Game changing mutation.

Abstract

We present a model of the effect of mutation on haploid sexually reproducing populations by modelling the reproductive dynamics as occurring in the context of a common interests game played by the loci, with the alleles in the role of pure actions. Absent mutations, the population will deterministically converge to a pure Nash equilibrium of the game. A novel mutation adds new alleles, hence is tantamount to a change of the game by the addition of new actions. If the new game defined by the mutation removes the former pure Nash equilibrium the game changing mutation becomes in addition a Nash equilibrium changing mutation, as the population will then move to a new equilibrium with an increase in fitness. A graph of common interests games is defined, and evolution by mutation is modelled as a path through this graph. We discuss two applications-fitness valley crossing and evolutionary contingency.