Journal article
Analysis of the Trojan Y-Chromosome eradication strategy for an invasive species
Journal of mathematical biology, Vol.68(7), pp.1731-1756
06/2014
Handle:
https://hdl.handle.net/2376/118218
PMID: 23702536
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.
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Details
- Title
- Analysis of the Trojan Y-Chromosome eradication strategy for an invasive species
- Creators
- Xueying Wang - Department of Mathematics Texas A & M University College Station TX 77843 USAJay Walton - Department of Mathematics Texas A & M University College Station TX 77843 USARana Parshad - Division of Mathematical and Computer Sciences and Engineering King Abdullah University of Science and Technology 23955 Thuwal Kingdom of Saudi ArabiaKatie Storey - Department of Mathematics Carleton College Northfield MN 55057 USAMay Boggess - Department of Mathematics Texas A & M University College Station TX 77843 USA
- Publication Details
- Journal of mathematical biology, Vol.68(7), pp.1731-1756
- Academic Unit
- Mathematics and Statistics, Department of
- Publisher
- Springer Berlin Heidelberg; Berlin/Heidelberg
- Identifiers
- 99900548276601842
- Language
- English
- Resource Type
- Journal article