Evolution of mutation rates in asexual populations

Abstract

The term“evolution” in the context of biology refers to the collective changes in the features of a population over a period of time [15]. Population genetics provides a framework to understand the processes and mechanisms by which evolutionary changes occur [16]. The main goal of theoretical population genetics is to gain an insight into how the interactions between the forces of mutation, natural selection, random genetic drift, and population structure result in the variations amongst the individuals of a population by formulating the problem into a workable mathematical model [17]. Since the inclusion of all the complexities that are part of the actual biological systems is not possible in a mathematical model, simplifications, which do not significantly alter the details of the real system, but using which a furthermathematical progress can be achieved, are required. In this thesis, the evolutionary forces are considered to be not changingwith time.Moreover, wemodelmutation and selection as simple processes [17, 18], though in reality,more complex scenarios are possible for themutation rate of an organismas well as the selection acting on it. It will be seen in the subsequent Chapters that despite the simplifications in our models, we encounter mathematically challenging problems. However, a mathematical approach is very helpful in obtaining quantitative predictions as well as a deep understanding of the mechanism behind the evolutionary processes [19].