Eco-Evolutionary Dynamics of a Population with Randomly Switching Carrying Capacity

Environmental variability greatly influences the eco-evolutionary dynamics of a population, i.e. it affects how its size and composition evolve. Here, we study a well-mixed population of finite and fluctuating size whose growth is limited by a randomly switching carrying capacity. This models the environmental fluctuations between states of resources abundance and scarcity. The population consists of two strains, one slightly faster than the other, competing under two scenarios: one in which competition is solely for resources, and one in which the slow (“cooperating”) strain produces a public good. We investigate how the coupling of demographic and environmental (external) noise affects the population’s eco-evolutionary dynamics. By analytical and computational means, we study the correlations between the population size and its composition, and discuss the cooperation dilemma arising in the “eco-evolutionary game” of public good production in a fluctuating environment. We determine in which conditions it is best to cooperate and produce a public good; when cooperating is beneficial but outcompeted by the non-producing strain, and when the public good production is detrimental for cooperators. By generalizing the linear noise approximation to populations of varying size, we also analyze the coupled effects of demographic and environmental noise on the size distribution.