Computational Methods for the Coalescent

Robert C. Griffiths
Simon Tavaré

To appear in Progress in Population Genetics and Human Evolution
ed. P. Donnelly and S. Tavaré
IMA Volumes in Mathematics and its Applications.
Springer Verlag, Berlin, 1996.

Abstract

This paper describes recent work on computational methods for the coalescent . We show how integro-recurrence relations for sampling distributions and related quantities may be solved by a simple Markov chain Monte Carlo method. We describe the method in the context of the coalescent process for a population that is evolving according to a deterministic population size function. The usual constant population size models appear as a special case of this approach. One of the appealing features of the approach is its generic nature: many apparently different problems may be attacked with this one approach. A wide variety of examples are discussed, among them maximum likelihood estimation of parameters.

Key words:

• Coalescent process
• Markov chain Monte Carlo
• Population genetics
• Sampling distributions
• Variable population size

AMS(MOS) subject classifications: 60G35, 92A05, 92A10.

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