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

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1 ICES CM 2011/H "Not be cited without prior reference to the author" Exploring larvae recruitment variability of Peruvian anchovy and sardine with modeling and data assimilation Olga Hernandez 1, Inna Senina 1, Patrick Lehodey 1, Patricia Ayon 3, Arnaud Bertrand 2,3, Vincent Echevin 2,4, Ramiro Castillo 3, Philippe Gaspar 1 1 MEMMS (Marine Ecosystems Modeling and Monitoring by Satellites), CLS, France 2 IRD, UMR EME IFREMER/IRD/UM2, Avenue Jean Monnet, BP 171, Sète, France 3 Instituto del Mar del Peru, Esquina Gamarra y Gral. Valle sn, Apartado 22, Callao, Lima 4 IRD, LOCEAN, Université Pierre et Marie Curie, Boite, 4 Place Jussieu, Paris, France A Spatial Eulerian Ecosystem and Population Dynamic Model (SEAPODYM) is used in a data assimilation study aiming to estimate model parameters that describe spawning conditions and dynamics of anchoveta and sardine larvae in the Humboldt Current system (HCS) off Peru. Initially developed for large pelagic fish (e.g., tuna), SEAPODYM was adapted for this study to small pelagic species, and configured to a regional domain using the ROMS-PISCES coupled physicalbiogeochemical 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 subsequent spatiotemporal variability of natural mortality during their drift with currents described by a system of Eulerian equations. We conducted a series of optimization experiments using data of anchovy and sardine larvae to estimate the parameters of the spawning habitat of both species. Different mechanisms proposed to control the fish larvae recruitment are explored: temperature, trade-off between presence/absence of prey and predators of larvae, retention or dispersion by currents. Key-words: end-to-end model, SEAPODYM, anchoveta, sardine, upwelling ecosystem, parameter optimization, population dynamics, spawning habitat Contact author: O. Hernandez, MEMMS (Marine Ecosystems Modeling and Monitoring by Satellites), CLS, Space Oceanography Division, 8-10 rue Hermes, Ramonville, France ohernandez@cls.fr

2 1 Introduction The Humboldt Current system (HCS) off Peru and Chile is one of the most productive coastal upwelling system in the world and the most productive system in terms of fish biomass (Bakun and Broad, 2003; Chavez et al., 2008). This system is submitted to climate variability at seasonal, interannual 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 growing and time to maturity (one and two years respectively) are well adapted to this variability and dominate the HCS waters. Within the last decades, different periods dominated either by anchovies or sardines occurred. The sardine population disappeared from the Peruvian coast after 1999 and did not reappear since. The Spatial Ecosystem And Populations Dynamics Model (SEAPODYM) has been adapted for the study of early life stages of anchovy in the Humboldt upwelling system (Hernandez et al., submitted). In this paper, we present the data assimilation approach developed for optimizing the model parameters, using anchovy and sardine eggs and larvae data collected by IMARPE. Different mechanisms proposed to control the fish larvae recruitment are explored: temperature, trade-off between presence and absence of prey and predators of larvae, retention and dispersion by currents. After a validation 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-like species) at basin-scale [Lehodey et al., 2008, 2010a]. We have adapted the model to study early life stages 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

3 The main causes proposed to explain the variability in spawning success and larvae survival include the combination of stock-recruitment relationship with more or less favorable environmental conditions. Recruitment dependence on the spawning biomass is considered to be weak except at low levels of parental biomass (Myers et al., 1999). Thus, we can expect that environmental variability explains a very large part of the fluctuations in the survival of anchovy larvae and the subsequent recruitment of juveniles in the adult population rather than by densitydependent processes (Brochier et al., 2008). In this study, the stock-recruitment relationship was not included. We assume that adults are present and distributed evenly within the spawning sites and hence that recruitment is proportional 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 f 1 (T ) = N(T 0, σ 0)with standard deviation σ 0 and optimal mean temperature T The match/mismatch (Cushing, 1975) between spawning and presence of prey for larvae; it is simulated by the Holling Type 2 functional response (Reynolds et al., 1959). Primary production (PP) is used as a proxy for the prey of larvae: f 2 (P P ) = ap P 1 + ahp P = P P 1 a + hp P (1) where a is the success rate, h the predator handling time per prey time, and PP is prey density. For numerical simplification, the second form of the equation is used with α = 1 a the steepness parameter and h as set to The prey-predator tradeoff mechanisms (Lehodey et al., 2008), expressed as the product of the previous function with a decreasing sigmoid function: f 3 (P P, P red) = f 2 (P P ) or can be also written as a functional response of Holling type II: f 4 (P P, P red) = exp b (P red c) (2) P P P red a + P P P red The redistribution of larvae by currents leading to higher or lower mortality according to the retention 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 mortality coefficient for anchovy larvae was set to 0.69 year 1 based on Cubillos et al. (2002). (3) Larvae transport by currents with associated mortality is computed for a time step of five days after spawning, i.e., roughly corresponding to the estimated mean age of larvae collected in a size range between 3 and 6 mm, and based on a length of hatching of 2 mm and a growth function (Marzloff et al., 2009). Various mechanisms or combination of mechanisms to define the spawning habitat have been explored (Table 1) and the results compared taking into account the number of parameters.

