Intermittent motion in desert locusts: behavioural complexity in simple environments

Revealing the mechanism and function underlying pairwise temporal coupling in collective motion

Coordinated motion in animal groups has predominantly been studied with a focus on spatial interactions, such as how individuals position and orient themselves relative to one another. Temporal aspects have, by contrast, received much less attention. Here, by studying pairwise interactions in juvenile zebrafish (Danio rerio)-including using immersive volumetric virtual reality (VR) with which we can directly test models of social interactions in situ-we reveal that there exists a rhythmic out-of-phase (i.e., an alternating) temporal coordination dynamic. We find that reciprocal (bi-directional) feedback is both necessary and sufficient to explain this emergent coupling. Beyond a mechanistic understanding, we find, both from VR experiments and analysis of freely swimming pairs, that temporal coordination considerably improves spatial responsiveness, such as to changes in the direction of motion of a partner. Our findings highlight the synergistic role of spatial and temporal coupling in facilitating effective communication between individuals on the move.

Pausing to swarm: locust intermittent motion is instrumental for swarming-related visual processing

Intermittent motion is prevalent in animal locomotion. Of special interest is the case of collective motion, in which social and environmental information must be processed in order to establish coordinated movement. We explored this nexus in locust, focusing on how intermittent motion interacts with swarming-related visual-based decision-making. Using a novel approach, we compared individual locust behaviour in response to continuously moving stimuli, with their response in semi-closed-loop conditions, in which the stimuli moved either in phase with the locust walking, or out of phase, i.e. only during the locust's pauses. Our findings clearly indicate the greater tendency of a locust to respond and 'join the swarming motion' when the visual stimuli were presented during its pauses. Hence, the current study strongly confirms previous indications of the dominant role of pauses in the collective motion-related decision-making of locusts. The presented insights contribute to a deeper general understanding of how intermittent motion contributes to group cohesion and coordination in animal swarms.

A lionfish-inspired predation strategy in planar structured environments. BIOINSPIRATION & BIOMIMETICS 2023;18:046022. [PMID: 37339652 DOI: 10.1088/1748-3190/ace016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

This paper investigates a pursuit-evasion game with a single pursuer and evader in a bounded environment, inspired by observations of predation attempts by lionfish (Pterois sp.). The pursuer tracks the evader with a pure pursuit strategy while using an additional bioinspired tactic to trap the evader, i.e. minimize the evader's escape routes. Specifically, the pursuer employs symmetric appendages inspired by the large pectoral fins of lionfish, but this expansion increases its drag and therefore its work to capture the evader. The evader employs a bioinspired randomly-directed escape strategy to avoid capture and collisions with the boundary. Here we investigate the trade-off between minimizing the work to capture the evader and minimizing the evader's escape routes. By using the pursuer's expected work to capture as a cost function, we determine when the pursuer should expand its appendages as a function of the relative distance to the evader and the evader's proximity to the boundary. Visualizing the pursuer's expected work to capture everywhere in the bounded domain, yields additional insights about optimal pursuit trajectories and illustrates the role of the boundary in predator-prey interactions.

Intermittent and temporally variable bioturbation by some terrestrial invertebrates: implications for ichnology

Bedding planes and vertical sections of many sedimentary rock formations reveal bioturbation structures, including burrows, produced by diverse animal taxa at different rates and durations. These variables are not directly measurable in the fossil record, but neoichnological observations and experiments provide informative analogues. Comparable to marine invertebrates from many phyla, a captive beetle larva burrowing over 2 weeks showed high rates of sediment disturbance within the first 100 h but slower rates afterwards. Tunnelling by earthworms and adult dung beetles is also inconstant-displacement of lithic material alternates with organic matter displacement, often driven by food availability with more locomotion when hungry. High rates of bioturbation, as with locomotion generally, result from internal and external drives, slowing down or stopping when needs are filled. Like other processes affecting sediment deposition and erosion, rates can drastically differ based on measured timescale, with short bursts of activity followed by hiatuses, concentrated in various seasons and ontogenetic stages for particular species. Assumptions of constant velocities within movement paths, left as traces afterward, may not apply in many cases. Arguments about energetic efficiency or optimal foraging based on ichnofossils have often overlooked these and related issues. Single bioturbation rates from short-term experiments in captivity may not be comparable to rates measured at an ecosystem level over a year or generalized across multiple time scales where conditions differ even for the same species. Neoichnological work, with an understanding of lifetime variabilities in bioturbation and their drivers, helps connect ichnology with behavioural biology and movement ecology.

Predicting age and mass at maturity from feeding behavior and diet in Manduca sexta: An empirical test of a life history model

Feeding for most animals involves bouts of active ingestion alternating with bouts of no ingestion. In insects, the temporal patterning of bouts varies widely with resource quality and is known to affect growth, development time, and fitness. However, the precise impacts of resource quality and feeding behavior on insect life history traits are poorly understood. To explore and better understand the connections between feeding behavior, resource quality, and insect life history traits, we combined laboratory experiments with a recently proposed mechanistic model of insect growth and development for a larval herbivore, Manduca sexta. We ran feeding trials for 4th and 5th instar larvae across different diet types (two hostplants and artificial diet) and used these data to parameterize a joint model of age and mass at maturity that incorporates both insect feeding behavior and hormonal activity. We found that the estimated durations of both feeding and nonfeeding bouts were significantly shorter on low-quality than on high-quality diets. We then explored how well the fitted model predicted historical out-of-sample data on age and mass of M. sexta. We found that the model accurately described qualitative outcomes for the out-of-sample data, notably that a low-quality diet results in reduced mass and later age at maturity compared with high-quality diets. Our results clearly demonstrate the importance of diet quality on multiple components of insect feeding behavior (feeding and nonfeeding) and partially validate a joint model of insect life history. We discuss the implications of these findings with respect to insect herbivory and discuss ways in which our model could be improved or extended to other systems.

