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Analysis of the Trojan Y-Chromosome eradication strategy for an invasive species.
MedLine Citation:
PMID:  23702536     Owner:  NLM     Status:  Publisher    
Abstract/OtherAbstract:
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.
Authors:
Xueying Wang; Jay R Walton; Rana D Parshad; Katie Storey; May Boggess
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Publication Detail:
Type:  JOURNAL ARTICLE     Date:  2013-5-24
Journal Detail:
Title:  Journal of mathematical biology     Volume:  -     ISSN:  1432-1416     ISO Abbreviation:  J Math Biol     Publication Date:  2013 May 
Date Detail:
Created Date:  2013-5-24     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7502105     Medline TA:  J Math Biol     Country:  -    
Other Details:
Languages:  ENG     Pagination:  -     Citation Subset:  -    
Affiliation:
Department of Mathematics, Texas A & M University, College Station, TX, 77843, USA, wxyfree2009@gmail.com.
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