Relative energy deficiency in dance (RED-D): a consensus method approach to REDs in dance.

Relative energy deficiency in sport (REDs) is a potentially severe, challenging, broad-spectrum syndrome with potential negative health and performance outcomes. The numerous research publications and International Olympic Committee consensus statements relating to REDs testify to the challenges faced in early identification or screening, diagnosis and management. Like sport, dance, in its simplest form, can be identified as an activity resulting in physiological energy demands and, as such, requires appropriate energy availability concerning energy expenditures. However, the specificity of physiological and psychological demands in dance must be considered when considering REDs. An environment where physical activity can exceed 30 hours per week and where culture may instil a value that thinness is required puts dancers at increased risk for REDs. The purpose of this study was to provide dance-specific guidance dance on this complex condition. An RAND/UCLA Delphi Panel method with nominal group technique was used to review the literature from REDs to evaluate how it may relate to dance. In addition to the EP, which was assembled from a multidisciplinary background with expertise in REDs and multiple genres of dance, six focus groups were commissioned. Four of the focus groups were drawn from the EP members and two additional focus groups formed by dancers and artistic leaders. These panels were used to guide the development of a RED-D diagnosis pathway, management plan and risk stratification and return to dance pathway. The dance-specific pathways are designed to be a practical tool for guiding and supporting clinicians managing RED-D. Furthermore, this paper represents an important focus of this area in dance and serves to stimulate discussion and further research within the sector.

Mosquito swarms shear harden.

Recently Cavagna et al. (Sci Rep 13(1): 8745, 2023) documented the swarming behaviors of laboratory-based Anopheles gambiae mosquitoes. Here key observations from this 3D-video tracking study are reproduced by a minimally structured (maximum entropy) stochastic trajectory model. The modelling shows that in contrast with midge swarms which are a form of collective behavior, unperturbed mosquito swarms are more like collections of individuals that independently circulate around a fixed location. The modelling predicts the observed response Anopheles gambiae mosquitoes in wild swarms to varying wind speeds (Butail et al. in J Med Entomol 50(3): 552-559, 2013). It is shown that this response can be attributed to shear hardening. This is because mosquitoes are found to be attracted to the centre of the swarm by an effective force that increases with increasing flight speed. Mosquitoes can therefore better resist the influence of environmental disturbances by increasing their flight speeds. This contrasts with other emergent mechanical-like properties of swarming which arise accidentally without a change in an individual's behavior. The new results add to the growing realization that perturbations can drive swarms into more robust states.

Phase transitions in insect swarms.

In contrast with laboratory insect swarms, wild insect swarms display significant coordinated behaviour. It has been hypothesised that the presence of a fluctuating environment drives the formation of transient, local order (synchronized subgroups), and that this local order pushes the swarm into a new state that is robust to environmental perturbations. The hypothesis is supported by observations of swarming mosquitoes. Here I provide numerical evidence that the formation of transient, local order is an accidental by-product of the strengthening of short-range repulsion which is expected in the presence of environmental fluctuations. The results of the numerical simulations reveal that this strengthening of the short-range can drive swarms into a crystalline phase containing subgroups that participate in cooperative ring exchanges-a new putative form of collective animal movement lacking velocity correlation. I thereby demonstrate that the swarm state and structure may be tuneable with environmental noise as a control parameter. Predicted properties of the collective modes are consistent with observations of transient synchronized subgroups in wild mosquito swarms that contend with environmental disturbances. When mutual repulsion becomes sufficiently strong, swarms are, in accordance with observations, predicted to form near stationary crystalline states. The analysis suggests that the many different forms of swarming motions observed across insect species are not distinctly different phenomena but are instead different phases of a single phenomenon.

Swarm formation as backward diffusion.

Considerable progress has been made in understanding insect swarms-forms of collective animal behaviour that unlike bird flocks, fish schools and animal herds do not possess global order. Nonetheless, little is known about swarm formation. Here we posit a mechanism for the formation of insect swarms that is consistent with recent empirical observations reported by (Patel and Ouellette 2022). It correctly predicts new features of swarm formation that have not been reported on previously. Our simple analytically tractable model shows how harmonic potential wells, a characteristic feature of swarming, and so swarm cohesion, arise from diffusion and local fission-fusion dynamics and how, in accord with observations, these wells deepen over time. The overall form of these potential wells is predicted to depend on the number and spatial distribution of all individuals, making them manifestly a collective phenomenon. Finally, swarms are predicted to 'cool' (that is, condense) as they form.