Visual processing and collective motion-related decision-making in desert locusts

Collectively moving groups of animals rely on the decision-making of locally interacting individuals in order to maintain swarm cohesion. However, the complex and noisy visual environment poses a major challenge to the extraction and processing of relevant information. We addressed this challenge by studying swarming-related decision-making in desert locust last-instar nymphs. Controlled visual stimuli, in the form of random dot kinematograms, were presented to tethered locust nymphs in a trackball set-up, while monitoring movement trajectory and walking parameters. In a complementary set of experiments, the neurophysiological basis of the observed behavioural responses was explored. Our results suggest that locusts use filtering and discrimination upon encountering multiple stimuli simultaneously. Specifically, we show that locusts are sensitive to differences in speed at the individual conspecific level, and to movement coherence at the group level, and may use these to filter out non-relevant stimuli. The locusts also discriminate and assign different weights to different stimuli, with an observed interactive effect of stimulus size, relative abundance and motion direction. Our findings provide insights into the cognitive abilities of locusts in the domain of decision-making and visual-based collective motion, and support locusts as a model for investigating sensory-motor integration and motion-related decision-making in the intricate swarm environment.

The velocity and quiescence distributions in spontaneous locomotion across animals vary between modes of movement

Locomotion in animals follows simple mathematical rules: when active, most time is spent at lower velocities and exponentially decreasing time is spent at increasing velocities; when inactive, there is an abundance of short quiescence periods decreasing by an inverse power function towards longer quiescence periods. We investigated whether these mathematical rules are ‘universal’, i.e. followed by all animals independently of their modes of movement (walking, gliding/crawling, swimming) or their habitat (land, water). Using automated video tracking with high temporal and spatial resolution, we investigated the velocity and quiescence period distributions in ten species representing major divisions of the animal kingdom (snails, woodlice, springtail, beetle, fish, reptile, chicken and mouse). We confirm that the two functions are followed by most species, although we also found important exceptions: the snails and woodlice showed uni- or bimodal velocity distributions; the snails did not follow the inverse power law of quiescence periods. Thus, most animals running on legs or swimming follow the expected distributions, while other runners (isopods) and substrate gliders/crawlers (snails) do not. We suggest a difference in velocity distribution between animals that use running to escape predators and those that do not (snails and woodlice).

Band movement and thermoregulation in Schistocerca cancellata

At high density, juvenile locusts create marching hopper bands. Understanding the roles of temperature and vegetation on the movement of these bands shall allow to better forecast and control them. Following a hopper band in North Argentina in November 2019, we explored the thermoregulation behaviours of the South American locust, Schistocerca cancellata. Gut-content samples informed about the feeding status at different time of the day. Hoppers' body temperature was above cold air temperature in the mornings during basking and group-basking activities and before the onset of marching behaviour. Marching by walking or hopping was dominant at body temperatures close to 40 °C. Jumping, stilting, shading and perching on plants were seen as thermoregulatory behaviours to avoid ground temperatures above 50 °C. Feeding was observed throughout the day with continuous high gut contents despite an intermittent pattern of feeding-resting-marching. Speed and daily travelled distance of the front of the hopper band was depending on the type of encountered vegetation. Daily behavioural patterns, thermoregulatory behaviours, walking speed and daily travelled distances of S. cancellata were similar to the ones observed for the Desert locust, S. gregaria, in Africa. High air temperatures recorded during the observation times could explain the continuous feeding patterns. These species may have evolved behaviours of alternating consuming a bit and marching as a migration strategy to avoid staying where no food is available after the havoc left behind large hopper bands. Recommendations made for the control of Desert locust hopper bands can be extended to South American locust ones.

Collective motion as a distinct behavioral state of the individual

The collective motion of swarms depends on adaptations at the individual level. We explored these and their effects on swarm formation and maintenance in locusts. The walking kinematics of individual insects were monitored under laboratory settings, before, as well as during collective motion in a group, and again after separation from the group. It was found that taking part in collective motion induced in the individual unique behavioral kinematics, suggesting the existence of a distinct behavioral mode that we term a "collective-motion-state." This state, characterized by behavioral adaptation to the social context, is long lasting, not induced by crowding per se, but only by experiencing collective motion. Utilizing computational models, we show that this adaptability increases the robustness of the swarm. Overall, our findings suggest that collective motion is not only an emergent property of the group but also depends on a behavioral mode, rooted in endogenous mechanisms of the individual.

