Population Dynamics in Spatially Heterogeneous Systems with Drift: the generalized contact process

TL;DR

This paper studies how populations evolve and stabilize in spatially heterogeneous environments with directional drift, revealing phase transitions between extinction, localization, and delocalization through simulations.

Contribution

It introduces a stochastic, spatially discrete model with drift, analyzing phase behavior in heterogeneous systems, extending previous deterministic models.

Findings

Population can be zero, localized, or delocalized depending on parameters.

Phase diagram resembles that of a deterministic convection model.

Simulations confirm the impact of drift and heterogeneity on population survival.

Abstract

We investigate the time evolution and stationary states of a stochastic, spatially discrete, population model (contact process) with spatial heterogeneity and imposed drift (wind) in one- and two-dimensions. We consider in particular a situation in which space is divided into two regions: an oasis and a desert (low and high death rates). Carrying out computer simulations we find that the population in the (quasi) stationary state will be zero, localized, or delocalized, depending on the values of the drift and other parameters. The phase diagram is similar to that obtained by Nelson and coworkers from a deterministic, spatially continuous model of a bacterial population undergoing convection in a heterogeneous medium.