Quantifying the Non-Linear Coupling Between Species: Copula and Rank Based Statistics

Esquerra-Ortells, Lledo

Graduate Thesis Or Dissertation

Quantifying the Non-Linear Coupling Between Species: Copula and Rank Based Statistics Public Deposited

Analytics

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Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/7m01bm14d

Abstract

Understanding the process of coevolution, the evolution of interacting species, is a major endeavor of evolutionary biology. Coevolution is a potent source of adaptive evolution, since it can sustain selection pressures indefinitely even in the absence of changes in the physical environment. In this work, we want to explain eco-evolutionary patterns in terms of adaptive behavior. Pursuant to this goal our methodology and the accompanying metrics are aimed at capturing different aspects of the dependence that has been shaped by evolution to respond in dynamic, adaptive ways to relevant features of the organisms environment. Previous studies, Nuismer et al. 2010[14], have shown that adaptive behavior does not fit in a linear model. Consequently, we must go beyond correlation analysis to track the population dynamics and the evolutionary changes over time. A variety of ways to measure dependence exist. We are interested in those which are capable of tracking non-linear dependence, since a vast amount of literature has been written about linear correlation meanwhile dealing with non-linear dependence seems almost an uncharted field. We studied different concepts that would allow us to find the coupling, if it exists, among the different species statistics. Among them, copula and rank based statistics turned out to be very promising. Hence, this work describes this copula concept, and how it is related to other rank statistic tools, giving some toy examples to explain how it helps in exploring the underlying structure of the data. Finally, we apply those concepts to analyze the dependence structure among the species of a simulated tritrophic system (predators- prey-resources or parasite-host-resources). We use the simulated data to explore two general questions. First, does coupling exist? And in the affirmative case, how is this dependence described? Second, does the underlying dependence structure of the predator-prey model describe the dependence between parasites and host; in other words, would we expect the two models to behave similarly in terms of adaptive behavior?

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