Extinction and viability of populations: Paradigms and concepts of extinction models

Abstract

Population Viability Analysis often relies on population dynamics models. In particular, extinction models aim at quantifying the risk of extinction of populations that are the subject of conservation concerns. Many such models are developed as simulation models, although the behaviour of stochastic models incorporating various types of variability (such as demographic and environmental stochasticity) can be complex and difficult to analyze. We present here, based on a simple example, a large class of stochastic models: Branching Processes. We summarize their key explicit mathematical properties as extinction models, in particular, in conditions realistic for conservation biology, the so-called “quasi-stationarity” (certainty of extinction, existence of stationary distribution of population size conditional on non-extinction, geometric distribution of time to extinction). Quasi-stationarity links decreasing populations and populations stabilized by density-dependence on a continuum of annual extinction probability. We then develop approximations of the annual probability of extinction and illustrate them for the Amsterdam Albatross (Diomedea amsterdamensis), a critically endangered species. As extinction models are clearly more useful for hierarchizing risks of extinction than for estimating in an absolute fashion a probability of extinction, we hope our approach will open the way to sensitivity analyses of the risk of extinction.