There's a new paper in PLoS ONE, Craniometric Data Supports Demic Diffusion Model for the Spread of Agriculture into Europe. That's fine. There are two extreme models about how farming might have spread in Europe. One model suggests that farmers replaced non-farmers genetically. Another model posits that there was no discernible movement of population, but ideas flowed. Apes are not the only ones who can imitate and emulate after all. Peruvians did not move with the potato, so there are cases of the latter. But the genetic data (see links) seem to imply some non-trivial contribution (for example, greater than 10% of post-Ice Age European distinctive genome content being derived from the Middle East) from Southwest Asia, so one would hope that the skulls would align.
Several years ago the geneticist Bryan Sykes made some waves by suggesting that in fact the majority of the ancestors of modern Europeans were resident in Europe during the last Ice Age. You can read Sykes' recollection of this episode in Seven Daughters of Eve. L. L. Cavalli-Sforza, who was the geneticist who first attempted to probe this question through biological methods, took issue with Sykes' characterization of his own position. After all, along a wave of advance one would expect dilution to be operative, so that the Southwest Asian genetic impact would be greater in Southeast Europe than in Northwest Europe. Cavalli-Sforza points out that he did not explicitly claims that the majority of the ancestors of Europeans were Middle Eastern farmers who rode the demographic wave of advance. But, to be fair I think it is correct that many people received this impression in some of his popularizations, e.g., The Great Human Diasporas.
A few years ago I read a bit on the spread of agriculture in Europe. Suffice it to say that the archaeological reality is quite complex, and in some regions there are seems to have been stable mosaic patterns of lifestyles (i.e., islands of agriculture surrounded by non-agriculturalists). Only later in history did the many regions switch wholesale to agriculture despite trading with agriculturalists for many generations (this was the case in southern Sweden). So even more nuanced models positing a uniform wave of advance leave something to be desired, though the stylized fact may be of some utility.
IMHO a mixed model is self-evident. Agriculture can support higher population densities than hunting&gathering. Such communities become trading places, where h&g people visit and learn the new technologies.
But at some point the community becomes too crowded for the resources of the land, and one or more groups move out to set up their own communities in unpopulated areas. Splits can happen e.g. when a chief dies, and the title goes to the eldest son. The younger sons have a political motive to leave.
lassi, but geographic barriers can result in demographic choke points. e.g., the spread of southeast asian crops in east africa, the movement of rice into south asia from southeast asia. this isn't an issue in europe until you read the north and baltic seas.