The classical wave-of-advance model is based on Fisher's equation. However, this approach leads to an unbounded wave-of-advance speed at high reproduction rates. In contrast, an integro-difference model leads to a finite upper bound for the speed, namely the maximum dispersal distance divided by the generation time. Intuitively, this is a very reasonable result. This demic model has been generalized to include cultural transmission (Fort, PNAS 2012). We apply this recent demic-cultural model to determine the percentages of demic and cultural diffusion in the Neolithic transition for two case studies: (i) Europe, and (ii) southern Africa (Jerardino et al., submitted 2014). The similarities and differences between both case studies are interpreted in terms of the three mechanisms at work (population reproduction, dispersal and acculturation).