The critical role of dependence among individuals in extinction models

Abstract

We analyze the potential effect of a general dependence among individuals in population extinction models. We conduct this analysis using Branching Processes as extinction models. In Branching Processes, each individual is replaced at each step of time, independently of all others, by a contribution to the population made of an integer random number of individuals. We introduce dependence among individuals as a uniform positive correlation between contributions of all pairs of individuals. This general form of dependence between individuals is shown to be equivalent to environmental stochasticity. The correlation coefficient among individuals' contributions is then shown to be equivalent to an Intraclass Correlation Coefficient in an analysis of variance with a random effect. This property makes it possible to estimate the intensity of environmental stochasticity in natural populations in a simple fashion. As an example, we show that in the Alsace (eastern France) white stork population the Intraclass Correlation Coefficient for fecundity is estimated to be 0.79. With such a high value one may expect environmental stochasticity to strongly influence extinction risk. We therefore analyze the impact of increasing correlation among individual contributions on extinction risk: first, conditional on population size and, second, incorporating all sources of variation in numbers through the Quasi-Stationary Distribution of population size. Our approach should facilitate the development of sensitivity analyses of extinction risk.