Efficient Lévy walks in virtual human foraging

Efficient foraging depends on decisions that account for the costs and benefits of various activities like movement, perception, and planning. We conducted a virtual foraging experiment set in the foothills of the Himalayas to examine how time and energy are expended to forage efficiently, and how foraging changes when constrained to a home range. Two hundred players foraged the human-scale landscape with simulated energy expenditure in search of naturally distributed resources. Results showed that efficient foragers produced periods of locomotion interleaved with perception and planning that approached theoretical expectations for Lévy walks, regardless of the home-range constraint. Despite this constancy, efficient home-range foraging trajectories were less diffusive by virtue of restricting locomotive search and spending more time instead scanning the environment to plan movement and detect far-away resources. Altogether, results demonstrate that humans can forage efficiently by arranging and adjusting Lévy-distributed search activities in response to environmental and task constraints.

What gaze direction can tell us about cognitive processes in invertebrates

Most visually guided animals shift their gaze using body movements, eye movements, or both to gather information selectively from their environments. Psychological studies of eye movements have advanced our understanding of perceptual and cognitive processes that mediate visual attention in humans and other vertebrates. However, much less is known about how these processes operate in other organisms, particularly invertebrates. We here make the case that studies of invertebrate cognition can benefit by adding precise measures of gaze direction. To accomplish this, we briefly review the human visual attention literature and outline four research themes and several experimental paradigms that could be extended to invertebrates. We briefly review selected studies where the measurement of gaze direction in invertebrates has provided new insights, and we suggest future areas of exploration.

Lévy Walk in Swarm Models Based on Bayesian and Inverse Bayesian Inference

While swarming behavior is regarded as a critical phenomenon in phase transition and frequently shows the properties of a critical state such as Lévy walk, a general mechanism to explain the critical property in swarming behavior has not yet been found. Here, we address this problem with a simple swarm model, the Self-Propelled Particle (SPP) model, and propose a way to explain this critical behavior by introducing agents making decisions via the data-hypothesis interaction in Bayesian inference, namely, Bayesian and inverse Bayesian inference (BIB). We compare three SPP models, namely, the simple SPP, the SPP with Bayesian-only inference (BO) and the SPP with BIB models. We show that only the BIB model entails coexisting tornado, splash and translation behaviors, and the Lévy walk pattern.

An insight on Drosophila myogenesis and its assessment techniques

Movement assisted by muscles forms the basis of various behavioural traits seen in Drosophila. Myogenesis involves developmental processes like cellular specification, differentiation, migration, fusion, adherence to tendons and neuronal innervation in a series of coordinated event well defined in body space and time. Gene regulatory networks are switched on-off, fine tuning at the right developmental stage to assist each cellular event. Drosophila is a holometabolous organism that undergoes myogenesis waves at two developmental stages, and is ideal for comparative analysis of the role of genes and genetic pathways conserved across phyla. In this review we have summarized myogenic events from the embryo to adult focussing on the somatic muscle development during the early embryonic stage and then on indirect flight muscles (IFM) formation required for adult life, emphasizing on recent trends of analysing muscle mutants and advances in Drosophila muscle biology.

Development of an automatic turntable-type multiple T-maze device and observation of pill bug behavior

In recent years, various animal observation instruments have been developed to support long-term measurement and analysis of animal behaviors. This study proposes an automatic observation instrument that specializes for turning behaviors of pill bugs and aims to obtain new knowledge in the field of ethology. Pill bugs strongly tend to turn in the opposite direction of a preceding turn. This alternation of turning is called turn alternation reaction. However, a repetition of turns in the same direction is called turn repetition reaction and has been considered a malfunction of turn alternation. In this research, the authors developed an automatic turntable-type multiple T-maze device and observed the turning behavior of 34 pill bugs for 6 h to investigate whether turn repetition is a malfunction. As a result, most of the pill bug movements were categorized into three groups: sub-diffusion, Brownian motion, and Lévy walk. This result suggests that pill bugs do not continue turn alternation mechanically but elicit turn repetition moderately, which results in various movement patterns. In organisms with relatively simple nervous systems such as pill bugs, stereotypical behaviors such as turn alternation have been considered mechanical reactions and variant behaviors such as turn repetition have been considered malfunctions. However, our results suggest that a moderate generation of turn repetition is involved in the generation of various movement patterns. This study is expected to provide a new perspective on the conventional view of the behaviors of simple organisms.

Quantifying flight aptitude variation in wild Anopheles gambiae in order to identify long-distance migrants

Background

In the West African Sahel, mosquito reproduction is halted during the 5–7 month-long dry season, due to the absence of surface waters required for larval development. However, recent studies have suggested that both Anopheles gambiae sensu stricto (s.s.) and Anopheles arabiensis repopulate this region via migration from distant locations where larval sites are perennial. Anopheles coluzzii engages in more regional migration, presumably within the Sahel, following shifting resources correlating with the ever-changing patterns of Sahelian rainfall. Understanding mosquito migration is key to controlling malaria—a disease that continues to claim more than 400,000 lives annually, especially those of African children. Using tethered flight data of wild mosquitoes, the distribution of flight parameters were evaluated as indicators of long-range migrants versus appetitive flyers, and the species specific seasonal differences and gonotrophic states compared between two flight activity modalities. Morphometrical differences were evaluated in the wings of mosquitoes exhibiting high flight activity (HFA) vs. low flight activity (LFA).

