Equilibrium and Nonequilibrium Concepts in Ecological Models

TLDR

Mathematical models and empirical studies reveal that nonlinear feedbacks, time‑lags, and stochastic environmental forcing can destabilize ecosystems, raising the question of how complex ecosystems persist. Our study analyzes the basic themes of this research and identifies five general hypotheses that theoretical ecologists have built into models to increase stability against disruptive feedback and stochasticity. To counter feedback instabilities, theorists use stabilizing functional interactions, disturbance patterns, and spatial integration, while to reduce stochasticity they invoke compensatory mechanisms at low densities and spatial heterogeneity. We show that these ideas can be systematically organized and that stable equilibrium emerges asymptotically from large spatial scales rather than being a fundamental property.

Abstract

Mathematical models and empirical studies have revealed two potentially disruptive influences on ecosystems; (1) instabilities caused by nonlinear feedbacks and time—lags in the interactions of biological species, and (2) stochastic forcings by a fluctuating environment. Because both of these phenomena can severely affect system survival, ecologists are confronted with the question of why complex ecosystems do, in fact, exist. Our study analyzes the basic themes of this research and identifies five general hypotheses that, in recent years, theoretical ecologists have built into models to increase their stability against disruptive feedback and stochasticity. To counter feedback instabilities, theoreticians have considered (1) functional interactions between species that act as stabilizers, (2) disturbance patterns that interrupt adverse feedback effects, and (3) the stabilizing effect of integrating small—spatial—scale systems into large landscapes. To decrease the influence of stochasticity, modelers have hypothesized (4) compensatory mechanisms operating at low population densities, and (5) the moderating effect of spatial extent and heterogeneity. We show that modeling based on these ideas can be organized in a systematic way. We also show that the stable equilibrium state should not be viewed as a fundamental property of ecological systems, but as a property that can emerge asymptotically from extrapolation to sufficiently large spatial scales.