1. Department of Ecology and Evolutionary Biology, University of Colorado, Boulder, Colorado 80309, USA
2. Department of Environmental Science and Policy, University of California, Davis, California 95616, USA

Correspondence to: Brett A. Melbourne¹ Correspondence and requests for materials should be addressed to B.A.M. (Email: brett.melbourne@colorado.edu).

Abstract

Extinction risk in natural populations depends on stochastic factors that affect individuals, and is estimated by incorporating such factors into stochastic models^{1, 2, 3, 4, 5, 6, 7, 8, 9}. Stochasticity can be divided into four categories, which include the probabilistic nature of birth and death at the level of individuals (demographic stochasticity²), variation in population-level birth and death rates among times or locations (environmental stochasticity^{1, 3}), the sex of individuals^{6, 8} and variation in vital rates among individuals within a population (demographic heterogeneity^{7, 9}). Mechanistic stochastic models that include all of these factors have not previously been developed to examine their combined effects on extinction risk. Here we derive a family of stochastic Ricker models using different combinations of all these stochastic factors, and show that extinction risk depends strongly on the combination of factors that contribute to stochasticity. Furthermore, we show that only with the full stochastic model can the relative importance of environmental and demographic variability, and therefore extinction risk, be correctly determined. Using the full model, we find that demographic sources of stochasticity are the prominent cause of variability in a laboratory population of Tribolium castaneum (red flour beetle), whereas using only the standard simpler models would lead to the erroneous conclusion that environmental variability dominates. Our results demonstrate that current estimates of extinction risk for natural populations could be greatly underestimated because variability has been mistakenly attributed to the environment rather than the demographic factors described here that entail much higher extinction risk for the same variability level.

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