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Analyse mathématique de modèles non-locaux en écologie évolutive.

Abstract : In this thesis we consider several nonlocal partial differential equations and integro-differential equations, arising from evolutionary biology models. We aim at performing a rigorous mathematical analysis of extinction, survival and invasion phenomena of these models that lead to relevant biological insights. Firstly, we look at a population facing a linear environmental gradient, that is the optimal trait is linearly dependent of the spatial position (say the temperature along a north-south axis). We show that, under certain conditions on the initial data, the solution spreads in space by accelerating. We also give precise estimates of the asymptotic position of the level sets of the solution. Secondly, we consider a model with a nonlinear environmental gradient. Using perturbative techniques, we construct steady states and, when the gradient is periodic, pulsating fronts. Our analysis reveals how the distribution of the population at equilibrium and its invasion dynamics are affected by the nonlinear gradient. Finally, we introduce new models with nonlocal, heterogeneous, anisotropic diffusion. We investigate their connections with local diffusion models found in the literature, as well as their steady states. Our approach involves the notion of “deciding factors”, and sheds light on the “preferential position of individuals”.
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Submitted on : Friday, October 22, 2021 - 4:31:10 PM
Last modification on : Friday, August 5, 2022 - 10:51:49 AM
Long-term archiving on: : Monday, January 24, 2022 - 4:59:12 PM


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  • HAL Id : tel-03396299, version 1


Gwenaël Peltier. Analyse mathématique de modèles non-locaux en écologie évolutive.. Ingénierie de l'environnement. Université Montpellier, 2021. Français. ⟨NNT : 2021MONTS007⟩. ⟨tel-03396299⟩



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