To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

Ewens's sampling formula

From Wikipedia, the free encyclopedia

In population genetics, Ewens's sampling formula, describes the probabilities associated with counts of how many different alleles are observed a given number of times in the sample.


Ewens's sampling formula, introduced by Warren Ewens, states that under certain conditions (specified below), if a random sample of n gametes is taken from a population and classified according to the gene at a particular locus then the probability that there are a1 alleles represented once in the sample, and a2 alleles represented twice, and so on, is

for some positive number θ representing the population mutation rate, whenever a1, ..., ak is a sequence of nonnegative integers such that

The phrase "under certain conditions" used above is made precise by the following assumptions:

  • The sample size n is small by comparison to the size of the whole population; and
  • The population is in statistical equilibrium under mutation and genetic drift and the role of selection at the locus in question is negligible; and
  • Every mutant allele is novel.

This is a probability distribution on the set of all partitions of the integer n. Among probabilists and statisticians it is often called the multivariate Ewens distribution.

Mathematical properties

When θ = 0, the probability is 1 that all n genes are the same. When θ = 1, then the distribution is precisely that of the integer partition induced by a uniformly distributed random permutation. As θ → ∞, the probability that no two of the n genes are the same approaches 1.

This family of probability distributions enjoys the property that if after the sample of n is taken, m of the n gametes are chosen without replacement, then the resulting probability distribution on the set of all partitions of the smaller integer m is just what the formula above would give if m were put in place of n.

The Ewens distribution arises naturally from the Chinese restaurant process.

See also


  • Warren Ewens, "The sampling theory of selectively neutral alleles", Theoretical Population Biology, volume 3, pages 87–112, 1972.
  • H. Crane. (2016) "The Ubiquitous Ewens Sampling Formula", Statistical Science, 31:1 (Feb 2016). This article introduces a series of seven articles about Ewens Sampling in a special issue of the journal.
  • J.F.C. Kingman, "Random partitions in population genetics", Proceedings of the Royal Society of London, Series B, Mathematical and Physical Sciences, volume 361, number 1704, 1978.
  • S. Tavare and W. J. Ewens, "The Multivariate Ewens distribution." (1997, Chapter 41 from the reference below).
  • N.L. Johnson, S. Kotz, and N. Balakrishnan (1997) Discrete Multivariate Distributions, Wiley. ISBN 0-471-12844-9.
This page was last edited on 24 August 2020, at 01:51
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.