Transport phenomena in collective dynamics: from micro to social hydrodynamics

Swarming Using Adaptive Long-range Interactions

Dan Gorbonos

Weizmann Institute of Science


The collective motion of groups of animals emerges from the net effect of the interactions between individual members of the group. In many cases, such as birds, fish, or ungulates, these interactions are mediated by sensory stimuli that predominantly arise from nearby neighbors. But not all stimuli in animal groups are short range. Here, we consider mating swarms of midges, which interact primarily via long-range acoustic stimuli. We exploit the similarity in form between the decay of acoustic and gravitational sources to build a model for swarm behavior. However, sensory mechanisms in biology, from cells to humans, have the property of adaptivity, whereby the sensitivity of the signal produced by the sensor is adapted to the overall amplitude of the signal. By appropriately accounting for the adaptive nature of the midges' acoustic sensing, we show that our “adaptive gravity” model makes mean-field predictions that agree well with experimental observations of laboratory swarm. Motivated by this model, we generalized it and explored the effective forces that organisms feel from others in the context of a uniform swarm, both in two and three dimensions. The interactions between the individuals are taken to be of power-law form. We find that the effects of adaptivity are dramatic: outside the swarm the effective interactions do not decay with distance for perfect adaptivity, while inside the swarm, the effective forces decrease (or remain constant) with increasing swarm density, unlike the stimulus or regular non-adaptive interactions which increase linearly with the density of the sources. Adaptivity therefore endows swarms with a natural mechanism for stabilization.