Analysis of the Trojan Y chromosome model for eradication of invasive species in a dendritic riverine system
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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.
KeywordsTrojan Y chromosome model Eradication Invasive species Population dynamics Global attractor Absorbing set
Mathematics Subject Classification (2000)35K57 35Q92 92D25
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- Charles S, de la Parra RB, Mallet J, Persat H, Auger P (1998) A density dependent model describing salmo trutta population dynamics in an arborescent river network. Effects of dams and channelling. Comptes Rendus de l’Acad des Sci Ser III Sci de la Vie 321(12): 979–990Google Scholar
- Fagan W, Grant EC, Lynch H, Unmack P (2009) Riverine landscapes: ecology for an alternative geometry. In: Cantrell RS, Cosner C, Ruan S Spatial ecology, chap. 5. CRC Press, Boca Raton, pp 85–100Google Scholar
- Gutierrez JB (2009) Mathematical analysis of the use of trojan sex chromosomes as means of eradication of invasive species. PhD thesis, Florida State University, Tallahassee, FLGoogle Scholar
- Hill J, Cichra C (2005) Eradication of a reproducing population of Convict Cichlids, Cichlasoma nigrofasciatum (Cichlidae) in North-Central Florida.. Florida Sci 68(2): 65–74Google Scholar
- Kaiser BA, Burnett KM (2010) Spatial economic analysis of early detection and rapid response strategies for an invasive species. Resour Energ Econ (in proof) (corrected proof)Google Scholar
- Okubo A, Levin S (2001) Diffusion and ecological problems: modern perspectives. Springer, New YorkGoogle Scholar
- OTA (1993) Harmful non-indigenous species in the United States. OTA-F-565 US Congress, Office of Technology Assessment, Washington, DCGoogle Scholar
- Quarteroni A, Sacco R, Salieri F (2000) Numerical mathematics. Springer, New YorkGoogle Scholar
- Shafland P, Foote K (1979) A reproducing population of Serrasalmus humeralis Valenciennes in southern Florida. Florida Sci 42(4): 206–214Google Scholar
- Strauss WA (1992) Partial differential equations: an intoduction. Wiley, NewyorkGoogle Scholar