4 Experiment Mechanism Function Parameters HS1 Temperature Hs = f 1(T ) σ, T HS2 Match-mismatch Hs = f 2(P P ) σ HS3 Temperature and Match-Mismatch Hs = f 1(T ) f 2(P P ) σ, T, α HS4 Prey-predator trade-off Hs = f 4(P P, P red) α HS5 Temperature and Prey-predator trade-off Hs = f 1(T ) f 4(P P, P red) σ, T, α HS6 Prey-predator trade-off Hs = f 3(P P, P red) α, b,c HS7 Temperature and Prey-predator trade-off Hs = f 1(T ) f 3(P P, P red) 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 sample anchovy/sardine eggs and larvae data. In 1983, IMARPE also started to monitor the adult biomass using regular acoustic sampling cruises. We use climatologies produced using all available data between (159 cruises) for eggs and larvae collected with the Hensen net, characterized by 0.33m 2 mouth area and 300 µm mesh 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 S and 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 particular region (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 this favorable 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 resolution of the grid model (1/6, cf. below) after removing the data collected during the most powerful El Niño events (between 04/ /1998 and 02/ /1992). A mask with five coastal and offshore 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 euphotic depth) were predicted from the Regional Ocean Modeling System (ROMS, [Shchepetkin and McWilliams, 2005]) coupled to a biological model (PISCES, [ Aumont and Bopp, 2006]). The model domain covers the Humboldt upwelling system in the region 5 N-25 S and 90 W-69.5 W, at a spatial resolution of 1/6 with 30 depth layers. Its configuration and validation has been described in (Penven 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 Quikscat wind stress, as in Albert et al. (2010). At the open boundaries the model is forced by the dynamical fields and biogeochemical tracers from a monthly climatology of the ORCA2 OGCM simulation at 2 resolution over 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 the mixed-layer depth where eggs and larvae are believed to concentrate (Mathiesen, 1989). Total primary production was integrated over all the vertical layers. Each simulation had the same resolution

5 in time and space as the input fields. To test the mechanisms of predation on larvae by the micronekton, the mid-trophic level model of SEAPODYM (Lehodey et al., 2010) has been used with this ROMS-PISCES physical-biogeochemical environmental forcing. This model includes 6 functional groups from surface to 1000 m with vertically migrant and non-migrant components (Lehodey et al., 2010). The biomass of larvae predators is calculated as the sum of biomass of the epipelagic group and the migrant groups coming into the 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) collected by the Instituto del Mar del Peru over the period (a and b) and (c). Circles radius are proportional to density values with the higher biggest circle corresponding to (a) (anchovy) and (sardine) eggs.m 2, (b) (anchovy) and (sardine) larvae.m 2 and (c) s A = (anchovy) and s A = (sardine) nm.m 2. All data were provided by IMARPE.

6 4 Data Assimilation approach The optimization method in SEAPODYM has been developed by Senina et al. (2008) using fishing data. The authors used the maximum likelihood method with fishing data to estimate the set of parameters that minimizes the differences between predictions and observations. Here we adapt the method 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 using Quantile-Quantile (QQ) plots (Fig. 3). If data distribution and tested theoretical distribution are identical, the Q-Q plot follows the 45 line y = x. Negative binomial and ZI negative binomial were found to be the best distribution fitting the data. We chose the Zero Inflated negative binomial because it allows 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 Inflated negative 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 is the correlation coefficient. 4.2 Likelihood function Larvae and eggs data are aggregated at the 5-day time step resolution of the model. Density of eggs and larvae data, d a,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, e a,n,t,i,j in square meters. Thus the abundance in observed samples of eggs or larvae Sn,t,i,j obs are given by the equation (4): S obs n,t,i,j = and associated to a total cell sampling effort E n,t,i,j : k d a,n,t,i,j e a,n,t,i,j (4) a E n,t,i,j = k e a,n,t,i,j (5) a

