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National audience; One of the difficulties with cultural group selection theory highlighted in the review by Smith (2020, Evol. Hum. Sci., 2, e7) is its inability to separate the evolutionary effects of selection of cultural traits based on biological fitness (Cultural Selection 1) from the effects of selection based on cultural fitness (Cultural Selection 2). Confusing these two processes can hinder the integration of adaptive explanations for human behaviour, which focus on biological fitness, and cultural evolution explanations, which often focus on social transmission. Recent empirical work is starting to bridge this gap, but progress in mathematical modelling has been considerably slower. Here, I suggest that modellers can contribute to achieving this integration by further developing models of Cultural Selection 1, where behaviours are influenced by culturally inherited traits selected on the basis of their effects on biological fitness. These models should build on existing social evolution theory methods and replace genetic relatedness with cultural relatedness, that is the probability that two individuals share a cultural variant.