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/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 sizes and small mutation rates, the relative reproductive rate of a successful replacer can be as low as 1/e.Author summary: Traditional mathematical models of evolution study how different types of reproducing individuals compete in a population. Reproduction is often treated as a random process where one individual gives birth and another random individual dies. However, this randomness means that an offspring might replace another individual of its own type, effectively resulting in a wasted reproductive event. Here we introduce a new type of an individual, called a “replacer”. Replacers are highly efficient competitors. When they reproduce, their offspring specifically target and replace individuals of a competing type, avoiding such wasted effort. We use mathematical models to explore how these replacers perform compared to “standard” individuals, in different regimes. We find that sometimes being a replacer does not help at all, but sometimes it gives a massive boost. For example, once established in the population, replacers are incredibly difficult to displace. This defensive advantage is so powerful that replacers can dominate even if they reproduce at a substantially lower rate than their standard competitors. Our findings highlight that efficiency can ultimately outweigh raw reproductive speed.