Multiple Sources of the European Neolithic: Mathematical Modelling   Constrained by Radiocarbon Dates
  We present a mathematical model, based on the compilation and statistical processing of radiocarbon dates, of the transition from the Mesolithic to the Neolithic, from about 7,000 to 4,000 BC in Europe. The arrival of the Neolithic is traditionally associated with the establishment of farming-based economies; yet in considerable areas of north-eastern Europe it is linked with the beginning of pottery-making in the context of foraging-type communities. Archaeological evidence, radiocarbon dates and genetic markers are consistent with the spread of farming from a source in the Near East. However, farming was less important in the East; the Eastern and Western Neolithic have distinct signatures. We use a population dynamics model to suggest that this distinction can be attributed to the presence of two waves of advance, one from the Near East, and another through Eastern Europe. Thus, we provide a quantitative framework in which a unified interpretation of the Western and Eastern Neolithic can be developed. 
K. Davison, P. M. Dolukhanov, G. R. Sarson, A. Shukurov, G. I.   Zaitseva