Extinction threshold in the spatial stochastic logistic model: space homogeneous case

Abstract

ABSTRACT We consider the extinction regime in the spatial stochastic logistic model in (a.k.a. Bolker–Pacala–Dieckmann–Law model of spatial populations) using the first-order perturbation beyond the mean-field equation. In space homogeneous case (i.e. when the density is non-spatial and the covariance is translation invariant), we show that the perturbation converges as time tends to infinity; that yields the first-order approximation for the stationary density. Next, we study the critical mortality – the smallest constant death rate which ensures the extinction of the population – as a function of the mean-field scaling parameter . We find the leading term of the asymptotic expansion (as ) of the critical mortality which is apparently different for the cases , d = 2, and d = 1.