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dc.contributor.advisor Magwene, Paul M en_US
dc.contributor.advisor McShea, Daniel W en_US
dc.contributor.author McCandlish, David Martin en_US
dc.date.accessioned 2012-05-25T20:18:32Z
dc.date.available 2013-05-20T04:30:05Z
dc.date.issued 2012 en_US
dc.identifier.uri http://hdl.handle.net/10161/5538
dc.description Dissertation en_US
dc.description.abstract <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> en_US
dc.subject Evolution & development en_US
dc.subject Genetics en_US
dc.subject Fitness landscape en_US
dc.subject Neutral network en_US
dc.subject Random walk en_US
dc.subject Reversible Markov chain en_US
dc.subject Spectral graph theory en_US
dc.subject Weak mutation en_US
dc.title Evolution on Arbitrary Fitness Landscapes when Mutation is Weak en_US
dc.type Dissertation en_US
dc.department Biology en_US
duke.embargo.months 12 en_US

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