Common sense, such as it is, tells us that the actual correlation in the
distant past was neither one nor zero, but somewhere in between, just as
has been observed in recent history.  Genetic analysis has started
providing evidence to back up common sense, and even provide some
evidence as to where this in-between point might be.  For example, see
the graphs at:

http://dienekes.blogspot.com/2010/11/multidimensional-scaling-and-admixture.html

Quote: "The correspondence [of genetics] with geography and language is
striking".

This particular study deals only with the genetics of modern Eurasian
populations, but recently people have been getting stuck into the
genetics of remains from thousands of years ago too.  For example, this
one on an LBK site in Germany:

http://dienekes.blogspot.com/2010/11/near-eastern-origin-of-european.html

Quote: "Either natural selection or later demographic events have led to
a quite different gene pool today than what existed in central Europe
thousands of years ago."