Towards a universal model for structured microbial populations

Most of the models studied in evolutionary dynamics consider a well-mixed population. However, this is rarely the case in nature where geographical structure plays a role: migrations and local competition contribute to maintain genetic diversity in a structured population, resulting in a complex evolutionary dynamics. In order to take geographical structure into account, we study a model proposed by Lieberman et al. in which individuals are arranged on a graph. This model considers a weighted directed graph where one individual is placed at each node and replacement probabilities are defined on each edge; the size of the population is kept constant since a birth and a death event occur at each time step. Important results from this model, however, strongly depend on details of the chosen dynamics (in particular, whether we choose first the individual who reproduces or the individual who dies), raising issues on the applicability of the model to experiments. We focus on the star graph which is a well known amplifier of selection in the birth-death case, and show that this property strongly depends on the chosen dynamics, the importance of self-replacement and the initial conditions. In order to make the model more realistic, we study and generalize a coarse-grained version proposed by Houchmandzadeh et al., where a well-mixed subpopulation is placed at each node of a graph and migration probabilities are defined on each edge. We show that it is possible, within this model, to reduce the dependence of the evolutionary outcome on the dynamics.