  Populations of replicating entities frequently experience sudden or cyclical
changes in environment. We explore the implications of this phenomenon via a
environmental switching parameter in several common evolutionary dynamics
models including the replicator dynamic for linear symmetric and asymmetric
landscapes, the Moran process, and incentive dynamics. We give a simple
relationship between the probability of environmental switching, the relative
fitness gain, and the effect on long term behavior in terms of fixation
probabilities and long term outcomes for deterministic dynamics. We also
discuss cases where the dynamic changes, for instance a population evolving
under a replicator dynamic switching to a best-reply dynamic and vice-versa,
giving Lyapunov stability results.
