Spatial dynamics of human dispersals: Constraints on modelling and archaeological validation

In recent years there has been growing interest in the application of travelling wave models to the spatial dynamics of human dispersals, and their archaeological validation. These models enable predictions of the velocity of population expansion, derived from estimates of reproductive rates and of individual mobility. In this paper we discuss some intrinsic constraints on the application of such models to dispersal events which have been documented in the archaeological record. There is significant uncertainty in radiocarbon dating of first occupation at different locations, and in the reconstruction of evolving population distributions from time-averaged archaeological distribution maps. We calculate some archaeological boundary conditions for the accurate estimation of travelling wave profiles and velocities, and demonstrate their significance for two archaeological case studies: the first peopling of the Americas, and the Neolithic transition in Europe.