Stochasticity may generate coherent motion in bird flocks.

Murmurations along with other forms of flocking have come to epitomize collective animal movements. Most studies into these stunning aerial displays have aimed to understand how coherent motion may emerge from simple behavioral rules and behavioral correlations. These studies may now need revision because recently it has been shown that flocking birds, like swarming insects, behave on the average as if they are trapped in elastic potential wells. Here I show, somewhat paradoxically, how coherent motion can be generated by variations in the intensity of multiplicative noise which causes the shape of a potential well to change, thereby shifting the positions and strengths of centres of attraction. Each bird, irrespective of its position in the flock will respond in a similar way to such changes, giving the impression that the flock behaves as one, and typically resulting in scale-free correlations. I thereby show how correlations can be an emergent property of noisy, confining potential wells. I also show how such wells can lead to high density borders, a characteristic of flocks, and I show how they can account for the complex patterns of collective escape patterns of starling flocks under predation. I suggest swarming and flocking do not constitute two distinctly different kinds of collective behavior but rather that insects are residing in relatively stable potential wells whilst birds are residing in unstable potential wells. It is shown how, dependent upon individual perceptual capabilities, bird flocks can be poised at criticality.

The 'Cruciform Test': A diagnostic tool to detect pectoralis major rupture.

Introduction: Pectoralis major (PM) rupture is a severe injury that untreated can lead to a profound functional deficit. Early surgical repair can greatly improve outcomes and give a more predictable timetable for recovery, making this the goal of current treatment. Surgical intervention is also essential to return professional athletes to their previous level of competition. However, there is no single, reliable and easily reproducible test that can be used to establish the diagnosis. We describe 'The Cruciform Test'; a method of identifying PM rupture that can be used for initial diagnosis either in clinic or a pitch-side environment, or to assess restoration of normal anatomy and function post-operatively. Methods: We studied a series of 14 patients who underwent open PM repair in order to evaluate this method of assessment. Results: All patients had a positive test pre-operatively. 5 were formally tested at post-operative follow-up and all had a negative result. Discussion: The Cruciform Test is a simple and reproducible diagnostic tool that has potential as a clinical indicator of both PM rupture and successful repair. It can therefore contribute to earlier diagnosis, prompt surgical intervention and facilitate return to play at the earliest opportunity.

Comment on 'A physics perspective on collective animal behavior' 2022Phys. Biol.19 021004.

In his insightful and timely review Ouellette (2022Phys. Biol.19021004) noted three theoretical impediments to progress in understanding and modelling collective animal behavior. Here through novel analyses and by drawing on the latest research I show how these obstacles can be either overcome or negated. I suggest ways in which recent advances in the physics of collective behavior provide significant biological information.

Stochastic modelling of bird flocks: accounting for the cohesiveness of collective motion.

Collective behaviour can be difficult to discern because it is not limited to animal aggregations such as flocks of birds and schools of fish wherein individuals spontaneously move in the same way despite the absence of leadership. Insect swarms are, for example, a form of collective behaviour, albeit one lacking the global order seen in bird flocks and fish schools. Their collective behaviour is evident in their emergent macroscopic properties. These properties are predicted by close relatives of Okubo's 1986 [Adv. Biophys.22, 1-94. (doi:10.1016/0065-227X(86)90003-1)] stochastic model. Here, we argue that Okubo's stochastic model also encapsulates the cohesiveness mechanism at play in bird flocks, namely the fact that birds within a flock behave on average as if they are trapped in an elastic potential well. That is, each bird effectively behaves as if it is bound to the flock by a force that on average increases linearly as the distance from the flock centre increases. We uncover this key, but until now overlooked, feature of flocking in empirical data. This gives us a means of identifying what makes a given system collective. We show how the model can be extended to account for intrinsic velocity correlations and differentiated social relationships.

Weierstrassian Lévy walks are a by-product of crawling.

