Highlights d We conducted a cultural evolution experiment using captive great tits d Gradual replacement of individuals promoted the spread of efficient cultural variants d Immigrants played a role as adopters rather than innovators of efficient variants d Turnover might be a general mechanism in the cultural evolution of efficiency

Recent studies in several taxa have demonstrated that animal culture can evolve to become more efficient in various contexts ranging from tool use to route learning and migration. Under recent definitions, such increases in efficiency might satisfy the core criteria of cumulative cultural evolution (CCE). However, there is not yet a satisfying consensus on the precise definition of efficiency, CCE or the link between efficiency and more complex, extended forms of CCE considered uniquely human. To bring clarity to this wider discussion of CCE, we develop the concept of efficiency by (i) reviewing recent potential evidence for CCE in animals, and (ii) clarifying a useful definition of efficiency by synthesizing perspectives found within the literature, including animal studies and the wider iterated learning literature. Finally, (iii) we discuss what factors might impinge on the informational bottleneck of social transmission, and argue that this provides pressure for learnable behaviours across species. We conclude that framing CCE in terms of efficiency casts complexity in a new light, as learnable behaviours are a requirement for the evolution of complexity. Understanding how efficiency greases the ratchet of cumulative culture provides a better appreciation of how similar cultural evolution can be between taxonomically diverse species—a case for continuity across the animal kingdom. This article is part of a discussion meeting issue ‘The emergence of collective knowledge and cumulative culture in animals, humans and machines’.

The ability to build upon previous knowledge—cumulative cultural evolution—is a hallmark of human societies. While cumulative cultural evolution depends on the interaction between social systems, cognition and the environment, there is increasing evidence that cumulative cultural evolution is facilitated by larger and more structured societies. However, such effects may be interlinked with patterns of social wiring, thus the relative importance of social network architecture as an additional factor shaping cumulative cultural evolution remains unclear. By simulating innovation and diffusion of cultural traits in populations with stereotyped social structures, we disentangle the relative contributions of network architecture from those of population size and connectivity. We demonstrate that while more structured networks, such as those found in multilevel societies, can promote the recombination of cultural traits into high-value products, they also hinder spread and make products more likely to go extinct. We find that transmission mechanisms are therefore critical in determining the outcomes of cumulative cultural evolution. Our results highlight the complex interaction between population size, structure and transmission mechanisms, with important implications for future research.