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Updated: Jun 14, 2026

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
Published on: July 30, 2019
An advection-diffusion-reaction size-structured fish population dynamics model combined with a statistical parameter
Blaise Faugeras1, Olivier Maury
1CNRS I3S, Les Algorithmes, 2000 route des lucioles, BP 121, 06903, Sophia Antipolis Cedex, France. Blaise.Faugeras@unice.fr or Blaise.Faugeras@ifremer.fr.
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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