Weierstrassian Lévy walks are one of the simplest random walks which do not satisfy the central limit theorem and have come to epitomize scale invariance even though they were initially regarded as being a mathematical abstraction. Here, I show how these Lévy walks can be generated intrinsically as a by-product of crawling, a common but ancient form of locomotion. This may explain why Weierstrassian Lévy walks provide accurate representations of the movement patterns of a diverse group of molluscs-certain mussels, mud snails and limpets. I show that such movements are not specific to molluscs as they are also evident in Drosophila larvae. The findings add to the growing realization that there are many idiosyncratic, seemingly accidental pathways to Lévy walking. And that the occurrence of Lévy walks need not be attributed to the execution of an advantageous searching strategy.

Understanding the thermodynamic properties of insect swarms.

Sinhuber et al. (Sci Rep 11:3773, 2021) formulated an equation of state for laboratory swarms of the non-biting midge Chironomus riparius that holds true when the swarms are driven through thermodynamic cycles by the application external perturbations. The findings are significant because they demonstrate the surprising efficacy of classical equilibrium thermodynamics for quantitatively characterizing and predicting collective behaviour in biology. Nonetheless, the equation of state obtained by Sinhuber et al. (2021) is anomalous, lacking a physical analogue, making its' interpretation problematic. Moreover, the dynamical processes underlying the thermodynamic cycling were not identified. Here I show that insect swarms are equally well represented as van der Waals gases and I attribute the possibility of thermodynamic cycling to insect swarms consisting of several overlapping sublayers. This brings about a profound change in the understanding of laboratory swarms which until now have been regarded as consisting of non-interacting individuals and lacking any internal structure. I show how the effective interactions can be attributed to the swarms' internal structure, the external perturbations and to the presence of intrinsic noise. I thereby show that intrinsic noise which is known to be crucial for the emergence of the macroscopic mechanical properties of insect swarms is also crucial for the emergence of their thermodynamic properties as encapsulated by their equation of state.

Scale-free movement patterns in termites emerge from social interactions and preferential attachments.

As the number or density of interacting individuals in a social group increases, a transition can develop from uncorrelated and disordered behavior of the individuals to a collective coherent pattern. We expand this observation by exploring the fine details of termite movement patterns to demonstrate that the value of the scaling exponent µ of a power law describing the Lévy walk of an individual is modified collectively as the density of animals in the group changes. This effect is absent when termites interact with inert obstacles. We also show that the network of encounters and interactions among specific individuals is selective, resembling a preferential attachment mechanism that is important for social networking. Our data strongly suggest that preferential attachments, a phenomenon not reported previously, and favorite interactions with a limited number of acquaintances are responsible for the generation of Lévy movement patterns in these social insects.

Intrinsic stochasticity and the emergence of collective behaviours in insect swarms.

Intrinsic stochasticity associated with finite population size is fundamental to the emergence of collective behaviours in insect swarms. It has been assumed that this intrinsic stochasticity is purely additive (position independent) in quiescent (unperturbed) swarms. Here, I identify the hallmarks of intrinsic multiplicative (position dependent) stochasticity and show that they are evident in quiescent laboratory swarms of the non-biting midge Chironomus riparius. In accordance with theoretical expectations, the smallest well-documented laboratory swarms (containing between 14 and 46 individuals) are found to have q-Gaussian density profiles with [Formula: see text] 1, whereas larger laboratory swarms have Gaussian ([Formula: see text]1) density profiles. I show that these newly identified states are analogous to interstellar clouds and thereby extend a long-standing analogy between insect swarms and self-gravitating systems. Smaller laboratory swarms have been observed and are predicted to be gas-like, filling the available space rather than occupying just a small proportion of it. The new results unify laboratory swarms with wild swarms. Unlike laboratory swarms, wild swarms must contend with environmental (extrinsic) noise and have density profiles that are accurately represented by q-Gaussians with [Formula: see text] 1. Finally, it is shown how intrinsic multiplicative noise allows for the nucleation of swarms away from prominent visual features (basins of attraction) known as swarm markers.

Linking Small-Scale Flight Manoeuvers and Density Profiles to the Vertical Movement of Insects in the Nocturnal Stable Boundary Layer.

