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# Balding–Nichols model

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 Title: Balding–Nichols model Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Balding–Nichols model

 Parameters Probability density function Cumulative distribution function 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) x \in (0; 1)\! \frac{x^{\alpha-1}(1-x)^{\beta-1}} {\mathrm{B}(\alpha,\beta)}\! I_x(\alpha,\beta)\! p\! I_{0.5}^{-1}(\alpha,\beta) no closed form \frac{F-(1-F)p}{3F-1} Fp(1-p)\! \frac{2F(1-2p)}{(1+F)\sqrt{F(1-p)p}} 1 +\sum_{k=1}^{\infty} \left( \prod_{r=0}^{k-1} \frac{\alpha+r}{\frac{1-F}{F}+r}\right) \frac{t^k}{k!} {}_1F_1(\alpha; \alpha+\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).

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.

\left\{F (x-1) x f'(x)+f(x) (F (-p)+3 F x-F+p-x)=0\right\}