A central question in behavioral and social sciences is understanding to what extent cultural traits are inherited from previous generations, transmitted from adjacent populations or produced in response to changes in socioeconomic and ecological conditions. As quantitative diachronic databases recording the evolution of cultural artifacts over many generations are becoming more common, there is a need for appropriate data-driven methods to approach this question. Here we present a new Bayesian method to infer the dynamics of cultural traits in a diachronic dataset. Our method called Evoked-Transmitted Cultural model (ETC) relies on fitting a latent-state model where a cultural trait is a latent variable which guides the production of the cultural artifacts observed in the database. The dynamics of this cultural trait may depend on the value of the cultural traits present in previous generations and in adjacent populations (transmitted culture) and/or on ecological factors (evoked culture). We show how ETC models can be fitted to quantitative diachronic or synchronic datasets, using the Expectation-Maximization algorithm, enabling estimating the relative contribution of vertical transmission, horizontal transmission and evoked component in shaping cultural traits. The method also allows to reconstruct the dynamics of cultural traits in different regions. We tested the performance of the method on synthetic data for two variants of the method (for binary or continuous traits). We found that both variants allow reliable estimates of parameters guiding cultural evolution. Overall, our method opens new possibilities to reconstruct how culture is shaped from quantitative data, with possible application in cultural history, cultural anthropology, archaeology, historical linguistics and behavioral ecology.
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