Pierre-Emmanuel Jabin

(Université de Nice Sophia-Antipolis, France)

"Selection-mutation Dynamics for the Evolution of Traits in a Population"

This talk aims at introducing some models describing the evolution of a large population of individuals with different biological "traits". The reproduction rate of each individual depends on its trait and on the competition for ressources within the population. In addition mutations may be included, enabling new traits to develop. These models leads to difficult asymptotic problems as the time scale of the mutations is usually much larger than the time scale of births and death. One such asymptotic will in particular be investigated, corresponding to frequent small mutations.