"Mean time to extinction in a fluctuating environment"Pande, JayantThe mean time to extinction of a species in a given ecosystem is a vital property which determines the future outlook of individual species as well as of the ecosystem as a whole. It relates to other important properties such as the ecosystem biodiversity, and is crucial to know for conservation efforts. Current approaches to calculate the mean time to extinction in a system subject to stochastic influences (environmental and/or demographic) employ the diffusion approximation, and rely on a separation of timescales between the attainment of quasi-equilibrium by the system and the subsequent loss of species. These assumptions fail to hold when the population numbers show large fluctuations. Here we present a new analytical method to calculate the mean time to extinction in a system of two species undergoing competitive dynamics, when the stochasticity in the system may be large. This builds on our previous work on the calculation of the chance of invasion of a species [1, 2], and involves a direct solution of the backward Kolmogorov equation describing the dynamics. We first rederive known expressions for the mean time to extinction in simple systems, and then use our method to present novel formulae in more complicated dynamics. Our results show good agreement with Monte Carlo simulations of the models for a wide parameter space. [1] Taming the diffusion approximation through a controlling-factor WKB method, J. Pande and N.M. Shnerb, Physical Review E 102, 062410 (2020) [2] Quantifying invasibility, J. Pande, Y. Tsubery and N.M. Shnerb, Ecology Letters 25, 1783 (2022) |
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