Quantifying species extinction risk under temporal environmental variance

Species populations are subjected to fluctuations in their surrounding environment, and the strength of these fluctuations has been hypothesized to be a major determinant of the extinction risk of these populations. Therefore, a key question is: How does temporal environmental variance affect the extinction risk of species populations? Previous theory based on the dynamics of single populations typically predicts an increased risk of extinction from the effects of environmental variance. However, previous studies have focused mainly on the case where environmental effects are temporally uncorrelated (white environmental noise), whereas such effects are typically correlated (colored environmental noise) in nature. Thus, further work on the case of colored environmental noise is required, but this has been hindered by the analytical intractability of corresponding stochastic models. In our study, we address this limitation by developing a new discrete-time Markov chain model of a species population fluctuating under colored environmental noise, with the simplification that the effects of demographic variance are manifested indirectly as an extinction threshold. This simplifying assumption allows us to derive analytical solutions, which show that the expected extinction time of model species declines with the strength of environmental variance under a variety of different scenarios, reflecting greater extinction risk. Our study thus clarifies the situations under which environmental variance tends to increase extinction risk, and provides a novel analytically tractable framework for modeling temporal environmental variance. We also discuss the possible implications of our results for species richness in ecological communities.