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EFFECTS OF PREDATOR DIET BREADTH ON STABILITY OF SIZE SPECTRA

Published online by Cambridge University Press:  05 April 2012

M. J. PLANK
M. J. PLANK*
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand (email: [email protected])
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Abstract

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Many marine ecosystems have the remarkable property that the abundance of organisms of a given body size is approximately proportional to the inverse square of that size. Size-structured models have been developed for which this “invariance-of-biomass” state is an equilibrium solution. These models are built on the coupling of predator growth to prey abundance, where prey suitability is determined by a size-based function referred to as a feeding kernel. In this paper, the local stability of the equilibrium state is investigated in a limiting case where predators only consume prey of a preferred size. In this special case, it is shown analytically that the equilibrium state is always unstable. It is concluded that some degree of diet breadth, in terms of the range of prey sizes consumed by a predator, is an essential prerequisite for the invariance-of-biomass state to be stable, as widely observed in the field.

Keywords

body massecosystem dynamicsMcKendrick–von Foerster equationpredatorpreysize-structured model

MSC classification

Secondary: 92D40: Ecology
Type
Research Article
Information
The ANZIAM Journal , Volume 53 , Issue 1 , July 2011 , pp. 38 - 47
Copyright
Copyright © Australian Mathematical Society 2012

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