Front propagation and cultural transmission. Theory and application to Neolithic transitions

We study the front propagation of a population that incorporates individuals of a second, pre-existing population. Previous models of such incorporation deal only with vertical cultural transmission (interbreeding) and horizontal cultural transmission (acculturation of individuals of the second population by members of the first one and of similar age). Here we present the first model of oblique transmission (acculturation by individuals of an older generation), which is more complicated because a model with age structure is necessary. We compare the new, age-structured model for oblique, horizontal and vertical transmission. The most powerful mechanism (fastest fronts) is oblique transmission. Two illustrative applications of Neolithic front propagation are presented. In one of them, the front was so fast that neither horizontal nor vertical transmission can explain it (but oblique transmission can). In the cases for which cultural transmission is a viable explanation, the observed front speed yields bounds on the intensity of cultural transmission. Our models are also of interest in many other Neolithic and non-Neolithic human range expansions, including major human migrations. Additionally, in future work the new agestructured models reported in this paper could be applied to model genetic gradients and, possibly, to similar phenomena in other species in which cultural transmission is well-known to occur. (c) 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )