Introduction

We've now seen the principles underlying Wright's $F$-statistics. I should point out that Gustave Malécot developed very similar ideas at about the same time as Wright, but since Wright's notation stuck,² population geneticists generally refer to statistics like those we've discussed as Wright's $F$-statistics.³

Neither Wright nor Malécot worried too much about the problem of estimating $F$-statistics from data. Both realized that any inferences about population structure are based on a sample and that the characteristics of the sample may differ from those of the population from which it was drawn, but neither developed any explicit way of dealing with those differences. Wright develops some very ad hoc approaches in his book [9], but they have been forgotten, which is good because they aren't very satisfactory and they shouldn't be used. There are now two reasonable approaches available:

1. Weir and Cockerham's $\theta$-statistics, which are ``method of moments'' estimates, and

2. Bayesian approaches to estimating $\theta$.⁴

There's also an approach due to Nei [4] that was widely used in the past, but less widely used now. You'll need to know how it differs from the approaches used now, so we'll discuss it, but I wouldn't recommend using Nei's method on your own data.⁵