Développement et ajustement d'un modèle de dynamique des populations structuré en longueur et spatialisé appliqué au stock Nord de merlu (Merluccius merluccius)

The biology of European hake has been largely studied, however some specific processes of its biology, especially growth and migration, are still poorly known. Those uncertainties have consequences on the quality of the stock assessments and on the stock management by limiting the possibility to assess the effect of spatial management measures. Therefore, we develop an integrated length-structured and spatialised model of population dynamics aiming at improving the estimation of unknown parameters of the population dynamic. The model relies on a state model describing the dynamics of the population and the fishing activity, and on an observation model describing the observation processes and providing a likelihood function. A review of the literature shows that modelling growth is a key point in length-structured model. Consequently, we develop a method to assess the impact of several assumptions of time and length discretisation and growth increments distribution in a length-structured population growth model. The method relies (i) on the construction of a design of experiments and (ii) on its analysis using linear models and multivariate regression trees. This generic approach is useful to assess the impact of any discretisation processes in a discret model. In our case, it shows that a quartertly time step, 1cm wide length classes and a gamma distribution of growth increments are appropriate for the Northern stock of hake. A specific attention to the likelihood function has been necessary during the development of the model to provide a robust function and to be consistent with the observation processes. A quasi-Newton algorithm has been selected among several optimisation algorithms to maximize the likelihood function. Estimations of migration and growth rates are obtained by fitting the model to available data. Migration rates are consistent with previous analysis while estimated growth rates are slightly lower than estimates obtained from tagging data. The diagnostic on the spawning stock biomass provided by the model is quite close to current diagnostics obtained from other assessments conducted by ICES. Some parameters of the model are still not identifiable. This, however, does not concerned parameters of interest.