Stochastic models for the time to the most recent common ancestor

A new area of recent research is inferring ancestral history from samples of DNA [11]. Most of this research has focused on the evolution of mitochondrial DNA. These molecules have a very high mutation rate, thereby allowing one to see differences in the DNA samples of two closely related individuals [11]. Mitochondria are maternally inherited which allows one to trace back female lineages. Also, male lineages can be traced back by using a specific locations on the Y chromosome. Estimates of the time to the origin of modern humans. Homo-sapiens, have been made by tracing back female lineages (referred to "the time to Mitochondria Eve") and by tracing back male lineages (referred to as "the time to Y-Adam") [1, 2. 4. 11. 13]. In theory, it is possible to trace back lineages for any species with information about mitochondrial DNA, population size, and mutation rates. Our research will be concerned with development of mathematical models and numerical techniques so that inferences can be made about the time to the most recent common ancestor (or TMRCA) given a data set from DNA samples taken from a population. Due to the fact that there is really no way of knowing the exact ancestral history from a given sample of DNA sequences we will use a probabilistic approach by developing a stochastic model for the TMRCA. We will generate a probability distribution for TMRCA from which we can calculate means, variances, or other summary statistics.