[SS13] Models in cultural evolution and the application to human prehistory

[SS13-02] The effect of domain shape on eco-cultural range expansion model

*Ryuichi Kumata¹, Joe Yuichiro Wakano² (1. CEFE, CNRS (France), 2. Meiji Univ. (Japan))

Keywords:

Reaction diffusion,Spatial domain,Wave

The dynamical expansion of the habitat of archaic and modern humans are considered within the framework of eco-culture, in which the carrying capacity of each species is linked to the cultural levels of each species. In a model in which the population density and density of skilled people of archaic humans and modern humans are spatially distributed, and the carrying capacity of the environment increases as the density of skilled people increases, the dynamics of the habitat expansion are found to consist of multiple wave fronts, including the wave front (first wave) of invading newcomers into the habitat of archaic humans and the wave front (second wave) of the replacement of the archaic humans with the low cultural level by the modern humans with the high cultural level (Wakano et al., 2017). In other words, the expansion dynamics of the modern humans are driven by the ecological expansion followed by the cultural cultural expansion (Eco-cultural range expansion). However, in reality, the human range expansion took place not in a one-dimensional uniform space but in a two-dimensional space with complicated domain shape. In this study, the effect of two-dimensional spatial domain on the eco-cultural range expansion is investigated with the Neuman boundary condition. . To express spatial bottlenecks, we consider a spatial domain in which two rectangular patches are connected by a narrow corridor (spatial bottleneck). Numerical analysis shows that spatial bottlenecks have little effect on the first wave, but have a significant effect on the second wave. At the exit of the spatial bottleneck, the second wave slows down, or if the spatial bottleneck is narrow enough, the second wave stops and a non-uniform stationary spatial pattern is observed. We then characterize the largest bottleneck width that stops the second wave, and relate it to actual archaeological scenarios.