Monday, October 6, 2014 (3:30 p.m. in Yost 306)

Title: Stochastic Modeling of Darwinian Evolution in a Chemostat

Speaker: Sylvie Méléard (École polytechnique)

Abstract: We are interested in modeling the Darwinian evolution
resulting from the interplay of phenotypic variation and natural
selection through ecological interactions, in the specific scales of
the biological framework of adaptive dynamics. We consider a
multi-resources chemostat model, where  the competition between
bacteria results from the sharing of several resources which have
their own dynamics. Starting from a stochastic birth and death process
model, we prove that, when advantageous mutations are rare, the
population behaves on the  mutational time scale as a jump process
moving between equilibrium states. An essential technical ingredient
is the study of the long time behavior of a chemostat multi-resources
dynamical system. In the small mutational steps limit this process in
turn gives rise to a differential equation in phenotype space called
canonical equation of adaptive dynamics. From this canonical equation
and still assuming small mutation steps, we prove a rigorous
characterization of the evolutionary branching points.