Balding–Nichols model

Balding-Nichols
Parameters 0 < F < 1(real)
0< p < 1 (real)
For ease of notation, let
\alpha=\tfrac{1-F}{F}p, and
\beta=\tfrac{1-F}{F}(1-p)
Support x \in (0; 1)\!
PDF \frac{x^{\alpha-1}(1-x)^{\beta-1}} {\mathrm{B}(\alpha,\beta)}\!
CDF I_x(\alpha,\beta)\!
Mean p\!
Median I_{0.5}^{-1}(\alpha,\beta) no closed form
Mode \frac{F-(1-F)p}{3F-1}
Variance Fp(1-p)\!
Skewness \frac{2F(1-2p)}{(1%2BF)\sqrt{F(1-p)p}}
MGF 1 %2B\sum_{k=1}^{\infty} \left( \prod_{r=0}^{k-1} \frac{\alpha%2Br}{\frac{1-F}{F}%2Br}\right) \frac{t^k}{k!}
CF {}_1F_1(\alpha; \alpha%2B\beta; i\,t)\!

In population genetics, the Balding–Nichols model is a statistical description of the allele frequencies in the components of a sub-divided population. With background allele frequency p the allele frequencies, in sub-populations separated by Wright's FST F, are distributed according to independent draws from

B\left(\frac{1-F}{F}p,\frac{1-F}{F}(1-p)\right)

where B is the Beta distribution. This distribution has mean p and variance Fp(1 – p).[1]

The model is due to David Balding and Richard Nichols and is widely used in the forensic analysis of DNA profiles and in population models for genetic epidemiology.

References

  1. ^ Alkes L. Price, Nick J. Patterson, Robert M. Plenge, Michael E. Weinblatt, Nancy A. Shadick & David Reich (2006). "Principal components analysis corrects for stratification in genome-wide association studies" (PDF). Nature Genetics 38 (8): 904–909. doi:10.1038/ng1847. PMID 16862161. http://genepath.med.harvard.edu/~reich/Price%20et%20al.pdf. 
Key concepts
Selection
Effects of selection
on genomic variation
Genetic drift
Founders
Related topics