Lactase persistence (LP) is common among people of European ancestry, but with the exception of some African, Middle Eastern and southern Asian groups, is rare or absent elsewhere in the world. Lactase gene haplotype conservation around a polymorphism strongly associated with LP in Europeans (-13,910 C/T) indicates that the derived allele is recent in origin and has been subject to strong positive selection. Furthermore, ancient DNA work has shown that the--13,910*T (derived) allele was very rare or absent in early Neolithic central Europeans. It is unlikely that LP would provide a selective advantage without a supply of fresh milk, and this has lead to a gene-culture coevolutionary model where lactase persistence is only favoured in cultures practicing dairying, and dairying is more favoured in lactase persistent populations. We have developed a flexible demic computer simulation model to explore the spread of lactase persistence, dairying, other subsistence practices and unlinked genetic markers in Europe and western Asias geographic space. Using data on--13,910*T allele frequency and farming arrival dates across Europe, and approximate Bayesian computation to estimate parameters of interest, we infer that the--13,910*T allele first underwent selection among dairying farmers around 7,500 years ago in a region between the central Balkans and central Europe, possibly in association with the dissemination of the Neolithic Linearbandkeramik culture over Central Europe. Furthermore, our results suggest that natural selection favouring a lactase persistence allele was not higher in northern latitudes through an increased requirement for dietary vitamin D. Our results provide a coherent and spatially explicit picture of the coevolution of lactase persistence and dairying in Europe.