Origin and spread of agriculture in prehistoric Europe.

Case Study 6

**Aim. **The aim of this case study is to formulate solutions that can explain some of the local variability at the expanding front of the Neolithic transition by introducing the influence of geography, or the interaction with Mesolithic populations. We also want to formulate new models that include cultural transmission in addition to demic diffusion.

**Background.** The transition from hunter-gathering economics to farming is known as the Neolithic transition. The spreading mechanism for the Neolithic transition in Europe is controversial with two main competing models: the demic diffusion model (spread of population) and the cultural diffusion model (spread of ideas). The demic diffusion model assumes that the driving mechanism for the Neolithic expansion was population dispersal, with farming populations basically outplacing the indigenous hunter-gatherer populations. The cultural diffusion model, on the other hand, considers that agriculture was spread mainly by means of imitation of the farming techniques by the hunter-gatherer indigenous populations.

**Questions.** To what extent can geographical factors explain the non-homogeneities observed in the Neolithic spread rate? To what extent can the slowdown of the Neolithic spread in northern Europe be explained by the opposing effect of indigenous populations? How does cultural diffusion change the predictions of purely demic models, and how do they compare to the archaeological data? How do the results change under distance-dependent and frequency-dependent dynamics, as typically observed for human cultural transmission? What is the relative importance of demic, vertical and horizontal/oblique diffusion effects in the geographical spread of the Neolithic transition in Europe?

**Methodology.** In this case study we are developing reaction-diffusion models to describe the spread of agriculture in prehistoric Europe. Reaction-diffusion equations are mathematical models that can be applied to explain the evolution in time and space of the density of particles, or individuals, when under the influence of two processes: a reaction process, which corresponds to reproduction for biological populations, and a diffusion process. In order to model the spread of the Neolithic transition, we also perform reaction random walk simulations. These numerical simulations follow the evolution of the population density in time in space within a two dimensional grid. At every time step (one generation) population density is recalculated at each point of the grid, according the population growth equation and the dispersion algorithm.