title: Sufficiency of the number of segregating sites in the limit under finite-sites mutation.
abstract: We show that the number of segregating sites is a sufficient statistic for the scaled mutation parameter (theta) in the limit as the number of sites tends to infinity and there is free recombination between sites. We assume that the mutation parameter at each site tends to zero such than the total mutation parameter (theta) is constant in the limit. Our results show that Watterson's estimator is the maximum likelihood estimator in this case, but that it estimates a composite parameter which is different for different mutation models. Some of our results hold when recombination is limited, because Watterson's estimator is an unbiased, method-of-moments estimator regardless of the recombination rate. The quantity it estimates depends on the details of how mutations occur at each site.
authors.affiliation: Department of Biostatistics, Columbia University, New York, NY 10032, United States. ar2946@columbia.edu
authors.forename: Arindam
authors.initials: A
authors.lastname: Roychoudhury
authors.forename: John
authors.initials: J
authors.lastname: Wakeley
mesh_terms: D000483:Alleles; D001499:Bayes Theorem; D005787:Gene Frequency; D005828:Genetics, Population / Q000379:methods*; D008957:Models, Genetic; D009154:Mutation