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

Handle URI:
http://hdl.handle.net/10754/562771
Title:
Analysis of the Trojan Y-Chromosome eradication strategy for an invasive species
Authors:
Wang, Xueying; Walton, Jay R.; Parshad, Rana ( 0000-0001-7443-8927 ) ; Storey, Katie; Boggess, May M.
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. © 2013 Springer-Verlag Berlin Heidelberg.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Springer Verlag
Journal:
Journal of Mathematical Biology
Issue Date:
24-May-2013
DOI:
10.1007/s00285-013-0687-1
Type:
Article
ISSN:
03036812
Sponsors:
This work was supported by the NSF-REU program DMS-0850470. This publication is based in part on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorWang, Xueyingen
dc.contributor.authorWalton, Jay R.en
dc.contributor.authorParshad, Ranaen
dc.contributor.authorStorey, Katieen
dc.contributor.authorBoggess, May M.en
dc.date.accessioned2015-08-03T11:05:08Zen
dc.date.available2015-08-03T11:05:08Zen
dc.date.issued2013-05-24en
dc.identifier.issn03036812en
dc.identifier.doi10.1007/s00285-013-0687-1en
dc.identifier.urihttp://hdl.handle.net/10754/562771en
dc.description.abstractThe 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. © 2013 Springer-Verlag Berlin Heidelberg.en
dc.description.sponsorshipThis work was supported by the NSF-REU program DMS-0850470. This publication is based in part on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSpringer Verlagen
dc.subjectAllee effecten
dc.subjectExtinctionen
dc.subjectRecoveryen
dc.subjectTrojan Y-Chromosome eradication strategyen
dc.subjectTuring instabilityen
dc.titleAnalysis of the Trojan Y-Chromosome eradication strategy for an invasive speciesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalJournal of Mathematical Biologyen
dc.contributor.institutionDepartment of Mathematics, Texas A and M University, College Station, TX, 77843, United Statesen
dc.contributor.institutionDepartment of Mathematics, Carleton College, Northfield, MN, 55057, United Statesen
kaust.authorParshad, Ranaen
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