Supporting Information for How perceived threat increases synchronization in collectively moving animal groups

Here we present supplementary information for the article ”How perceived threat increases synchronization in collectively moving animal groups” in the Proceedings of the Royal Society B. 1 Theoretical methods 1.1 Justification for asynchronous updating scheme Asynchronous updates are integral to our model. Consider a synchronous analogue of our model in which all individuals update at the same time but still choose the behavioural rule they follow at random. If p = 0.5 such a model will always result in symmetric distributions of individual speeds for long simulations. Such speed distributions do not have a positive skewness as observed in empirical data. Furthermore, adding a symmetric error or noise term to the desired movement of individuals in the model (as commonly done in the literature) will not result in positively skewed speed distributions for long simulations. However, if we relax the assumption that collectively