Understanding the evolution and role of cultural inheritance in animal biology is a challenge. Central questions are: How does cultural inheritance arise? How does it depend on learning mechanisms? How do cultures evolve and diversify? We address these issues by considering diet learning in ``monkeys''. We use a bottom-up modeling approach and implement a few straightforward biological features, namely: living in groups, learning what to eat and foraging selectively in rich spatial environments with many resource species. We then study interactions and self-organizing processes that arise, and explore what this means for cultural inheritance. Surprisingly, we find that simply living in groups is sufficient for generating traditional inheritance of diet preferences and cumulative cultural diet improvement. Traditions arise when naive individuals passively inherit group specific diet preferences by following their group, and learn in patches visited by their group. Moreover, if naive individuals are sufficiently selective in their foraging, they can be selective within the feeding context of their group and are better able to select high quality resources. If this continues over generations, diets improve culturally. Trial-and-error learning in groups is therefore sufficient for allowing cultural phenomena to self-organize. Crucial is how the environment structures learning opportunities. In patchy environments, individuals automatically share local learning opportunities and spontaneously converge in learning. This generates group-level diets. In contrast, in uniform environments local depletion of resources causes individuals to forage on, and learn from, resources not eaten by other individuals, causing divergence in diet. This emphasizes the role of the environment, rather than cognition, in structuring the nature of social influences on learning that arise as side-effects of grouping. Given what we find for trial-and-error learning in groups, we next considered the additional role of more explicit social learning, namely copying. We find that can improve diet learning and enhance cumulative cultural diet improvement. Copying allows individuals to share information about high quality resources, and when it is effective such collective learning is extended over the generations. The short-term impact of copying depends on the difficulty of preference development, the potential for copying to overrule individual selectivity, and the difficulty of copying itself. How these factors relate depends on resource distributions. Next to cumulative cultural change, we find cultural diversification in response to environmental change. This is because different learning histories cause groups to adapt differently to change. Surprisingly, copying increases the rate of divergence by enhancing the rate of diet innovation, especially when groups live together in the same environment. This is because competition for shared resources enhances feeding on differently preferred resources. In conclusion, our model provides a simple bottom-up framework to understand how cultural inheritance can come about, evolve and diversify as side-effects of grouping. We provide a highly parsimonious explanation based on self-organization, and do not require adaptive explanations for their origin. Moreover, the ease with which cultural phenomena arise, suggest that they could be common in group foragers, playing a role in their ecology and evolution
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