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Volume 6,     Number 3,     Fall 1998

 

ON THE STABILIZING EFFECT OF
SPECIALIST PREDATORS ON
FOUNDER-CONTROLLED COMMUNITIES
SEBASTIAN J. SCHREIBER

Abstract. We study a generalized model of 2n interacting species consisting of n competing prey and n predators, each of which feeds exclusively upon one of the prey species. Under the assumption that the prey community is founder-controlled (the positive equilibria determined by single prey species are asymptotically stable in prey phase space), it is shown that then predators can mediate uniform persistence when their mortality rates are sufficiently small. When this occurs, a repelling heteroclinic network on the boundary of the positive orthant is formed in which the removal of any predator leads to a system with a globally asymptotically stable equilibrium that only supports a single species.

 

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