Effects of Discreteness on Population Persistence in an Oasis

Abstract eng:
Determining the conditions for persistence of species and populations is a question of paramount importance in population biology. The problem was first theoretically investigated adopting a continuous reaction-diffusion equation for population dynamics in a patch of finite size surrounded by a completely hostile environment, representing an oasis in a desert. The main result of this model, today known as the KiSS model (after Kierstead, Slobodkin and Skellam), is that patches need to be larger than a critical size to let the population survive. To explore the effects of discreteness and demographic stochasticity, here we propose an individual-based formulation of the KiSS model. We investigate population dynamics in our discrete model, focusing on the average time to extinction (above and below the critical patch size of the continuous model) and on the quasi-stationary distribution of the number of individuals for patch sizes larger than the critical value.

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