Equilibrium and Nonequilibrium Concepts in Ecological Models

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 ofbiological 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.

Reforming Watershed Restoration: Science in Need of Application and Applications in Need of Science

“…Problems include: application of the concept requires that there is some form of self-regulation that governs system dynamics; the concept typically does not apply at the small spatial and temporal scales in which most ecologists work; and the concept minimizes the importance of history, disturbance, and stochastic factors (DeAngelis and Waterhouse 1987;Wu and Loucks 1995). There is usually very little understanding of what, if any, internal regulating processes control the state of an ecosystem in need of restoration (Mayer and Rietkerk 2004).…”

Trophic interactions in open systems: Effects of predators and nutrients on stream food chains

“…et al 1981). Many ecological communities are, however, open and/or nonequilibrial (Pickett and White 1985;DeAngelis and Waterhouse 1987), and there is growing evidence that local food webs are strongly influenced by the exchange of materials and organisms with adjacent habitats (Bustamante et al 1995;Polis and Hurd 1996;Menge et al 1997a). Recent theoretical analyses predict that the effects of consumers and resources on food chains in open systems may differ from those in closed systems (Nisbet et al 1997), but there is very little empirical information that can be used to test those predictions.…”

Forest Economics, Natural Disturbances and the New Ecology

“…Separation of the mathematically tractable concept(s) of equilibrium from the more vague notions of balanceof-nature has allowed ecologists to test equilibrium theories and models, at least in principle. However, even fundamental mathematical models of population equilibrium, such as density dependent regulation of population size, are often empirically untestable because the scale at which density dependence operates may be much broader than the scale at which observations are typically made (DeAngelis and Waterhouse 1987). Notably, when models of static ecosystem stability have been tested, they often fail (Wu and Loucks 1995).…”

“…An alternative perspective argues that because ecosystems are open systems under the influence of stochastic processes, they are best characterized as nonequilibrium systems (DeAngelis et al 1985, DeAngelis andWaterhouse 1987). This view is supported by historical evidence on wildfires and pest epidemics.…”