The duality of stability: towards a stochastic theory of species interactions

Understanding the dynamics of ecological systems using stability concepts has been a key driver in ecological research from the inception of the field. Despite the tremendous effort put into this area, progress has been limited due to the bewildering number of metrics used to describe ecological stability. Here, we seek to resolve some of the confusion by unfolding the dynamics of a simple consumer-resource interaction module. In what follows, we first review common dynamical metrics of stability (CV, eigenvalues). We argue using the classical type II consumer-resource model as an example where the empirical stability metric, CV, hides two different, but important, aspects of stability: (i) stability due to mean population density processes and (ii) stability due to population density variance processes. We then employ a simple stochastic consumer-resource framework in order to elucidate (i) when we expect these two different aspects of stability to arise in ecological systems and, importantly, highlight (ii) the fact that these two different aspects of stability respond differentially, but predictably, to changes in fundamental parameters that govern biomass flux and loss in any consumer-resource interaction (e.g., attack rates, carrying capacity, mortality).