Editing Ewens's sampling formula (section)

==Definition==
Ewens's sampling formula, introduced by [[Warren Ewens]], states that under certain conditions (specified below), if a random sample of ''n'' [[gamete]]s is taken from a population and classified according to the [[gene]] at a particular [[locus (genetics)|locus]] then the [[probability]] that there are ''a''<sub>1</sub> [[allele]]s represented once in the sample, and ''a''<sub>2</sub> alleles represented twice, and so on, is

:<math>\operatorname{Pr}(a_1,\dots,a_n; \theta)={n! \over \theta(\theta+1)\cdots(\theta+n-1)}\prod_{j=1}^n{\theta^{a_j} \over j^{a_j} a_j!},</math>

for some positive number ''θ'' representing the [[population mutation rate]], whenever <math>a_1, \ldots, a_n</math> is a sequence of nonnegative integers such that

:<math>a_1+2a_2+3a_3+\cdots+na_n=\sum_{i=1}^{n} i a_i = n.\,</math>

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. {{See also|Infinite-alleles model}}

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