The speed-curvature power law in Drosophila larval locomotion

Application of scaling to mouse spontaneous movement: Path curvature varies with speed and linear distance features isochrony

To conserve sequential behavior in relation to the topographic challenges of space, it is proposed that humans and nonhuman animals can organize behavior using different scaling principles. To deal with increases in linear distance, isochrony suggest that there is a corresponding increase in speed, whereas to deal with changes in curvature, speed is adjusted according to a power function. The present study investigates whether these principles provide a framework for describing the organization of mouse behavior in a variety of standard experimental tasks. The structure of movement was examined in ambulation during open field exploration; manipulation in a string-pulling task, in which a string is advanced hand over hand to retrieve food; and rung-walking, in which the limbs successively step from rung to rung on a horizontal ladder. Both principles were found to be conserved in the organization of mouse behavior across scales of movement. These principles provide novel measures of the temporal and geometric features of movement in the mouse and insights into how the temporal and geometric features of movement are conserved within different species.

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

Pesticide exposure has been cited as a key threat to insect pollinators. Notably, a diverse range of potential sublethal effects have been reported in bee species, with a particular focus on effects due to exposure to neonicotinoid insecticides. Here, a purpose-built thermal-visual arena was used in a series of pilot experiments to assess the potential impact of approximate sublethal concentrations of the next generation sulfoximine insecticide sulfoxaflor (5 and 50 ppb) and the neonicotinoid insecticides thiacloprid (500 ppb) and thiamethoxam (10 ppb), on the walking trajectory, navigation and learning abilities of the buff-tailed bumblebee (Bombus terrestris audax) when subjected to an aversive conditioning task. The results suggest that only thiamethoxam prevents forager bees from improving in key training parameters (speed and distanced travelled) within the thermal visual arena. Power law analyses further revealed that a speed-curvature power law, previously reported as being present in the walking trajectories of bumblebees, is potentially disrupted under thiamethoxam (10 ppb) exposure, but not under sulfoxaflor or thiacloprid exposure. The pilot assay described provides a novel tool with which to identify subtle sublethal pesticide impacts, and their potential causes, on forager bees, that current ecotoxicological tests are not designed to assess.

Behavioral illusions: The Snark is a Boojum

A behavioral illusion is a regularity of behavior that appears to reflect something about the functional characteristics of an organism when it does not. This illusion occurs when the methods appropriate to the study of an open-loop or zero feedback (Z)-system are used to study the behavior of what is, in fact, a closed-loop or negative feedback (N)-system. The situation is like the one described in Lewis Carroll’s The Hunting of the Snark, where the sought-after Snark—analogous to the actual organism function—looks just like the feared Boojum—analogous to the illusory one. This article describes examples of three different kinds of behavioral illusion and explains how researchers can avoid the mistake of taking a Boojum for a Snark by reorienting the study of behavior toward identifying the perceptual variables that organisms control and away from seeking regularities in their overt behavior.

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

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.

Bioinspired Implementation and Assessment of a Remote-Controlled Robot

Daily activities are characterized by an increasing interaction with smart machines that present a certain level of autonomy. However, the intelligence of such electronic devices is not always transparent for the end user. This study is aimed at assessing the quality of the remote control of a mobile robot whether the artefact exhibits a human-like behavior or not. The bioinspired behavior implemented in the robot is the well-described two-thirds power law. The performance of participants who teleoperate the semiautonomous vehicle implementing the biological law is compared to a manual and nonbiological mode of control. The results show that the time required to complete the path and the number of collisions with obstacles are significantly lower in the biological condition than in the two other conditions. Also, the highest percentage of occurrences of curvilinear or smooth trajectories are obtained when the steering is assisted by an integration of the power law in the robot's way of working. This advanced analysis of the performance based on the naturalness of the movement kinematics provides a refined evaluation of the quality of the Human-Machine Interaction (HMI). This finding is consistent with the hypothesis of a relationship between the power law and jerk minimization. In addition, the outcome of this study supports the theory of a CNS origin of the power law. The discussion addresses the implications of the anthropocentric approach to enhance the HMI.

Modelling the mechanics of exploration in larval Drosophila

The Drosophila larva executes a stereotypical exploratory routine that appears to consist of stochastic alternation between straight peristaltic crawling and reorientation events through lateral bending. We present a model of larval mechanics for axial and transverse motion over a planar substrate, and use it to develop a simple, reflexive neuromuscular model from physical principles. The mechanical model represents the midline of the larva as a set of point masses which interact with each other via damped translational and torsional springs, and with the environment via sliding friction forces. The neuromuscular model consists of: 1. segmentally localised reflexes that amplify axial compression in order to counteract frictive energy losses, and 2. long-range mutual inhibition between reflexes in distant segments, enabling overall motion of the model larva relative to its substrate. In the absence of damping and driving, the mechanical model produces axial travelling waves, lateral oscillations, and unpredictable, chaotic deformations. The neuromuscular model counteracts friction to recover these motion patterns, giving rise to forward and backward peristalsis in addition to turning. Our model produces spontaneous exploration, even though the nervous system has no intrinsic pattern generating or decision making ability, and neither senses nor drives bending motions. Ultimately, our model suggests a novel view of larval exploration as a deterministic superdiffusion process which is mechanistically grounded in the chaotic mechanics of the body. We discuss how this may provide new interpretations for existing observations at the level of tissue-scale activity patterns and neural circuitry, and provide some experimental predictions that would test the extent to which the mechanisms we present translate to the real larva.

