Eco-evolutionary dynamics of a population with randomly switching carrying capacity

Abstract

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 growing 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 (PG) that benefits also the fast (free-riding) strain. 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 social-dilemma-like 'eco-evolutionary game' characterizing the PG production. We determine in what conditions it is best to produce a PG; when cooperating is beneficial but outcompeted by free riding, and when the PG production is detrimental for cooperators. Within a linear noise approximation to populations of varying size, we also accurately analyse the coupled effects of demographic and environmental noise on the size distribution.

Fixation properties of rock-paper-scissors games in fluctuating populations

“…Here, the DMN is always at stationary: Its average vanishes, ξ(t) = 0, and its autocorrelation is ξ(t)ξ(t ) = exp (−2ν|t − t |) [63,62] (here, · denotes the ensemble average over the DMN). The randomly switching carrying capacity therefore reads [55,56]…”

“…is the harmonic mean of K ± and ξ is the multiplicative dichotomous noise ( The PDMP defined by Eq. (20) [62,63,42,55,56] is characterized by the following stationary marginal probability density function (pdf) [55]:…”

“…As shown in Ref. [56], the actual width of the N-QSD can be accurately computed with a linear-noise approximation about the PDMP process (20).…”

“…While EN and IN are naturally interdependent in many biological applications, the theoretical understanding of their coupling is still limited. Recently, progress has been made in simple two-species models [55,56], but the analysis of EN and IN coupling in populations consisting of many interacting species is a formidable task. Here, we study the coupled effect of environmental and internal noise on the fixation properties of three-species rock-paper-scissors games in a population of fluctuating size, when the resources continuously vary between states of scarcity and abundance.…”

Trait-space patterning and the role of feedback in antigen-immunity coevolution

“…In existing generic models where both ecological and evolutionary processes are considered, a separation of timescales is often assumed so that the fast dynamics is slaved to the slow one (reviewed in [16]). In cases where timescales are not treated as separated [17][18][19][20][21][22][23][24], the feedback between changes in diversity and population dynamics tends to be ignored. The goal of this paper is to consider inseparable timescales and at the same time account for feedback effect in order to address the questions raised above.…”