The shape of the cultural transmission of shapes

Cultural evolutionary theory has long modeled offspring trait variance as constant across generations, an assumption borrowed from quantitative genetics that has remained largely untested. We tested it by comparing a Parental Variability-Dependent Inheritance (PVDI) model, in which offspring trait variance scales with parental trait variance, against the classic Galton-Pearson model and a null model. Participants designed artifacts on a tablet configurator by adjusting five dimension sliders, in one of three tasks: an averaging task, an aesthetic task, and an engineering task. Aesthetic and engineering artifacts were 3D-printed and passed along independent three-generation chains varying in parental set size and selection pressure. Data were collected at three field sites: Molyko and Bokwango, two neighborhoods of Buea, Cameroon, and Prague, Czech Republic. Of 658 participants recruited, 600 were retained for analysis. Models were fitted as Bayesian beta regressions and compared by WAIC. In the inheritance analysis the variance-proportional model outperformed the null model in all three tasks, most clearly in the averaging task, and variance proportionality depended more on which group the learner belonged to, by country and by gender, than on the task domain. In the performance analysis the null model won: neither mean parental performance nor the best parent's performance predicted offspring performance. Engineering performance nonetheless rose across generations, implicating individual innovation rather than inherited performance. Educational background did not emerge as a meaningful predictor in any task. These findings challenge a foundational assumption of the field and make the case for cross-cultural designs in cultural evolution research.