“…Before presenting this model, let us briefly describe the other two mechanisms mentioned above. A mathematical model of the third mechanism (horizontal cultural transmission [27,28,31,35]) will not be tackled in this paper because it would require substantial additional calculations since (i) it is well known from empirical data that human individuals often use the frequency of a trait as an indirect evaluation of its merit (biased transmission [26]), and (ii) horizontal transmission takes place at much longer distances than vertical transmission, even for pre-industrial populations [36], and this will lead to a distance-dependent probability of transmission. Finally, the fourth mechanism (local innovation) will not be analyzed here either, for the following reasons: (i) such local processes are probably not amenable to mathematical modeling, and (ii) a gradual front propagation in the Southeast-Northwest direction, with fairly constant speed, is observed for the Neolithic transition in Europe at the continental scale according to the archaeological data [37,38], thus, local innovations probably did not have an important effect on the global spread rate.…”