First generation modelling of cultural systems, as applied in archaeology, frequently invoked linear, deterministic relationships as well as privileging concepts such as stability and an assumed cumulative evolution towards increasing complexity. But can the world of human affairs with its numerous reversals and unintended consequences really be captured by such models? Recent advances in the natural sciences have demonstrated the central role of non-linear phenomena, discontinuities and unpredictable breaks from established patterns and events. It is argued that such findings can form the basis for a new theoretical framework, human ecodynamics.