Mutator Gene Model with Three Classes of Evolutionary States

The mutator gene model is one of the fundamental models of modern evolutionary dynamics. Usually, one considers a transition between two evolutionary regimes: the wild-type and mutator type. In this study, we introduce a hierarchy of three types with the transitions between them, considering an extra allele for the mutator gene. We examine both the unidirectional transitions between types and symmetric transition case. The analytical solution obtained is supported by numerical simulations.