Balding–Nichols model

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 F_ST 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.

Differential equation

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