Extinction threshold in the spatial stochastic logistic model: space homogeneous case. Issue 7 (3rd May 2022)

• Record Type: Journal Article
• Authors: Finkelshtein, Dmitri
• Is Part Of: Applicable analysis. Volume 101:Issue 7(2022)
• Page Start: 2726
• Page End: 2753
• Publication Date: 2022-05-03
• Subjects: Extinction threshold -- spatial logistic model -- mean-field equation -- population density -- perturbation -- correlation function -- asymptotic behaviour; 34E10 -- 92D25 -- 34D10 -- 58C15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1820996
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We consider the extinction regime in the spatial stochastic logistic model in R d (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 ε > 0 . We find the leading term of the asymptotic expansion (as ε → 0 ) of the critical mortality which is apparently different for the cases d ≥ 3, d = 2, and d = 1.