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