Applying invasion criterion to cultural evolution

Cultural diversity is a fundamental aspect of human life; however, it is still challenging to understand mechanisms that promote cultural diversity. While previous studies tended to focus on how innovation generates cultural diversity, we investigated whether the invasion criterion, originally developed for understanding species coexistence in community ecology, can predict the maintenance of cultural diversity in a finite population under various transmission biases. Using mathematical and individual-based models, we show that the invasion criterion reliably predicts the duration of coexistence of multiple cultural traits in stochastic dynamics under content-, conformity-, and anticonformity-biased social learning. The invasion criterion also predicted cultural coexistence under prestige- and success-bias social learning, but the predictability was lower than in the above cases. Similarity-biased social learning, where people tend to learn from those with the same "tag" traits (e.g., gender), lowered the predictive power because the cultural traits were associated with the tag traits with a certain probability, violating the rarity assumption. Our results, therefore, demonstrate that the invasion criterion offers valuable tools for quantitatively predicting cultural coexistence, but predictability varied across transmission biases, suggesting that modifications are needed to improve the predictability in cultural dynamics. Our model also showed that increasing the number of cultural models, from which an individual copies a cultural trait, can prolong cultural coexistence under certain biases, with implications for fostering innovation and preserving culture. These findings suggest that the invasion criterion can be useful for understanding the maintenance of cultural diversity, as it is for species diversity.