Determining asymptotically large population sizes in insect swarms

Abstract

Social animals commonly form aggregates that exhibit emergent collective behaviour, with group dynamics that are distinct from the behaviour of individuals. Simple models can qualitatively reproduce such behaviour, but only with large numbers of individuals. But how rapidly do the collective properties of animal aggregations in nature emerge with group size? Here, we study swarms of Chironomus riparius midges and measure how their statistical properties change as a function of the number of participating individuals. Once the swarms contain order 10 individuals, we find that all statistics saturate and the swarms enter an asymptotic regime. The influence of environmental cues on the swarm morphology decays on a similar scale. Our results provide a strong constraint on how rapidly swarm models must produce collective states. But our findings support the feasibility of using swarms as a design template for multi-agent systems, because self-organized states are possible even with few agents.

Intrinsic Fluctuations and Driven Response of Insect Swarms

“…2b) show that the dominant response of the swarm is indeed at ω d for all frequencies we tested (up to ω d /2π = 32 Hz). We find that the response is insensitive to the number of midges participating in the swarm, consistent with our previous results [23].…”

Time-Frequency Analysis Reveals Pairwise Interactions in Insect Swarms

“…2(c)), though it is small. But even though their mean-field statistical weight is small, characterizing these interactions is necessary for fully understanding the swarm dynamics, since they are not particularly rare events; aside from very small swarms, which may exhibit different behavior [18], we find that midges spend about 15% of their time engaged in these pairwise interactions (Fig. 3).…”

“…Briefly, our midge colony is maintained in a cubical enclosure measuring 91 cm on a side that is exposed to overhead light on a circadian cycle with 16 hours of light and 8 hours of darkness per day. Twice daily, at "dawn" and "dusk", male midges spontaneously form swarms, with sizes ranging from just a few individuals up to about 100 [15,18]. To promote swarm nucleation, we place a black felt swarm marker measuring 30 × 30 cm 2 in the center of the enclosure.…”

Discovery of Parameters for Animation of Midge Swarms

“…Male chironomids form mating swarms. A typical swarm is an aggregation of males "dancing" back and forth in a certain location [10]. Swarms tend to form in certain preferred locations, often based on visual cues or air currents [4,7].…”

“…For this alternative approach, we require a way of scoring the quality of a behaviour model based on the results of a simulation run or runs. Conveniently, in three recent studies, Puckett, Kelley, and Ouellette have described in detail the movement of individual midges (Chironomus riparius) in a swarm [6,9,10]. We suggest specific criteria that allow us to assess the fidelity of the model to nature, based on this quantitative data and separate qualitative observations of midge behaviour [4,7].…”