Evolution of a Fluctuating Population in a Randomly Switching Environment

Abstract

Environment plays a fundamental role in the competition for resources, and hence in the evolution of populations. Here, we study a well-mixed, finite population consisting of two strains competing for the limited resources provided by an environment that randomly switches between states of abundance and scarcity. Assuming that one strain grows slightly faster than the other, we consider two scenarios--one of pure resource competition, and one in which one strain provides a public good--and investigate how environmental randomness (external noise) coupled to demographic (internal) noise determines the population's fixation properties and size distribution. By analytical means and simulations, we show that these coupled sources of noise can significantly enhance the fixation probability of the slower-growing species. We also show that the population size distribution can be unimodal, bimodal or multimodal and undergoes noise-induced transitions between these regimes when the rate of switching matches the population's growth rate.

15 pages, 8 figures: Main text (5+ pages, 4 figures) followed by Supplemental Material (10 pages, 4 supplementary figures). To appear in Physical Review Letters. Supporting mp4 and ogv videos are available at https://doi.org/10.6084/m9.figshare.5082712 and http://www1.maths.leeds.ac.uk/~amtmmo/KEM_videos/index.html

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• Cooperation in Microbial Populations: Theory and Experimental Model Systems
• Fixation in Fluctuating Populations
• Game-environment feedback dynamics in growing population: Effect of finite carrying capacity