The ANZIAM Journal

Table of Contents - July 2011 - Volume 53, Issue 01  

Research Article

EFFECTS OF PREDATOR DIET BREADTH ON STABILITY OF SIZE SPECTRA

M. J. PLANKa1

a1 Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand (email: michael.plank@canterbury.ac.nz)

Abstract

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.

(Received October 13 2011)

(Revised January 11 2012)

2010 Mathematics subject classification

  • 92D40

Keywords and phrases

  • body mass;
  • ecosystem dynamics;
  • McKendrick–von Foerster equation;
  • predator;
  • prey;
  • size-structured model