A phylogenetic estimator of effective population size or mutation rate

The natural Wright-Fisher model, without recombination and population subdivision and with effective population size, Ne and mutation rate per locus per generation, mu, provides a new estimator of the essential parameter theta having the value 4Ne-mu from DNA polymorphism data. The minimum variance of all possible unbiased estimators of the parameter is only marginally smaller than the new estimator. The variance of any currently used estimator is much bigger than the new estimator's variance.