Hi Farhad Alizadeh,

To known if the genetic difference between populations increase with increasing geographic distance, you can test for isolation by distance (IBD) with a Mantel test and using the Kendall correlation coefficient. For this, you can calculate the correlation between the genetic distance (d) and the Euclidian geographic distance (in km) generated from the geographic coordinates of each collected locality.

More than due to geographical distances, populations can get structure (genetic differences) for reasons, among others, such as zero migration and zero genetic flow.

Distance predict an increase in genetic differentiation with geographic distance.

Yes. With a few notable exceptions, the bulk of DNA differentiation purely relates to distance. This is why PCA works on genetic samples - the first two principal components almost always describe spatial x and y, and can be typically used to reproduce the locations of populations on the map. I'm really surprised hardly anyone seems to know this.

I don't think anyone has done the work, but it should fall away as with a gravity model or similar.

If PCA DOESNT reproduce space, then you have clear evidence of bottlenecking or exogamy.

As to your question, the answer is "usually yes, unless something else is going on".

What Khadim suggests is basically what I'd do as well: a Mantel test of genetic distance on geographic distance, but I would be careful as to how I would express geographic distances.

Over relatively short distances, Euclidean is fine, but as you go further you'll have to consider that the earth is a ball ;-)

A somewhat better, generic solution is therefore to calculate the great circle distance: https://en.wikipedia.org/wiki/Great-circle_distance (there are R packages that help with this).

Even if the environmental conditions at those separated places are similar ?

Environment should usually make little difference to the typical inactive areas of the genome we use. If however you are looking for a selective sweep, it may well have not just an environmental component, but an environmental history component. This is also true of "linkage disequilibrium" effects - and, more surprisingly, to the genome as a whole.

This is because repeated bottlenecks accelerate genetic drift , causing minor and possibly unhelpful mutations to accumulate while eliminating rarer lines and leading the population to accumulate in a few genetic clumps. The classic example is at the north edge of the habitable zone in Siberia, where the border periodically expands and contracts. Ireland also shows signs of a major bottleneck just prior to the arrival of the Romans.

Individual variation within a population is much greater than between-population differences. Following a bottleneck, the population can therefore appear to be very substantially genetically different.

dear Khadim Kebe and Diego F. Villanueva-Mejía

thank you for your help

dear Niketan Deshmukh

Is it also true for ancestral populations?

Do you know of an article that I can refer to?