Stochasticity‐induced stabilization in ecology and evolution: a new synthesis

Abstract

The ability of random environmental variation to stabilize competitor coexistence was pointed out long ago and, in recent years, has received considerable attention. Analyses have focused on variations in the log abundances of species, with mean logarithmic growth rates when rare, Er, used as metrics for persistence. However, invasion probabilities and the times to extinction are not single‐valued functions of Er and, in some cases, decrease as Er increases. Here, we present a synthesis of stochasticity‐induced stabilization (SIS) phenomena based on the ratio between the expected arithmetic growth normalμ and its variance g. When the diffusion approximation holds, explicit formulas for invasion probabilities and persistence times are single‐valued, monotonic functions of μ/g. The storage effect in the lottery model, together with other well‐known examples drawn from population genetics, microbiology, and ecology (including discrete and continuous dynamics, with overlapping and non‐overlapping generations), are placed together, reviewed, and explained within this new, transparent theoretical framework. We also clarify the relationships between life‐history strategies and SIS, and study the dynamics of extinction when SIS fails.

Intraspecific variability in fluctuating environments: mechanisms of impact on species diversity

“…We further assumed a mode of competition that (in the absence of ITV) does not lead by itself to a disadvantage or advantage of rare species (Chesson and Warner 1981) so it does not support stochasticity‐induced stabilization (Dean and Shnerb 2020). As a result, an increase in the amplitude of temporal environmental fluctuations has only negative effect on species richness, and this allows us to identify the influence of the portfolio effect unambiguously.…”

“…With this duel competition scheme, both mortality and reproduction are identically affected by fitness. This keeps the model linear (Meyer and Shnerb 2018) and avoids stochasticity‐induced stabilization effects (Chesson and Warner 1981, Chesson 2000, Dean and Shnerb 2020). For two homogeneous species competition, where all individuals in a species have the same fitness, the mean frequency of species 1, x , satisfies the classical logistic equation…”

Stochasticity-induced stabilization weakens in diverse communities

“…Second, the single-species probability distribution function P ( x ), which is the chance to find a given species with n = Nx individuals (i.e., at frequency x ), must decay close to x = 0. When P ( x ) diverges at x = 0 – even if the probability distribution is still normalizable – the chance of extinction (due to the combined effect of environmental stochasticity which widens P ( x ) and demographic fluctuations which lead to extinction at small abundances) is quite large and the rate at which S decreases is relatively high [9, 11].…”

“…To resolve this problem, a few mechanisms that may facilitate coexistence have been presented and analyzed in the literature [7]. One of the most important has to do with the ability of stochastic temporal fluctuations to stabilize an otherwise unstable, or weakly stable, coexistence state [8, 9]. This counterintuitive phenomenon was discovered about forty years ago [10–12] and has been discussed since then by many authors.…”

Invasion growth rate and its relevance to persistence: a response to Technical Comment by Ellner et al.

“…IGR also neglects the effect of environmentally induced abundance variations, which play an important role in driving a population towards low frequencies. This issue was analysed by Dean and Shnerb (2020), who showed that, when demographic stochasticity is negligible and the diffusion approximation holds, and are determined by the ratio between IGR and the strength of environmental stochasticity.…”