Watterson estimator - AbsoluteAstronomy.com

Population genetics

Population genetics is the study of allele frequency distribution and change under the influence of the four main evolutionary processes: natural selection, genetic drift, mutation and gene flow. It also takes into account the factors of recombination, population subdivision and population...

, the Watterson estimator is a method for estimating the population mutation rate,

, where

is the effective population size

Effective population size

In population genetics, the concept of effective population size Ne was introduced by the American geneticist Sewall Wright, who wrote two landmark papers on it...

and

is the per-generation mutation rate

Mutation rate

In genetics, the mutation rate is the chance of a mutation occurring in an organism or gene in each generation...

of the population of interest . 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

Coalescent theory

In genetics, coalescent theory is a retrospective model of population genetics. It attempts to trace all alleles of a gene shared by all members of a population to a single ancestral copy, known as the most recent common ancestor...

. Watterson's estimator is commonly used for its simplicity. When its assumptions are met, the estimator is unbiased

Bias of an estimator

In statistics, bias of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. Otherwise the estimator is said to be biased.In ordinary English, the term bias is...

and the variance

Variance

In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...

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

Exponential growth

Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...

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.

See also