The Research Of Evolutionary Graphs Based On Neutral Drift

Evolutionary graph theory is a new active fields that combine evolutionary biology,mathematics graph theory and other subjects. At the same time it is a kind of useful way whichdescribes the consequent of the structured population on the evolutionary dynamics.Evolutionary graph theory has been developed to a kind of mature scientific theoretical systemsince Lieberman and on proposed the concept of evolution graph theory in2005. Evolutionarydynamics theory provides a strong theoretical foundation for the evolution graph theory whichdescribes the effect of the structured population on the evolutionary dynamics. Based on theresearches on the evolutionary graph theory, the fixation probability and the fixation time whichare very important features describe the dynamic evolution of the population.In Chapter3, we make use of the related knowledge of evolution graph theory to give acalculation method of fixation probability based on neutral drift with an arbitrary initial state ofline graph and we get the fixation probability and the average fixation probability of any mutantsin the end. In chapter4, based on birth-death updating rule，we explores the average time to fixof three isothermal graphs which are directed circle, undirected circle and the complete graph,especially the average fixation time on condition of quasi-neutral drift. The results are that whenthe fitness of mutants is more than one, the average fixation time is monotonically decreasingwith the fitness of mutants r; when the fitness of mutants is less than one, it is monotonicallyincreasing with the fitness of mutants r. In the end, the evolutionary graph theory is furtherextended.