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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 mutation, assumed to have arisen uniquely in the history of the population. A rigorous theoretical study of this conditional genealogy is given using coalescent methods. Particular results include the mean, variance, and density of the age of the m...

Genetic variation at most loci examined in human populations indicates that the (effective) population size has been approximately 10(4) for the past 1 Myr and that individuals have been genetically united rather tightly. Also suggested is that the population size has never dropped to a few individuals, even in a single generation. These impose important requirements for the hypotheses for the ...