The Complexity-Stability Continuum: Calculating Collapse

Abstract.  Starting 45 years ago, Bob May’s landmark paper generated large and continuing debates about whether and how it is possible to have large complex systems that are also stable. Conventional ecological wisdom held that complexity would be stabilizing, but May used theory to show complexity can lead to instability. May’s conclusions have been both challenged and confirmed over the years in terms of questioning the underlying model assumptions and confronting the model with empirical data. In this talk, we will revisit May’s original calculations to show the instability that arises is much more of a continuum than has been previously described. Using analytic, asymptotic, and numerical methods, we show that species start to go extinct well before the instability point predicted by May, yet the system does not actually collapse, meaning loss of majority of the species, until well after the instability point predicted by May. Apart from clarifying and detailing the process of extinctions and collapse in May’s original model, we argue this may more generally suggest an intermediate region for ecological and other systems that  exist between first extinctions and collapse and represents the sweet spot of system complexity and size. For these reasons, we propose there should be more study of the complexity-stability continuum, as opposed to the more binary view that has predominated.