7 with k the number of samples in the cell i, j during time step t. Using this sampling effort E n,t,i,j, the predicted abundance of eggs or larvae S pred n,t,i,j (in numbers) at time t, for the net n, and in cell i,j is given by equation (6): S pred n,t,i,j = E n,t,i,j q n N t,i,j (6) with N t,i,j the predicted density of larvae or eggs per square meter and q n the catchability coefficient characterizing 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 averaged at the resolution of the grid model (1/6 ) and collected with one single type of net (cf. paragraph 3.1), the sampling effort E n,t,i,j was set to 1 with eggs or larvae abundance equal to equation (7): S obs m,i,j = k a d a,n,t,i,j a and predicted eggs or larvae densities were averaged by month (eq. 8): (7) S pred with nts the number of time step in the month m. L m,i,j = (q N t,i,j nts ) (8) t Finally, using a zero inflated negative binomial distribution, the cost function is defined by Eq. 9: ( p f + (1 p f ) L eggs or larvae (θ S obs) tfij ( = ( Γ (1 p f ) ( tfij Γ ( ) βf pred S tfij βf 1+β f ) Stfij obs + β f S pred tfij 1 p f ( βf β f S pred ) tfij S 1 p obs f tfij! 1 p f ), if Stfij obs = 0, ) βf pred S tfij 1+β f ( ) 1 p f 1 Sobs tfij 1+β f ), if S obs tfij > 0, f = 1, 2. (9) where parameter β f is the negative binomial parameter which will be estimated in the optimization process and parameter p f is the probability of getting a null observation. β f is inversely related to the variance σ 2 = S pred (1 + 1 β f ) and (1 + 1 β f ) 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 be minimized (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 likelihood function 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 of automatic code differentiation library AUTODIFF - Otter Research LTd., 1994) was identical to the gradient calculated by the adjoint code. Then we verify that equation (11) is correct, i.e., that the discrepancy between each gradient component (obtained by analytic differentiation (adjoint code) and its finite difference approximation changes parabolically with step h (Senina et al., 2008).

8 L (θ k + h) L (θ k h) k L = O(h 2 ) (11) 2h Finally, the approach was validated with a twin experiment. Starting from larvae and eggs pseudoobservations simulated with a fixed set of parameter values, we verify that after changing the parameter values, the model can converge and find the exact original values of the parameters. Six twin experiments with randomly created sets of perturbed parameters were conducted and all successfully recovered the original values with a relative error below <1%. Furthermore, we verified that the hessian 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 Hernandez et al. (submitted). Highest abundance of anchovy eggs was observed along the coast in region 3 and 4, with density starting to increase after July, decreasing in October, and increasing again from December to February to peak in March. Density decreased when moving towards the south (region 5). A single small peak appeared off coast in region 2 in August (Fig. 4) and almost no eggs were sampled far offshore in region 1. Figure 4: Seasonal variability in anchovy (top) and sardine (bottom) eggs and larvae density after removing 0.5 per cent of outliers (all regions) with box plots showing the median and the 25th and 75th percentiles, the green 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 between monthly samples (Mann-Withney U test; p>0.05) The significant abundance and scarce periods are illustrated with yellow and blue shading highlighting. The seasonal pattern for larvae was very similar to the one described for eggs, with a major peak of density in September and a secondary peak between December and March (Fig. 4). The northern

9 coastal region 3 had the highest observed density, followed by region 4. In the intermediate offshore region 2, the highest density of larvae occurred in September and March. Interestingly, in the southern 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. However though anchovy abundance of eggs and larvae show a peak in September followed by a plateau until March, for sardines, one main peak and a secondary peak in February are more clearly separated by 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 function to parameters. Since we cannot test the n-dimensional space, we computed sensitivity for 6 random set of parameters using the climatological ROMS-PISCES. Figure 5: Log-scaled measures of sensitivity obtained for each parameters for 5 random experiments. The values 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 measures for model parameters using model predictions. Of course, the parameters β n, and p n which are the likelihood parameters 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

10 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. Results were quite similar between these experiments. Table 2 shows the estimated values of parameters found 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 that a local minimum was achieved. Anchovy Sardine T σ α a p b p q 1 q 2 β 1 β 2 p 1 p 2 L end Hs Hs Hs Hs Hs Hs Hs Hs Hs Hs Hs Hs Hs Hs Table 2: Results of optimization experiments using eggs and larvae climatological data for anchovy an 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 temperature function reached the maximum boundary, but the optimal mean value was well estimated between the boundaries, around 21 C for sardine and 17 C for anchovy, in good agreement with the literature, 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 data sets used is not sufficient or the model configuration not realistic enough to estimate these parameters. 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 estimates a very high value of the parameter α ( 100) for anchovy, thus leading to a quasi linear relationship 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 values of this range, a more rapid increase of index at weaker primary production (Fig 6 ). The impact of adding predation (Hs7) is estimated to occur earlier at low predator concentration for anchovy than for sardine (Table 2 ; Fig 6 ). Indeed, this effect could reflect the more dispersed distribution offshore of sardine eggs and larvae where mesopelagic organism concentration is higher than in the coastal zone.

