To be confirmed

Swarming is a non-equilibrium phenomenon observed throughout the animal kingdom; flocking in birds, swarming in insects, shoaling in fish and herding in mammals. Our understanding of this process in real animal systems is remarkably undeveloped. Most previous models involve members of a swarm aligning their velocities with those of their immediate neighbours (plus some noise). However, both metric-based and metric-free versions of these {local} models have fundamental pathologies that are frequently overlooked, e.g. the swarm evaporates in the absence of an ad hoc long-range attraction unless confined within an artificial box. Here we analyse how individuals might respond to a visual projection of the swarm and argue why this is biologically plausible. A simple class of candidate models then arises naturally in which there is a single additional scalar parameter controlling the tendency of all individuals to fly in a direction that is characteristic of the particular projection pattern that they see. This naturally leads to swarms that remain localized. Our model supports a surprisingly rich variety of qualitative behaviour that is reminiscent of birds, fish and insects respectively. It also exhibits an intriguing emergent property - swarms self-select a particular density at which they are marginally opaque, a property that is apparent in real bird flocks. This implies a non-trivial mean field scaling relationship between the swarm density and the number of individuals: ρ ≈ N^(-1) in 2D and ρ ≈ N^(-1/2) in 3D. Some evidence for the latter scaling result already exists. Our model therefore makes several experimentally testable predictions and may even provide a mechanism for classifying the behaviour of different swarming animals according to the relative strength of their alignment and projection terms. Finally, it would also appear to provide emergent biological fitness, given that marginal opacity provides for rapid, long-range information transfer, another feature not present in local models with diffusive dynamics. Further experiments on shoaling fish are currently underway in my lab.