By Michel Benaim (Université de Neuchâtel)
An important issue in ecology is to understand under which conditions a
group of interacting species - whether they are plants, animals, or
viral particles - can coexist over long periods of time. A fruitful
approach to this question has been the development of nonlinear models
of deterministic interactions, leading to what is now known as the
Mathematical theory of persistence.
Persistence amounts to saying that the dynamical system describing the
species interactions admits an attractor bounded away from
extinction (i.e. the subset of the state-space where the abundance of
one or more species vanishes).
Beside biotic interactions, environmental fluctuations play a key role
in population dynamics. In order to take into account these fluctuations
and to understand how they may affect persistence, deterministic models
need to be replaced by stochastic ones and the theory needs to be
This talk will survey recent results in this direction laying the
groundwork for a mathematical theory of stochastic persistence.
Part of this work stems from a close collaboration between Neuchatel’s
research group in probability and UC Davis department of Evolution and