Methods

A novel tethered-flight assay was used to characterize flight in the three primary malaria vectors- An. arabiensis, An. coluzzii and An. gambiae s.s. The flights of tethered wild mosquitoes were audio-recorded from 21:00 h to 05:00 h in the following morning and three flight aptitude indices were examined: total flight duration, longest flight bout, and the number of flight bouts during the assay.

Results

The distributions of all flight indices were strongly skewed to the right, indicating that the population consisted of a majority of low-flight activity (LFA) mosquitoes and a minority of high-flight activity (HFA) mosquitoes. The median total flight was 586 s and the maximum value was 16,110 s (~ 4.5 h). In accordance with recent results, flight aptitude peaked in the wet season, and was higher in gravid females than in non-blood-fed females. Flight aptitude was also found to be higher in An. coluzzii compared to An. arabiensis, with intermediate values in An. gambiae s.s., but displaying no statistical difference. Evaluating differences in wing size and shape between LFA individuals and HFA ones, the wing size of HFA An. coluzzii was larger than that of LFAs during the wet season—its length was wider than predicted by allometry alone, indicating a change in wing shape. No statistically significant differences were found in the wing size/shape of An. gambiae s.s. or An. arabiensis.

Conclusions

The partial agreement between the tethered flight results and recent results based on aerial sampling of these species suggest a degree of discrimination between appetitive flyers and long-distance migrants although identifying HFAs as long-distance migrants is not recommended without further investigation.

Post-contact immobility and half-lives that save lives

A wide variety of animals become completely immobile after initial contact with a potential predator. This behaviour is considered to be a last-ditch escape strategy. Here, we test the hypothesis that such immobility should have an extremely unpredictable duration. We find that it spans more than three orders of magnitude in antlion larvae. We also analyse the second period of immobility that follows the first bout of immobility, and consider the distributions of both first and second immobility periods within the context of the intermittence that characterizes the movement of most organisms. Both immobility durations were fitted best by exponential distributions. Therefore, both were characterized by high variability and hence, unpredictability. The immobility half-life, its mean duration and standard deviation were greater for the first than the second immobility. Furthermore, individual consistency was weak or absent in repeated measures of the first immobility and between the first and second immobilities. Our quantitative approach can be replicated across taxa and would help link an understanding of immobility after an initial predator contact in both vertebrates and invertebrates. To facilitate this, we contend that the terminology should be simplified, and we advocate the use of the term post-contact immobility (PCI).

Four-Types of IIT-Induced Group Integrity of Plecoglossus altivelis

Integrated information theory (IIT) was initially proposed to describe human consciousness in terms of intrinsic-causal brain network structures. Particularly, IIT 3.0 targets the system's cause-effect structure from spatio-temporal grain and reveals the system's irreducibility. In a previous study, we tried to apply IIT 3.0 to an actual collective behaviour in Plecoglossus altivelis. We found that IIT 3.0 exhibits qualitative discontinuity between three and four schools of fish in terms of Φ value distributions. Other measures did not show similar characteristics. In this study, we followed up on our previous findings and introduced two new factors. First, we defined the global parameter settings to determine a different kind of group integrity. Second, we set several timescales (from Δ t = 5 / 120 to Δ t = 120 / 120 s). The results showed that we succeeded in classifying fish schools according to their group sizes and the degree of group integrity around the reaction time scale of the fish, despite the small group sizes. Compared with the short time scale, the interaction heterogeneity observed in the long time scale seems to diminish. Finally, we discuss one of the longstanding paradoxes in collective behaviour, known as the heap paradox, for which two tentative answers could be provided through our IIT 3.0 analysis.

Modeling navigation by weaver ants in an unfamiliar, featureless environment

The motion of individual weaver ants from Oecophylla smaragdina was tracked within a small arena to study the algorithm that these ants use for navigation. The arena, a floor tile, was either clean or partly covered by a mild chemical repellent. Statistical properties of the observed motion of the ant can be described by a model that is analogous to the Langevin theory of the motion of Brownian particles. With each time step, the velocity of the ant changes by a random vector with a robust probability distribution. When the average ant encounters the chemical repellent it responds, like a particle seeing a potential energy barrier, by initially slowing before recovering towards its equilibrium state of motion. The model accounts for most qualitative properties of motion with a small number of parameters.

Agent-based and continuous models of hopper bands for the Australian plague locust: How resource consumption mediates pulse formation and geometry

Locusts are significant agricultural pests. Under favorable environmental conditions flightless juveniles may aggregate into coherent, aligned swarms referred to as hopper bands. These bands are often observed as a propagating wave having a dense front with rapidly decreasing density in the wake. A tantalizing and common observation is that these fronts slow and steepen in the presence of green vegetation. This suggests the collective motion of the band is mediated by resource consumption. Our goal is to model and quantify this effect. We focus on the Australian plague locust, for which excellent field and experimental data is available. Exploiting the alignment of locusts in hopper bands, we concentrate solely on the density variation perpendicular to the front. We develop two models in tandem; an agent-based model that tracks the position of individuals and a partial differential equation model that describes locust density. In both these models, locust are either stationary (and feeding) or moving. Resources decrease with feeding. The rate at which locusts transition between moving and stationary (and vice versa) is enhanced (diminished) by resource abundance. This effect proves essential to the formation, shape, and speed of locust hopper bands in our models. From the biological literature we estimate ranges for the ten input parameters of our models. Sobol sensitivity analysis yields insight into how the band's collective characteristics vary with changes in the input parameters. By examining 4.4 million parameter combinations, we identify biologically consistent parameters that reproduce field observations. We thus demonstrate that resource-dependent behavior can explain the density distribution observed in locust hopper bands. This work suggests that feeding behaviors should be an intrinsic part of future modeling efforts.

