One model for the spread of the agricultural way of life into Europe is of inexorable "demic diffusion" via a "wave of advance" of farming populations met by a land surplus. Conceptually and analytically it's an elegant model. It's also fundamentally methodologically individualistic, and so in keeping with the spirit of the age. There's no need to appeal to higher order social structure or organization, farmers who have a specific cultural toolkit drive the dynamic through endogenous growth in pre-state cultures through the production of large families. This growth washes over the frontier of the advance, and the original locus of the demographic pulse synthesizes across a transect with the indigenous substrate. In the early aughts historical geneticists Bryan Sykes and L. L. Cavalli-Sforza sparred over whether demic diffusion was useful or not as a conceptual framework. Sykes reported chromosomal results which implied that 75 percent of the ancestry of Europeans derives from Pleistocene hunter-gatherers. Cavalli-Sforza's riposte was that the original model did not specify a particular Paleolithic-Neolithic ratio, but rather characterized a dynamic which emphasized the necessity of migration as a mediator for cultural changes (the two perspectives are outlined in Seven Daughters of Eve and A Genetic and Cultural Odyssey). In the end the debate did seem semantic quibbling. And today it also is likely outmoded and irrelevant. There is a high probability that the basic fundamental assumptions of the original diffusionist model, whether cultural or genetic, were pushed too far. It neglected the profound discontinuities introduced into the equation by the protean tendencies of human culture. Empirically there is evidence of this in works such as Lawrence Keeley's War Before Civilization of this in the European context. As farmers impinged upon the territories of Mesolithic populations which utilized marine resources the advance of agriculture often stalled, and there are archaeological remains which are suggestive of violent conflict across Northern Europe's maritime fringe. Additionally, when humans advance into "virgin" territory the landscape can often seem "patchy." Instead of a spatially uniform wave of advance one almost certainly saw farmers race up favorable valleys and avoid zones of decreased fertility. In the United States the Far West was understood to be more amenable to agricultural techniques than the Great Plains in the 19th century, so one notes a "leap frog" to California and Oregon in the decades before the Civil War, leaving the intervening lands to native populations (at least temporarily). It is with this in mind that we must take in results being published more recently which suggest a more confused and irregular shift of peoples and cultures in Neolithic Europe. For example, at the symposium on Modern Human Genetic Variation Mattias Jakobsson is reporting on results of ancient DNA from ~5,000 year old samples from Scandinavia. The individual who was a farmer resembles Southern Europeans, while the two hunter-gatherers resemble modern Northern Europeans. Jakobsson observes that most modern European populations span the gamut between the two extremes. A few years ago a paper came out which reported that the mtDNA lineages of LBK individuals from Central Europe (the earliest farming culture) resembled Near Easterners more than modern Europeans. A similar discontinuity seems evident in France. At this point I think there are enough data to force us to move past an simple Neolithic demic diffusion wave of advance, and any model which posits pure cultural diffusion or total replacement of the indigenous populations. We should be careful about making grand pronouncements for the next few years, because the outlines will be clear and pegged down within 5 years due to the impending surfeit of ancient DNA studies. Rather, let's switch back to the question of clines and gradual shifts. The problem here may be the granularity of the archaeological data. It seems likely that the expansion of agriculture was more spatially patchy, and exhibited more starts and stops, then the samples we have allow us to infer with any confidence. The arrival of startlingly distinctive populations genetically and culturally across which likely rapidly traversed territory in a point-to-point fashion, and their subsequent extinction or assimilation into local substrate, is less surprising when we keep in mind the discontinuous nature of much of cultural change.