Why insect swarms seem unduly complicated

Eur. Phys. J. Plus (2024) 139:610 https://doi.org/10.1140/epjp/s13360-024-05401-x Regular Article Why insect swarms seem unduly complicated Andy M. Reynoldsa Rothamsted Research, Harpenden, Hertfordshire AL5 2JQ, UK Received: 10 May 2024 / Accepted: 24 June 2024 © The Author(s) 2024 Abstract Mating swarms of flying male insects are a form of collective behaviour, albeit one different from flocks and schools as they do not display ordered collective movements. In recent years, much progress has been made in uncovering the emergent mechanical-like and thermodynamic-like of such swarms. Nonetheless, two basic properties of this swarming behaviour remain unexplained. Namely, why do individual insects have erratic rather than regular flight patterns? And why are the swarms elliptical rather than circular? Here I account for this seemingly undue complexity. I show that regular flight patterns weaken an individual’s attraction to the swarm centre, making swarms less resilient to the presence of environmental disturbances. I then show that the elliptical shape of swarms of the non-biting midge Chironomus riparius optimizes the trade-off between maximizing swarm size (target size for females) and maximizing swarm stability. Finally, I show that the observed excess velocity kurtosis of swarming C. riparius maximizes swarm cohesiveness. Taken together the new results provide the first tentative evidence for fine-tuning in insect mating swarms driven by selection pressure for advantageous behaviours. 1 Introduction Collective motion of social animals is ubiquitous in nature. Birds, fish, ungulates, and other species of animal routinely exhibit coherent and often organized movement. These striking examples of self-organization in natural far-from-equilibrium systems are drawing the attention of physicists [1]. With very few exceptions, animal groups have been characterized almost exclusively by their morphology and by their degree of directional order. Not all collective animal groups, however, show macroscopic order. The most notable outliers are mating swarms of flying insects which are generally assumed to be collective, but which can nonetheless lack positional and orientational order [2–8]. These stationary swarms are usually comprised almost entirely of males and typically form over prominent visual features known as swarm ‘markers’. They function as leks, i.e. as areas where males congregate to secure mates [8]. Many species of insect form mating swarms and do so in a variety of ways [8]. But in all cases their lack of order challenges conventional notion of collective behaviour. Here I show how this lack order together with the incumbent complexity of swarming can be understood and brought into the fold of collective behaviour studies. For the most part attention is focused on recordings of laboratory swarms of the non-biting midge Chironomus riparius made under carefully controlled conditions, free from environmental disturbances [5, 9]. Mating swarms of flying insects typically show a high degree of spatial cohesion and are a form of collective animal behaviour, albeit one different from flocks and schools as they do not display ordered collective movements [2, 3, 5–7]. Flying insects do not circulate around the centre of the swarm in an orderly fashion but instead have more complicated erratic flight patterns [4–6, 8]. I show that this may be attributed to circular trajectories weakening an individual’s attraction to the swarm centre, making the swarm less resilient to the presence of environmental disturbances. I then show that the elliptical shape of laboratory swarms of the non-biting midge Chironomus riparius [5, 9], an emergent collective property of the swarming behaviour, can be attributed to swarms optimizing the trade-off between maximizing their perimeter/major axis length and maximizing their resilience to environmental disturbances. Maximizing perimeter length/major axis length increases the likelihood that the swarm is detected by females that are close by/far afield. The modelling predicts that the trade-off is optimized when, as observed [9], the swarm aspect ratio is about 1.2. The much larger elongation in the vertical direction can be attributed to the stacking of near circular swarms [10]. Finally, I show that the observed value of the excess velocity kurtosis laboratory swarms of C. riparius midges maximizes swarm cohesiveness. From a physical perspective, the swarm aspect ratio and excess velocity kurtosis are free parameters and so, in principle, can take on any values. Herein, their values are determined by purely biological considerations. The new results thereby provide the first provisional evidence for fine-tuning in insect mating swarms driven by selection pressure for advantageous behaviours. Remarkably, this fine-tuning first occurs when swarms of C. riparius midges contain order 10 individuals, i.e. when all statistics saturate, and the a e-mail: (corresponding author) 0123456789().: V,-vol 123 610 Page 2 of 8 Eur. Phys. J. Plus (2024) 139:610 swarms enter an asymptotic regime [9]. It occurs even though individuals are sporadically entering and exiting the swarm [5], and despite the fact that swarm dynamics are inherently noisy [10, 11]. Hereafter, unless stated otherwise, attention is focused exclusively on horizontal movements. Results are obtained with the aid of stochastic models for simulating the trajectories of individual insects within swarms. These models are generalizations of Okubo’s [6] classic, pioneering model and are in close agreement with numerous measurements of swarming behaviours made in carefully controlled laboratory settings and in the wild [6, 10–20]. These models account for: laboratory swarms of the non-biting midge Chironomus riparius surprisingly having macroscopic mechanical properties similar to solids, including a finite Young’s modulus and yield strength, and for the swarms not flowing like viscous fluids [14, 21]; swarms of Chironomus riparius midges displaying a collective viscoelastic response to applied oscillatory visual stimuli characterized by a negative storage modulus [19]; environmental perturbations inducing correlations in swarms of Chironomus riparius midges [20], thereby reconciling seeming contradictory observations of laboratory swarms [22] made under quiescent conditions with observations of wild swarms which must contend with environmental disturbances [2]; the ability of swarms of Chironomus riparius midges to be driven through ‘thermodynamic cycles’ by external perturbations, during which an equation of state holds throughout [10, 23]; the collective response of Anopheles gambiae mosquito swarms to environmental disturbances which resembles shear hardening [17]. By construction, simulated trajectories produced by these models are necessarily consistent with parameterizations of both observed swarm density profiles and observed velocity distributions of swarming insects; quant (...truncated)