Unstructured Individual Variation and Demographic Stochasticity

Demographic stochasticity increases the variance in the growth rate of small populations, and is an important factor to consider when predicting the fates of such populations. Unfortunately, the concept has been treated inconsistently. It is often defined verbally as representing chance variation among individuals in both traits (such as survival probability) and fates (such as whether the individual survived or not). In practice it is modeled as variation in fates only, with all individuals having identical underlying traits. In previous work we demonstrated that structured (but unmodeled) individual variability in survival traits can reduce the variance in population survivorship associated with demographic stochasticity, but that unstructured random variability in survival traits has no such effect. We implicitly generalized the latter result to fecundity, without offering proof. Robert et al. (2003) have demonstrated, using simulations, that unstructured individual variability in fecundity traits can increase the extinction risk of a small population when demographic stochasticity in fecundity is modeled as following a Poisson distribution. In this paper we extend our earlier theory to correct our mistaken speculations and analytically show the source of Robert et al.’s results. We also provide general predictions about the circumstances under which both structured and unstructured individual trait variation should either increase or decrease the magnitude of demographic stochasticity in the population.