Manuel Esser

We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with
mutation. To depict repeating changes of the environment, all of the model parameters vary over time as piecewise
constant and periodic functions, on an intermediate time scale between those of stabilization of the resident population
(fast) and exponential growth of mutants (slow). This can biologically interpreted as the influence of seasons or the
deviation of drug concentration during medical treatment. The typical evolutionary behaviour can be studied by looking
at limits of large populations and rare mutations.
Analysing the influences of the changing environment carefully on each time scale, we are able to determine the
effective growth rates of emergent mutants and their invasion of the resident population. We describe this growth as a
mesoscopic scaling-limit of the orders of population sizes, where we observe an averaging effect of the invasion fitness.
Moreover, we prove a limit result for the sequence of consecutive macroscopic resident traits that is similar to the socalled
trait-substitution-sequence.
This talk is based on joint work with Anna Kraut.