A statistical method for identifying different rules of interaction between individuals in moving animal groups

The emergent patterns of collective motion are thought to arise from application of individual-level rules that govern how individuals adjust their velocity as a function of the relative position and behaviours of their neighbours. Empirical studies have sought to determine such rules of interaction applied by 'average' individuals by aggregating data from multiple individuals across multiple trajectory sets. In reality, some individuals within a group may interact differently from others, and such individual differences can have an effect on overall group movement. However, comparisons of rules of interaction used by individuals in different contexts have been largely qualitative. Here we introduce a set of randomization methods designed to determine statistical differences in the rules of interaction between individuals. We apply these methods to a case study of leaders and followers in pairs of freely exploring eastern mosquitofish (Gambusia holbrooki). We find that each of the randomization methods is reliable in terms of: repeatability of p-values, consistency in identification of significant differences and similarity between distributions of randomization-based test statistics. We observe convergence of the distributions of randomization-based test statistics across repeat calculations, and resolution of any ambiguities regarding significant differences as the number of randomization iterations increases.