Abstract
Local interactions, when individuals meet, can regulate collective behaviour. In a system without any central control, the rate of interaction may depend simply on how the individuals move around. But interactions could in turn influence movement; individuals might seek out interactions, or their movement in response to interaction could influence further interaction rates. We develop a general framework to address these questions, using collision theory to establish a baseline expected rate of interaction based on proximity. We test the models using data from harvester ant colonies. A colony uses feedback from interactions inside the nest to regulate foraging activity. Potential foragers leave the nest in response to interactions with returning foragers with food. The time series of interactions and local density of ants show how density hotspots lead to interactions that are clustered in time. A correlated random walk null model describes the mixing of potential and returning foragers. A model from collision theory relates walking speed and spatial proximity with the probability of interaction. The results demonstrate that although ants do not mix homogeneously, trends in interaction patterns can be explained simply by the walking speed and local density of surrounding ants.