This workshop aims at bringing together several experts of different fields of mathematical biology, in order to explore new results and new research directions, from population dynamics to kinetic modelling of ecosystems and game theory .
It will take place in Amphitheatre Hermite, Institut Henri Poincaré, Paris, from the 3rd to the 5th of December.
Program
Wednesday 3/12
14h-14h50 : Laura Kanzler (Laboratoire Jacques-Louis Lions, CNRS, Sorbonne Université) « Modelling the evolution of the size-distribution in aquatic ecosystems »
14h50-15h40 : Elisa Affili (LMRS, Université de Rouen Normandie)
With support from: Sorbonne Université, LJLL (Emergence grant), Paris Dauphine Université PSL, CEREMADE (PSL Young Researcher Grant), Institut Henri Poincaré.
Abstracts
This section will be updated regularly.
Laura Kanzler (Laboratoire Jacques-Louis Lions, CNRS, Sorbonne Université) Modelling the evolution of the size-distribution in aquatic ecosystems
Trophic interactions between animals in aquatic ecosystems were matter of interest since the 1960s, where it was quickly discovered that the body size of individuals acts as ’master trait’ in food webs of animals, giving rise to emergent distributions of biomass, abundance and production of organisms. We propose and investigate a deterministic jump-growth model, which is given by a kinetic equation for coalescing particles, aiming to capture this emergence phenomenon in aquatic ecosystems. The equation of interest is derived from individual based dynamics governed by a stochastic process. Following the observation of the body mass being the crucial trait in these dynamics it is based on the assumption that binary interactions between individuals in the ecosystem take place: A predator feeding on a prey, which then results in growth of the predator with assimilating a certain (usually very small) amount of its prey’s mass as well as plankton production. Analytical results in various parameter regimes are discussed and numerical simulations underlying these observations are given.
Cécile Taing (LMA, Université de Poitiers, INRIA Paris) On the Fisher infinitesimal model without variability
We study the long-time behavior of solutions to a model of sexual populations structured in phenotypes. The model features a nonlinear integral reproduction operator derived from the Fisher infinitesimal operator and a linear trait-dependent selection term. The reproduction operator describes here the inheritance of the mean parental traits to the offspring without variability. First, we show that, under assumptions on the growth of the selection rate, Dirac masses are stable around phenotypes for which the difference between the selection rate and its minimum value is less than 1/2. Then, we prove the convergence in some Fourier-based distance of the centered and rescaled solution to a stationary profile under some conditions on the initial moments of the solution. The use of the Fourier-distance for probability measures has been inspired from the work of Lorenzo Pareschi and Giuseppe Toscani in 2006 for kinetic models of Boltzmann-Maxwell type. This work has been done in collaboration with Amic Frouvelle (Université Paris Dauphine).
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