An AMOVA example

Excoffier et al. [1] illustrate the approach by presenting an analysis of restriction haplotypes in human mtDNA. They analyze a sample of 672 mitochondrial genomes representing two populations in each of five regional groups (Figure 2). They identified 56 haplotypes in that sample. A minimum spanning tree illustrating the relationships and the relative frequency of each haplotype is presented in Figure 3.

Figure 2: Locations of human mtDNA samples used in the example analysis (from [1]).

Figure 3: Minimum spanning network of human mtDNA samples in the example. The size of each circle is proportional to its frequency (from [1]).

It's apparent from the figure that haplotype 1 is very common. In fact, it is present in substantial frequency in every sampled population. An AMOVA using the minimum spanning network in Figure 3 to measure distance produces the results shown in Table 1. Notice that there is relatively little differentiation among populations within the same geographical region ( $\Phi_{SC} = 0.044$). There is, however, substantial differentiation among regions ( $\Phi_{CT} = 0.220$). In fact, differences among populations in different regions is responsible for nearly all of the differences among populations ( $\Phi_{ST} = 0.246$). Notice also that $\Phi$-statistics follow the same rules as Wright's $F$-statistics, namely

$$\begin{eqnarray*} 1 - \Phi_{ST} &=& (1 - \Phi_{SC})(1 - \Phi_{CT}) \\ 0.754 &=& (0.956)(0.78) \quad , \end{eqnarray*}$$

within the bounds of rounding error.¹

Table 1: AMOVA results for the human mtDNA sample (from [1]).

Component of differentiation	$\Phi$-statistics
Among regions	$\Phi_{CT} = 0.220$
Among populations within regions	$\Phi_{SC} = 0.044$
Among all populations	$\Phi_{ST} = 0.246$