Gene-culture shock waves

A hyperbolic model is presented which generalises Aokiʼs parabolic system for the combined propagation of a mutant gene together with a cultural innovation. It is shown that this model allows for the propagation of a shock wave and the shock amplitude is calculated numerically. Particular attention is paid to the case where the shock moves into a region where the frequencies of the mutant gene and of the individuals adopting the innovation are zero.