An efficient estimator of the mutation parameter and analysis of polymorphism from the 1000 genomes project

The mutation parameter θ is fundamental and ubiquitous in the analysis of population samples of DNA sequences. This paper presents a new highly efficient estimator of θ by utilizing the phylogenetic information among distinct alleles in a sample of DNA sequences. The new estimator, called Allelic BLUE, is derived from a generalized linear model about the mutations in the allelic genealogy. This estimator is not only highly accurate, but also computational efficient, which makes it particularly useful for estimating θ for large samples, as well as for a large number of cases, such as the situation of analyzing sequence data from a large genome project, such as the 1000 Genomes Project. Simulation shows that Allelic BLUE is nearly unbiased, with variance nearly as small as the minimum achievable variance, and in many situations, it can be hundreds- or thousands-fold more efficient than a previous method, which was already quite efficient compared to other approaches. One useful feature of the new estimator is its applicability to collections of distinct alleles without detailed frequencies. The utility of the new estimator is demonstrated by analyzing the pattern of θ in the data from the 1000 Genomes Project.