Evolution of large populations under the joint action of deleterious and beneficial mutations

Abstract

The present state of life on earth is the outcome of millions of years of biological evolution. All organisms evolve to develop traits which make them better suited to their environment. Biological evolution is driven by several forces such as mutations (beneficial, deleterious and neutral), recombination, migration, genetic drift and natural selection. The main aim of this work is to understand the effect of beneficial mutations in the presence of deleterious mutations and other evolutionary forces. Many theoretical studies consider the effect of either one of these mutations only, but the combined effect of both beneficial and deleterious mutations is much less explored. However, it is important to take both into account because in a real biological system, they occur together. In this thesis, we focus on two biological questions, namely, evolution of sex and recombination and dynamics of adaptation process in which beneficial mutations play a crucial role. A summary of the different models studied in this thesis is given in Table 1. The thesis is divided into six chapters as described below: In Chapter 1, we introduce various evolutionary forces such as mutation, recombination, migration, genetic drift and natural selection. Two theoretical models (Wright-Fisher process and Moran process) used to study the role of these forces in evolution are discussed here. Further, different fitness landscapes considered in our study are also explained in this Chapter. Recombination is very common in nature as a primary mechanism of reproduction. The reason why it is so widespread in spite of all its disadvantages is however not properly understood. Irreversible accumulation of deleterious mutations (Muller’s ratchet)[1] in finite asexual populations is considered to be one of the reasons for the evolution of sex and recombination. But theoretical studies of Muller’s ratchet [2] completely ignore the presence of beneficial