Partitioning the effects of deterministic and stochastic processes on species extinction risk

Species populations are subjected to deterministic and stochastic processes, both of which contribute to their risk of extinction. However, current understanding of the relative contributions of these processes to species extinction risk is far from complete. Here, we address this knowledge gap by analyzing a suite of models representing species populations with negative intrinsic growth rates, to partition extinction risk according to deterministic processes and two broad classes of stochastic processes - demographic and environmental variance. Demographic variance refers to random variations in population abundance arising from random sampling of events given a particular set of intrinsic demographic rates, whereas environmental variance refers to random abundance variations arising from random changes in intrinsic demographic rates over time. When the intrinsic growth rate was not close to zero, we found that deterministic growth was the main driver of mean time to extinction, even when population size was small. This contradicts the intuition that demographic variance is always an important determinant of extinction risk for small populations. In contrast, when the intrinsic growth rate was close to zero, stochastic processes exerted substantial negative effects on the mean time to extinction. Demographic variance had a greater effect than environmental variance at low abundances, with the reverse occurring at higher abundances. In addition, we found that the combined effects of demographic and environmental variance were often substantially lower than the sum of their effects in isolation from each other. This sub-additivity indicates redundancy in the way the two stochastic processes increase extinction risk, and probably arises because both processes ultimately increase extinction risk by boosting variation in abundance over time.