Understanding mechanisms that control fish spawning and larval recruitment: Parameter optimization of an Eulerian model (SEAPODYM-SP) with Peruvian anchovy and sardine eggs and larvae data
Introduction
The largest commercial fishing fleet of small pelagic fish corresponds to the Peruvian anchovy (Engraulis ringens) fishery, which represents 30–35% of the worldwide fishmeal and fish oil (IFFO, 2009). This species inhabits the Humboldt Current System (HCS) off the Peruvian coast, the most productive oceanic system in terms of fish biomass (Bakun and Broad, 2003, Chavez et al., 2008). With less than 0.1% of the world ocean surface, the annual landings of Peruvian anchovy represent about 10% of the world fish catches.
In such coastal upwelling systems, small pelagic stocks vary under the influence of the natural climate variability (Lehodey et al., 2006) as a result of changes in recruitment and mortality. In the HCS, several climatic factors operate at different time scales: large-scale variations of the Eastern Pacific ITCZ at secular scale (Gutiérrez et al., 2009), the Pacific decadal oscillation (PDO) at multi-decadal scale, El Niño Southern Oscillation (ENSO) at the interannual scale, and seasonal and intraseasonal variability (Chavez et al., 2008). This strong variability makes the management of the fisheries a challenging task. In this context, a stock assessment spatial population dynamics model accounting for both fishing and climate-driven variability (Lehodey et al., 2008, Senina et al., 2008) could help us to better understand and possibly forecast the impact of the environment on these exploited populations.
There is a large diversity of approaches to integrate the dynamics of exploited fish populations in an end-to-end ecosystem modeling framework (Plagányi, 2007, Fulton, 2010, Goethel et al., 2011). A first critical issue is to include a representation of fish early life history controlling the subsequent recruitment in the population. A second one is to provide realistic quantitative estimates fitting observations and based on robust statistical methods. For example, Heath (2012) included fish early life history traits as well as a statistical method to optimize the model parameters. When a more explicit treatment of spatial dynamics is researched, it is often to the detriment of statistical method for quantitative estimates. The Individual-based (i.e., Lagrangian) modeling (IBM) framework was the basis of a large variety of studies investigating how the oceanic environment controls the early life history of pelagic species (e.g., Heath and Gallego, 1998, Mullon et al., 2002, Lett et al., 2007, Brochier et al., 2008). Some of these studies focused on larvae but also simulated the growth of young and adult fish (Megrey et al., 2007, Rose et al., 2007). Studies attempting to describe in detail the complete fish life cycle (Ito et al., 2007, Okunishi et al., 2009, Xi, 2009) or multi-species interactions (Travers et al., 2009) are less frequent. In these cases, the optimization of model parameters is highly complex and few solutions have been proposed. Brickman et al. (2007) used probability density function (PDF) to condense the results of tens of thousands of particle trajectories and integrate them into an optimization framework allowing to choose the best case among several fixed parameterizations. Other approaches are mostly based on genetic algorithms (e.g., Huse et al., 1999, Duboz et al., 2010).
The Eulerian approach that computes fluxes of fish density with advection–diffusion-reaction (ADR) equations is another category of spatial dynamics modeling with multiple examples (e.g., Okubo et al., 1980, MacCall, 1990, Richards et al., 1995, Bertignac et al., 1998, Turchin, 1998, Sibert et al., 1999, Magnússon et al., 2004). It can offer an advantageous framework for spatial population dynamics modeling and stock assessment. Indeed, such models have a limited number of parameters and continuous functions for the transport model, which greatly facilitates the development of inverse models for optimization (Senina et al., 2008). One such Eulerian modeling approach of population dynamics has been successfully developed to link the spatial population dynamics of large pelagic species (i.e. tuna and tuna-like species) to a simplified 3D basin-scale ecosystem (Lehodey et al., 2008, Lehodey et al., 2010a). The main features of this Spatial Ecosystem And POpulation DYnamics Model (SEAPODYM) are: (i) forcing by environmental data (temperature, currents, primary production and dissolved oxygen concentration) in 3 vertical biological layers, (ii) prediction of both temporal and spatial distribution of mid-trophic (micronekton) functional groups (Lehodey et al., 2010b), (iii) prediction of both temporal and spatial distribution of age-structured predator populations, (iv) prediction of total catch and size frequencies by fleet when fishing effort is available, and (v) parameter optimization based on fishing data assimilation techniques (Senina et al., 2008).
