Coexistence and extinction in a competitive exclusion Leslie/Gower model with harvesting and stocking

Ziyad AlSharawi, Mohamed Rhouma

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The principle of competitive exclusion states that when the competition between species is sufficiently strong, only the dominant species survives. In this paper, we examine the strategies of using stocking and harvesting to prevent the extinction of the weak species in a competitive exclusion environment. We find that in a system governed by the Leslie/Gower model careful stocking will ensure the coexistence between all species. We also find that constant harvesting of the dominant species may guarantee the survival of the weaker species when the parameters of the model are in a certain range. Mixed strategies and conditional harvesting strategies are also discussed.

Original languageEnglish
Pages (from-to)1031-1053
Number of pages23
JournalJournal of Difference Equations and Applications
Volume15
Issue number11-12
DOIs
Publication statusPublished - 2009

Fingerprint

Leslie model
Competitive Exclusion
Harvesting
Coexistence
Extinction
Mixed Strategy

Keywords

  • Coexistence
  • Competitive exclusion
  • Extinction
  • Harvesting
  • Leslie/Gower model
  • Stocking

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics
  • Analysis

Cite this

Coexistence and extinction in a competitive exclusion Leslie/Gower model with harvesting and stocking. / AlSharawi, Ziyad; Rhouma, Mohamed.

In: Journal of Difference Equations and Applications, Vol. 15, No. 11-12, 2009, p. 1031-1053.

Research output: Contribution to journalArticle

@article{89d0b1db26d745199cba943130e65df5,
title = "Coexistence and extinction in a competitive exclusion Leslie/Gower model with harvesting and stocking",
abstract = "The principle of competitive exclusion states that when the competition between species is sufficiently strong, only the dominant species survives. In this paper, we examine the strategies of using stocking and harvesting to prevent the extinction of the weak species in a competitive exclusion environment. We find that in a system governed by the Leslie/Gower model careful stocking will ensure the coexistence between all species. We also find that constant harvesting of the dominant species may guarantee the survival of the weaker species when the parameters of the model are in a certain range. Mixed strategies and conditional harvesting strategies are also discussed.",
keywords = "Coexistence, Competitive exclusion, Extinction, Harvesting, Leslie/Gower model, Stocking",
author = "Ziyad AlSharawi and Mohamed Rhouma",
year = "2009",
doi = "10.1080/10236190802459861",
language = "English",
volume = "15",
pages = "1031--1053",
journal = "Journal of Difference Equations and Applications",
issn = "1023-6198",
publisher = "Taylor and Francis Ltd.",
number = "11-12",

}

TY - JOUR

T1 - Coexistence and extinction in a competitive exclusion Leslie/Gower model with harvesting and stocking

AU - AlSharawi, Ziyad

AU - Rhouma, Mohamed

PY - 2009

Y1 - 2009

N2 - The principle of competitive exclusion states that when the competition between species is sufficiently strong, only the dominant species survives. In this paper, we examine the strategies of using stocking and harvesting to prevent the extinction of the weak species in a competitive exclusion environment. We find that in a system governed by the Leslie/Gower model careful stocking will ensure the coexistence between all species. We also find that constant harvesting of the dominant species may guarantee the survival of the weaker species when the parameters of the model are in a certain range. Mixed strategies and conditional harvesting strategies are also discussed.

AB - The principle of competitive exclusion states that when the competition between species is sufficiently strong, only the dominant species survives. In this paper, we examine the strategies of using stocking and harvesting to prevent the extinction of the weak species in a competitive exclusion environment. We find that in a system governed by the Leslie/Gower model careful stocking will ensure the coexistence between all species. We also find that constant harvesting of the dominant species may guarantee the survival of the weaker species when the parameters of the model are in a certain range. Mixed strategies and conditional harvesting strategies are also discussed.

KW - Coexistence

KW - Competitive exclusion

KW - Extinction

KW - Harvesting

KW - Leslie/Gower model

KW - Stocking

UR - http://www.scopus.com/inward/record.url?scp=70449657212&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449657212&partnerID=8YFLogxK

U2 - 10.1080/10236190802459861

DO - 10.1080/10236190802459861

M3 - Article

AN - SCOPUS:70449657212

VL - 15

SP - 1031

EP - 1053

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

SN - 1023-6198

IS - 11-12

ER -