Type of Document	Dissertation
Author	Gutierrez, Juan Bernardo
URN	etd-09152009-163757
Title	Mathematical Analysis of the Use of Trojan Sex Chromosomes as Means of Eradication of Invasive Species
Degree	Doctor of Philosophy
Department	Mathematics, Department of
Advisory Committee	Advisor Name Title Monica Hurdal Committee Chair Betty Case Committee Member Dewet sumners Committee Member Jack Quine Committee Member Nick Cogan Committee Member Richard Bertram Committee Member Joseph Travis University Representative
Keywords	Species Eradication Trojan Invasive
Date of Defense	2009-09-03
Availability	unrestricted
Abstract This dissertation presents and evaluates a theoretical method of eradication of invasive species through the use of Trojan Y chromosomes. The mathematical analysis of the Trojan Y chromosome eradication strategy is presented for the ODE case and the PDE case in R. It is shown that is possible to cause local extinction of species that have XY sex determination systems as long as they are susceptible to sex reversal. The existence of global attractors is shown for this system, and global attractors are proposed as descriptors of the dynamics of the innite dimensional system. The case of Poecilia formosa is studied as a natural case of Trojan X chromosomes; it is shown in this case that the combination of stochastic-dependent dissipation and high sensitivity to perturbations can lead to coexistence of P. formosa and P. mexicana. Similarities between the Trojan X chromosomes and Trojan Y chromosomes cases indicate that local extinction could occur in practice for the latter.
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