Stability of complex ecosystems

Abstract

ECOLOGISTS have generally held that a complex ecosystem is more likely to be stable than is a simpler one. Gardner and Ashby¹ have shown, however, that for randomly connected linear systems the probability that the equilibrium will be stable actually decreases as the complexity increases. Of course, whether or not this is a contradiction depends very much on what is meant by stability. It is doubtful that field ecologists are really thinking of the relative likelihoods that systems of different types will persist; it is, after all, only those systems which persist which are observed and about which generalisations are made. The reason for connecting stability and complexity seems rather to have been the observation that large scale population oscillations are much more common in simple ecosystems than in complex ones^2,3. We have therefore considered the following problem: Given that a system is near a stable steady state, will increased complexity tend to increase or to decrease the rate at which perturbations die out?