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].
