Statistical properties of segregating sites

A mutation leading to a segregating site of a sample can be classified by the number of sequences in the sample that inherits the mutant nucleotide; it can also be classified by the frequencies of the two segregating nucleotides at the resulting segregating side. We define the size of a mutation to be the number of sequences in the sample that inherits the mutant nucleotide and the type of mutation (segregating site) to be the smallest value of the frequencies of segregating nucleotides. Each of these two classifications of mutations is analogous to allelic types in a sample of genes. Assuming the neutral Wright-Fisher model, we derived in this paper the mean and variance of the frequency of mutations of each size and type, and the covariance between the numbers of mutations of two different sizes and two different types. Potential applications of these results are discussed.