The synergistic effects of interaction strength and lags on ecological stability

Uncovering the fundamental properties of ecological stability is a central question in theoretical biology since its inception at the turn of the century. Here, motivated by simple modular theory (e.g., population models to few species models), we review the role of interactions strength and lags on dynamics and stability. Specifically, we argue that modular theory consistently finds that lags combined with high growth rates or strong interaction strengths underly all forms of instability in ecological models. To fully explore this relationship, we first need to understand the role of both explicit lags—using lagged versions of classical models, such as the lagged logistic population model, as well as the more subtle role of implicit lags that arise in all biological models of growth. Given this, and the realization that nature is replete with lags (e.g., age structure, stage structure, predator-prey, reproductive lags, recycling lags), it becomes important to understand how lags, both implicit and explicit, interact. With an eye towards correcting the frequently overlooked role of lags on stability we review existing mathematical examples that argue lags can combine to drive instability (lag excitation) or inhibit the expression of instability by cancelling each other out effectively (lag cancellation). We suggest that further understanding the role of lags and how they interact within whole webs and ecosystems remains an important research area for the future.