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At mutation-drift balance, the increased heterozygosity brought by new mutations is exactly equal to the loss of heterozygosity due to genetic drift. At equilibrium, the expected heterozygosity for a given locus is:
$$\hat h = \frac{4Nu}{1+4Nu}$$
The expected heterozygosity is only the first moment of the whole distribution of locus specific heterozygosity. What is the (among loci) variance in heterozygosity?
In The Distribution of Gene Frequencies in Populations, Sewall Wrights derivates a continuous approximation to the probability distribution for the frequency of an allele in a panmictic population under the pressure of drift and mutation on a bi-allelic locus. In his paper, he reports several version of the same equation. Below is one of them, where $\phi(q)$ is the probability density of the one specified allele to be at frequency $q$.
$$\phi(q) = C q^{4N\nu -1}(1-q)^{4N\mu -1}$$
, where $C=\frac{\Gamma(4N\mu+4N\nu)}{\Gamma (4N\mu) \cdot \Gamma (4N\nu)}$ is a constant, $\mu$ and $\nu$ and the forward and backward mutation rate The heterozygosity is then a simple one-to-one function of the allele frequency.
