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Stability Analysis of Male Aggression Levels in a Coercive Mating Model
Udiani, Oyita B.C.

2012, Master of Science, Ohio State University, Mathematics.
The evolution of sexually antagonistic behavior is an inherent consequence of the often diverging reproductive interests of the sexes. When males are the principal aggressors, there will be evolutionary pressure on females to develop a number of morphological and/or behavioral adaptations that mitigate aggression costs and maximize reproductive fitness. Correspondingly, selection will also favor males whose aggression strategies are best attuned to the changing fitness landscape. Previously, Bokides et al. (2012) presented a replicator dynamics model of female movement in response to male aggression. Their results indicated that under spatial restrictions, selection for high or low aggression strategists largely depends on the proximity of aggression types to an intermediate level a*. This paper is a continuation of that work addressing the questions of degeneracy at monomorphic equilibria when males adopt a*. First, we prove that the system admits no closed orbit solutions and show that monomorphic equilibria where males use a* are locally stable in the sense of Lyapunov. Next, we show, as a consequence of Poincaré-Bendixson Theorem, that all locally stable equilibria are in fact globally asymptotically stable for all parameters. Finally, we argue based on our results that these equilibria correspond to Evolutionary Stable States and that adopting a* is an Evolutionary Stable Strategy as conceived by Maynard Smith (1982).
Yuan Lou, PhD (Advisor)
Ian Hamilton, PhD (Advisor)
38 p.

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Udiani, O. (2012). Stability Analysis of Male Aggression Levels in a Coercive Mating Model. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Udiani, Oyita. "Stability Analysis of Male Aggression Levels in a Coercive Mating Model." Electronic Thesis or Dissertation. Ohio State University, 2012. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Udiani, Oyita "Stability Analysis of Male Aggression Levels in a Coercive Mating Model." Electronic Thesis or Dissertation. Ohio State University, 2012. https://etd.ohiolink.edu/

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