Spatially distributed stochasticity and the constancy of ecosystems

Abstract

Ifconstancy is a measure of an ecosystem's (in) variability through time andstability is a measure of the system's ability to damp and recover from environmental perturbations, then constancy depends not only on stability but also on the frequency and amplitude of perturbations—theenvironmental “noise level”. The stability of an ecosystem reflects its texture, extent, and viscosity (fine-scale structure); the noise level experienced by the system (“effective” noise level) reflects the level at any point (“ambient” noise level), the spectrum of stochastic scale (regional distribution of stochasticity), and the system's spatial extent (size, or number of patches included). The coefficient of variation of a limiting stochastic variate is a measure of the effective noise level. Ifp is the total number of patches in the system (its extent) andn is the number of contiguous patches with noise signals correlated through time (its stochastic scale), then the coefficient of variation is directly proportional to$\sqrt {(n/p)}$ whenevern<p. Thus ecosystems of small stochastic scalen or large sizep damp out environmental noise by “spreading the risk” in space, thereby reducing their variability in time.