Abstract:
Population genetics and population demography are classically studied separately. We introduce a new probabilistic model aiming at combining the two approaches, through the definition of the behaviour of individuals forming a given population. We consider a population of individuals characterized by their genotype at a bi-allelic locus. The population is modelled by a 3-type birth-and-death process with Mendelian reproduction and competition. This process is studied under a large population and fast reproduction scaling, and is shown to converge toward a slow-fast dynamics, whose slow component is a two dimensional diffusion process giving the joint dynamics of population demography and population genetics. This diffusion process gets extinct almost surely in finite time and its quasi-stationary behaviour is studied.
Biography:
Since September 2014 Camille Coron has been a maître de conférences, at Laboratoire de Mathématiques d'Orsay (Université Paris Sud). She is a member of the team Probability and statistics. She is interested in probability and statistics applied to ecology. In particular, she studies the respective roles of demography and mating systems, on Darwinian evolution. She did her Ph.D. thesis at the Center for Applied Mathematics of École Polytechnique, under the supervision of Sylvie Méléard. During one year she was a Hadamard Lecturer, at Laboratoire de Mathématiques d'Orsay. She is also a member of the Chaire Modélisation Mathématique et Biodiversité.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai