Inference of Cultural Transmission Modes Based on Incomplete Information

In this article we explore the theoretical limits of the inference of cultural transmission modes based on sparse population-level data. We approach this problem by investigating whether different transmission modes produce different temporal dynamics of cultural change. In particular, we explore whether different transmission modes result in sufficiently different distributions of the average time a variant stays the most common variant in the population, tmax, so that their inference can be guaranteed on the basis of an estimate of tmax. We assume time series data detailing the frequencies of different variants of a cultural trait in a population at different points in time and investigate the temporal resolution (i.e., the length of the time series and the distance between consecutive time points) that is needed to ensure distinguishability between transmission modes. We find that under complete information most transmission modes can be distinguished on the basis of the statistic tmax; however, we should not expect the same results if only infrequent information about the most common cultural variant in the population is available.