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
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1.
CNRS I3S, Les Algorithmes, 2000 route des lucioles, BP 121, 06903, Sophia Antipolis Cedex
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2.
Institut de Recherche pour le Développement, Centre de Recherche Halieutique, avenue Jean Monnet, BP 171, 34200 Sète
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Received:
01 February 2005
Accepted:
29 June 2018
Published:
01 October 2005
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MSC :
92D25, 92D40, 86A05, 35K15, 35K20, 35K57,65M06, 86A22, 65K10, 93B30.
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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.
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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