The role of waterways in the spread of the Neolithic Kate Davison a, * , Pavel Dolukhanov b , Graeme R. Sarson a , Anvar Shukurov a a School of Mathematics and Statistics, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, UK b School of Historical Studies, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, UK Received 31 March 2005; received in revised form 25 August 2005; accepted 27 September 2005 Abstract The causes and implications of the regional variations in the spread of the incipient agriculture in Europe remain poorly understood. We use population dynamics models to study the dispersal of the Neolithic in Europe from a localised 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 DanubeeRhine 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 and hence lead to an effective advection. The standard reaction-diffusion equation is thus supplemented with an advection term, 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, 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 data, and reproduces a time delay in the spread of farming to the Eastern Europe, Britain and Scandinavia. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Neolithic; Population dynamics; Environmental effects; Expansion rate; Europe 1. Introduction The transition from hunter-gathering to early forms of agri- culture and stock breeding, when humankind entered the Neo- lithic epoch, was a quantum leap that ultimately shaped the later civilisations. The nature of the Neolithic and the mecha- nism of the spread of agriculture in the Old World remain top- ical issues in archaeology and related disciplines [26,34,36]. One viewpoint, first proposed and advocated by Gordon Childe [11], treats the spread of agriculture in Europe as a result of demic expansion, wherein farmers immigrated to Europe from the Near East, bringing with them new technol- ogies and subsistence strategies. An alternative approach at- taches more importance to cultural transmission; i.e., the adoption of cultural traits not necessarily associated with massive long-range travel of individuals [46]. Despite their fundamental difference, both processes represent gradual spread driven by individual random events, either human mi- grations or cultural exchange. Therefore, both processes can be modelled with (almost) the same mathematical equations involving the diffusion operator (or its appropriate generalisa- tion), albeit with different parameters. It is appealing to apply population dynamics models to de- scribe quantitatively the spread of the Neolithic. The simplest model of this type was suggested by Ammerman and Cavalli- Sforza [3], who chose parameter values appropriate for demic expansion. This model neglected any heterogeneity of the envi- ronment (and only suggested a mild latitudinal gradient in the rate of spread); even coastlines were neglected at that level of ap- proximation. Nevertheless, the model was remarkably success- ful in explaining the constant rate of spread of incipient farming over the vast area from the Near East to Western Europe. The constant speed of front propagation is a salient feature of solu- tions to one of the most popular equations of population dynam- ics, the FishereKolmogorovePetrovskyePiskunov (FKPP) * Corresponding author. E-mail addresses: kate.davison@newcastle.ac.uk (K. Davison), pavel. dolukhanov@newcastle.ac.uk (P. Dolukhanov), g.r.sarson@newcastle.ac.uk (G.R. Sarson), anvar.shukurov@newcastle.ac.uk (A. Shukurov). 0305-4403/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jas.2005.09.017 Journal of Archaeological Science 33 (2006) 641e652 http://www.elsevier.com/locate/jas