The speed–curvature power law in Drosophila larval locomotion

Abstract

We report the discovery that the locomotor trajectories of Drosophila larvae follow the power-law relationship between speed and curvature previously found in the movements of human and non-human primates. Using high-resolution behavioural tracking in controlled but naturalistic sensory environments, we tested the law in maggots tracing different trajectory types, from reaching-like movements to scribbles. For most but not all flies, we found that the law holds robustly, with an exponent close to three-quarters rather than to the usual two-thirds found in almost all human situations, suggesting dynamic effects adding on purely kinematic constraints. There are different hypotheses for the origin of the law in primates, one invoking cortical computations, another viscoelastic muscle properties coupled with central pattern generators. Our findings are consistent with the latter view and demonstrate that the law is possible in animals with nervous systems orders of magnitude simpler than in primates. Scaling laws might exist because natural selection favours processes that remain behaviourally efficient across a wide range of neural and body architectures in distantly related species.

Mechanics of exploration inDrosophila melanogaster

“…We calculated the mean . We also note that our COM trajectories display the power-law 574 relationship between angular speed and curvature reported by [55], with a scaling 575 exponent (β ≈ 0.8) falling within the range reported for freely exploring larvae (S4 Fig). 576 We next investigated the rate at which the simulated larvae explored their 577 environment.…”

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

“…Walking is distinctly different from the crawling movements made by limbless larvae [17]. Therefore, we might predict that walking bee trajectories would adhere more closely to the two-thirds power law exponent reported for unconstrained movements such as human drawing and walking [1,6], than the three-quarters exponent reported for the mechanically constrained movements of larvae [5].…”

“…The law also holds true across a diverse range of taxa. The law has been observed in the motor cortical control of Rhesus monkey hand movements whilst drawing [8], and even in the larval movement of the fruit fly (Drosophila melanogaster) [5] albeit with a marginally different power-law exponent, three quarters rather than two thirds.…”

“…where k is a constant of proportionality. Maximally-smooth movements, which minimize rates of change of acceleration (i.e., jerks and jolts), are generated under the two-thirds power law [3][4][5], which holds true across a range of voluntary human movements, including drawing, walking and pursuit eye movements [1,3,6,7]. The law also holds true across a diverse range of taxa.…”

“…One hypothesis suggests that the law results from central planning constraints imposed by the nervous system [8,9]. Another, that the law arises due to physiological constraints conferred by muscular properties and kinematics [2,5,10]. A further view, that the law exists to maximize movement smoothness and minimize jerk [3,9].…”