  Environmental changes greatly influence the evolution of populations. Here,
we study the dynamics of a population of two strains, one growing slightly
faster than the other, competing for resources in a time-varying binary
environment modeled by a carrying capacity switching either randomly or
periodically between states of abundance and scarcity. The population dynamics
is characterized by demographic noise (birth and death events) coupled to a
varying environment. We elucidate the similarities and differences of the
evolution subject to a stochastically- and periodically-varying environment.
Importantly, the population size distribution is generally found to be broader
under intermediate and fast random switching than under periodic variations,
which results in markedly different asymptotic behaviors between the fixation
probability of random and periodic switching. We also determine the detailed
conditions under which the fixation probability of the slow strain is maximal.
