Table 1.

Summary of problematic issues found in the models by Acerbi et al. (2016) and Van Leeuwin et al.¹⁶.

Issue	Explanation
Starting conditions	The population was always initiated with a probability of 0.5 for each behaviour. This is unrealistic from empirical perspective, as a natural spreading process would start with one innovator (proportions near 0 or 1). This assumption exacerbates the potential for an artefactual sigmoidal response. Had a range of initial conditions been used to assess model robustness, which is common practice in agent-based modelling, the strong claims made by the modelling papers would not have been supported.
Pooling data	All of the frequency data across each of the 1000 replicates were pooled, without noting variation across replicates. This aggregates multiple categories of response into a single category. This practice can eliminate discovery of multimodal data and provides no information on the range of outcomes that are possible. This approach can graft different responses together, such as combining two linear responses that then appear as an artefactual sigmoid. More generally, data with categorically different starting conditions should not be pooled.
Full behaviour history	The full history of all behaviours was used to calculate frequency of behaviours used by agents in the model when making a behavioural choices. This approach misrepresents what has been done in existing empirical studies. It also describes a biologically implausible process that assumes individuals respond to a distant past that potentially includes thousands of observations. Using data restricted to recent history when calculating the state of the system alleviates any potential mistaken results.
What counts as ‘copying’ events	Every event was counted in which an individual encountered behavioural variant A, including when an individual did not change what action it performs. However, events in which an individual retained variant A after encountering variant B were not counted. This increases the appearance of a sigmoidal acquisition curve (as opposed to either a linear or r-shaped curve) because individuals that continuously perform variant A when the population behaviour becomes entrenched are all counted as copying action A. Defining social learning events is challenging, so striving for consistency and robustness is important.
Individuals are their own targets for social learning	Individuals could select themselves as demonstrators, which confounds data on social learning. Similarly, a focal individual’s behaviours were counted in its assessment of the historical frequency of observed events. Whilst in a population of 100 or more individuals this issue had relatively little impact on the results, the effect may be much greater in a smaller population.

These issues result in the incorrect or misleading conclusions drawn from the simulations. While some issues do not strongly affect the shapes of the curve in the results of the papers, they incorrectly implement the biological process that the papers seek to investigate (for example, animals do not copy themselves) or incorrectly represent the analytical approaches used by empirical studies (for example studies count only the first demonstration by an individual).