Replicator Dynamics

The replicator dynamics are the canonical differential equations of evolutionary dynamics, describing how the frequencies of competing types in a population change under selection pressure. Formulated by Taylor and Jonker in 1978, the equation states that a type's per-capita growth rate equals its fitness excess over the population mean — a deceptively simple rule that produces equilibria, limit cycles, and chaos on the population simplex. The replicator dynamics are mathematically equivalent to the Lotka-Volterra equations of ecology, suggesting that competition between biological species and competition between behavioral strategies are instances of the same underlying dynamical grammar. Extensions incorporating mutation, spatial structure, and adaptive dynamics with continuous strategy spaces have broadened the framework far beyond its original game-theoretic context.