Volume 6, Number 3, Fall 1998
ON THE STABILIZING EFFECT OF
SPECIALIST PREDATORS ON
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.