Competitive Exclusion in a Discrete Stage-Structured Two Species Model

A. S. Ackleh; P. Zhang

Mathematical Modelling of Natural Phenomena (2009)

  • Volume: 4, Issue: 6, page 156-175
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Ackleh, A. S., and Zhang, P.. "Competitive Exclusion in a Discrete Stage-Structured Two Species Model." Mathematical Modelling of Natural Phenomena 4.6 (2009): 156-175. <http://eudml.org/doc/222295>.

@article{Ackleh2009,
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. },
author = {Ackleh, A. S., Zhang, P.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {stage-structured model; net reproductive number; competitive exclusion; net reproductive number},
language = {eng},
month = {11},
number = {6},
pages = {156-175},
publisher = {EDP Sciences},
title = {Competitive Exclusion in a Discrete Stage-Structured Two Species Model},
url = {http://eudml.org/doc/222295},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Ackleh, A. S.
AU - Zhang, P.
TI - Competitive Exclusion in a Discrete Stage-Structured Two Species Model
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/11//
PB - EDP Sciences
VL - 4
IS - 6
SP - 156
EP - 175
AB - 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.
LA - eng
KW - stage-structured model; net reproductive number; competitive exclusion; net reproductive number
UR - http://eudml.org/doc/222295
ER -

References

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