Any studies on language change rate vs. population density?

I suspect there may be a correlation between population density and language change rate. In other words, I suspect that language change might be slow when population density is very low - and vice versa (higher density causes faster changes).

This may seem intuitive: the more people you have a chance to bump into, the more language diversity you're likely to be exposed to.

However, I have not been able to find any studies that:

1) try to verify whether this correlation exists or not

2) try to measure this correlation quantitatively, in case it does exist

If you know any research on this topic, can you please point me to it?

Thanks!