Huge numbers of insects migrate over considerable distances in the stably-stratified night-time atmosphere with great consequences for ecological processes, biodiversity, ecosystem services and pest management. We used a combination of meteorological radar and lidar instrumentation at a site in Oklahoma, USA, to take a new look at the general assistance migrants receive from both vertical and horizontal airstreams during their long-distance flights. Movement in the nocturnal boundary layer (NBL) presents very different challenges for migrants compared to those prevailing in the daytime convective boundary layer, but we found that Lagrangian stochastic modelling is effective at predicting flight manoeuvers in both cases. A key feature for insect transport in the NBL is the frequent formation of a thin layer of fast-moving air - the low-level jet. Modelling suggests that insects can react rapidly to counteract vertical air movements and this mechanism explains how migrants are retained in the jet for long periods (e.g. overnight, and perhaps for several hours early in the morning). This results in movements over much longer distances than are likely in convective conditions, and is particularly significant for the reintroduction of pests to northern regions where they are seasonally absent due to low winter temperatures.

On the emergence of gravitational-like forces in insect swarms.

Okubo (Okubo 1986 Adv. Biophys.22, 1-94. (doi:10.1016/0065-227X(86)90003-1)) was the first to propose that insect swarms are analogous to self-gravitating systems. In the intervening years, striking similarities between insect swarms and self-gravitating systems have been uncovered. Nonetheless, experimental observations of laboratory swarms provide no conclusive evidence of long-range forces acting between swarming insects. The insects appear somewhat paradoxically to be tightly bound to the swarm while at the same time weakly coupled inside it. Here, I show how resultant centrally attractive gravitational-like forces can emerge from the observed tendency of insects to continually switch between two distinct flight modes: one that consists of low-frequency manoeuvres and one that consists of higher-frequency nearly harmonic oscillations conducted in synchrony with another insect. The emergent dynamics are consistent with 'adaptive' gravity models of swarming and with variants of the stochastic models of Okubo and Reynolds for the trajectories of swarming insects: models that are in close accord with a plethora of observations of unperturbed and perturbed laboratory swarms. The results bring about a radical change of perspective as swarm properties can now be attributed to known biological behaviours rather than to elusive physical influences.

On the origin of the tensile strength of insect swarms.

Traditionally animal groups have been characterized by the macroscopic patterns that they form. It is now recognised that such patterns convey limited information about the nature of the aggregation as a whole. Aggregate properties cannot be determined by passive observations alone; instead one must interact with them. One of the first such dynamical tests revealed that swarms of flying insects have macroscopic mechanical properties similar to solids, including a finite Young's modulus and yield strength. Here I show, somewhat counterintuitively, that the emergence of these solid-like properties can be attributed to centre-of-mass movements (heat). This suggests that perturbations can drive phase transitions.

Harmonic radar tracking reveals random dispersal pattern of bumblebee (Bombus terrestris) queens after hibernation.

The dispersal of animals from their birth place has profound effects on the immediate survival and longer-term persistence of populations. Molecular studies have estimated that bumblebee colonies can be established many kilometers from their queens' natal nest site. However, little is known about when and how queens disperse during their lifespan. One possible life stage when dispersal may occur, is directly after emerging from hibernation. Here, harmonic radar tracking of artificially over-wintered Bombus terrestris queens shows that they spend most of their time resting on the ground with intermittent very short flights (duration and distance). We corroborate these behaviors with observations of wild queen bees, which show similar prolonged resting periods between short flights, indicating that the behavior of our radar-monitored bees was not due to the attachment of transponders nor an artifact of the bees being commercially reared. Radar-monitored flights were not continuously directed away from the origin, suggesting that bees were not intentionally trying to disperse from their artificial emergence site. Flights did not loop back to the origin suggesting bees were not trying to remember or get back to the original release site. Most individuals dispersed from the range of the harmonic radar within less than two days and did not return. Flight directions were not different from a uniform distribution and flight lengths followed an exponential distribution, both suggesting random dispersal. A random walk model based on our observed data estimates a positive net dispersal from the origin over many flights, indicating a biased random dispersal, and estimates the net displacement of queens to be within the range of those estimated in genetic studies. We suggest that a distinct post-hibernation life history stage consisting mostly of rest with intermittent short flights and infrequent foraging fulfils the dual purpose of ovary development and dispersal prior to nest searching.

Incorporating terminal velocities into Lagrangian stochastic models of particle dispersal in the atmospheric boundary layer.

