Watterson estimator

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In population genetics, the Watterson estimator is a method for estimating the population mutation rate, $θ = 4 N e μ$ , where $N e$ is the effective population size and $μ$ 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 an infinitely many alleles possible, and that $n \ll N_e$ .

The estimate of $θ$ , often denoted as ${\hat \theta_w}$ , is

${\hat \theta_w} = { K \over a_n },$

where K is the number of segregating sites in the sample and

$a_n = \sum^{n-1}_{i=1} {1 \over i}$

is the (n − 1)th harmonic number.

This estimate is based on coalescent theory. Watterson's estimator is commonly used for its simplicity. The estimator is unbiased and the variance of the estimator decreases with increasing sample size and/or recombination rate. However, the estimator can be biased by population structure. For example, ${\hat\theta_w}$ is downwardly biased in an exponentially growing population.