Abstract
• Invasion of a population that incorporates individuals of a pre-existing population. • First model of oblique transmission (acculturation by older individuals). • Oblique transmission is the most powerful mechanism (fastest fronts). • Example of a Neolithic front can be only explained by oblique transmission. • We obtain bounds on the intensity of cultural transmission. 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 age-structured 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.
Highlights
The propagation of reaction-diffusion fronts has been widely studied, both theoretically [1,2,3] and in many physical and interdisciplinary applications [3,4] such as cancer tumors [5,6], virus infections [7,8], the spread of genetic mutations [9,10] and human range expansions [11,12]
Let us stress that our purpose is mainly to model oblique transmission (Section 3.1), but in doing so we have realized that the new framework makes it possible to improve previous models of horizontal and vertical transmission, so it is worth to develop all three cases
Our main conclusion is that the effect of oblique transmission on front propagation, which has been analyzed in this paper for the first time, is much more powerful than those of both horizontal and vertical transmission
Summary
The propagation of reaction-diffusion fronts has been widely studied, both theoretically [1,2,3] and in many physical and interdisciplinary applications [3,4] such as cancer tumors [5,6], virus infections [7,8], the spread of genetic mutations [9,10] and human range expansions [11,12]. All equations above belong to the so-called demic case, i.e., that in which a front ( called wave of advance) of a population spreads due only to dispersal and reproduction, but not via cultural transmission (i.e., by incorporation of individuals from another population). In the opposite limit (q p), the first equation yields p = p(1 + η), so the bound η ≤ 1 implies that p ≤ 2p, which is reasonable because each farmer is assumed to mate with a single person in this model [34], so the number of HGs (ηp) incorporated per unit area is at most (for η = 1) equal to the initial number of farmers (p). In the last equation the number density of adults of the second population (qA) is smaller by the same amount, relative to the case in which no children are converted (i.e., vanishing oblique cultural transmission, g = 0). First we need to develop a realistic age-dependent model without cultural transmission (Section 2)
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