An advection-diffusion-reaction size-structured fish population dynamics model combined with a statistical parameter estimation procedure: Application to the Indian Ocean skipjack tuna fishery - Blaise Faugeras; Olivier Maury (Mathematical Biosciences and Engineering)
We develop an advection-diffusion size-structured fish populationdynamics model and apply it to simulate the skipjack tunapopulation in the Indian Ocean. The model is fully spatialized, andmovements are parameterized with oceanographical and biologicaldata; thus it naturally reacts to environment changes.We first formulate an initial-boundary valueproblem and prove existence of a unique positive solution. We thendiscuss the numerical scheme chosen for the integration of thesimulation model.In a second step we address the parameter estimation problem for such a model.With the help of automatic differentiation, we derive the adjoint code which is usedto compute the exact gradient of a Bayesian cost functionmeasuring the distance between the outputs of the model and catch and length frequency data.A sensitivity analysis shows that not all parameters can be estimated from the data.Finally twin experiments in which pertubated parameters are recoveredfrom simulated data are successfully conducted.