I'd like to add a word of caution here. To test whether there is isolation by distance, you need several data points along a geographical range (either several populations or individuals at a range of distances). Because you are testing only two populations, you cannot infer there is a pattern of isolation by distance--your regression line is just connecting the two populations.

Well, I am no specialist, but basically Mantel test measured and tested the correlation between you two matrix. According to your distance plot, you seem to have two groups of individuals isolated from each other, with a very limited genetic differentiation between those two groups.

The test indicate a slight correlation between the two matrix (0.148) which is anyway significantly different from 0 (P=0.009), according to your permutations.

That is how I would interpret it.

Gregoire Leroy I see, thank you so much for the insight :D

I would like to clarify if there is a significant correlation between the two matrix that means there is isolation by distance, and that the genetic differentiation (though very limited) between the two populations can be attributed to their spatial distance? Another question (sorry for asking a lot), how can you say that there is a very limited genetic differentiation between the two groups by just looking at the distance plot? Thank you so much. I am an aspiring genetic conservationists and I am still learning to understand population genetics in the context of PGRFA conservation :)

Unless I am completely wrong, your isolation by distance plot just show geographic vs genetic distance, with a regression line right? (ignore the heat color which just indicate the density of points).

We see two groups largely isolated in term of geographical distance. However if the trend line is fine, the left group show average genetic distance around 0.57 and the right one around 0.6. Basically you can interpret that as "if two individuals are geographically close, their genetic distance would be on average around 0.57, while the two are far from each other (around 25,000) their genetic distance will be on average around 0.6". The statistic test indicate that given the number of points that you have, this difference is too large to be due to randomness.

This said, given the large variance in genetic distance that shows the two groups of points, you can absolutely not predict if two individuals are from the same geographical origin or not, based on their genetic distance. You may anyway hypothesize that there is some isolation by distance between your two groups.

Gregoire Leroy yes it is geographic vs genetic distance. it is actually two populations of wild rice which are geographically isolate around 25km apart. the first population can be found around 600 m above sea level while the other one is about 1000 m above sea level.

So you are saying that based on this result, the two population‘s genetic diversity were somehow affected by their geographic distance. That genetic diversity is postivitely correlated to geographic distance, i.e. the more geographically distant the populations, the more genetically diverse also?

Talking about genetic diversity can be very misleading here: you cannot say anything about the genetic diversity within your two populations. You may hypothesize that geographical distance impacted the genetic differentiation between the two populations.

Gregoire Leroy thank you so much. I get it now. I learned a lot from this discussion :)

I'd like to add a word of caution here. To test whether there is isolation by distance, you need several data points along a geographical range (either several populations or individuals at a range of distances). Because you are testing only two populations, you cannot infer there is a pattern of isolation by distance--your regression line is just connecting the two populations.

I would echo Stephanie's point. I don't see any evidence for or against isolation by distance in the figures you provided because their is no way to know if the 2 populations are close or far apart relative to gene flow distances or localized regions of dispersal obstruction.

In addition to all above advice, I would actually split your data into two populations (based on the geographcal split presented in the heatmap), and re-analyzed for IBD each - separately. This would likely uncover within-subpop IBD.