Finding continuity and discontinuity in fish schools via integrated information theory

Collective behaviours are known to be the result of diverse dynamics and are sometimes likened to living systems. Although many studies have revealed the dynamics of various collective behaviours, their main focus has been on the information processing performed by the collective, not on interactions within the collective. For example, the qualitative difference between three and four elements in a system has rarely been investigated. Tononi et al. proposed integrated information theory (IIT) to measure the degree of consciousness Φ. IIT postulates that the amount of information loss caused by the minimum information partition is equivalent to the degree of information integration in the system. This measure is not only useful for estimating the degree of consciousness but can also be applied to more general network systems. Here, we obtained two main results from the application of IIT (in particular, IIT 3.0) to the analysis of real fish schools (Plecoglossus altivelis). First, we observed that the discontinuity on 〈Φ(N)〉 distributions emerges for a school of four or more fish. This transition was not observed by measuring the mutual information or the sum of the transfer entropy. We also analysed the IIT on Boids simulations with respect to different coupling strengths; however, the results of the Boids model were found to be quite different from those of real fish. Second, we found a correlation between this discontinuity and the emergence of leadership. We discriminate leadership in this paper from its traditional meaning (e.g. defined by transfer entropy) because IIT-induced leadership refers not to group behaviour, as in other methods, but the degree of autonomy (i.e. group integrity). These results suggest that integrated information Φ can reveal the emergence of a new type of leadership which cannot be observed using other measures.

Optimal searching behaviour generated intrinsically by the central pattern generator for locomotion

Efficient searching for resources such as food by animals is key to their survival. It has been proposed that diverse animals from insects to sharks and humans adopt searching patterns that resemble a simple Lévy random walk, which is theoretically optimal for 'blind foragers' to locate sparse, patchy resources. To test if such patterns are generated intrinsically, or arise via environmental interactions, we tracked free-moving Drosophila larvae with (and without) blocked synaptic activity in the brain, suboesophageal ganglion (SOG) and sensory neurons. In brain-blocked larvae, we found that extended substrate exploration emerges as multi-scale movement paths similar to truncated Lévy walks. Strikingly, power-law exponents of brain/SOG/sensory-blocked larvae averaged 1.96, close to a theoretical optimum (µ ≅ 2.0) for locating sparse resources. Thus, efficient spatial exploration can emerge from autonomous patterns in neural activity. Our results provide the strongest evidence so far for the intrinsic generation of Lévy-like movement patterns.

Adaptive switch to sexually dimorphic movements by partner-seeking termites

How should females and males move to search for partners whose exact location is unknown? Theory predicts that the answer depends on what they know about where targets can be found, raising the question of how actual animals update their mate search patterns to increase encounter probability when conditions change. Here, we show that termites adaptively alternate between sexually monomorphic and dimorphic movements during mate search. When the location of potential mates was completely unpredictable, both sexes moved in straight lines to explore widely. In contrast, when the stray partner was at least nearby, males moved while females paused. Data-based simulations confirmed that these movements increase the rate of successful encounters. The context-dependent switch of search modes is a key to enhance random encounters.

Lévy walk process in self-organization of pedestrian crowds

Similar to other animal groups, human crowds exhibit various collective patterns that emerge from self-organization. Recent studies have emphasized that individuals anticipate their neighbours' motions to seek their paths in dynamical pedestrian flow. This path-seeking behaviour results in deviation of pedestrians from their desired directions (i.e. the direct path to their destination). However, the strategies that individuals adopt for the behaviour and how the deviation of individual movements impact the emergent organization are poorly understood. We here show that the path-seeking behaviour is performed through a scale-free movement strategy called a Lévy walk, which might facilitate transition to the group-level behaviour. In an experiment of lane formation, a striking example of self-organized patterning in human crowds, we observed how flows of oppositely moving pedestrians spontaneously separate into several unidirectional lanes. We found that before (but not after) lane formation, pedestrians deviate from the desired direction by Lévy walk process, which is considered optimal when searching unpredictably distributed resources. Pedestrians balance a trade-off between seeking their direct paths and reaching their goals as quickly as possible; they may achieve their optimal paths through Lévy walk process, facilitating the emergent lane formation.

Asynchrony induces polarization in attraction-based models of collective motion

Animal groups frequently move in a highly organized manner, as represented by flocks of birds and schools of fish. Despite being an everyday occurrence, we do not fully understand how this works. In particular, what social interactions between animals give rise to the flock structures we observe? This question is often investigated using self-propelled particle models where particles represent the individual animals. These models differ in the social interactions used, individual particle properties, and various technical assumptions. One particular technical assumption relates to whether all particles update their headings and positions at exactly the same time (synchronous update) or not (asynchronous update). Here, we investigate the causal effects of this assumption in an attraction-only model and find that it has a dramatic impact. Polarized groups do not form when synchronous update is used, but are produced with asynchronous update, and this phenomenon is robust with respect to variation in particle displacements and inclusion of noise. Given that many important models have been implemented with synchronous update only, we speculate that our understanding of the social interactions on which they are based may be incomplete. Perhaps previously unobserved phenomena will emerge if other potentially more realistic update schemes are used.

