sensitivity for 6 randomset of parameters using the climatological ROMS-PISCES.

Figure 5: Log-scaled measures of sensitivity obtained for each parameters for 5 random experiments. The val-ues below the dashed line correspond to less than 5% sensitivity of cost function to corresponding parameters.Top: Sensitivity measures for model parameters using sensitivity of cost function - Down: Sensitivity measuresfor model parameters using model predictions. Of course, the parameters βn, and pn which are the likelihoodparameters to be estimated are not sensitive to model predictions, then not show.

The results (Fig. 5) showed that parameters are sensitive using either the cost function or the model

predictions. These parameters can be then estimated in the optimization process.

Optimization experiments were carried out for different definitions of spawning habitat (table 1 ).We made different simulation using either only eggs dataset, larvae dataset or both datasets. Resultswere quite similar between these experiments. Table 2 shows the estimated values of parametersfound using Zero Inflated Negative Binomial Log likelihood distribution for anchovy and sardine,using both eggs and larvae data. The hessian was definite positive for each experience indicating thata local minimum was achieved.

T σ α ap bp q1 q2 β1 β2 p1 p2 Lend

Anc

hovy

Hs1 13.0 5.5 - - - 33810 10413 0.00036 0.0031 0.42 0.30 43730.4Hs2 - - 100 - - 57648 18438 0.00028 0.0029 0.0 0.22 43306.8Hs3 14.34 5.5 100 - - 85024 27186 0.00032 0.0029 0.16 0.20 43074.8Hs4 - - 100 - - 112580 36916 0.00033 0.003 0.2 0.19 42972Hs5 17.49 5.5 11.9 - - 115420 37678 0.00034 0.0030 0.24 0.19 42949.1Hs6 - - 100 7.59 0.001 218211 72978 0.00035 0.0031 0.25 0.21 42947.8Hs7 17.79 5.5 100 6.36 0.001 209021 69612 0.00035 0.0031 0.25 0.21 42955.6

Sard

ine

Hs1 18.9 4.5 - - - 1486 528 0.0017 0.0115 0.84 0.79 10859.4Hs2 - - 7.78 - - 4006 1463 0.0018 0.0104 0.84 0.73 10792.8Hs3 19.1 5.5 3.29 - - 3950 1437 0.0018 0.0104 0.84 0.73 10792.4Hs4 - - 0.30 - - 3281 1195 0.0019 0.011 0.84 0.76 10790.7Hs5 21.26 5.5 0.39 - - 4223 1558 0.0019 0.0108 0.84 0.74 10786.1Hs6 - - 2.46 25.01 0.34 3693 1343 0.0019 0.0106 0.84 0.74 10786.2Hs7 20.7 5.5 1.4 7.34 0.29 4837 1784 0.0019 0.0107 0.84 0.74 10787.5

Table 2: Results of optimization experiments using eggs and larvae climatological data for anchovyan sardine (ZI Negative Log Likelihood). Grey shaded cells showed best likelihood solutions.

In both cases, for sardine and anchovies, the optimized values for standard deviation of temper-ature function reached the maximum boundary, but the optimal mean value was well estimatedbetween the boundaries, around 21°C for sardine and 17°C for anchovy, in good agreement with theliterature, where sardine thermal habitat has been always proposed to be higher than for anchovy[Schwartzlose et al., 1999]. However, the large standard deviation could suggest that either the datasets used is not sufficient or the model configuration not realistic enough to estimate these parame-ters. Consequently though the temperature has certainly a effect in the final definition of the habitat,it is relatively weak in its combination with the other mechanisms.

When temperature is combined with the match-mismatch mechanism (Hs3), the optimization es-timates a very high value of the parameter α (∼ 100) for anchovy, thus leading to a quasi linearrelationship between primary production (the proxy for food of larvae) and the spawning index (Fig.6). The values obtained for sardines is much lower, between 0.3 and 2.5, that is for the lower valuesof this range, a more rapid increase of index at weaker primary production (Fig 6 ). The impact ofadding predation (Hs7) is estimated to occur earlier at low predator concentration for anchovy thanfor sardine (Table 2 ; Fig 6 ). Indeed, this effect could reflect the more dispersed distribution offshoreof sardine eggs and larvae where mesopelagic organism concentration is higher than in the coastalzone.