We investigate the relationship between brain, body and environment in the exploratory behaviour of fruitfly larva. A larva crawls forward by propagating a wave of compression through its segmented body, and changes its crawling direction by bending to one side or the other. We show first that a purely mechanical model of the larva’s body can produce travelling compression waves, sideways bending, and unpredictable, chaotic motions. For this body to locomote through its environment, it is necessary to add a neuromuscular system to counteract the loss of energy due to friction, and to limit the simultaneous compression of segments. These simple additions allow our model larva to generate life-like forward and backward crawling as well as spontaneous turns, which occur without any direct sensing or control of reorientation. The unpredictability inherent in the larva’s physics causes the model to explore its environment, despite the lack of any neural mechanism for rhythm generation or for deciding when to switch from crawling to turning. Our model thus demonstrates how understanding body mechanics can generate and simplify neurobiological hypotheses as to how behaviour arises.

A Neuronal Pathway that Commands Deceleration in Drosophila Larval Light-Avoidance

When facing a sudden danger or aversive condition while engaged in on-going forward motion, animals transiently slow down and make a turn to escape. The neural mechanisms underlying stimulation-induced deceleration in avoidance behavior are largely unknown. Here, we report that in Drosophila larvae, light-induced deceleration was commanded by a continuous neural pathway that included prothoracicotropic hormone neurons, eclosion hormone neurons, and tyrosine decarboxylase 2 motor neurons (the PET pathway). Inhibiting neurons in the PET pathway led to defects in light-avoidance due to insufficient deceleration and head casting. On the other hand, activation of PET pathway neurons specifically caused immediate deceleration in larval locomotion. Our findings reveal a neural substrate for the emergent deceleration response and provide a new understanding of the relationship between behavioral modules in animal avoidance responses.

Residual Limb Revision Surgery Alters Velocity-Curvature Coupling During Stepping and Turning of a Transfemoral Amputee

Two-Thirds Power Law is a frequently observed relationship in human movement, relating velocity and curvature of movement trajectory. These movements span handwriting, larvae crawling, and human-robot interaction. Despite vast acceptance as a common principle of biology, it is unknown if the power law applies to interaction between amputees and prostheses, and if interventions to augment the physical connection between amputees and prostheses influence this speed-curvature coupling during demanding forms of human locomotion. The purpose of this study was to determine if individuals with transfemoral amputation exhibit a biologically-appropriate power law relationship during non-steady-state locomotion, and if a surgical intervention to reduce residual limb soft tissue would influence the observed coupling. We hypothesized that a power regression would well characterize amputee locomotion, and that limb revision surgery would result in a non-linear power coupling close to one-third and overall increased speed (i.e., higher linear coupling) in each non-steady-state movement. The subject performed repeated trials of left and right 90° turns during walking, as well as Foursquare Step Test (FSST), while whole-body kinematics were captured. After fitting center-of-mass velocity and curvature to the power law, the power coupling in FSST was similar to the Two-Thirds Power Law, while turning was not. Finally, the intervention was shown to increase linear coupling suggesting an overall improvement in movement tempo characterized by modest changes in velocity, enabling tasks to be achieved more quickly.

The power law as behavioral illusion: reappraising the reappraisals

Marken and Shaffer (Exp Brain Res 235:1835-1842, 2017) have argued that the power law of movement, which is generally thought to reflect the mechanisms that produce movement, is actually an example of what Powers (Psychol Rev 85:417-435, 1978) dubbed a behavioral illusion, where an observed relationship between variables is seen as revealing something about the mechanisms that produce a behavior when, in fact, it does not. Zago et al. (Exp Brain Res. https://doi.org/10.1007/s0022-017-5108-z , 2017) and Taylor (Exp Brain Res, https://doi.org/10.1007/s00221-018-5192-8 , 2018) have "reappraised" this argument, claiming that it is based on logical, mathematical, statistical and theoretical errors. In the present paper we answer these claims and show that the power law of movement is, indeed, an example of a behavioral illusion. However, we also explain how this apparently negative finding can point the study of movement in a new and more productive direction, with research aimed at understanding movement in terms of its purposes rather than its causes.

The speed-curvature power law of movements: a reappraisal

Several types of curvilinear movements obey approximately the so called 2/3 power law, according to which the angular speed varies proportionally to the 2/3 power of the curvature. The origin of the law is debated but it is generally thought to depend on physiological mechanisms. However, a recent paper (Marken and Shaffer, Exp Brain Res 88:685-690, 2017) claims that this power law is simply a statistical artifact, being a mathematical consequence of the way speed and curvature are calculated. Here we reject this hypothesis by showing that the speed-curvature power law of biological movements is non-trivial. First, we confirm that the power exponent varies with the shape of human drawing movements and with environmental factors. Second, we report experimental data from Drosophila larvae demonstrating that the power law does not depend on how curvature is calculated. Third, we prove that the law can be violated by means of several mathematical and physical examples. Finally, we discuss biological constraints that may underlie speed-curvature power laws discovered in empirical studies.

The power law of movement: an example of a behavioral illusion

The curved movements produced by living organisms follow a power law where the velocity of movement is a power function of the degree of curvature through which the movement is made. The exponent of the power function is close to either 1/3 or 2/3 depending on how velocity and curvature are measured. This power law is thought to reflect biological and/or kinematic constraints on how organisms produce movements. The present paper shows that the power law is actually a statistical artifact that results from mistaking a correlational for a causal relationship between variables. The power law implies that curvature influences the velocity of movement. In fact, the power law is a mathematical consequence of the way that these variables are calculated. The appearance that curvature affects the velocity of movement is shown to be an example of a "behavioral illusion" that results from ignoring the purpose of behavior.