Quantifying Evolutionary Dynamics
by Lukas Geyrhofer
Date of Examination:2014-06-24
Date of issue:2015-06-04
Advisor:Dr. Oskar Hallatschek
Referee:Dr. Oskar Hallatschek
Referee:Prof. Dr. Annette Zippelius
Persistent Address:
http://dx.doi.org/10.53846/goediss-5112
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Abstract
English
Adaptation is a central process in evolution: populations adapt to their environment by accumulating beneficial mutations over the course of generations. Microbial populations present an excellent experimental system that allows to observe the adaptation process on reasonable timescales. Recent results of evolutionary experiments with microbes expose an intricate dynamics: beneficial mutations appear continuously and often many of them are present simultaneously. These different clones interfere on their way to fixation or extinction in the mostly asexually reproducing populations. This dynamical regime, termed clonal competition, has been observed in various laboratory populations. In recent years traveling wave models gained considerable attention as possible description of the ensuing dynamics in the experimental microbial populations. There, the population is represented as a density in fitness space. Individuals are grouped by their growth rate. The size of these groups, called fitness classes, changes over time via mutation and selection. In many implementations genetic drift is considered to correctly account for the dynamics of very fit clones that are still low in number. If the influx of beneficial mutations is large enough, the bell-shaped density moves to higher fitness as soliton-like traveling wave: the population adapts. In this thesis, we investigate the dynamical behavior of these traveling wave models. In particular, we try to quantify the fluctuations in the adaptation process that are inherent due to the discreteness of individuals and individual mutations. Even very fit clones can go extinct due to genetic drift. Successful clones sweep to fixation and eradicate much of the genetic diversity. In order to describe these fluctuations, we use a special version of traveling wave models. Based on branching random walks, we couple the dynamics to a specific tuned constraint that allows to construct exactly solvable equations. As a particularly interesting extension, we show that slightly modifying this formalism yields all moments of the population density, giving access to the complete fluctuation spectrum. Based on simulation data, we extract relevant timescales of the adaptation process in our model. An almost universal scaling is indicated: the time of large scale oscillations in fitness variance appears to depend largely on the product of adaptation speed and mutational scale alone. When applied to experimental data, we can infer the mutational scale, a value that is usually obscured by the dynamics of interfering mutations.
Keywords: Populations Genetics; Evolution; Adaptation; Traveling wave models; Microbial experimental evolution