Figure 6: Functions of match-mismatch (left) and predation (right) for the control parameters obtained afteroptimization experiments

The final likelihood value needs to be considered in relation with the number of parameters usedin the model to define which model definition is the most parcimonious. The Akaike informationcriterion (AIC) (eq. 12) allows to account for the number of parameters and variables in the measureof the relative goodness of fit of a statistical model. Amongst different models, the best one will bethe model leading to the minimum AIC value.

AIC = −2ln(L) + 2µ (12)

whith µ the number of degrees of freedom (i.e., the total number of parameters and variables) andL the maximal likelihood.

Using this criteria, the best definition of habitat index for this configuration of model and data isobtained with Hs5 and Hs6, which combines respectively temperature and prey-predator tradeoffeffects (using Eq.3) and prey-predator tradeoff effect alone using (Eq. 2).

Lend Nb parameters Nb Variables AIC

Anc

hovy

Hs1 43730.4 8 1 87478.8Hs2 43306.8 7 1 86629.6Hs3 43074.8 9 2 86171.6Hs4 42972 7 2 85962Hs5 42949.1 9 3 85922.2Hs6 42947.8 9 2 85917.6Hs7 42955.6 11 2 85937.24

Sard

ine

Hs1 10859.4 8 1 21736.8Hs2 10792.8 7 1 21601.6Hs3 10792.4 9 2 21606.8Hs4 10790.7 7 2 21599.4Hs5 10786.1 9 3 21596.2Hs6 10786.2 9 2 21594.4Hs7 10787.5 11 2 21601.0

Table 3: Results of AIC for anchovy and sardine optimization experiments using different spawninghabitat functions

As noted above the choice in the definition of the upper layer where eggs and larvae can be con-centrated may lead to different impacts by the currents. Therefore we also replayed this series ofoptimization experiments using a different definition of this upper layer: instead of using the mixed-

layer depth, we took the euphotic depth, which is everywhere deeper than mixed-layer depth. Inthis case, the best fit to data is obtained with Hs5 and Hs7 (Table 4), which combine respectivelytemperature and prey-predator effects using function 4 (Eq. 3 ) and temperature and prey-predatoreffects using function 3 (Eq. 2). In addition, for all definitions of habitat, the likelihood was improved,meaning that physics averaged on the euphotic depth provide better dynamics for our observations.

T σ α ap bp q1 q2 β1 β2 p1 p2 Lend AICHs4 - - 100 - - 112580 34468 0.00033 0.0029 0.20 0.15 42916.2 85850.4Hs5 15.6 4.90 1.3 - - 89336 27086 0.00033 0.0029 0.22 0.15 42854 85732Hs6 - - 3.10 7.72 0.001 189097 59030 0.00034 0.0029 0.26 0.17 42892 85806Hs7 15.38 5.5 3.37 5.98 0.001 191694 59646 0.00034 0.003 0.23 0.16 42866.5 85759

Table 4: Anchovy optimization using vertical definition based on euphotic depth. Work on sardine isstill on going

Spatial distributions obtained with the optimal parameterization is shown on figure 7 for anchovyand sardine. The simulations suggested that concentration of eggs and larvae differ during the twofavourable seasons in September and February. In this latter, the concentration occurred all alongthe coast for both species, while in September, the favourable area is clearly in the region coastalnorther region (region 3). In June, the spawning habitat and larvae concentration are at there weakestintensity. Overall, it should be noted that the spatial agreement between predictions and observationsis quite good (an example of this comparison for eggs is shown for the february month in fig 8).These predictions agree with observed cycles (Fig. 4 ) but when integrated by area the predictedtotal abundances do not reproduce very well the observed climatological cycles (Fig 9) . Possibleexplanations are explored in the discussion.

