Evolutionary dynamics on multi-dimensional fitness landscapes
Evolution is the common theme linking everything in biology from individual alleles to languages. Darwin believed that those who were mathematically inclined had a different insight and he regretted not having it. He probably would feel gratified knowing that now evolution has gained a solid mathematical foundation. The general principles of evolution can be represented by precise mathematical equations. Simplicity is invoked by making use of the minimum factors that matter. But we cannot even imagine how many factors a single honeybee takes into account to vouch for a particular flower. How can we take this complexity into account if we aim at retrieving simple tractable explanations of biological principles? This thesis addresses this problem particularly in two scenarios: Static and dynamic fitness landscapes. A fitness landscape is a tool for visualising the the fitness of a population in a space in which each dimension is a trait affecting the fitness. The population is ever searching for fitness maxima on this landscape. This is the process of adaptation. In a static fitness landscape the fitness is fixed, determined by the trait combination. Here we present results pertaining to the time required for a population to move from one point to another on this landscape if the paths consists of broad valleys or narrow ridges. In dynamic fitness landscapes the fitness is a function of the population composition. Hence as the population moves over the landscape the landscape changes shape and the fitness maxima can be eternally moving. To analyse frequency dependence we employ evolutionary game theory. Traditional evolutionary game theory deals with two player games with two strategies. This thesis invokes higher dimensions and non-linearities by studying multiple players and strategies. Important results from the two player two strategy case are generalised to multiple players. Finally we employ this theoretical development to analyse a possible evolutionary application in genetic pest management.