We performed extensive and realistic simulations of the colonization process of Europe by Neolithic farmers, as well as their potential admixture and competition with local Palaeolithic hunter-gatherers. We find that minute amounts of gene flow between Palaeolithic and Neolithic populations should lead to a massive Palaeolithic contribution to the current gene pool of Europeans. This large Palaeolithic contribution is not expected under the demic diffusion (DD) model, which postulates that agriculture diffused over Europe by a massive migration of individuals from the Near East. However, genetic evidence in favour of this model mainly consisted in the observation of allele frequency clines over Europe, which are shown here to be equally probable under a pure DD or a pure acculturation model. The examination of the consequence of range expansions on single nucleotide polymorphism (SNP) diversity reveals that an ascertainment bias consisting of selecting SNPs with high frequencies will promote the observation of genetic clines (which are not expected for random SNPs) and will lead to multimodal mismatch distributions. We conclude that the different patterns of molecular diversity observed for Y chromosome and mitochondrial DNA can be at least partly owing to an ascertainment bias when selecting Y chromosome SNPs for studying European populations.