The field of population genetics relies on mathematical models to describe genetic variations among individuals. One question of interest is to understand the behavior of a mutant that has a higher fitness, defined as an ability to spread or reproduce. Fundamental models apply to well-mixed populations, where all individuals interact equally. While these models can be theoretically analyzed, they are of limited interest to describe natural systems, where spatial structure plays an important role (e.g. microbial communities or ecological systems). We introduce a new model of population on graphs, where subpopulations are placed on the nodes of a graph structure and can migrate along the edges of the graph, following Markovian updates. We apply a branching process approximation, a stochastic process analysis that allows us to derive several results on the dynamics of the spread of a mutant. In particular, we compute the key quantity of the fixation probability of a mutant, i.e. how likely it is for mutants to take over the whole graph population, for any graph structure. We show that any graph structure makes it more likely for mutants to take over the population. We support our results with stochastic simulations.

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