Inferring processes of cultural transmission: the critical role of rare variants in distinguishing neutrality from novelty biases (1702.08506v2)

Abstract: Neutral evolution assumes that there are no selective forces distinguishing different variants in a population. Despite this striking assumption, many recent studies have sought to assess whether neutrality can provide a good description of different episodes of cultural change. One approach has been to test whether neutral predictions are consistent with observed progeny distributions, recording the number of variants that have produced a given number of new instances within a specified time interval: a classic example is the distribution of baby names. Using an overlapping generations model we show that these distributions consist of two phases: a power law phase with a constant exponent of -3/2, followed by an exponential cut-off for variants with very large numbers of progeny. Maximum likelihood estimations of the model parameters provide a direct way to establish whether observed empirical patterns are consistent with neutral evolution. We apply our approach to a complete data set of baby names from Australia. Crucially we show that analyses based on only the most popular variants, as is often the case in studies of cultural evolution, can provide misleading evidence for underlying transmission hypotheses. While neutrality provides a plausible description of progeny distributions of abundant variants, rare variants deviate from neutrality. Further, we develop a simulation framework that allows for the detection of alternative cultural transmission processes. We show that anti-novelty bias is able to replicate the complete progeny distribution of the Australian data set.