Albert Christian Soewongsono

One of the interesting topics to be examined in the field of theoretical population genetics is to find the most recent common ancestor of the current population. In this thesis, firstly we proceed by finding the common ancestor of two randomly chosen individuals at the current time s, thus we will build a mathematical model to illustrate this situation using a Galton-Watson process which allows the population to grow stochastically over time, and only genetic drift affects the model. We then generalise the model into modelling the common ancestor for n randomly chosen individuals at the current time step. Later, we derive the joint estimate of having a common ancestor from n chosen individuals and the current population at time s does not exceed the observed population. Hence, this will be used to determine the estimate of the initial population size and the time of the most recent common ancestor for the case of n = 2. Lastly, we will compare the coalescent time with result found ...

We consider the problem of estimating the elapsed time since the most recent common ancestor of a finite random sample drawn from a population which has evolved through a Bienaymé-Galton-Watson branching process. More specifically, we are interested in the diffusion limit appropriate to a supercritical process in the near-critical limit evolving over a large number of time steps. Our approach differs from earlier analyses in that we assume the only known information is the mean and variance of the number of offspring per parent, the observed total population size at the time of sampling, and the size of the sample. We obtain a formula for the probability that a finite random sample of the population is descended from a single ancestor in the initial population, and derive a confidence interval for the initial population size in terms of the final population size and the time since initiating the process. We also determine a joint likelihood surface from which confidence regions can ...