R. C. Griffiths - Ancestral inference from gene trees

A unique gene tree describing the mutation history of a sample of DNA sequences can be can be constructed as a perfect phylogeny under an assumption of non-recurrent point mutations. The tree is equivalent to the DNA sequence data and because of ancestry there is much interest in thinking of the data as a tree.

The likelihood of a gene tree under a stochastic coalescent model of evolution can be found by an advanced simulation technique of importance sampling on genealogies, thus allowing maximum likelihood estimation of parameters using the full information in the data.

The distribution of the time to the most recent common ancestor, ages of mutations in the gene tree, and other ancestral characteristics conditional on the gene tree topology can also be found by the simulation technique.