Watterson estimator

In population genetics, the Watterson estimator is a method for describing the genetic diversity in a population. It was developed by Margaret Wu and G. A. Watterson in the 1970s. 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. θ = 4 N e μ {displaystyle heta =4N_{e}mu } , where N e {displaystyle N_{e}} is the effective population size and μ {displaystyle mu } is the per-generation mutation rate of the population of interest (Watterson (1975) ). The assumptions made are that there is a sample of n {displaystyle 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 n ≪ N e {displaystyle nll N_{e}} .Because the number of segregating sites counted will increase with the number of sequences looked at, the correction factor a n {displaystyle a_{n}} is used. In population genetics, the Watterson estimator is a method for describing the genetic diversity in a population. It was developed by Margaret Wu and G. A. Watterson in the 1970s. 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. θ = 4 N e μ {displaystyle heta =4N_{e}mu } , where N e {displaystyle N_{e}} is the effective population size and μ {displaystyle mu } is the per-generation mutation rate of the population of interest (Watterson (1975) ). The assumptions made are that there is a sample of n {displaystyle 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 n ≪ N e {displaystyle nll N_{e}} .Because the number of segregating sites counted will increase with the number of sequences looked at, the correction factor a n {displaystyle a_{n}} is used. The estimate of θ {displaystyle heta } , often denoted as θ ^ w {displaystyle {widehat { heta ,}}_{w}} , is where K {displaystyle 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 ) {displaystyle (n-1)} th harmonic number. This estimate is based on coalescent theory. 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, θ ^ w {displaystyle {widehat { heta ,}}_{w}} 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.