Cultural Transmission and Stochastic Network Growth

Abstract

Archaeological theory has traditionally presupposed the existence of “battleship curves” in stylistic evolution, with little understanding about what governs the width (variant frequency) or length (variant lifespan) of these curves. In terms of these variables, we propose that there is a testable difference between independent decisions, unbiased transmission, and biased transmission in cultural evolution. We expect independent decision making to be represented by an exponential distribution of variant prevalence in the population. In contrast, unbiased transmission tends to be characterized by a power law or log-normal distribution of prevalence, while biased transmission should deviate significantly from the unbiased case. The difference between these categories may be fundamental to how cultural traits spread and persist. In order to make analytical predictions for unbiased transmission, we adapt a model of stochastic network growth that, by quantitatively demonstrating the inherent nonlinearity in unbiased transmission, can explain why a few highly popular styles can be expected to emerge in the course of cultural evolution. For the most part, this model predicts the frequencies of pottery decorations remarkably well over a 400-year span of Linearbandkeramik settlement in the Merzbach valley. Because the highest frequencies of actual motifs are somewhat less than predicted by our unbiased transmission model, we identify an anti-conformist, or pro-novelty, bias in the later phases of the Neolithic Merzbach Valley.