Long-term evolutionary dynamics on graphs : Space voyages exploring new stars

Evolutionary dynamics in well-mixed populations have been studied quite extensively. While the respective studies provide a good starting point for a mathematical analysis, populations in the wild are rarely well-mixed. Natural populations often come with spatial structures, resulting in dynamics different from the well-mixed case. Therefore, it is crucial to understand evolution on spatial structures. To this end, we use the framework of evolutionary graph theory, where nodes represent asexually reproducing entities, and links define the neighborhood of nodes. First, we develop a model to study population structures adapting to a single-peaked fitness landscape. The mutation rates are considered very low, making the mutation-selection dynamics sequential. Surprisingly, a structure with a poor ability to fix beneficial mutants outcompetes the well-mixed population in the long run by achieving higher fitness. This result is explained by the structure’s ability to reject disadvantageous mutants more efficiently. Subsequently, we discovered that this phenomenon occurs in the majority of randomly generated spatial structures. Consequently, it is not only the beneficial mutant regime that is relevant for adaptive evolution, but the deleterious mutant regime is equally important.