How and why life on earth evolved to the present state is one of the main questions in biological research ever since the history of science. Though this is a very old field of research, we have not completely understood the mechanics of evolution even for the simplest microorganisms. The process of evolution is driven by the combined effect of different biological forces such as mutation, selection, recombination and drift. The stochasticity associated with this process facilitates the application of statistical mechanics in the study of evolution. The motivation of my study is to understand the evolution of microbial populations using mathematical models such as Wright-Fisher model and Moran model. The main focus of the study is on the role of beneficial/back mutations in the attainment of an equilibrium state. In my work, I have been using Wright-Fisher model to study the evolution of a linked genome. The main questions we want to address are, Does the asexual population attain an equilibrium state in the presence of beneficial mutations? If it does, what is the equilibrium frequency of deleterious mutations/ mutation load the population carry at a steady state? How does this fraction depend on the rate of recombination? In the last part of my talk, I will briefly explain how we can make use of adaptation dynamics to predict the distribution of beneficial fitness effects (DBFEs).