Abstract
Some human fronts spread faster than expected by models based on dispersal and reproduction. The only explanation proposed so far assumes that some autochthonous individuals are incorporated by the expanding populations, leading to faster front speeds. Here we show that simple models without this effect are also consistent with the observed speeds of two fronts (a Khoi-khoi expansion of herders and a Bantu expansion of farmers), provided that the dispersal of individuals is biased (i.e., more probable) in directions closer to the front propagation direction. The physical models presented may also be applied to other kinds of social phenomena, including innovation diffusion, rumor propagation, linguistic fronts, epidemic spread, diffusion in economic space and the evolution of cooperation in spatial systems. They can be also adapted to non-human systems with biased dispersal, including biological invasions, cancer tumors and virus treatment of tumors.