Will a Large Complex System be Stable?
A short Nature paper on the relation between stability and complexity in ecological systems with many interacting species, with a sharp result for large systems assembled at random: once complexity exceeds a critical value, they are almost certainly unstable. May takes up a suggestion by Gardner and Ashby, from computer studies of small systems, that large complex systems connected at random may be expected to be stable up to a critical level of connectance and then suddenly become unstable, and investigates it analytically for many variables. In his model each species would by itself return to equilibrium after a disturbance; interactions are then switched on at random, equally likely to be positive or negative, with a common average strength, and connectance is the probability that any pair of species interact. For large numbers of species, the system is almost certainly stable if the average interaction strength is below one over the square root of the product of the number of species and the connectance, and almost certainly unstable above it.
May offers two corollaries, of no more than qualitative significance by his own account. The first, roughly speaking, suggests that species that interact with many others should do so weakly, and those that interact strongly should do so with but a few, a tendency in many natural ecosystems, May says, citing Margalef. And Gardner and Ashby's computations, at one fixed interaction strength, show for example that 12-species communities with 15% connectance have essentially no chance of being stable, while 35% of those arranged into three separate blocks of four species, each with 45% connectance, are stable; such examples, May suggests, favour interactions arranged in blocks. The models are random ensembles of individually stable parts, examined near an equilibrium; the analysis assumes many variables, yet agrees with Gardner and Ashby's results to within 30% even for four variables. Nothing in it concerns organisations; the bridge to psychological safety is ours. We read it as a corrective to the idea that more connection is always better: in May's models, the number of parts, their connectance and the strength of their interactions together set the threshold beyond which a large system is almost certainly unstable, and his examples suggest that how the interactions are arranged changes the odds.
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