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; Blaise Faugeras; Olivier Maury

doi:10.3934/mbe.2005.2.719

Mathematical Biosciences and Engineering

2005, Volume 2, Issue 4: 719-741. doi: 10.3934/mbe.2005.2.719

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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 ¹,
Olivier Maury ²

1.
CNRS I3S, Les Algorithmes, 2000 route des lucioles, BP 121, 06903, Sophia Antipolis Cedex
2.
Institut de Recherche pour le Développement, Centre de Recherche Halieutique, avenue Jean Monnet, BP 171, 34200 Sète

Received: 01 February 2005 Accepted: 29 June 2018 Published: 01 October 2005
MSC : 92D25, 92D40, 86A05, 35K15, 35K20, 35K57,65M06, 86A22, 65K10, 93B30.

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.

Keywords:

tuna fisheries,
well-posed initial- boundary value problem,
statistical parameter estimation,
stock-assessment.,
Population dynamics model,
size structure

Citation: Blaise Faugeras, Olivier Maury. 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[J]. Mathematical Biosciences and Engineering, 2005, 2(4): 719-741. doi: 10.3934/mbe.2005.2.719

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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.

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