Adaptation of a population to a changing environment under the light of quasi-stationarity

Aurélien Velleret

Published 2019-03-25Version 1

We consider a model of diffusion with jumps intended to illustrate the adaptation of a population to the variation of its environment. Assuming that our deterministic environment is changing regularly towards a constant direction, we obtain the existence and uniqueness of the quasi-stationary distribution, the associated survival capacity and the Q-process. Our approach provides moreover several results of exponential convergence (in total variation for the measures). From these summary information, we can characterize the efficiency at which adaptation occurs, and see if this adaptation is rather internal (renewal of the population from the invasions of mutants) or external (survival would be too low otherwise).