Demographic interactions between the last hunter-gatherers and the first farmers.

Demographic interaction processes play a pivotal role during episodes of cultural diffusion between different populations, particularly when these episodes can lead to competition for the same resources and geographic space. The diffusion of farming is one prototypical case within this broader scenario, where groups of incumbent hunter-gatherers occupied a space which would later be claimed by expanding farmers. In this work, we tackle such processes through a two-population mathematical model, where farmers and foragers compete and interact in the same geographic space. We present this work as a conceptual approach where, first, we assess the implications of our theoretical model and its general applicability and, second, we empirically test it on three case studies: Denmark, Eastern Iberia, and the island of Kyushu (Japan). While these regional case studies do not encompass the full range of processes observed in the interaction between migrant farmers and incumbent hunter-gatherers they provide reasonable variation to illustrate how our model can be fitted to a diverse range of empirical data and provide insights into these demographic processes. In particular, our theoretical model and case studies illustrate how endogenous interaction processes alone can explain the demographic fluctuations observed in the archaeological record during this transition, highlighting how these should be accounted for before invoking external forces as primary drivers.