Evolutionary invasion analysis

This article is about modelling the invasion of rare mutants using differential equations. For a related article, see Evolutionary dynamics.

Evolutionary invasion analysis is a set of mathematical modeling techniques that use differential equations to study the long-term evolution of traits in asexually and sexually reproducing populations. It is a branch of mathematical evolutionary theory that overlaps with evolutionary dynamics and adaptive dynamics. All three fields use differential equations and sometimes produce identical results, but different researchers prefer different terms.

Evolutionary invasion analysis makes it possible to identify conditions on model parameters for which the mutant population dies out, replaces the resident population, and/or coexists with the resident population. Long-term coexistence of the two phenotypes is known as evolutionary branching. When branching occurs, the mutant establishes itself as a second resident in the environment.

Central to evolutionary invasion analysis is the mutant's invasion fitness. This is a mathematical expression for the long-term exponential growth rate of the mutant subpopulation when it is introduced into the resident population in small numbers. If the invasion fitness is positive (in continuous time), the mutant population can grow in the environment set by the resident phenotype. If the invasion fitness is negative, the mutant population swiftly goes extinct.

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