Spatial evolution of human dialects

The geographical pattern of human dialects is a result of history. Here, we formulate a simple spatial model of language change which shows that the final result of this historical evolution may, to some extent, be predictable. The model shows that the boundaries of language dialect regions are controlled by a length minimizing effect analogous to surface tension, mediated by variations in population density which can induce curvature, and by the shape of coastline or similar borders. The predictability of dialect regions arises because these effects will drive many complex, randomized early states toward one of a smaller number of stable final configurations. The model is able to reproduce observations and predictions of dialectologists. These include dialect continua, isogloss bundling, fanning, the wave-like spread of dialect features from cities, and the impact of human movement on the number of dialects that an area can support. The model also provides an analytical form for S\'{e}guy's Curve giving the relationship between geographical and linguistic distance, and a generalisation of the curve to account for the presence of a population centre. A simple modification allows us to analytically characterize the variation of language use by age in an area undergoing linguistic change.