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. (English) Zbl 1097.92058
Summary: We develop an advection-diffusion size-structured fish population dynamics model and apply it to simulate the skipjack tuna population in the Indian Ocean. The model is fully spatialized, and movements are parameterized with oceanographical and biological data; thus it naturally reacts to environmental changes. We first formulate an initial-boundary value problem and prove existence of a unique positive solution. We then discuss the numerical scheme chosen for the integration of the simulation 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 used to compute the exact gradient of a Bayesian cost function measuring 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 recovered from simulated data are successfully conducted.
MSC:
92D40 | Ecology |
35K57 | Reaction-diffusion equations |
91B76 | Environmental economics (natural resource models, harvesting, pollution, etc.) |
86A05 | Hydrology, hydrography, oceanography |
35K15 | Initial value problems for second-order parabolic equations |
35K20 | Initial-boundary value problems for second-order parabolic equations |
65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
65K10 | Numerical optimization and variational techniques |
93B30 | System identification |
65C20 | Probabilistic models, generic numerical methods in probability and statistics |
62P10 | Applications of statistics to biology and medical sciences; meta analysis |