Journal of Mathematical Biology

, Volume 64, Issue 1–2, pp 319–340 | Cite as

Analysis of the Trojan Y chromosome model for eradication of invasive species in a dendritic riverine system

  • Juan B. Gutierrez
  • Monica K. Hurdal
  • Rana D. Parshad
  • John L. Teem
Article

Abstract

The use of Trojan Y chromosomes has been proposed as a genetic strategy for the eradication of invasive species. The strategy is particularly relevant to invasive fish species that have XY sex determination system and are amenable to sex-reversal. In this paper we study the dynamics of an invasive fish population occupying a dendritic domain in which Trojan individuals bearing multiple Y chromosomes have been released as a means of eradication. We demonstrate the existence of a bounded absorbing set that represents extinction of the invasive species irrespective of the dendritic configuration. The method of analysis used to obtain global estimates could be applied to other population problems and other geometries.

Keywords

Trojan Y chromosome model Eradication Invasive species Population dynamics Global attractor Absorbing set 

Mathematics Subject Classification (2000)

35K57 35Q92 92D25 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Juan B. Gutierrez
    • 1
  • Monica K. Hurdal
    • 2
  • Rana D. Parshad
    • 3
  • John L. Teem
    • 4
  1. 1.Mathematical Biosciences InstituteOhio State UniversityColumbusUSA
  2. 2.Department of MathematicsFlorida State UniversityTallahasseeUSA
  3. 3.Department of Mathematics and Computer ScienceClarkson UniversityPotsdamUSA
  4. 4.Division of AquacultureFlorida Department of Agriculture and Consumer ServicesTallahasseeUSA

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