11 Figure 6: Functions of match-mismatch (left) and predation (right) for the control parameters obtained after optimization experiments The final likelihood value needs to be considered in relation with the number of parameters used in the model to define which model definition is the most parcimonious. The Akaike information criterion (AIC) (eq. 12) allows to account for the number of parameters and variables in the measure of the relative goodness of fit of a statistical model. Amongst different models, the best one will be the 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) and L the maximal likelihood. Using this criteria, the best definition of habitat index for this configuration of model and data is obtained with Hs5 and Hs6, which combines respectively temperature and prey-predator tradeoff effects (using Eq.3) and prey-predator tradeoff effect alone using (Eq. 2). Anchovy Sardine L end Nb parameters Nb Variables AIC Hs Hs Hs Hs Hs Hs Hs Hs Hs Hs Hs Hs Hs Hs Table 3: Results of AIC for anchovy and sardine optimization experiments using different spawning habitat functions As noted above the choice in the definition of the upper layer where eggs and larvae can be concentrated may lead to different impacts by the currents. Therefore we also replayed this series of optimization experiments using a different definition of this upper layer: instead of using the mixed-

12 layer depth, we took the euphotic depth, which is everywhere deeper than mixed-layer depth. In this case, the best fit to data is obtained with Hs5 and Hs7 (Table 4), which combine respectively temperature and prey-predator effects using function 4 (Eq. 3 ) and temperature and prey-predator effects 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 a p b p q 1 q 2 β 1 β 2 p 1 p 2 L end AIC Hs Hs Hs Hs Table 4: Anchovy optimization using vertical definition based on euphotic depth. Work on sardine is still on going Spatial distributions obtained with the optimal parameterization is shown on figure 7 for anchovy and sardine. The simulations suggested that concentration of eggs and larvae differ during the two favourable seasons in September and February. In this latter, the concentration occurred all along the coast for both species, while in September, the favourable area is clearly in the region coastal norther region (region 3). In June, the spawning habitat and larvae concentration are at there weakest intensity. Overall, it should be noted that the spatial agreement between predictions and observations is 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 predicted total abundances do not reproduce very well the observed climatological cycles (Fig 9). Possible explanations are explored in the discussion. 6 Discussion Spawning and larvae recruitment mechanisms largely determine the dynamics of the populations of small pelagic fishes. In upwelling regions and for small pelagic fishes, spawning success is mainly due to environmental conditions (Bertrand et al., 2004; Cole, 1999), but stock recruitment relationship and availability of mature adults also need to be taken into account. In this study we only take into account the environmental conditions, so we cannot then expect a perfect concordance with the observations. In addition the environmental forcing provided by a coupled physical-biogeochemical model may lack of realism, and the spatial resolution of 1/6 is likely still too coarse for these species that have a very coastal habitat, especially anchovy. The SEAPODYM model also introduces some approximations. Physical variables are averaged on the mixed layer depth, and vertical resolution is suppressed. The simulated micronekton has not yet been validated for Peruvian region. Finally, the climatology was built with data covering a long period ( ) that may include different regimes in the seasonal patterns, and sources of uncertainty and variability in the methodology for net sampling and manual counting. As for the comparison between the climatology (fig 8), and the monthly predictions, it should be noted that the climatology is obtained by averaging a large number of highly variable spatial observations and is therefore affected by a high monthly uncertainty. However, the optimization procedure did not take into account these uncertainties. Therefore, part of the discrepancy between the observed climatology and the predicted climatology could be explained by these errors. Whether it is possible to 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-

13 tion optimization approach to investigate the mechanisms of spawning habitat and early life history of anchovy and sardines. The approach has been first validated by twin experiments and tested for two different species with real data sets. These first results provided reasonable estimates of thermal habitat in agreement with previous studies from the litterature, suggesting that the overall thermal habitat of Peruvian anchovy is in the range of C ( Bertrand et al., 2008, Gutierrez et al., 2007), but likely shifted to warmer values for sardine (Schwartzlose et al., 1999). Overall, this new eulerian modeling approach seems very promising to achieve a reasonable optimized simulation of population 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 indicate that more than one mechanism is needed to approach observations. Further simulations will have to consider the combination of these environmental mechanisms with those of a local stock-recruitement relationship and spatial change in adult density due to feeding and spawning behaviour. The use of long time series including internanual variability related to ENSO should also help in the optimization, providing contrasted signals associated to the strong environmental changes 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 (Collecte Localisation 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 providing the climatological simulations of ROMS-PISCES.

14 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 0 and 1)

15 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, log10 transformation only for observation (right) )

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

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