Analysis of the Trojan Y-Chromosome eradication strategy for an invasive species

Xueying Wang, Jay R. Walton, Rana D. Parshad, Katie Storey, May Boggess

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

The Trojan Y-Chromosome (TYC) strategy, an autocidal genetic biocontrol method, has been proposed to eliminate invasive alien species. In this work, we analyze the dynamical system model of the TYC strategy, with the aim of studying the viability of the TYC eradication and control strategy of an invasive species. In particular, because the constant introduction of sex-reversed trojan females for all time is not possible in practice, there arises the question: What happens if this injection is stopped after some time? Can the invasive species recover? To answer that question, we perform a rigorous bifurcation analysis and study the basin of attraction of the recovery state and the extinction state in both the full model and a certain reduced model. In particular, we find a theoretical condition for the eradication strategy to work. Additionally, the consideration of an Allee effect and the possibility of a Turing instability are also studied in this work. Our results show that: (1) with the inclusion of an Allee effect, the number of the invasive females is not required to be very low when the introduction of the sex-reversed trojan females is stopped, and the remaining Trojan Y-Chromosome population is sufficient to induce extinction of the invasive females; (2) incorporating diffusive spatial spread does not produce a Turing instability, which would have suggested that the TYC eradication strategy might be only partially effective, leaving a patchy distribution of the invasive species.

Original languageEnglish (US)
Pages (from-to)1731-1756
Number of pages26
JournalJournal Of Mathematical Biology
Volume68
Issue number7
DOIs
StatePublished - Jun 2014
Externally publishedYes

Keywords

  • Allee effect
  • Extinction
  • Recovery
  • Trojan Y-Chromosome eradication strategy
  • Turing instability

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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