Do bumblebees have signatures? Demonstrating the existence of a speed-curvature power law in Bombus terrestris locomotion patterns

Abstract

We report the discovery that Bombus terrestris audax (Buff-tailed bumblebee) locomotor trajectories adhere to a speed-curvature power law relationship which has previously been found in humans, non-human primates and Drosophila larval trajectories. No previous study has reported such a finding in adult insect locomotion. We used behavioural tracking to study walking Bombus terrestris in an arena under different training environments. Trajectories analysed from this tracking show the speed-curvature power law holds robustly at the population level, displaying an exponent close to two-thirds. This exponent corroborates previous findings in human movement patterns, but differs from the three-quarter exponent reported for Drosophila larval locomotion. There are conflicting hypotheses for the principal origin of these speed-curvature laws, ranging from the role of central planning to kinematic and muscular skeletal constraints. Our findings substantiate the latter idea that dynamic power-law effects are robust, differing only through kinematic constraints due to locomotive method. Our research supports the notion that these laws are present in a greater range of species than previously thought, even in the bumblebee. Such power laws may provide optimal behavioural templates for organisms, delivering a potential analytical tool to study deviations from this template. Our results suggest that curvature and angular speed are constrained geometrically, and independently of the muscles and nerves of the performing body.

A Sublethal Concentration of Sulfoxaflor Has Minimal Impact on Buff-Tailed Bumblebee (Bombus terrestris) Locomotor Behaviour under Aversive Conditioning

“…The thermal–visual arena ( Figure 1 ) is an aversive place learning assay for bumblebees [ 2 ]. The arena is based upon a design used by Ofstad, Zuker, and Reiser [ 80 ] to study walking Drosophila trajectories.…”

“…Further study of the speed–curvature power law in relation to bee movement patterns may therefore provide a key diagnostic tool to determine the underlying drivers of observed sublethal effects, allowing us to unpick potential causation and impact of biological stressors at a finer physiological scale. We predict that some pesticide exposure regimes may lead to non-optimal movements in B. terrestris , and this would be reflected in a change in the optimal power law relationships observed in James et al [ 2 ].…”

“…To address this deficit, we recently developed and optimised a thermal–visual arena experimental platform for aversive (place-learning) conditioning of the buff-tailed bumblebee ( Bombus terrestris audax). The laboratory assay was used to demonstrate the existence of underlying movement regularities within the trajectories of walking bumblebees, directed via the speed–curvature power law, whereby motor control dictates a constrained relation between the kinematic property of speed and the geometric property of curvature [ 2 ]. This novel aversive conditioning (heat avoidance) and movement analysis (adherence to the speed–curvature power law) assay is further utilised here to assess the potential impacts of three common Group 4 insecticides [ 3 ], sulfoxaflor, thiamethoxam and thiacloprid, on the locomotion, navigation and learning abilities of buff-tailed bumblebees.…”

“…Power laws (i.e., relationships in which a relative change in one quantity gives rise to a proportional relative change in the other quantity, independent of the initial size of those quantities) governing movement are said to be ‘scale-free’ i.e., both short and long values can occur, and no scale is more frequent (dominant) than another [ 68 ]. Increasingly, power law distributions have been found in the movement patterns of a wide range of animals [ 61 , 68 , 69 , 70 , 71 ], including B. terrestris [ 2 ]. The discovery of power laws (the speed–curvature power law) in the movement trajectories of bees facilitates the study of how a bees’ movement patterns may change in response to stressors such as pesticides.…”

“…The robustness of the Lévy search patterns observed in honeybees may be due to Lévy flights being fundamental characteristics of neuronal processes, which are therefore unaffected by the physiological impacts of stressors such as disease. However, as we discussed extensively in James et al [ 2 ], it is likely that the speed–curvature power law is governed by biomechanical constraints [ 78 , 79 ] and may therefore be responsive to physiological stressors. Further study of the speed–curvature power law in relation to bee movement patterns may therefore provide a key diagnostic tool to determine the underlying drivers of observed sublethal effects, allowing us to unpick potential causation and impact of biological stressors at a finer physiological scale.…”