The evolutionary advantage of replacers in the Moran process

Evolution occurs in populations of reproducing individuals. In stochastic descriptions of evolutionary dynamics, such as the Moran process, individuals are chosen randomly for birth and for death. If the same type is chosen for both steps, then the reproductive event is wasted, because the composition of the population remains unchanged. Here we introduce a new phenotype, which we call a replacer. Replacers are efficient competitors. When a replacer is chosen for reproduction, the offspring will always replace an individual of another type (if available). We determine the selective advantage of replacers in well-mixed populations and on one-dimensional lattices. We find that being a replacer substantially boosts the fixation probability of neutral and deleterious mutants. In particular, fixation probability of a single neutral replacer who invades a well-mixed population of size $N$ is of the order of $1/\sqrt N$ rather than the standard $1/N$. Even more importantly, replacers are much better protected against invasions once they have reached fixation. Therefore, replacers dominate the mutation selection equilibrium even if the phenotype of being a replacer comes at a substantial cost: curiously, for large population size and small mutation rate the relative reproductive rate of a successful replacer can be as low as $1/e$.