# Understanding F-statistics in population genetics

I am reading the classic Weir and Cockerham 1984 paper about $F_{ST}$ estimation. At the beginning (first page, right column), they define 3 statistics.

• $F$ is the correlation of genes within individuals ("inbreeding")

• $\theta$ is the correlation of genes of different individuals in the same population ("coancestry")

• $f$ is the correlation of genes within individuals within populations.

They also state that the 3 statistics are related by

$$f = (F-\theta)(1-\theta)$$

I don't quite understand those 3 statistics and especially I don't understand why this relationship holds true. Can you help me with that?

• I find the 1984 paper to be a bit dense in some places. I don't have time at the moment to explicate this, but I found Bruce Weir's book very illuminating. You don't need to read it straight through. There are two or three relevant chapters. However, for your question, a good population genetics textbook such as Hartl and Clark might be sufficient.
– Mars
Commented Oct 29, 2015 at 5:49

• Thanks for the answer. Solving $1-F(1-f)(1-\theta)$ for $f$ gives $f=\frac{\theta-F}{\theta-1}$. Commented Aug 6, 2016 at 17:17