Nonlinearity, Disorder, the Spread of Neolithic Farming, and the Origin of the Indo-European Languages

Abstract

The replacement of mesolithic hunters and gatherers by neolithic farmers in Europe is a very clean example of technology-based growth and change in human society. Recently, a remarkable quantitative model, the wave-of-advance model, has been put forward by Ammerman and Cavalli-Sforza (AC)[1,2,3] to describe this transition and its genetic consequences. Renfrew has elaborated the model to provide first an explanation of the origin of the Indo-European languages [4] and subsequently of the other two members of the Nostratic superfamily of languages.[5] The Fisher equation employed by AC does not, however, incorporate the spatial inhomogeneity of the food production potential of the neolithic farming technology within Europe. We generalize the Fisher equation to include the effects of such heterogeneity on demic diffusion and population growth. Our most important result is the prediction of internal boundaries, subsistence boundaries, around, e.g., mountain ranges and in the North within which the farming population density vanishes. These boundaries offer the possibility of explaining within the framework of the wave-of-advance model, such anomalies as the Basque language.