Effective leadership in animal groups when no individual has pertinent information about resource locations: How interactions between leaders and followers can result in Lévy walk movement patterns

Much progress has been made in understanding how a few informed individuals are able to influence the foraging behaviour of a group and enhance its ability to navigate towards a resource. This research has provided valuable insights into the mechanisms of effective leadership. Here using a simple exactly solvable model we show how effective leadership could operate when no individual in the group has pertinent information about the locations of resources. Simple interactions between an ignorant leader and its followers are found to result in Lévy walk movement patterns that can optimize random searches. The findings may account for the Lévy walk movement patterns seen in some marine predators and for the frequent formation of groups of 2 or 3 ungulates when resources become scarce