Survival and complete convergence for a spatial branching system with local regulation

Abstract

We study a discrete time spatial branching system on ${\mathbb{Z}}^d$ with logistic-type local regulation at each deme depending on a weighted average of the population in neighboring demes. We show that the system survives for all time with positive probability if the competition term is small enough. For a restricted set of parameter values, we also obtain uniqueness of the nontrivial equilibrium and complete convergence, as well as long-term coexistence in a related two-type model. Along the way we classify the equilibria and their domain of attraction for the corresponding deterministic coupled map lattice on ${\mathbb{Z}}^d$.

Published in at http://dx.doi.org/10.1214/105051607000000221 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• A microscopic probabilistic description of a locally regulated population and macroscopic approximations
• Coexistence in locally regulated competing populations and survival of branching annihilating random walk
• Ergodic behavior of locally regulated branching populations

Cited by in corpus (5)

• Random walks in dynamic random environments and ancestry under local population regulation
• Interacting diffusions and trees of excursions: convergence and comparison
• Branching random walk with non-local competition
• Ancestral lineages in spatial population models with local regulation
• Spreading speed of locally regulated population models in macroscopically heterogeneous environments