Navigation Links
Ewens's sampling formula


In population genetics, 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, whenever a1, ..., an is a sequence of nonnegative integers such that

The phrase "under certain conditions", used above, must of course be made precise. The assumptions are (1) the sample size n is small by comparison to the size of the whole population, and (2) the population is in statistical equilibrium under mutation and genetic drift and the role of selection at the locus in question is negligible, and (3) 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 Ewens distribution.

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 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.

References

  • Warren Ewens, "The sampling theory of selectively neutral alleles", Theoretical Population Biology, volume 3, pages 87—112, 1972.
  • J.F.C. Kingman, "Random partitions in population genetics", Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, volume 361, number 1704, 1978.

'"/>


(Date:1/4/2017)... LAS VEGAS , Jan. 4, 2017  For the thousands of ... , a global leader in connected health and biometric measurement devices and ... pressure monitors. On display in A&D Medical,s special CES ... monitors represent the ongoing expansion of the company,s WellnessConnected product ... ...
(Date:12/20/2016)... , Dec. 20, 2016 The ... sharing, rental and leasing is stoking significant interest ... radio frequency technology, Bluetooth low energy (BLE), biometrics ... as the next wave of wireless technologies in ... access system to advanced access systems opens the ...
(Date:12/16/2016)... 2016 The global wearable medical device market, in terms ... from USD 5.31 billion in 2016, at a CAGR of 18.0% ... ... advancements in medical devices, launch of a growing number of smartphone-based ... among healthcare providers, and increasing focus on physical fitness. ...
Breaking Biology News(10 mins):
Other biology definition