Stochasticity-induced-stabilization: a quantitative analysis

The coexistence of multiple interacting and competing species within natural communities has long posed a challenging theoretical puzzle. Prevailing arguments, including the competitive exclusion principle and May's complexity-diversity relationships, suggest that such coexistence should be unlikely or unstable. However, observations in nature demonstrate that this coexistence is common and persistent. A promising solution to this conundrum involves the role of temporal environmental variations—whether periodic or stochastic—in promoting species coexistence.
To quantitatively analyze this phenomenon and enhance our understanding of stability in such systems, we employ a combination of the diffusion approximation, large-deviation theory (WKB), and numerical analysis. This endeavor enabled the development of novel formulas for invasibility [1,2], a crucial metric for assessing stable coexistence, and exploring the dependence of stability parameters on various factors such as the number of species and the number of temporal niches [3,4]. 

[1] Pande, Fung, Chisholm & Shnerb, Ecology letters 23, 274-282 (2020)
[2] Pande, Tsubery & Shnerb, Ecology Letters 25, 1783-1794 (2022)
[3] Pande & Shnerb, Journal of Theoretical Biology 539, 111053 (2022)
[4] Meyer, Steinmetz & Shnerb, PLOS Computational Biology 18, e1009971 (2022).