Demographic stochasticity and the variance reduction effect

Demographic stochasticity is almost universally modeled as sampling variance in a homogeneous population, although it is defined as arising from random variation among individuals, This can lead to serious misestimation of the extinction risk in small populations. Here, we derive analytical expressions showing that the misestimation for each demographic parameter is exactly (in the case of survival.) or approximately (in the case of fecundity) proportional to the among-individual variance in that parameter. We also show why this misestimation depends on systematic variation among individuals, rather than random variation. These results indicate that correctly assessing the importance of demographic stochasticity requires (1) an estimate of the variance in each demographic parameter; (2) information on the qualitative shape (convex or concave) of the mean-variance relationship; and (3) information on the, mechanisms generating among-individual variation. An important consequence is that almost all population viability analyses (PVAS) overestimate the importance of demographic stochasticity and, therefore, the risk of extinction.