According to Guns, Germs, and Steel, how was the rise in human population density linked to the origins of food production starting around 8500 BC?...

The answer
to this can be found in Chapter 6.  Specifically, it starts on p. 111 in the paperback version
of the book and ends on p. 112.  Diamonds argument can be summed up when he says

A fourth factor was the two-way link between the rise in human population density and
the rise in food production. 

What that means is that neither was the cause
or the effect.  They were both causes and they were both effects.

Diamond
says that human populations were already rising in the late Pleistocene, even
before...