# Why is Fst/1-Fst used when calculating isolation by distance?

In population genetics a common analysis when considering the genetic structure of a population is to examine isolation by distance - the relationship between the genetic difference and the geographic distance between populations. Commonly Fst (the P of variation attributable to differences between rather than within populations) is used as a measure of genetic distance and the analysis is usually some form of regression, however actual variable used for genetic distance is often Fst/1-Fst rather than the raw Fst estimate.

This practice I can generally trace back to Rousset 1997 (doi: 10.1093/genetics/145.4.1219) who appears to have set this standard, however I can find no satisfactory explanation as to why this is - the explanation provided in Rousset's paper uses a far higher level of math than I can interpret.

I assume that somewhere it has to do with a non-linear, more logarithmic relationship between Fst and geographic distance but I am hoping someone can provide a bit more detail on this (or correct me entirely!)

• Hi, rainbird. Did you happen to see this and does it help? I'd try to help, but I really stink at math. Jan 4, 2022 at 0:34
• Hi, @anongoodnurse, yes I have had a look at the wiki but this entry really only discusses the calculation of Fst itself, not the relationship with distance. There is actually a separate wiki on isolation by distance but all of the Fst examples there use raw Fst. Actually so do quite a few of the recent papers it references, so perhaps this use of a modified Fst isn't quite ubiquitous, but it's still common enough to make me curious. Jan 4, 2022 at 12:37
• I do wish I could help. It's a valid question. Jan 4, 2022 at 15:35