Spatial enhancement of population uncertainty near the extinction threshold

Abstract

Ecosystem dynamics can be studied using model populations. Perturbation experiments have often been applied to simulated populations in order to study the uncertainty in ecosystem dynamics. Most of these studies have predicted a stationary state. We report on the uncertainty in the dynamics near extinction. In particular, we explore fluctuation enhancements, i.e., enhanced variability in dynamics of paths to extinction. We examine two dynamic models on a two-dimensional lattice of finite size: (1) the contact process (CP) in which interactions are restricted to occur between adjacent lattice points, and (2) mean-field simulation (MFS), where interactions occur globally, between any pair of lattice points. Computer simulation reveals that, for both CP and MFS, the random drift of density about a stationary state increases with the decrease of steady-state density. Drift is much more pronounced in the vicinity of the critical mortality rate, at the transition to extinction. Simulation demonstrates that MFS shows greater variability when relative mortality rate is low whereas CP shows much more pronounced variability when mortality is near the critical threshold. The CP process shows wider fluctuations while the MFS process shows minimal increases following perturbations that lead to extinction. Because interactions are local for CP, there are a variety of different paths to extinction.