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Every now and then the cultural paradigm of a society changes. Human historycan be regarded as a sequence of long periods of cultural stasis punctuated byparadigm shifts that transform culture upside-down over the turn of a fewgenerations. We propose here a population dynamics model devised to analyseparadigm shifts. In this model individuals are defined by a vector of culturaltraits that can change mainly through imitation of other individuals' traits.The novelty of the model is that cultural traits may interact reinforcing orhindering each other. Imitation is then biased by the 'cultural fitness'landscape thus defined. Our main result is that abrupt paradigm shifts occur,as a response to weak changes in the landscape, only when cultural traits dointeract---whereas adaptation is smooth if there is no interaction. Borrowingthe genetic term, this interaction is called 'cultural epistasis'. The resultis robust to the way that epistasis is implemented, to whether imitation isbiased by homophily, or to changes in other model parameters. Finally, arelevant consequence of this dynamics is the irreversible nature of paradigmshifts: the old paradigm cannot be restored even if the external changes areundone. Our model puts the phenomenon of paradigm shifts in cultural evolutionin the same category as catastrophic shifts in ecology or phase transitions inphysics.

Epistasis between cultural traits drives paradigm shifts in cultural evolution