  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.
