Allele frequency spectrum

In population genetics, the allele frequency spectrum, sometimes called the site frequency spectrum, is the distribution of the allele frequencies of a given set of loci (often SNPs) in a population or sample.^[1][2][3][4] Because an allele frequency spectrum is often a summary of or compared to sequenced samples of the whole population, it is a histogram with size depending on the number of sequenced individual chromosomes. Each entry in the frequency spectrum records the total number of loci with the corresponding derived allele frequency. Loci contributing to the frequency spectrum are assumed to be independently changing in frequency. Furthermore, loci are assumed to be biallelic (that is, with exactly two alleles present), although extensions for multiallelic frequency spectra exist.^[5]

Many summary statistics of observed genetic variation are themselves summaries of the allele frequency spectrum, including estimates of ${\displaystyle \theta }$ such as Watterson's ${\displaystyle \theta _{W}}$ and Tajima's ${\displaystyle \theta _{\pi }}$, Tajima's D, Fay and Wu's H and the fixation index ${\displaystyle F_{ST}}$.^[6]