A Stochastic Adaptive Dynamics Model for Bacterial Populations with Mutation, Dormancy and Transfer

Abstract

This paper introduces a stochastic adaptive dynamics model for the interplay of several crucial traits and mechanisms in bacterial evolution, namely dormancy, horizontal gene transfer (HGT), mutation and competition. In particular, it combines the recent model of Champagnat, M\'el\'eard and Tran (2021) involving HGT with the model for competition-induced dormancy of Blath and T\'obi\'as (2020). Our main result is a convergence theorem which describes the evolution of the different traits in the population on a `doubly logarithmic scale' as piece-wise affine functions. Interestingly, even for a relatively small trait space, the limiting process exhibits a non-monotone dependence of the success of the dormancy trait on the dormancy initiation probability. Further, the model establishes a new `approximate coexistence regime' for multiple traits that has not been observed in previous literature.