Several challenging issues need to be addressed to adapt this model to small pelagic fish. First, the model domain for tuna applications is at basin-scale, thus the model can run at relatively low spatial (∼1° to 2°) and temporal (∼1 month) resolution for parameter optimization. Conversely, the small pelagic species like anchovy and sardines are mainly located in coastal areas where the main factors driving the variability in eggs and larvae abundances (enrichment, concentration and retention), as identified by Bakun (1996), are likely to be strongly influenced by mesoscale activity. Thus, the approach requires a high resolution regional model that accurately represents mesoscale physical and biogeochemical patterns. Another key difference is the type of available observation that can be used in the parameter estimation approach. For tuna application, fishing data is used since there is a long historical (50 years) fishing period with relatively well detailed (spatially-disaggregated) records of catch, effort and size distribution of catch over all the oceanic basin. For anchovies and sardines, as historical catch data is often based on port landings (i.e., no detailed spatial information), and the fishing effort can be huge but during short periods of time, this data provides scarce information on yearly dynamics (Fréon et al., 2008). Therefore, for these species we used eggs and larvae data collected during scientific cruises to apply data assimilation techniques.
Early life history and recruitment mechanisms, that are strongly influenced by the environmental conditions, largely determine the dynamics of adult fish population (Beverton and Holt, 1957). Since early life history is a critical period, this first modeling effort to develop a SEAPODYM application to small pelagics focuses on the spawning habitat and eggs and larvae dynamics of the Peruvian anchovy (Engraulis ringens, know also as “anchoveta”) and sardine (Sardinops sagax) in the HCS. These two species have a relatively short life span (around 4 and 8 years, respectively) with a maximum size of 20 cm and 40 cm respectively, a fast growth and early maturity (one and two years, respectively) (Gutiérrez et al., 2007). Both anchovy and sardine adult feed mainly on zooplankton. However, sardines are primarily filter-feeders and consume preferentially small size zooplankton (small copepods and fewer euphausiids), while anchovies mainly forage on large copepods and euphausiids (Espinoza and Bertrand, 2008, Espinoza et al., 2009).
This model will allow us to identify the mechanisms that define favorable conditions in habitats and to describe why other areas are less optimal. For clarity sake, the version for small pelagics is named SEAPODYM-SP. This paper presents the model and the methodology developed to use eggs and larvae data in a robust statistical framework for the optimization of the parameters controlling the spawning habitat and early life history of small pelagic fishes. It allows to discriminate the different mechanisms controlling fish spawning habitat and larval recruitment for small pelagic fish. The approach is based on climatological series of environmental variables and eggs and larvae data. In the next section, the data, modeling and optimization methodology are described. The optimized parameters and associated functional relationships describing the fish habitat, and the resulting spatial patterns of eggs and larvae are presented in the result section. A discussion of the results and conclusions are drawn in the fourth and fifth section.
Section snippets
Eggs and larvae data
Since 1961, the Peruvian Sea Research Institute (Instituto del Mar del Peru, IMARPE) has been conducting regular research cruises to sample anchovy eggs and larvae along the Peruvian coast between 5°S and 18°S. In the present study, data collected from 1961 to 2008 were used. Fig. 1a shows a typical cruise in March–April 2001. Samples were collected using different types of net. To avoid dealing with sampling differences between nets, only data collected with the Hensen net (characterized by
Eggs and larvae distributions
The anchovy and sardine eggs and larvae collected all along the Peruvian coast were mainly concentrated between 6°S and 14°S. The highest concentrations were observed near the coast, at the edge of the continental shelf (Fig. 3). Though anchovy eggs were found all along the coast without particular concentration patterns (Fig. 3a), anchovy larvae appeared frequently in higher density in the northern region from 6°S to 10°S (Fig. 3c). A possible enrichment by larval drift from nearby regions or
Discussion
Since pioneering works from a century ago (e.g., Hjort, 1914) marine biologists have searched to explain the variability in larvae survival and the mechanisms that drive the recruitment of juvenile fish (Fréon et al., 2005). Despite substantial sampling efforts, the mechanisms at work in the highly dynamic marine environment remain partly unclear. Laboratory experiments have been used to identify the optimal temperature range for larval growth (Llanos-Rivera and Castro, 2006), and measure the
Conclusion
The majority of biophysical models of fish larvae are Lagrangian individual based-models (Miller, 2007, Gallego et al., 2007), for which there are still only a few examples of parameter optimization. The present study provides a different approach using an Eulerian model of eggs and larvae dynamics with an inverse parameter optimization method. This modeling framework is a promising tool to investigate the mechanisms responsible for the strong interannual variability of small pelagic
Acknowledgments
This study formed part of the Ph.D dissertation of O. Hernandez funded by CLS, France (Collecte Localisation Satellites) and a research grant supported by the French National Research Agency (ANR) within the Peru Ecosystem Projection Scenarios ANR-VCMS08 Project. This work is a contribution to the cooperative agreement between the Instituto del Mar del Peru (IMARPE), the Institut de Recherche pour le Développement (IRD), and of the LMI DISCOH. We thank Aurélie Albert for providing the
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