Mutability as an altruistic trait in finite asexual populations

Mutation rate (MR) is a crucial determinant of the evolutionary process. Optimal MR may enable efficient evolutionary searching and therefore increase the fitness of the population over time. Nevertheless, individuals may favor MRs that are far from being optimal for the whole population. Instead, each individual may tend to mutate at rates that selfishly increase its own relative fitness. We show that in some cases, undergoing a mutation is altruistic, i.e., it increases the expected fitness of the population, but decreases the expected fitness of the mutated individual itself. In this case, if the population is uniform (completely mixed, undivided), immutability is evolutionary stable and is probably selected for. However, our examination of a segregated population, which is divided into several groups (or patches), shows that the optimal, altruistic MR may out-compete the selfish MR if the coupling between the groups is neither too strong nor too weak. This demonstrates that the population structure is crucial for the succession of the evolutionary process itself. For example, in a uniform population, the evolutionary process may be stopped before the highest fitness is reached, as demonstrated in a one-pick fitness landscape. In addition, we show that the dichotomy between evolutionary stable and optimal MRs can be seen as a special case of a more general phenomenon in which optimal behaviors may be destabilized in finite populations, since optimal sub-populations may become extinct before the benefit of their behavior is expressed.