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
