Résumé

Cultural transmission occurs when individuals copy the cultural variants of other individuals. During transmission, individuals may have biases concerning which members of their population, or which variants, they imitate. Frequency-dependent bias occurs when the probability that a naive individual acquires a cultural variant depends on the frequency of the variant among his role models. An example is conformist bias, which occurs when naive individuals are disproportionately likely to adopt the more common variant. Boyd and Richerson (1985) and more recently Denton, Ram, Lieberman, and Feldman (2020) have proposed and analysed mathematical models of frequency-dependent bias, and used them to explain the cultural evolution of large-scale human cooperation. Here, I revisit the mathematical foundations of these models by making use of techniques borrowed from approximation theory and computer aided-geometric design. I show how previous results are easily recovered and extended beyond the simple cases usually considered in the literature.

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Référence

Jorge Peña ( IAST), « Revisiting mathematical models of frequency-dependent biased cultural transmission », IAST Lunch Seminar, Toulouse : IAST, 9 mars 2021, 12h45–13h45, salle Zoom Meeting.