Watterson estimator

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In population genetics, the Watterson estimator is a method for describing the genetic diversity in a population. It is estimated by counting the number of polymorphic sites. It is a measure of the "population mutation rate" (the product of the effective population size and the neutral mutation rate) from the observed nucleotide diversity of a population. , where is the effective population size and is the per-generation mutation rate of the population of interest (Watterson (1975) ). The assumptions made are that there is a sample of n haploid individuals from the population of interest, that there are infinitely many sites capable of varying (so that mutations never overlay or reverse one another), and that .

The estimate of , often denoted as , is

where K is the number of segregating sites (an example of a segregating site would be a single-nucleotide polymorphism) in the sample and

is the (n − 1)th harmonic number.

This estimate is based on coalescent theory. The number of segregating sites counted will increase with the number of bases looked at, and so the correction factor a_n is used. Watterson's estimator is commonly used for its simplicity. When its assumptions are met, the estimator is unbiased and the variance of the estimator decreases with increasing sample size or recombination rate. However, the estimator can be biased by population structure. For example, is downwardly biased in an exponentially growing population. It can also be biased by violation of the infinite-sites mutational model; if multiple mutations can overwrite one another, Watterson's estimator will be biased downward.

Comparing the value of the Watterson estimator, to nucleotide diversity is the basis of Tajima's D which allows inference of the evolutionary regime for a population of alleles.

See also[edit]


  • Watterson, G.A. (1975), "On the number of segregating sites in genetical models without recombination.", Theoretical Population Biology, 7 (2): 256–276, doi:10.1016/0040-5809(75)90020-9, PMID 1145509 
  • McVean, Gil; Awadalla, Philip; Fearnhead, Paul (2002) "A Coalescent-Based Method for Detecting and Estimating Recombination From Gene Sequences", Genetics, 160, 1231–1241.