On randomly changing conformity bias in cultural transmission

Significance Animals, from humans to Drosophila, display conformity and anticonformity. Population dynamics under (anti)conformity may explain emergent properties of groups including fads, norms, and collective behavior. Although empirical evidence suggests that a population’s level of conformity can vary over time, most mathematical models have not included time-varying conformity coefficients. To potentially improve applicability to real-world systems, we allow conformity coefficients, numbers of sampled “role models,” and weak selection to vary stochastically in an established conformity model. Novel dynamics are possible, including simultaneous stochastic local stability of monomorphisms and polymorphism. Interpreting real-world population differences in terms of (anti)conformity may therefore not be straightforward. Under some conditions, however, the deterministic model provides a useful approximation to the stochastic model. Humans and nonhuman animals display conformist as well as anticonformist biases in cultural transmission. Whereas many previous mathematical models have incorporated constant conformity coefficients, empirical research suggests that the extent of (anti)conformity in populations can change over time. We incorporate stochastic time-varying conformity coefficients into a widely used conformity model, which assumes a fixed number n of “role models” sampled by each individual. We also allow the number of role models to vary over time (nt). Under anticonformity, nonconvergence can occur in deterministic and stochastic models with different parameter values. Even if strong anticonformity may occur, if conformity or random copying (i.e., neither conformity nor anticonformity) is expected, there is convergence to one of the three equilibria seen in previous deterministic models of conformity. Moreover, this result is robust to stochastic variation in nt. However, dynamic properties of these equilibria may be different from those in deterministic models. For example, with random conformity coefficients, all equilibria can be stochastically locally stable simultaneously. Finally, we study the effect of randomly changing weak selection. Allowing the level of conformity, the number of role models, and selection to vary stochastically may produce a more realistic representation of the wide range of group-level properties that can emerge under (anti)conformist biases. This promises to make interpretation of the effect of conformity on differences between populations, for example those connected by migration, rather difficult. Future research incorporating finite population sizes and migration would contribute added realism to these models.