The causes and implications of the regional variations in the spread of the incipient agriculture in Europe remain poorly understood. We apply population dynamics models to study the dispersal of the Neolithic in Europe from a localized area in the Near East, solving the two-dimensional reaction-diffusion equation on a spherical surface. We focus on the role of major river paths and coastlines in the advance of farming to model the rapid advances of the Linear Pottery (LBK) and the Impressed Ware traditions along the Danube-Rhine corridor and the Mediterranean coastline respectively. We argue that the random walk of individuals, which results in diffusion of the population, can be anisotropic in those areas. The standard reaction-diffusion equation is thus supplemented with advection-like terms confined to the proximity of major rivers and coastlines. The model allows for the spatial variation in both the human mobility (diffusivity) and the carrying capacity of landscapes, reflecting the local altitude and latitude. This approach can easily be generalised to include other environmental factors, such as the bioproductivity of landscapes. Our model successfully accounts for the regional variations in the spread of the Neolithic, consistent with the radiocarbon dated data, and reproduces a time delay in the spread of farming to the Eastern Europe and Scandinavia.
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