Fixation and absorption in a fluctuating environment

Abstract

A fundamental problem in the fields of population genetics, evolution, and community ecology, is the fate of a single mutant, or invader, introduced in a finite population of wild types. For a fixed-size community of N individuals, with Markovian, zero-sum dynamics driven by stochastic birth-death events, the mutant population eventually reaches either fixation or extinction. The classical analysis, provided by Kimura and his coworkers, is focused on the neutral case, [where the dynamics is only due to demographic stochasticity (drift)], and on time-independent selective forces (deleterious/beneficial mutation). However, both theoretical arguments and empirical analyses suggest that in many cases the selective forces fluctuate in time (temporal environmental stochasticity). Here we consider a generic model for a system with demographic noise and fluctuating selection. Our system is characterized by the time-averaged (log)-fitness s and zero-mean fitness fluctuations. These fluctuations, in turn, are parameterized by their amplitude γ and their correlation time δ. We provide asymptotic (large N) formulas for the chance of fixation, the mean time to fixation and the mean time to absorption. Our expressions interpolate correctly between the constant selection limit γ → 0 and the time-averaged neutral case s=0.

Neutral competition in a deterministically changing environment: Revisiting continuum approaches

“…Incorporating the effects of a changing environment using deterministic periodic fitness fluctuations as above allows for simplified analysis when compared to stochastic fluctuations. Of course, there are many environmental changes that are modeled stochastically [9,10,11,12,13,14,15,16,17]. We therefore present a comparison of our results with those from an analogous competition model with a stochastically varying environment, and show that the qualitative behaviors of the two models match.…”

“…We have investigated the effects of a continuously fluctuating environment on two neutrally-competitive species by allowing each species' reproductive fitness to vary periodically over time, while maintaining the same long-term average. Our framework can be considered a simplification of recent and classic methods for analyzing competition within a stochastically variation environment [9,10,11,12,13,14,15,16,17]. By considering continuous-time environmental variation, we are better able to adapt and utilize standard analytical approaches to calculating the probability of fixation and mean time to fixation of either species in the competitive process.…”

“…More recently, and as a direct consequence of the criticisms of the results stemming from neutral theory, emphasis has been given to neutral models that incorporate fluctuating selective pressure due to a changing environment [9,10,11,12,13,14,15,16,17,18]. These models generally assume that the population-level fitness of each species changes (positively or negatively) due to changes in the environment.…”

Intra-Specific variability in fluctuating environments - mechanisms of impact on species diversity

“…We study the dynamics of a continuous time process, having in mind a community of J competing individuals. To avoid nonlinear effects that may stabilize coexistence states via the storage mechanism [8], we use (as in [27,38]) a simple model in which the relationships between fitness and growth rate are linear. We consider competition between two or more populations, where a chance encounter between two individuals may end up in a struggle over, say, a piece of food, a mate or a territory.…”

“…In particular, demographic stochasticity refers to stochastic events acting on individuals independently of each other while environmental stochasticity, or environmental fluctuations, reflect erratic changes affecting entire populations synchronously. Environmental fluctuations have been shown to play a central role in shaping species abundances in multiple communities [20][21][22][23], and their effect on species diversity [24] and persistence [25][26][27][28] have been the focus of much contemporary work.…”