Stochastic dynamics for adaptation and evolution of microorganisms

TL;DR

This paper models microbial population dynamics incorporating competition, horizontal transfer, and mutations, demonstrating how transfer rates influence long-term evolution and fixation probabilities through stochastic and deterministic analyses.

Contribution

It introduces a stochastic individual-based model for microbial evolution with horizontal transfer, analyzing its large population limit and effects of transfer on evolution and fixation.

Findings

Transfer rates critically affect long-term behavior.

Horizontal transfer can lead to evolutionary suicide.

Rare mutations and transfer influence fixation probabilities.

Abstract

We present a model for the dynamics of a population of bacteria with a continuum of traits, who compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait with possible mutations. Competition influences individual demographics, affecting population size, which feeds back on the dynamics of transfer. We consider a stochastic individual-based pure jump process taking values in the space of point measures, and whose jump events describe the individual reproduction, transfer and death mechanisms. In a large population scale, the stochastic process is proved to converge to the solution of a nonlinear integro-differential equation. When there are only two different traits and no mutation, this equation reduces to a non-standard two-dimensional dynamical system. We show how crucial the forms of the transfer rates are for the long-term behavior of its solutions. We describe the dynamics of invasion and fixation when one of the two traits is initially rare, and compute the invasion probabilities. Then, we study the process under the assumption of rare mutations. We prove that the stochastic process at the mutation time scale converges to a jump process which describes the successive invasions of successful mutants. We show that the horizontal transfer can have a major impact on the distribution of the successive mutational fixations, leading to dramatically different behaviors, from expected evolution scenarios to evolutionary suicide. Simulations are given to illustrate these phenomena.