On modeling cognition and culture How formal models of social learning can inform our understanding of cultural evolution

Formal models of cultural evolution analyze how cognitive and affective processes combine with patterns of social interaction to generate the distributions and dynamics of ‘representations’— ideas, beliefs, schemas, or mental models. Recently, cognitive anthropologists have made three criticisms of such models: First, mental representations are non-discrete. Second, cultural transmission is highly inaccurate because public representations provide only incomplete information to social learners. And third, mental representations are not replicated, but rather are ‘reconstructed’ through an inferential process that is strongly affected by cognitive ‘attractors,’ which shape the kinds of representations that are likely to be acquired. Based on these three claims, critics have concluded that: 1) models that assume use replication or replicators are inappropriate, 2) selective cultural learning cannot account for ‘cultural inertia’ (stable traditions), and 3) selective cultural learning also cannot generate cumulative adaptive evolution. Here we analyze three formal models to show that even if the three premises of this critique are correct, the deductions that have been drawn from them are false. In the first model, we assume continuously varying representations under the influence of weak selective transmission and strong attractors. We show that if the attractors are sufficiently strong relative to selective forces, the continuous representation model reduces to the standard discrete-trait replicator model, and the weak selective component determines the final equilibrium of the system. In the second model, we assume representations are discrete, but that replication is very inaccurate. We show that very low fidelity replication of representations at the individual level does not preclude accurate replication at the population level, and therefore, accurate individuallevel replication of representations is not necessary for selective forces to generate either cultural inertia or cumulative cultural adaptation. In the third model, we assume continuous (nondiscrete) cultural representations, incomplete transmission and substantial inferential transformations. We derive the conditions for cumulative adaptive evolution.