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Environmental variation can play an important role in ecological competitionby influencing the relative advantage between competing species. Here, weconsider such effects by extending a classical, competitive Moran model toincorporate an environment that fluctuates periodically in time. We adaptmethods from work on these classical models to investigate the effects of themagnitude and frequency of environmental fluctuations on two importantpopulation statistics: the probability of fixation and the mean time tofixation. In particular, we find that for small frequencies, the system behavessimilar to a system with a constant fitness difference between the two species,and for large frequencies, the system behaves similar to a neutrallycompetitive model. Most interestingly, the system exhibits nontrivial behaviorfor intermediate frequencies. We conclude by showing that our results agreequite well with recent theoretical work on competitive models with astochastically changing environment, and discuss how the methods we developease the mathematical analysis required to study such models.

Neutral competition in a deterministically changing environment: revisiting continuum approaches