Abstract
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 environment 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.
Highlights
Fish population dynamics models together with parameter estimation techniques are essential to provide assessment of the fish abundance and fishery exploitation level
The classical data used in fishery science to calibrate models are fishing effort, catch and length frequency data
We developed an advection-diffusion size-structured fish population dynamics model and applied it to simulate the skipjack tuna population in the Indian Ocean
Summary
Fish population dynamics models together with parameter estimation techniques are essential to provide assessment of the fish abundance and fishery exploitation level. Population dynamics model, size structure, well-posed initialboundary value problem, statistical parameter estimation, tuna fisheries, stock-assessment. Because of non-uniform mortality over sizes, bias on growth and mortality estimates may result from this procedure [5] Another point concerning tuna fisheries is that they are highly heterogeneous in space and time. The dynamics of the population of fish is described through a density function p(x, y, s, t), where position (x, y) ∈ Ω the bounded domain representing the ocean, size or length s ∈ (S0, S1) and time t ∈ (0, T ). The parameterizations of the processes involved in the time evolution of the population are described in detail in the following subsections
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