Introduction

In the last 8-10 years a different approach to the analysis of genetic structure has emerged: analysis of individual assignment. Although the implementation details get a little hairy, the basic idea is fairly simple. Suppose we have genetic data on a series of individuals. Label the data we have for each individual $x_i$. Suppose that all individuals belong to one of $K$ populations and let the genotype frequencies in population $k$ be represented by $\gamma_k$. Then the likelihood that individual $i$ comes from population $k$ is just

$$\mbox{P}(i\vert k) = \frac{\mbox{P}(x_i\vert\gamma_k)}{\sum_k \mbox{P}(x_i\vert\gamma_k)} \quad .$$

So if we can specify prior probabilities for $\gamma_k$, we can use Bayesian methods to estimate the posterior probability that individual $i$ belongs to population $k$, and we can associate that assignment with some measure of its reliability.¹