The effect of spatial bottleneck on human eco-cultural range expansion
The spatial spread of humans and culture is shaped by feedback between demography and cultural accumulation, as captured by the eco-cultural range expansion model. Yet, the effect of the geographical boundaries on this process remains poorly understood. Here, we extend the model to a two dimensional space where two large habitats are connected by a narrow corridor (spatial bottleneck) with reflecting boundaries. We find that a wave of ecological invasion is unaffected by the bottleneck, whereas a cultural wave can be blocked by sufficiently narrow corridors. The maximum bottleneck width that prevents propagation depends on the domain shape, and it converges to the threshold value when the habitat to be invaded gets larger. Our results align with mathematical results on a bistable reaction-diffusion equation, particularly mean curvature flow, based on which we provide an approximate formula of the threshold bottleneck width. Applied to the Middle- Upper Paleolithic transition, the findings suggest that while the spread of modern humans was robust to spatial bottlenecks, the expansion of advanced Upper Paleolithic culture could be delayed or halted by narrow corridors. Archaeological records point to potential cases where such geographic bottlenecks constrained cultural dispersal.