Resilience and local stability in a nutrient-limited resource-consumer system |
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Authors: | H Nakajima D L DeAngelis |
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Institution: | (1) Ritsumeikan University, 603 Kyoto, Japan;(2) Oak Ridge National Laboratory, 37831 Oak Ridge, TN, USA |
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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. |
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Keywords: | |
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