Inferential power in identifying frequency-dependent social learning strengthened by increasing behavioural options

Abstract

Two-option choice experimental designs are the most commonly employed framework for identifying evidence of social learning or social learning strategies in captive and wild populations. In nature, however, animals often choose from more than two behaviours, and multiple innovations may arise simultaneously. Studies of animal social learning are often constrained by small sample sizes, which limit researchers' ability to convincingly identify the proposed social learning strategy responsible for behavioural choice. In this study, I examine whether expanding behavioural options from k = 2 to k > 2 and increasing sample size affects inferential power in identifying social learning strategies. I focus on three frequency-dependent learning strategies: conformist transmission, unbiased transmission and anti-conformist transmission. I simulate 100 datasets for 72 parameter combinations, yielding 7200 simulations. I evaluate number of options (k = 2, 3, 4, 5), population size (n = 5, 10, 25, 50, 100, 250) and the logarithmic strength of frequency dependence (log(f) = log(1∕3), log(1), log(3)). I then fit a Bayesian social learning model to simulated data to evaluate the percent of the posterior consistent with type of frequency dependence, posterior standard deviations, highest posterior density intervals and posterior medians relative to the true simulated value of log(f). I show that increasing the number of options an animal can choose from increases the accuracy and certainty of identifying the type and magnitude of frequency-dependent social learning. These effects are particularly pronounced at small to intermediate sample sizes, which are common in empirical studies of animal social learning. These findings suggest that knowing what an animal did not choose is equally important as knowing what an animal did choose when identifying social learning strategies. By strategically increasing the number of behaviours from which an animal can choose, researchers can increase inferential power in identifying social learning strategies without increasing sample size, that is, adding additional animals or collecting more data.

Keywords: conformist transmission; conformity; cultural evolution; frequency dependence; multinomial; social learning.