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Thesis Format

Integrated Article

Degree

Master of Science

Program

Mathematics

Supervisor

Wahl, Lindi M.

Abstract

The process of adaptation has been of interest since the XIX century, when Darwin first proposed the idea of natural selection. Since then, there has been a myriad of theoretical and empirical works that have expanded the field. From the many evolutionary insights these works have produced, a foundational idea is that spontaneous mutations in the genome of organisms can produce changes to their reproductive success that might confer an advantage for the mutant organisms with respect to their peers. Therefore, mutations drive adaptive evolution by virtue of their heritable effects on fitness. Empirical measures of the distribution of these fitness effects of new mutations (the DFE) have been increasingly successful, and have recently highlighted the fact that the DFE changes during adaptation. Here, we analyze these dynamic changes to the DFE during a simplified adaptive process: an adaptive walk across a well-studied fitness landscape. First, we derive analytical approximations for the fitness distributions of both available and previously fixed alleles, and use these to derive expressions for the DFE at each step of the adaptive walk. We then confirm these predictions with independent simulations that relax several simplifying assumptions made in the analysis. Along with these quantitative predictions, we find that as de novo mutations accumulate, the DFE is reshaped in two important qualitative ways: the fraction of deleterious mutations increases (a shift to the left), and the variance of the distribution decreases. Our analysis makes the surprising prediction that, at least in additive fitness landscapes, adaptation may be more limited by the availability of low-fitness alleles to be replaced, rather than by the availability of beneficial mutations.

Summary for Lay Audience

The key idea of natural selection is that organisms that are better adapted to their environment will be able to reproduce more than organisms that are more poorly adapted. Furthermore, the offspring of those better adapted organisms will also reproduce more, increasing the frequency of that type of organism on the population, which is known as adaptation. In order to quantify this process, the term ``fitness" was defined as a quantitative measure for organismal reproductive success, in other words, fitness measures how well adapted an organism is to their environment. At the level of the genetic sequence, changes in the genome of the offspring, known as mutations, can lead to differences in their fitness with respect to their progenitors, referred as the fitness effects of said mutations. In this context, adaptation is driven by mutations that increase the fitness of mutant individuals. Therefore, the study of the fitness effects of new mutations is of great importance to predict adaptation. Using models that correlate genotypic sequences with fitness values, we study the mathematical properties of the distribution of fitness effects of new mutations, while adaptation acts on a simulated population. We derive analytical approximations for the distribution of fitness effects, as mutations accumulate, as well as provide independent computational simulations of the same process in order to confirm the predictions obtained in the analysis. We find that, as adaptation acts, the distribution of fitness effects exhibits a reduction in the fraction of mutations that confer a fitness advantage.

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

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