–
June 30, 2016
We consider a stochastic model of population dynamics where each individual is characterized by a natural birth rate, a logistic death rate due to age or competition and a probability of mutation at each birth event. Our trait space is finite and we choose parameters such that the induced fitness landscape consists in a double-well : mutant individuals with negative fitness have to be created in order for the population to reach a trait with positive fitness. We focus on the limit of large population and rare mutations with the aim of creating a metastability framework : for a well chosen speed of convergence, the exit time of the double-well is random and its law can be explicitely computed.
This is a work in progress in collaboration with Anton Bovier (Bonn University).
