# A Third Look at F-Statistics

## Hierarchical Components of Genetic Diversity

We have seen a number of estimates or quantities based on pairwise comparisons of genotypes or sequences and calculated for all pairs of individuals.

Figure 8.1

(A) Two locations in the South of Fiance distant by 3° of longitude. (B) The two locations showing that the distance between them is approximately a straight line.

Table 8.1

Comparison of F-statistics and Ф-statistics

 Index Distribution of Fis alleles among genotypes within populations Fst alleles among populations Fit alleles among genotypes across all populations \$sc genetic variation among populations within a continent Фет genetic variation among continents Фет genetic variation among populations across all continents

Consider for example the nucleotide diversity introduced in Section 5.2.2. Suppose the n individuals are distributed in several populations: the pair (i,j) may come from the same population or from two populations. There are thus two possible nucleotide diversities: ят is the global nucleotide diversity (calculated with all pairs) and 7rs calculated only with the pairs from the same population (i.e., this is the within-population nucleotide diversity). If the sequences are distributed randomly (i.e., the population structure has no effect on the nucleotide diversity), then we expect that тгт = 7Гу. Let us define:

This is similar, but not identical, to Fst (p- 187) and can be interpreted in a similar way (Table 8.1). Of course, if 7Гт = tts the Ф\$т = 0.

Suppose there is an additional level and let us call it ‘continent’ (though this could be ‘metapopulation’, ‘region’, or else): there is now a third way to calculate nucleotide diversity: for the pairs of individuals from two populations but on the same continent, and we denote it as яу;. Now, 7rT is calculated over all populations across the different continents. We can define two new Ф-statistics:

The comparison with the F-statistics shows the similarities and differences with the Ф-statistics: the former considers diploidy (or higher levels of ploicly) as the first structuring level, whereas ploidy is not important in the latter (Fig. 8.2). Fst appears now similar to Фет as being related to the second level of the structure (Table 8.1). Similarly to (7.3), the three Ф-statistics are related by:

Figure 8.2

Comparison of the structures with two levels considered by (A) F-statistics and (B) Ф-statistics.