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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. [ABSTRACT FROM AUTHOR]

Abstract: We show that the number of segregating sites is a sufficient statistic for the scaled mutation parameter 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 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. [ABSTRACT FROM AUTHOR]

Abstract: We develop here an analytical evolutionary model based on a trinucleotide mutation matrix with six substitution parameters associated with the transitions and transversions in the three trinucleotide sites. It generalizes the previous models based on the nucleotide mutation matrices and the trinucleotide mutation matrix with three parameters. It determines at some time t the exact occurrence probabilities of trinucleotides mutating randomly according to six substitution parameters. An application of this model allows an evolutionary study of the common circular code COM and the 15 archaeal circular codes X which have been recently identified in several archaeal genomes. The main property of a circular code is the retrieval of the reading frames in genes, both locally, i.e. anywhere in genes and in particular without a start codon, and automatically with a window of a few nucleotides. In genes, the circular code is superimposed on the traditional genetic one. Very unexpectedly, the evolutionary model demonstrates that the archaeal circular codes can derive from the common circular code subjected to random substitutions with particular values for six substitutions parameters. It has a strong correlation with the statistical observations of three archaeal codes in actual genes. Furthermore, the properties of these substitution rates allow proposal of an evolutionary classification of the 15 archaeal codes into three main classes according to this model. In almost all the cases, they agree with the actual degeneracy of the genetic code with substitutions more frequent in the third trinucleotide site and with transitions more frequent that transversions in any trinucleotide site. [Copyright &y& Elsevier]