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Stochastic interactions in ecological dynamics: microscopic models, macroscopic approximations and inference - Abstract:
Interactions between individuals, whether of the same or different species, drive ecological dynamics through mechanisms such as competition, predation, or mutualism. In most dynamical models, including the well-known Lotka-Volterra equations, the mathematical form of interaction rates is often chosen without justifications about the underlying biological processes. This leads to both theoretical and empirical challenges: implicit assumptions are made regarding time, space, and system scales, and it becomes difficult to estimate the parameters of these functional forms from data. In this talk, I will present an alternative approach: first, we develop stochastic microscopic models that describe individual-level interactions—for example, between predator and prey; second, we derive approximations for the distributions of interaction rates; and finally, we use these approximations to estimate parameters and perform inference from experimental data. - Affiliation:
Evo-Eco-Paléo UMR CNRS 8198 – University of Lille
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Team MacBes, Inria center at Université Côte d’Azur (France)
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Laboratoire J.A. Dieudonné, Université Côte d’Azur (France)
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Laboratoire de Mathématiques (LAMA) at Université Savoie Mont-Blanc (France)
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Team MUSCLEES at Inria Paris (France) and at the Jacques-Louis Lions Laboratory at Paris Sorbonne University (France)
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Mathematics Institute at the University of Warwick (United Kingdom)
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