Is the neighborhood of interaction in human crowds metric, topological, or visual?

Global patterns of collective motion in bird flocks, fish schools, and human crowds are thought to emerge from local interactions within a neighborhood of interaction, the zone in which an individual is influenced by their neighbors. Both metric and topological neighborhoods have been reported in animal groups, but this question has not been addressed for human crowds. The answer has important implications for modeling crowd behavior and predicting crowd disasters such as jams, crushes, and stampedes. In a metric neighborhood, an individual is influenced by all neighbors within a fixed radius, whereas in a topological neighborhood, an individual is influenced by a fixed number of nearest neighbors, regardless of their physical distance. A recently proposed alternative is a visual neighborhood, in which an individual is influenced by the optical motions of all visible neighbors. We test these hypotheses experimentally by asking participants to walk in real and virtual crowds and manipulating the crowd's density. Our results rule out a topological neighborhood, are approximated by a metric neighborhood, but are best explained by a visual neighborhood that has elements of both. We conclude that the neighborhood of interaction in human crowds follows naturally from the laws of optics and suggest that previously observed "topological" and "metric" interactions might be a consequence of the visual neighborhood.

Local interactions underlying collective motion in human crowds.

It is commonly believed that global patterns of motion in flocks, schools and crowds emerge from local interactions between individuals, through a process of self-organization. The key to explaining such collective behaviour thus lies in deciphering these local interactions. We take an experiment-driven approach to modelling collective motion in human crowds. Previously, we observed that a pedestrian aligns their velocity vector (speed and heading direction) with that of a neighbour. Here we investigate the neighbourhood of interaction in a crowd: which neighbours influence a pedestrian's behaviour, how this depends on neighbour position, and how the influences of multiple neighbours are combined. In three experiments, a participant walked in a virtual crowd whose speed and heading were manipulated. We find that neighbour influence is linearly combined and decreases with distance, but not with lateral position (eccentricity). We model the neighbourhood as (i) a circularly symmetric region with (ii) a weighted average of neighbours, (iii) a uni-directional influence, and (iv) weights that decay exponentially to zero by 5 m. The model reproduces the experimental data and predicts individual trajectories in observational data on a human 'swarm'. The results yield the first bottom-up model of collective crowd motion.

Follow the leader: visual control of speed in pedestrian following.

When people walk together in groups or crowds they must coordinate their walking speed and direction with their neighbors. This paper investigates how a pedestrian visually controls speed when following a leader on a straight path (one-dimensional following). To model the behavioral dynamics of following, participants in Experiment 1 walked behind a confederate who randomly increased or decreased his walking speed. The data were used to test six models of speed control that used the leader's speed, distance, or combinations of both to regulate the follower's acceleration. To test the optical information used to control speed, participants in Experiment 2 walked behind a virtual moving pole, whose visual angle and binocular disparity were independently manipulated. The results indicate the followers match the speed of the leader, and do so using a visual control law that primarily nulls the leader's optical expansion (change in visual angle), with little influence of change in disparity. This finding has direct applications to understanding the coordination among neighbors in human crowds.