  Environmental variation can play an important role in ecological competition
by influencing the relative advantage between competing species. Here, we
consider such effects by extending a classical, competitive Moran model to
incorporate an environment that fluctuates periodically in time. We adapt
methods from work on these classical models to investigate the effects of the
magnitude and frequency of environmental fluctuations on two important
population statistics: the probability of fixation and the mean time to
fixation. In particular, we find that for small frequencies, the system behaves
similar to a system with a constant fitness difference between the two species,
and for large frequencies, the system behaves similar to a neutrally
competitive model. Most interestingly, the system exhibits nontrivial behavior
for intermediate frequencies. We conclude by showing that our results agree
quite well with recent theoretical work on competitive models with a
stochastically changing environment, and discuss how the methods we develop
ease the mathematical analysis required to study such models.
