From Foll and Gagiotti (2008) (software BayeScan). They consider a model where several subpopulation are derived from a unique ancestral population.
We consider a set of $I$ loci and let $K_i$ be the number of alleles at the $i^{th}$ locus. The extent of differentiation at locus $i$ between subpopulation $j$ and the ancestral population is measured by $F^{ij}_{ST}$ and is the result of its demographic history. Let $p_i=\{p_{ik}\}$ denote the allele frequencies of the ancestral population at locus $i$, where $p_{ik}$ is the frequency of the allele $k$ at locus $i$ $\left(\sum_k p_{ik} = 1\right)$. We use $\mathbf {p} = \{\mathbf {p_i}\}$ to denote the entire set of allele frequencies of the ancestral population and $\mathbf {\tilde p_{ij}} = \{ \tilde p_{ijk}\}$ to denote the current allele frequencies at locus $i$ for subpopulation $j$. Under these assumptions, the allele frequencies at locus $i$ in subpopulation $j$ follow a Dirichlet distribution with parameters $\theta_{ij}\mathbf {p_i}$,
$$\mathbf {\tilde p_{ij}} \space \tilde \space\space \text{Dir}(\theta_{ij} p_{i1}, ..., \theta_{ij}p_{iK_i})$$
, where
$$\theta_{ij} = \frac{1}{F^{ij}_{ST}}-1$$
(I don't have much experience with Dirichlet distributions but I understand its definition and its usefulness in bayesian statistics).
Can you please help me to understand why $\mathbf {\tilde p_{ij}}$ follows this Dirichlet distribution?
Calling the $j^{th}$ parameter of the Dirichlet distribution, $\alpha_j$, I typically don't understand why they "chose" $\alpha_j = \left(\frac{1}{F^{ij}_{ST}}-1\right) p_{ij}$ and not, say just $\alpha_j = F^{ij}_{ST} p_{ij}$ or anything else.