We estimate a spread rate of 7.5–10.6 km/year for the Neolithic expansion along the northern shore of the western Mediterranean. Comparing to theory and numerical simulations of demic-cultural waves of advance, we find that the length of coastal jumps was $$240\le \Delta \le 427$$
240
≤
Δ
≤
427
km. We also derive what we believe are the first analytical equations for spread rates of waves of advance along a coast, and they agree with the simulation results. We show that the importance of cultural diffusion in this Neolithic spread was less than 21%, so demic diffusion was responsible for at least 79% of the observed spread rate. We argue that these results suggest that the spread took place using boats, and also a limited interaction between the incoming farmers and the autochthonous hunter-gatherers.