A classical question in population genetics is to understand the spread of a mutant with a fitness advantage in a population, in  particular its fixation probability. This question has been thoroughly studied through mathematical models for well-mixed populations, where all individuals interact the same way. However, natural microbial populations often have complex structure. This can impact their evolution, notably the ability of mutants to take over. Mutant fixation probabilities are known to be unaffected by structures which are sufficiently symmetric. To model more complex structures, works from evolutionary graph theory consider individuals on the nodes of a graph. They show that some structures can amplify or suppress natural selection, but this result depends on the detail of the interaction, known as update rule. Here, we propose a model of spatially structured populations on graphs directly inspired by batch culture experiments, alternating local growth on nodes and migration-dilution steps, and yielding successive bottlenecks. This model bridges a gap between the approach of evolutionary graph theory, and Wright-Fisher models. Using a branching process approach, we show that spatial structure with frequent migrations between nodes can only yield suppression of natural selection, but can accelerate fixation and extinction. We discuss the effect of symmetry in the graph. We also show that amplification of natural selection can only happen in a restructed regime of rare migrations and very small fitness advantage.

 

Refererence: "Frequent asymmetric migrations suppress natural selection in spatially structured populations", Alia Abbara and Anne-Florence Bitbol, PNAS Nexus (2023).