  Environmental variations can significantly influence how populations compete
for resources, and hence shape their evolution. Here, we study population
dynamics subject to a fluctuating environment modeled by a varying carrying
capacity changing continuously in time according to either binary random
switches, or by being driven by a noise of continuous range. We consider a
prototypical example of two competing strains, one growing slightly slower than
the other, and consider also the scenario where the slow strain is a public
goods producer. By systematically comparing the effect of binary- versus
continuously-varying environment, we study how different noise statistics
(mean, variance) influence the population size and fixation properties. We show
that the slow strain fixation probability can be greatly enhanced for a
continuously-varying environment compared to binary switches, even when the
first two moments of the carrying capacity coincide.
