In mathematics, the replicator equation is a type of dynamical system used in evolutionary game theory to model how the frequency of strategies in a population changes over time. It is a deterministic, monotone, non-linear, and non-innovative dynamic that captures the principle of natural selection in strategic interactions.
The replicator equation describes how strategies with higher-than-average fitness increase in frequency, while less successful strategies decline. Unlike other models of replication—such as the quasispecies model—the replicator equation allows the fitness of each type to depend dynamically on the distribution of population types, making the fitness function an endogenous component of the system. This allows it to model frequency-dependent selection, where the success of a strategy depends on its prevalence relative to others.
