Stochastic model of seed dispersal with homogeneous and non-homogeneous Poisson processes under habitat reduction conditions

This study presents a stochastic model of seed dispersal based on a branching random walk (BRW) framework, incorporating both homogeneous and non-homogeneous Poisson point processes (PPP). Building on the model introduced by Coletti et al. (2023), we examine the effects of habitat reduction on seed dispersal dynamics. We analyze the phase transition behavior of the BRW model under varying conditions of habitat fragmentation, focusing on how these conditions influence the critical dispersal rate. Specifically, we study a BRW on the real line with a non-homogeneous PPP driven by a log-normal density, constrained between spatial barriers. Our simulations localize the critical dispersal rate with respect to barrier positions and compare this dependence between homogeneous and non-homogeneous models.