Replicator Equation - Generalizations

Generalizations

A generalization of the replicator equation which incorporates mutation is given by the replicator-mutator equation, which takes the following form in the continuous version:

where the matrix gives the transition probabilities for the mutation of type to type . This equation is a simultaneous generalization of the replicator equation and the quasispecies equation, and is used in the mathematical analysis of language.

The replicator equation can easily be generalized to asymmetric games. A recent generalization that incorporates population structure is used in evolutionary graph theory.