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All species experience temporal fluctuations in environmental conditions e.g. temperature or mortality risk. These fluctuations often are autocorrelated e.g. warmer years tending to be followed by warmer years. How these autocorrelations influence extinction risk and species coexistence remains, largely, an open problem. In this talk, I review recent mathematical techniques for characterizing extinction and coexistence for stochastic difference equations. These techniques rely on non-zero Lyapunov exponents (growth rates when rare) at stationary distributions of the models. Using diffusion style approximations of these exponents, I illustrate how autocorrelated fluctuations can (i) promote population persistence in a landscape of sink habitats, and (ii) mediate coexistence (or stochastic priority effects) for species sharing a common resource or predator.

Also on Zoom: https://ucdavis.zoom.us/j/92718892837