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Competitive Exclusion in a Discrete Stage-Structured Two Species Model

Published online by Cambridge University Press:  27 November 2009

A. S. Ackleh  and
P. Zhang
A. S. Ackleh*
Affiliation:
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504
P. Zhang
Affiliation:
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504
*
ackleh@louisiana.edu
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Abstract

We develop a stage-structured model that describes the dynamics of two competing species each of which have sexual and clonal reproduction. This is typical of many plants including irises. We first analyze the dynamical behavior of a single species model. We show that when the inherent net reproductive number is smaller than one then the population will go to extinction and if it is larger than one then an interior equilibrium exists and it is globally asymptotically stable. Then we analyze the two-species model and establish conditions on the reproduction and survivorship rates that lead to competitive exclusion. We show that the winner species is the one that attains higher density at which its net reproductive number equals unity. Numerical results corroborating the theoretical ones are also presented.

Keywords

stage-structured modelnet reproductive numbercompetitive exclusion
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 6: Ecology (Part 1) , 2009 , pp. 156 - 175
Copyright
© EDP Sciences, 2009

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