<p>Evolutionary dynamics can be notoriously complex and difficult to analyze. In this dissertation I describe a population genetic regime where the dynamics are simple enough to allow a relatively complete and elegant treatment. Consider a haploid, asexual population, where each possible genotype has been assigned a fitness. When mutations enter a population sufficiently rarely, we can model the evolution of this population as a Markov chain where the population jumps from one genotype to another at the birth of each new mutant destined for fixation. Furthermore, if the mutation rates are assigned in such a manner that the Markov chain is reversible when all genotypes are assigned the same fitness, then it is still reversible when genotypes are assigned differing fitnesses. </p><p>The key insight is that this Markov chain can be analyzed using the spectral theory of finite-state, reversible Markov chains. I describe the spectral decomposition of the transition matrix and use it to build a general framework with which I address a variety of both classical and novel topics. These topics include a method for creating low-dimensional visualizations of fitness landscapes; a measure of how easy it is for the evolutionary process to `find' a specific genotype or phenotype; the index of dispersion of the molecular clock and its generalizations; a definition for the neighborhood of a genotype based on evolutionary dynamics; and the expected fitness and number of substitutions that have occurred given that a population has been evolving on the fitness landscape for a given period of time. I apply these various analyses to both a simple one-codon fitness landscape and to a large neutral network derived from computational RNA secondary structure predictions.</p> / Dissertation
| Identifer | oai:union.ndltd.org:DUKE/oai:dukespace.lib.duke.edu:10161/5538 |
| Date | January 2012 |
| Creators | McCandlish, David Martin |
| Contributors | Magwene, Paul M, McShea, Daniel W |
| Source Sets | Duke University |
| Detected Language | English |
| Type | Dissertation |
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