Resilience and local stability in a nutrient-limited resource-consumer system

Abstract

The “paradox of enrichment” predicts that increasing the growth rate of the resource in a resource-consumer dynamic system, by nutrient enrichment, for example, can lead to local instability of the system—that is, to a Hopf bifurcation. The approach to the Hopf bifurcation is accompanied by a decrease in resilience (rate of return to equilibrium). On the other hand, studies of nutrient cycling in food webs indicate that an increase in the nutrient input rate usually results in increased resilience. Here these two apparently conflicting theoretical results are reconciled with a model of a nutrient-limited resource-consumer system in which the tightly recycled limiting nutrient is explicitly modelled. It is shown that increasing nutrient input may at first lead to increased resilience and that resilience decreases sharply only immediately before the Hopf bifurcation is reached.