'Loop tracing' feedback reveals mechanisms that drive instabilities in resource-host-parasite dynamics

Abstract

How and why do species interactions produce unstable dynamics? In the simplest models, the answers are straightforward. In the Rosenzweig-MacArthur predator-prey model, resource self-facilitation due to predation mortality triggers oscillations; in Lotka-Volterra competition, positive feedback from stronger interspecific competition underlies alternative states. However, when unstable dynamics arise with three or more species, how and why answers become more opaque. We propose that dissection of feedback loops, chains of direct species interactions, can answer these questions in meso-scale models. To demonstrate, we disentangle instabilities in epidemics using three variations of a general yet mechanistic resource-host-parasite model. Resources introduce destabilizing self-facilitation but also positive interspecific direct effects on propagule production and transmission rate. Those direct effects then produce instabilities through feedback loops. First, we trace how resource self-facilitation catalyzes oscillations by weakening faster, shorter, lower levels of feedback relative to longer, slower feedback of the whole system. Then, we show how resource-dependent propagule yield introduces positive cascade fueling feedback, creating an Allee threshold inhibiting invasion of parasites. In a third variant, we traced how both resource-dependent components produced those unstable dynamics and more complex behaviors, including a period-doubling route to chaos to which we apply a form of loop tracing. Hence, we show how and why direct, positive effects of resources modulate feedbacks underlying oscillations, Allee effects, and more during epidemics. We propose that loop tracing, a generally applicable method, could empower ecologists to glean much deeper insight into dynamics of species interactions.