Cultural transmission and cultural evolution are important for animals, especially for humans. I developed a new analytical model of cultural evolution, in which each newborn learns cultural traits from multiple individuals (exemplars) in parental generation, individually explores around learned cultural traits, judges the utility of known cultural traits, and adopts a mature cultural trait. Cultural evolutionary speed increases when individuals explore a wider range of cultural traits, accurately judge the skill level of cultural traits (strong direct bias), do not strongly conform to the population mean, increase the exploration range according to the variety of socially learned cultural traits (condition dependent exploration), and make smaller errors in social learning. Number of exemplars, population size, similarity of cultural traits between exemplars, and one-to-many transmission have little effect on cultural evolutionary speed. I also investigated how cultural interaction between two populations with different mean skill levels affects their cultural evolution. A population sometimes increases in skill level more if it encounters a less skilled population than if it does not encounter anyone. A less skilled population sometimes exceeds a more skilled population in skill level by cultural interaction between both populations. The appropriateness of this analytical method is confirmed by individual-based simulations.
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