Weir and Cockerham's $\theta$

Weir and Cockerham [5] describe the fundamental ideas behind this approach. Weir and Hill [6] bring things up to date. We'll be using the implementation from GDA in this course. The most important difference between $\theta$ and $G_{st}$ and the reason why $G_{st}$ has fallen into disuse is that $G_{st}$ ignores an important source of sampling error that $\theta$ incorporates.

In many applications, especially in evolutionary biology, the subpopulations included in our sample are not an exhasutive sample of all populations. Moreover, even if we have sampled from every population there is now, we may not have sampled from every population there ever was. And even if we've sampled from every population there ever was, we know that there are random elements in any evolutionary process. Thus, if we could run the clock back and start it over again, the genetic composition of the populations we have might be rather different from that of the populations we sampled. In other words, our populations are, in many cases, best regarded as a random sample from a much larger set of populations that could have been sampled.

• Use $G_{st}$ to summarize the distribution of variation within and among populations when you're interested in the characteristics of the particular populations included in your sample - fixed-effect sampling.

• Use $\theta$ to summarize the distribution of variation within and among populations when you're using your sampled populations to represent the characteristics of a larger set of populations from which they were drawn - random-effect sampling.¹⁰