My recent focus on the lack of genetic continuity between hunter-gatherer and farming populations genetically and culturally is primarily due to the fact that we’re not in theory-land; the extraction of ancient DNA samples is steady-as-it-goes and is sharpening and overturning our understanding of the past. The relationship between culture and genetics is of particular importance in this case, genes serve not only as markers which we can track population movements, but genes themselves are embedded in dynamics which need not be connected to population movements.
Consider lactase persistence, which confers the ability to digest milk as an adult. In the 20th century “lactose intolerance” was assumed to be a pathology, but it turns out that most human populations can not digest milk sugar as adults due to the lack of production of the lactase enzyme. This is the ancestral type. Rather, different mutations which result in the persistence of lactase production into adulthood seem to have arisen independently in several regions of western Eurasia and Africa. This suggests that the mutational target zone here is large, that is, given particular selection pressures (cattle culture) mutants will arise in the background and increase in frequency which produce the phenotype of lactase persistence.