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Modeling Mutualism and Competition in Interactive Population Dynamics: How Ants and Aphids Affect Lycaenid Butterfly Ecology
AuthorKoontz, Elliot D.
Mathematics and Statistics
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Modeling population dynamics that include mutualistic interactions is an important and complex problem in theoretical biology and quantitative ecology. Mutualistic interactions, which are generally considered relationships in which two or more species benefit from each other’s presence, play a significant role in determining population dyanmics, and are essential to fully understanding the dynamics of interacting species. However, mutualistic interactions are a historically understudied topic in ecology; accurately describing populations in multi-species interactions is inherently challenging (Hastings & Powell, 1991), and models describing these populations increase greatly in complexity as the intricacy and interdependence of the relationship increases. As such, there have been relatively few attempts within the field to fully account for the particulars of these relationships. Through numerical simulation of lycaenid butterfly and aphid populations together with deterministic and stochastic mathematical models, this research aims to more thoroughly explore the facets of mutualistic and competitive interactions in population dynamics. By refining a previous model for lycaenid butterfly populations (Forister, Gompert, Nice, & Fordyce, 2010) and by adapting the models to include the dynamics of two interactive species, ants and aphids, we hope to generate a model which simultaneously predicts the fluctuation in the focal species while providing insight to the rich and complex interplay of mutualistic and competitive interactions in theoretical ecology. By using this model to examine the population dynamics of these species, we hope to generate a method which will be useful in explaining endangered lycaenid butterfly populations as well as understanding the role of mutualism in the context of quantitative and theoretical ecology.