The Metastability of the Double-Tripod Gait in Locust Locomotion

Insect locomotion represents a fundamental example of neuronal oscillating circuits generating different motor patterns or gaits by controlling their phase coordination. Walking gaits are assumed to represent stable states of the system, often modeled as coupled oscillators. This view is challenged, however, by recent experimental observations, in which in vitro locust preparations consistently converged to synchronous rhythms (all legs oscillating as one), a locomotive pattern never seen in vivo. To reconcile this inconsistency, we developed a modeling framework to capture the trade-off between the two competing mechanisms: the endogenous neuronal circuitry, expressed in vitro, and the feedback mechanisms from sensory and descending inputs, active only in vivo. We show that the ubiquitously observed double-tripod walking gait emerges precisely from this balance. The outcome is a short-lived meta-stable double-tripod gait, which transitions and alternates with stable idling, thus recovering the observed intermittent bouts of locomotion, typical of many insects' locomotion behavior.

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Isolated in vitro locust preparations indicate that idling is a stable fictive gait

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This is in contrast to the dominant in vivo locomotive pattern (i.e., double tripod)

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Hence functional locomotion behavior is dependent on descending and sensory inputs

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The presented model generates intermittent double-tripod bouts as seen empirically

Intra- versus intergroup variance in collective behavior

Animal collective motion arises from the intricate interactions between the natural variability among individuals, and the homogenizing effect of the group, working to generate synchronization and maintain coherence. Here, these interactions were studied using marching locust nymphs under controlled laboratory settings. A novel experimental approach compared single animals, small groups, and virtual groups composed of randomly shuffled real members. We found that the locust groups developed unique, group-specific behavioral characteristics, reflected in large intergroup and small intragroup variance (compared with the shuffled groups). Behavioral features that differed between single animals and groups, but not between group types, were classified as essential for swarm formation. Comparison with Markov chain models showed that individual tendencies and the interaction network among animals dictate the group characteristics. Deciphering the bidirectional interactions between individual and group properties is essential for understanding the swarm phenomenon and predicting large-scale swarm behaviors.

Traveling pulse emerges from coupled intermittent walks: A case study in sheep

Monitoring small groups of sheep in spontaneous evolution in the field, we decipher behavioural rules that sheep follow at the individual scale in order to sustain collective motion. Individuals alternate grazing mode at null speed and moving mode at walking speed, so cohesive motion stems from synchronising when they decide to switch between the two modes. We propose a model for the individual decision making process, based on switching rates between stopped / walking states that depend on behind / ahead locations and states of the others. We parametrize this model from data. Next, we translate this (microscopic) individual-based model into its density-flow (macroscopic) equations counterpart. Numerical solving these equations display a traveling pulse propagating at constant speed even though each individual is at any moment either stopped or walking. Considering the minimal model embedded in these equations, we derive analytically the steady shape of the pulse (sech square). The parameters of the pulse (shape and speed) are expressed as functions of individual parameters. This pulse emerges from the non linear coupling of start/stop individual decisions which compensate exactly for diffusion and promotes a steady ratio of walking / stopped individuals, which in turn determines the traveling speed of the pulse. The system seems to converge to this pulse from any initial condition, and to recover the pulse after perturbation. This gives a high robustness to this coordination mechanism.

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.

A random acceleration model of individual animal movement allowing for diffusive, superdiffusive and superballistic regimes

Patterns of individual animal movement attracted considerable attention over the last two decades. In particular, question as to whether animal movement is predominantly diffusive or superdiffusive has been a focus of discussion and controversy. We consider this problem using a theory of stochastic motion based on the Langevin equation with non-Wiener stochastic forcing that originates in animal’s response to environmental noise. We show that diffusive and superdiffusive types of motion are inherent parts of the same general movement process that arises as interplay between the force exerted by animals (essentially, by animal’s muscles) and the environmental drag. The movement is superballistic with the mean square displacement growing with time as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle {x}^{2}(t)\rangle \sim {t}^{4}$$\end{document}〈x2(t)〉∼t4 at the beginning and eventually slowing down to the diffusive spread \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle {x}^{2}(t)\rangle \sim t$$\end{document}〈x2(t)〉∼t. We show that the duration of the superballistic and superdiffusive stages can be long depending on the properties of the environmental noise and the intensity of drag. Our findings demonstrate theoretically how the movement pattern that includes diffusive and superdiffusive/superballistic motion arises naturally as a result of the interplay between the dissipative properties of the environment and the animal’s biological traits such as the body mass, typical movement velocity and the typical duration of uninterrupted movement.

