The paper is concerned with methods for the estimation of the coalescence time (time since the most recent common ancestor) of a sample of intraspecies DNA sequences. The methods take advantage of prior knowledge of population demography, in addition to the molecular data. While some theoretical results are presented, a central focus is on computational methods. These methods are easy to implement, and, since explicit formulae tend to be either unavailable or unilluminating, they are also more useful and more informative in most applications. Extensions are presented that allow for the effects of uncertainty in our knowledge of population size and mutation rates, for variability in population sizes, for regions of different mutation rate, and for inference concerning the coalescence time of the entire population. The methods are illustrated using recent data from the human Y chromosome.

The sampling distribution of a collection of DNA sequences is studied under a model where recombination can occur in the ancestry of the sequences. The infinitely-many-sites model of mutation is assumed where there may only be one mutation at a given site. Ancestral inference procedures are discussed for: estimating recombination and mutation rates; estimating the times to the most recent common ancestors along the sequences; estimating ages of mutations; and estimating the number of recombination events in the ancestry of the sample. Inferences are made conditional on the configuration of the pattern of mutations at sites in observed sample sequences. A computational algorithm based on a Markov chain simulation is developed, implemented, and illustrated with examples for these inference procedures. This algorithm is very computationally intensive.

Kimura and Ohta showed that the expected age of a neutral mutation observed t o be offrequency x in a population is -2a:(1-2)-' log x. We put this classical result in a general coalescent process context that allows questions t o be asked about mutations in a sample, as well as in the population. In the general context the population size may vary back in time. Assuming an infinitely-many-sites model of mutation, we find the distribution of the number of mutant genes at a particular site in a sample; the probability that an allele at that site of a given frequency is ancestral; the distribution of the age of a mutation given its frequency in a sample, or population; and the distribution of the time t o the most recent common ancestor, given the frequency of a mutation in a sample, or in the population.

We surveyed nine diallelic polymorphic sites on the Y chromosomes of 1,544 individuals from Africa, Asia, Europe, Oceania, and the New World. Phylogenetic analyses of these nine sites resulted in a tree for 10 distinct Y haplotypes with a coalescence time of approximately 150,000 years. The 10 haplotypes were unevenly distributed among human populations: 5 were restricted to a particular continent, 2 were shared between Africa and Europe, 1 was present only in the Old World, and 2 were found in all geographic regions surveyed. The ancestral haplotype was limited to African populations. Random permutation procedures revealed statistically significant patterns of geographical structuring of this paternal genetic variation. The results of a nested cladistic analysis indicated that these geographical associations arose through a combination of processes, including restricted, recurrent gene flow (isolation by distance) and range expansions. We inferred that one of the oldest events in the nested cladistic analysis was a range expansion out of Africa which resulted in the complete replacement of Y chromosomes throughout the Old World, a finding consistent with many versions of the Out of Africa Replacement Model. A second and more recent range expansion brought Asian Y chromosomes back to Africa without replacing the indigenous African male gene pool. Thus, the previously observed high levels of Y chromosomal genetic diversity in Africa may be due in part to bidirectional population movements. Finally, a comparison of our results with those from nested cladistic analyses of human mtDNA and beta-globin data revealed different patterns of inferences for males and females concerning the relative roles of population history (range expansions) and population structure (recurrent gene flow), thereby adding a new sex-specific component to models of human evolution.

Haplotypes constructed from Y-chromosome markers were used to trace the origins of Native Americans. Our sample consisted of 2,198 males from 60 global populations, including 19 Native American and 15 indigenous North Asian groups. A set of 12 biallelic polymorphisms gave rise to 14 unique Y-chromosome haplotypes that were unevenly distributed among the populations. Combining multiallelic variation at two Y-linked microsatellites (DYS19 and DXYS156Y) with the unique haplotypes results in a total of 95 combination haplotypes. Contra previous findings based on Y- chromosome data, our new results suggest the possibility of more than one Native American paternal founder haplotype. We postulate that, of the nine unique haplotypes found in Native Americans, haplotypes 1C and 1F are the best candidates for major New World founder haplotypes, whereas haplotypes 1B, 1I, and 1U may either be founder haplotypes and/or have arrived in the New World via recent admixture. Two of the other four haplotypes (YAP+ haplotypes 4 and 5) are probably present because of post-Columbian admixture, whereas haplotype 1G may have originated in the New World, and the Old World source of the final New World haplotype (1D) remains unresolved. The contrasting distribution patterns of the two major candidate founder haplotypes in Asia and the New World, as well as the results of a nested cladistic analysis, suggest the possibility of more than one paternal migration from the general region of Lake Baikal to the Americas.