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 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 always passes the bottleneck, whereas the subsequent transition to a high-density/high-culture equilibrium 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 for the threshold bottleneck width. Applied to the Middle-Upper Palaeolithic transition, the findings suggest that while the spread of modern humans was robust to spatial bottlenecks, the expansion of advanced Upper Palaeolithic culture could be delayed or halted by narrow corridors. Archaeological records point to potential cases where such geographic bottlenecks constrained cultural dispersal.