The evolutionary origins of Lévy walk foraging

We study through a reaction-diffusion algorithm the influence of landscape diversity on the efficiency of search dynamics. Remarkably, the identical optimal search strategy arises in a wide variety of environments, provided the target density is sparse and the searcher’s information is restricted to its close vicinity. Our results strongly impact the current debate on the emergentist vs. evolutionary origins of animal foraging. The inherent character of the optimal solution (i.e., independent on the landscape for the broad scenarios assumed here) suggests an interpretation favoring the evolutionary view, as originally implied by the Lévy flight foraging hypothesis. The latter states that, under conditions of scarcity of information and sparse resources, some organisms must have evolved to exploit optimal strategies characterized by heavy-tailed truncated power-law distributions of move lengths. These results strongly suggest that Lévy strategies—and hence the selection pressure for the relevant adaptations—are robust with respect to large changes in habitat. In contrast, the usual emergentist explanation seems not able to explain how very similar Lévy walks can emerge from all the distinct non-Lévy foraging strategies that are needed for the observed large variety of specific environments. We also report that deviations from Lévy can take place in plentiful ecosystems, where locomotion truncation is very frequent due to high encounter rates. So, in this case normal diffusion strategies—performing as effectively as the optimal one—can naturally emerge from Lévy. Our results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

How organisms improve the search for food, mates, etc., is a key factor to their survival. Mathematically, the best strategy to look for randomly distributed re-visitable resources—under scarce information and sparse conditions—results from Lévy distributions of move lengths (the probability of taking a step ℓ is proportional to 1/ℓ²). Today it is well established that many animal species in different habitats do perform Lévy foraging. This fact has raised a heated debate, viz., the emergent versus evolutionary hypotheses. For the former, a Lévy foraging is an emergent property, a consequence of searcher-environment interactions: certain landscapes induce Lévy patterns, but others not. In this view, the optimal strategy depends on the particular habitat. The evolutionary explanation, in contrast, is that Lévy foraging strategies are adaptations that evolved via natural selection. In this article, through simulations we exhaustively analyze the influence of distinct environments on the foraging efficiency. We find that the optimal procedure is the same in all situations, provided density is low and landscape information is scarce. So, the best search strategy is remarkably independent of details. These results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

Intermittence and connectivity of interactions in pigeon flock flights

Collective circular motion is a common yet spectacular behavior of pigeon flocks. Efficient and robust inter-individual communication is required for flock coordination during this widely-spreaded movement pattern. When a flock hovers near the home loft, the rotational direction undergoes regular spontaneous variations. Based on intensive analyses of high spatial-temporal resolution GPS data, we quantified the intensity of velocity alignment among different individuals in terms of their velocity fluctuations. It is found that pigeon flocks employ an intermittent interaction (alignment) mechanism, where intra-group information transmission is not required at every instant. However, the union of the topologies of several consecutive interaction networks always keeps connected. This biological observation strongly suggests the presence of a jointly connected topology in pigeon flocks, which helps substantially reduce the communication and/or information processing requirements while retaining the agility and stability of the group. Finally, we conducted extensive investigation on the interaction mechanism as well as the spontaneous changes in rotational direction of pigeon flocks. These results shed some light onto the coordination mechanism exploration of bird flocks’ collective motions.

Kinetic order-disorder transitions in a pause-and-go swarming model with memory

A two dimensional model of self-propelled particles combining both a pause-and-go movement pattern and memory is studied in simulations. It is shown, that in contrast to previously studied agent based models in two-dimensions, order and disorder are metastable states that can co-exist at some parameter range. In particular, this implies that the formation and decay of global order in swarms may be kinetic rather than a phase transition. Our results explain metastability recently observed in swarming locust and fish.

Emergence of a coherent and cohesive swarm based on mutual anticipation

Collective behavior emerging out of self-organization is one of the most striking properties of an animal group. Typically, it is hypothesized that each individual in an animal group tends to align its direction of motion with those of its neighbors. Most previous models for collective behavior assume an explicit alignment rule, by which an agent matches its velocity with that of neighbors in a certain neighborhood, to reproduce a collective order pattern by simple interactions. Recent empirical studies, however, suggest that there is no evidence for explicit matching of velocity, and that collective polarization arises from interactions other than those that follow the explicit alignment rule. We here propose a new lattice-based computational model that does not incorporate the explicit alignment rule but is based instead on mutual anticipation and asynchronous updating. Moreover, we show that this model can realize densely collective motion with high polarity. Furthermore, we focus on the behavior of a pair of individuals, and find that the turning response is drastically changed depending on the distance between two individuals rather than the relative heading, and is consistent with the empirical observations. Therefore, the present results suggest that our approach provides an alternative model for collective behavior.

Nonstationary Stochastic Dynamics Underlie Spontaneous Transitions between Active and Inactive Behavioral States

The neural basis of spontaneous movement generation is a fascinating open question. Long-term monitoring of fish, swimming freely in a constant sensory environment, has revealed a sequence of behavioral states that alternate randomly and spontaneously between periods of activity and inactivity. We show that key dynamical features of this sequence are captured by a 1-D diffusion process evolving in a nonlinear double well energy landscape, in which a slow variable modulates the relative depth of the wells. This combination of stochasticity, nonlinearity, and nonstationary forcing correctly captures the vastly different timescales of fluctuations observed in the data (∼1 to ∼1000 s), and yields long-tailed residence time distributions (RTDs) also consistent with the data. In fact, our model provides a simple mechanism for the emergence of long-tailed distributions in spontaneous animal behavior. We interpret the stochastic variable of this dynamical model as a decision-like variable that, upon reaching a threshold, triggers the transition between states. Our main finding is thus the identification of a threshold crossing process as the mechanism governing spontaneous movement initiation and termination, and to infer the presence of underlying nonstationary agents. Another important outcome of our work is a dimensionality reduction scheme that allows similar segments of data to be grouped together. This is done by first extracting geometrical features in the dataset and then applying principal component analysis over the feature space. Our study is novel in its ability to model nonstationary behavioral data over a wide range of timescales.

