Conditional genealogies and the age of a neutral mutant

This paper is concerned with the structure of the genealogy of a sample in which it is observed that some subset of chromosomes carries a particular m utation, assumed to have arisen uniquely in the history of the population. A rigorous theoretical study of this conditional genealogy is given using c oalescent methods. Particular results include the mean, variance, and densi ty of the age of the mutation conditional on its frequency in the sample. M ost of the development relates to populations of constant size, but we disc uss the extension to populations which have grown exponentially to their pr esent size. (C) 1999 Academic Press.