[The first part is here]

In a successive series of models, published in Scientific Reports, we considered whether other individual-level mechanisms could potentially be mistaken for conformity, generating relations between frequency of a trait and probability to copy it that *looked like* sigmoids. We choose a few simple and plausible mechanisms (you can refer to the paper for details) and we found that two of them – on a total of seven tested, plus three controls – generated relations for which a sigmoid function produced a better fit than a linear one (see figure below). The codes for running all simulations (written in Matlab) are available through the Open Science Framework.

The first one (a) implements what we called “Demonstrators subgroup”. The idea is that individuals copy only a limited and fixed subset of the population, which is randomly chosen at the beginning of the simulation. Copying is, inside this group, unbiased. Why does this setting produce a sigmoid? The reason is that a subset of a population will be more homogeneous and will converge faster than the whole population to one of the two traits. Imagine an extreme case in which the subgroup is represented by only one individual. The frequency of traits will be at the beginning around 50-50, but the probability to copy will be 0-100, generating a step function.

We called the second individual level mechanism (b in the figure above) “Variant preference”. This means that individuals had a consistent preference for one of the two variants. In our model this was implemented by having one of the two variants being always copied when encountered (so equivalent to unbiased copying) and the other copied with a lower probability.

There are a couple of things to notice about this result. First, the relation produced is not a “good” sigmoid (see again the figure b) but a combination of two linear functions with different slopes: one in the top-right part of the figure, which tracks the “preferred” trait and it is equivalent to unbiased copying, and one in the bottom-left of the figure, which tracks the “unpreferred” trait. The slope of the former depends on how much unpreferred is the trait. As above, let’s take an extreme case: if the probability to copy the unpreferred trait is zero, this part of the function will be an horizontal line at y=0.

For our purpose, however, the point is that this relation can be mistakenly taken for a sigmoid when tested against a linear function, which is the test that is likely to be done for empirical data. In addition, these details of the relation depend on the specific implementation of the preference. For example one could proceed the other way around, and assume that one variant is encountered and copied with a probability higher than its frequency, and the other is copied only when encountered. My bet is that all scenarios in which some form of imbalance is present will generate comparable results.

Second (an email exchange with Paul Smaldino after the publication helped me to identify this possible confusion in our paper), this result holds only when successive experiments, or simulations, in which different traits are alternatively preferred/unpreferred, are pooled together. If, each time, all individuals prefer the same trait there is no sigmoid. In fact, we modelled this scenario thinking exactly about the former situation. Experiments testing conformity, especially with non-human animals, tend to present two-action problems (see a review here) such as sliding a door to the left or right, or push or pull a rope etc. and it is not implausible that one of the two variants may become more salient during each trial (say because the sliding mechanism of the door becomes smoother on one side – more on this in our paper).

To conclude, we are not claiming that studies that found a sigmoid relation between frequency of a trait and probability to copy did not find a conformist bias at individual level. They might have. However there are few (and possibly many others) scenarios that seem plausible and that do not require individuals – being them humans, chimpanzees, or great tits – to be *disproportionate majority copiers *to generate the same population-level effect. At this point, there are more questions than answers: are there other mechanisms, beside the ones we explored, generating sigmoids? Can these mechanisms have the same “stabilising” effects on cultural differences that conformity is supposed to have? How strong is the empirical case for the existence of conformity in humans and other animals?

**References**

Acerbi, A.*, van Leeuwen, E.J.C.*, Tennie, C., Haun, D.B.M. (2016), Conformity cannot be identified based on population-level signatures, *Scientific Reports,* 6, 36068* *(*equal contribution)

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