Extinction dynamics of a discrete population in an oasis.
Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 1950s with the Kierstead, Slobodkin, and Skellam (KiSS) model, namely a continuous reaction-diffusion equation for a population growing on a patch of finite size L surrounded by a deadly environment with infinite mortality, i.e., an oasis in a desert. The main outcome of the model is that only patches above a critical size allow for population persistence. Here we introduce an individual-based analog of the KiSS model to investigate the effects of discreteness and demographic stochasticity. In particular, we study the average time to extinction both above and below the critical patch size of the continuous model and investigate the quasistationary distribution of the number of individuals for patch sizes above the critical threshold.
Laboratoire de Mécanique de Lille, CNRS/UMR 8107, Université Lille 1, 59650 Villeneuve d'Ascq, France.
Stefano
S
Berti
Istituto dei Sistemi Complessi, CNR, Via dei Taurini 19, 00185, Rome, Italy.
Massimo
M
Cencini
Istituto per le Applicazioni del Calcolo, CNR, Via dei Taurini 19, 00185, Rome, Italy.
Davide
D
Vergni
Dipartimento di Fisica, Università "La Sapienza," Piazzale Aldo Moro 2, I-00185 Roma, Italy and Istituto dei Sistemi Complessi, CNR, Via dei Taurini 19, 00185, Rome, Italy.
Angelo
A
Vulpiani
D018533:Biomass; D004777:Environment; D053476:Extinction, Biological; D008954:Models, Biological; D016011:Normal Distribution; D011157:Population Dynamics; D011336:Probability; D013269:Stochastic Processes; D013997:Time Factors