Dominance patterns in dynamic environments

Natural environments are seldom static and therefore it is important to ask how a population adapts in a changing environment. We consider a finite, diploid population with intermediate dominance evolving in a periodically changing environment and study how the fixation probability of a rare mutant depends on its dominance coefficient and the rate of environmental change. We find that in slowly changing environments, the dominance patterns are the same as in the static environment, that is, if a mutant is beneficial (deleterious) when it arrives, it is more (less) likely to fix if it is dominant. But in fast changing environments, these patterns depend on the mutants fitness on arrival as well as that in the time-averaged environment. We find that in a rapidly varying environment that is neutral or deleterious on-average, an initially beneficial (deleterious) mutant that arises while selection is decreasing (increasing) has a fixation probability lower (higher) than that for a neutral mutant leading to a reversal in the standard dominance patterns. We also find that recurrent mutations decrease the phase lag between the environment and the allele frequency, irrespective of the level of dominance.