Evolutionary Dynamics in a Varying Environment: Continuous versus Discrete Noise

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.