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Reliance on generative AI can reduce cultural variance and diversity, especially in creative work. This reduction in variance has already led to problems in model performance, including model collapse and hallucination. In this paper, we examine the long-term consequences of AI use for human cultural evolution and the conditions under which widespread AI use may lead to "cultural collapse", a process in which reliance on AI-generated content reduces human variation and innovation and slows cumulative cultural evolution. Using an agent-based model and evolutionary game theory, we compare two types of AI use: complement and substitute. AI-complement users seek suggestions and guidance while remaining the main producers of the final output, whereas AI-substitute users provide minimal input, and rely on AI to produce most of the output. We then study how these use strategies compete and spread under evolutionary dynamics. We find that AI-substitute users prevail under individual-level selection despite the stronger reduction in cultural variance. By contrast, AI-complement users can benefit their groups by maintaining the variance needed for exploration, and can therefore be favored under cultural group selection when group boundaries are strong. Overall, our findings shed light on the long-term, population-level effects of AI adoption and inform policy and organizational strategies to mitigate these risks.