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Volume 19,     Number 3,     Fall 2011

 

A REFUGE-MEDIATED APPARENT
COMPETITION MODEL
Dedicated to Professor Herb Freedman on the occasion of his 70th birthday
SZE-BI HSU AND LIH-ING WU ROEGER

Abstract. We analyze a competition model of two plant species for a single-limited resource while the competition is apparent: an indirect interaction where the invading plants provide a refuge for a shared consumer, subsequently increasing the consumer pressure on the resident plant species. When there is no refuge effect, the resident species is a superior species. As the refuge effect increases, the coexistence state appears as a saddle point with a two-dimensional stable manifold while the two extinction equilibria are locally stable. Thus the refuge- mediated apparent competition creates an Allee effect for both the invading and the resident species. A Lyapunov function is found to show the global stability of the equilibrium in which only the resident species survives.

 

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