6 Discussion

Spawning and larvae recruitment mechanisms largely determine the dynamics of the populations ofsmall pelagic fishes. In upwelling regions and for small pelagic fishes, spawning success is mainlydue to environmental conditions (Bertrand et al., 2004; Cole, 1999), but stock recruitment relationshipand availability of mature adults also need to be taken into account. In this study we only takeinto account the environmental conditions, so we cannot then expect a perfect concordance with theobservations. In addition the environmental forcing provided by a coupled physical-biogeochemicalmodel may lack of realism, and the spatial resolution of 1/6° is likely still too coarse for these speciesthat have a very coastal habitat, especially anchovy. The SEAPODYM model also introduces someapproximations. Physical variables are averaged on the mixed layer depth, and vertical resolutionis suppressed. The simulated micronekton has not yet been validated for Peruvian region. Finally,the climatology was built with data covering a long period (1961-2008) that may include differentregimes in the seasonal patterns, and sources of uncertainty and variability in the methodology fornet sampling and manual counting.

As for the comparison between the climatology (fig 8), and the monthly predictions, it should benoted that the climatology is obtained by averaging a large number of highly variable spatial observa-tions and is therefore affected by a high monthly uncertainty. However, the optimization proceduredid not take into account these uncertainties. Therefore, part of the discrepancy between the observedclimatology and the predicted climatology could be explained by these errors. Whether it is possibleto better take into account these uncertainties during the optimization procedure is not clear yet.

Despite these limitations, we have developed a modeling framework with rigorous parameteriza-

tion optimization approach to investigate the mechanisms of spawning habitat and early life historyof anchovy and sardines. The approach has been first validated by twin experiments and tested fortwo different species with real data sets. These first results provided reasonable estimates of thermalhabitat in agreement with previous studies from the litterature, suggesting that the overall thermalhabitat of Peruvian anchovy is in the range of 13-23°C ( Bertrand et al., 2008, Gutierrez et al., 2007),but likely shifted to warmer values for sardine (Schwartzlose et al., 1999). Overall, this new eulerianmodeling approach seems very promising to achieve a reasonable optimized simulation of popula-tion dynamics of small pelagic species using a small number of parameters.

Our results still did not allowed to select the best definition of spawning habitat, but clearly in-dicate that more than one mechanism is needed to approach observations. Further simulationswill have to consider the combination of these environmental mechanisms with those of a localstock-recruitement relationship and spatial change in adult density due to feeding and spawningbehaviour. The use of long time series including internanual variability related to ENSO shouldalso help in the optimization, providing contrasted signals associated to the strong environmentalchanges and fish population impacts that these events induce in this region.

Acknowledgments

This study formed part of the Ph.D dissertation of O. Hernandez funded by CLS, France (CollecteLocalisation Satellites) and a research grant under the Peru Ecosystem Projection Scenarios ANR-VCMS08 project (Institut de Recherche pour le Développement). We thank Aurélie Albert for pro-viding the climatological simulations of ROMS-PISCES.

Figure 7: Anchovy (top) and sardine (bottom) predicted spawning habitat index (∼ eggs abundance)and larvae density for February, June and September Months. (Abundance normalized between 0and 1)

Figure 8: Anchovy (top) and sardine (bottom) predicted spawning habitat index (∼ eggs abundance)(left) and observed eggs (right) for February month (Abundance normalized between 0 and 1, log10transformation only for observation (right) )

Figure 9: Seasonality of anchovy (top) and sardine (bottom) spawning habitat index (left) and anchovy larvaeabundance (right) in coastal regions (3, 4 and 5; solid lines) and offshore regions (1 and 2; dashed lines) usingthe different definition of spawning habitat index and parameters found during optimization process. It shouldbe noted that no main difference are observed between Hs4, Hs5, Hs6 and Hs7 spawning habitat definition.

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