I will present two different approaches to modeling cultural evolution. The first approach uses epidemiological models for describing the dynamics of cultural content in a single population of humans. Using techniques from the mathematical framework of adaptive dynamics, I show how this approach can be used to study cultural diversification. The second framework is being developed for studying multi-level selection on cultural content. This approach requires birth-death processes at different levels of selection, and can for example be used to study cultural group selection and the problem of cooperation.
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