Evolutionary Dynamics

Evolutionary dynamics treats the growth and decay of populations under conditions that influence reproduction, competition, predation and selection. The Lotka–Volterra equations are population equations that describe population cycles between predators and prey. Symbiotic dynamics can lead to stable ecosystems among a wide variety of species. Natural selection operates through the principle of relative fitness among species. A simple frequency-dependent fitness model is the replicator equation, which follows a zero-sum game among multiple species whose total populations reside within a simplex. Many closely related species, connected by mutation, are called quasispecies. The quasispecies equation includes mutation among quasispecies through a mutation matrix that drives diffusion in a multidimensional fitness landscape. Adding frequency-dependent fitness to the quasispecies equation converts it to the replicator–mutator equation, which captures collective group dynamics. Game theory provides a different perspective on the adoption of strategies for species evolving on a fitness landscape.