Extinction risk depends strongly on factors contributing to stochasticity

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Abstract
Extinction risk in natural populations depends on stochastic factors that affect individuals, and is estimated by incorporating such factors into stochastic models1,2,3,4,5,6,7,8,9. 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 stochasticity1,3), the sex of individuals6,8 and variation in vital rates among individuals within a population (demographic heterogeneity7,9). 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.