The potential for behaviours to spread via cultural transmission has profound implications for our understanding of social dynamics and evolution. Several studies have provided empirical evidence that local traditions can be maintained in animal populations via conformist learning (i.e. copying the majority). A conformist bias can be characterized by a sigmoidal relationship between a behavior's prevalence in the population and an individual's propensity to adopt that behavior. For this reason, the presence of conformist learning in a population is often inferred from a sigmoidal acquisition curve in which the overall rate of adoption for the behavior is taken as the dependent variable. However, the validity of sigmoidal acquisition curves as evidence for conformist learning has recently been challenged by models suggesting that such curves can arise via alternative learning rules that do not involve conformity. We review these models, and find that the proposed alternative learning mechanisms either rely on faulty or unrealistic assumptions, or apply only in very specific cases. We therefore recommend that sigmoidal acquisition curves continue to be taken as evidence for conformist learning. Our paper also highlights the importance of understanding the generative processes of a model, rather than only focusing solely on the patterns produced. By studying these processes, our analysis suggests that current practices by empiricists have provided robust evidence for conformist transmission in both humans and non-human animals.Arising from: Acerbi, A. et al. Sci. Rep. 6, 36068 (2016); https://doi.org/10.1038/srep36068 .