  Every now and then the cultural paradigm of a society changes. Human history
can be regarded as a sequence of long periods of cultural stasis punctuated by
paradigm shifts that transform culture upside-down over the turn of a few
generations. We propose here a population dynamics model devised to analyse
paradigm shifts. In this model individuals are defined by a vector of cultural
traits that can change mainly through imitation of other individuals' traits.
The novelty of the model is that cultural traits may interact reinforcing or
hindering 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 do
interact---whereas adaptation is smooth if there is no interaction. Borrowing
the genetic term, this interaction is called 'cultural epistasis'. The result
is robust to the way that epistasis is implemented, to whether imitation is
biased by homophily, or to changes in other model parameters. Finally, a
relevant consequence of this dynamics is the irreversible nature of paradigm
shifts: the old paradigm cannot be restored even if the external changes are
undone. Our model puts the phenomenon of paradigm shifts in cultural evolution
in the same category as catastrophic shifts in ecology or phase transitions in
physics.