Lagrangian stochastic models for simulation of tracer-particle trajectories in turbulent flows can be adapted for simulation of particle trajectories. This is conventionally done by replacing the zero-mean fall speed of a tracer-particle with the terminal speed of the particle. Such models have been used widely to predict spore and pollen dispersal. Here I show that this modification predicts that particles become uniformly distributed throughout the air column, which is at variance with the seminal experimental studies of Hirst et al. (1967) that demonstrated spore concentrations (and pollen concentrations) declined exponentially with height in unstable air. This discrepancy arises because the terminal speed, which is a Lagrangian property of a particle, has always been treated as if it were an Eulerian property of an ensemble of particles. In this study models are formulated correctly. I show that the mean acceleration of a tracer-particle should be replaced by the mean acceleration of a particle. Model predictions for aerial density profiles then agreed with the observations of Hirst et al. (1967) and with observations of ground-level concentrations but differed significantly from predictions obtained using conventional models. In accordance with the results of numerical simulations, the models also predict that particles are moving downwind marginally more slowly than the wind itself. Finally, the new modelling approach can be extended to predict the dispersal of small insects with active flight behaviours.

Olfactory-cued navigation in shearwaters: linking movement patterns to mechanisms.

After foraging in the open ocean pelagic birds can pinpoint their breeding colonies, located on remote islands in visually featureless seascapes. This remarkable ability to navigate over vast distances has been attributed to the birds being able to learn an olfactory map on the basis of wind-borne odors. Odor-cued navigation has been linked mechanistically to displacements with exponentially-truncated power-law distributions. Such distributions were previously identified in three species of Atlantic and Mediterranean shearwaters but crucially it has not been demonstrated that these distributions are wind-speed dependent, as expected if navigation was olfactory-cued. Here we show that the distributions are wind-speed dependent, in accordance with theoretical expectations. We thereby link movement patterns to underlying generative mechanisms. Our novel analysis is consistent with the results of more traditional, non-mathematical, invasive methods and thereby provides independent evidence for olfactory-cued navigation in wild birds. Our non-invasive diagnostic tool can be applied across taxa, potentially allowing for the assessment of its pervasiveness.

Distinguishing between apparent and actual randomness: a preliminary examination with Australian ants.

ABSTRACT: The correlated random walk paradigm is the dominant conceptual framework for modeling animal movement patterns. Nonetheless, we do not know whether the randomness is apparent or actual. Apparent randomness could result from individuals reacting to environmental cues and their internal states in accordance with some set of behavioral rules. Here, we show how apparent randomness can result from one simple kind of algorithmic response to environmental cues. This results in an exponential step-length distribution in homogeneous environments and in generalized stretched exponential step-length distributions in more complex fractal environments. We find support for these predictions in the movement patterns of the Australian bull ant Myrmecia midas searching on natural surfaces and on artificial uniform and quasi-fractal surfaces. The bull ants spread their search significantly farther on the quasi-fractal surface than on the uniform surface, showing that search characteristics differed as a function of the substrate on which ants are searching. Further tentative support comes from a re-analysis of Australian desert ants Melophorus bagoti moving on smoothed-over sand and on a more strongly textured surface. Our findings call for more experimental studies on different surfaces to test the surprising predicted linkage between fractal dimension and the exponent in the step-length distribution. SIGNIFICANCE STATEMENT: Animal search patterns often appear to be irregular and erratic. This behavior is captured by random walk models. Despite their considerable successes, extrapolation and prediction beyond observations remain questionable because the true nature and interpretation of the randomness in these models have until now been elusive. Here, we show how apparent randomness can result from simple algorithmic responses to environmental cues. Distinctive predictions from our theory find support in analyses of the search patterns of two species of Australian ants.

Lévy foraging patterns of rural humans.

Movement patterns resembling Lévy walks, often attributed to the execution of an advantageous probabilistic searching strategy, are found in a wide variety of organisms, from cells to human hunter-gatherers. It has been suggested that such movement patterns may be fundamental to how humans interact and experience the world and that they may have arisen early in our genus with the evolution of a hunting and gathering lifestyle. Here we show that Lévy walks are evident in the Me'Phaa of Mexico, in Brazilian Cariri farmers and in Amazonian farmers when gathering firewood, wild fruit and nuts. Around 50% of the search patterns resemble Lévy walks and these are characterized by Lévy exponents close to 1.7. The other search patterns more closely resemble bi-phasic walks. We suggest potential generative mechanisms for the occurrence of these ubiquitous Lévy walks which can be used to guide future studies on human mobility. We show that frequent excursions and meanderings from pre-existing trails can account for our observations.