A non-equilibrium neutral model for analysing cultural change

• Non-equilibrium model for analysing frequency changes between different time points.
• Model accounts for temporally varying population size and mutation rates.
• Considered statistic: probability of the number of remaining initial variants under different evolutionary hypotheses.
• This probability is a good indicator for detecting departures from the hypotheses.
• Frequency changes in LBK data set cannot be explained by neutral evolution.

Neutral evolution is a frequently used model to analyse changes in frequencies of cultural variants over time. Variants are chosen to be copied according to their relative frequency and new variants are introduced by a process of random mutation. Here we present a non-equilibrium neutral model which accounts for temporally varying population sizes and mutation rates and makes it possible to analyse the cultural system under consideration at any point in time. This framework gives an indication whether observed changes in the frequency distributions of a set of cultural variants between two time points are consistent with the random copying hypothesis. We find that the likelihood of the existence of the observed assemblage at the end of the considered time period (expressed by the probability of the observed number of cultural variants present in the population during the whole period under neutral evolution) is a powerful indicator of departures from neutrality. Further, we study the effects of frequency-dependent selection on the evolutionary trajectories and present a case study of change in the decoration of pottery in early Neolithic Central Europe. Based on the framework developed we show that neutral evolution is not an adequate description of the observed changes in frequency.