Establishment probability in newly founded populations

Abstract

Background: Establishment success in newly founded populations relies on reaching the established phase, which is defined by characteristic fluctuations of the populations state variables. Stochastic population models can be used to quantify the establishment probability of newly founded populations; however, so far no simple but robust method for doing so existed. To determine a critical initial number of individuals that need to be released to reach the established phase, we used a novel application of the "Wissel plot", where ln(1 P ω(t)) is plotted against time t. This plot is based on the equation P ω(t) = 1 - c1e- ω1t , which relates the probability of extinction by time t, P ω (t), to two constants: c 1 describes the probability of a newly founded population to reach the established phase, whereas ω 1 describes the populations probability of extinction per short time interval once established. Results: For illustration, we applied the method to a previously developed stochastic population model of the endangered African wild dog (Lycaon pictus). A newly founded population reaches the established phase if the intercept of the (extrapolated) linear parts of the "Wissel plot" with the y-axis, which is ln(c 1), is negative. For wild dogs in our model, this is the case if a critical initial number of four packs, consisting of eight individuals each, are released. Conclusions: The method we present to quantify the establishment probability of newly founded populations is generic and inferences thus are transferable to other systems across the field of conservation biology. In contrast to other methods, our approach disaggregates the components of a populations viability by distinguishing establishment from persistence. © 2012 Gusset et al.; licensee BioMed Central Ltd.