The effect of changing topography on the coordinated marching of locust nymphs

Collective motion has traditionally been studied in the lab in homogeneous, obstacle-free environments, with little work having been conducted with changing landscapes or topography. Here, the impact of spatial heterogeneity on the collective motion exhibited by marching desert locust nymphs was studied under controlled lab conditions. Our experimental circular arenas, incorporating a funnel-like narrowing followed by re-widening, did not constitute a major barrier to the locusts but, rather, mimicked a changing topography in the natural environment. We examined its effects on macroscopic features of the locust collective behavior, as well as the any changes in their marching kinematics. A major finding was that of the limited extent to which the changing topography affected system-level features of the marching locust group, such as the order parameter and the fraction of walking individuals, despite increased crowding at the funnel. Overall, marching kinematics was also very little affected, suggesting that locust marching bands adjust to the environment, with little effect on the overall dynamics of the group. These findings are in contrast to recent theoretical results predicting that environmental heterogeneities qualitatively alter the dynamics of collectively moving particles; and highlight the crucial role of rapid individual plasticity and adaptability in the dynamics of flocks and swarms. Our study has revealed other important features of the marching behavior of the desert locust in addition to its robustness: the locusts demonstrated both, clear thigmotaxis and a tendency to spread-out and fill the available space.

Variability in individual activity bursts improves ant foraging success

Using experimental and computational methods, we study the role of behavioural variability in activity bursts (or temporal activity patterns) for individual and collective regulation of foraging in A. senilis ants. First, foraging experiments were carried out under special conditions (low densities of ants and food and absence of external cues or stimuli) where individual-based strategies are most prevalent. By using marked individuals and recording all foraging trajectories, we were then able to precisely quantify behavioural variability among individuals. Our main conclusions are that (i) variability of ant trajectories (turning angles, speed, etc.) is low compared with variability of temporal activity profiles, and (ii) this variability seems to be driven by plasticity of individual behaviour through time, rather than the presence of fixed behavioural stereotypes or specialists within the group. The statistical measures obtained from these experimental foraging patterns are then used to build a general agent-based model (ABM) which includes the most relevant properties of ant foraging under natural conditions, including recruitment through pheromone communication. Using the ABM, we are able to provide computational evidence that the characteristics of individual variability observed in our experiments can provide a functional advantage (in terms of foraging success) to the group; thus, we propose the biological basis underpinning our observations. Altogether, our study reveals the potential utility of experiments under simplified (laboratory) conditions for understanding information-gathering in biological systems.

Foraging success under uncertainty: search tradeoffs and optimal space use

Understanding the structural complexity and the main drivers of animal search behaviour is pivotal to foraging ecology. Yet, the role of uncertainty as a generative mechanism of movement patterns is poorly understood. Novel insights from search theory suggest that organisms should collect and assess new information from the environment by producing complex exploratory strategies. Based on an extension of the first passage time theory, and using simple equations and simulations, we unveil the elementary heuristics behind search behaviour. In particular, we show that normal diffusion is not enough for determining optimal exploratory behaviour but anomalous diffusion is required. Searching organisms go through two critical sequential phases (approach and detection) and experience fundamental search tradeoffs that may limit their encounter rates. Using experimental data, we show that biological search includes elements not fully considered in contemporary physical search theory. In particular, the need to consider search movement as a non-stationary process that brings the organism from one informational state to another. For example, the transition from remaining in an area to departing from it may occur through an exploratory state where cognitive search is challenged. Therefore, a more comprehensive view of foraging ecology requires including current perspectives about movement under uncertainty.

Signatures of chaos in animal search patterns

One key objective of the emerging discipline of movement ecology is to link animal movement patterns to underlying biological processes, including those operating at the neurobiological level. Nonetheless, little is known about the physiological basis of animal movement patterns, and the underlying search behaviour. Here we demonstrate the hallmarks of chaotic dynamics in the movement patterns of mud snails (Hydrobia ulvae) moving in controlled experimental conditions, observed in the temporal dynamics of turning behaviour. Chaotic temporal dynamics are known to occur in pacemaker neurons in molluscs, but there have been no studies reporting on whether chaotic properties are manifest in the movement patterns of molluscs. Our results suggest that complex search patterns, like the Lévy walks made by mud snails, can have their mechanistic origins in chaotic neuronal processes. This possibility calls for new research on the coupling between neurobiology and motor properties.

Ants determine their next move at rest: motor planning and causality in complex systems

To find useful work to do for their colony, individual eusocial animals have to move, somehow staying attentive to relevant social information. Recent research on individual Temnothorax albipennis ants moving inside their colony's nest found a power-law relationship between a movement's duration and its average speed; and a universal speed profile for movements showing that they mostly fluctuate around a constant average speed. From this predictability it was inferred that movement durations are somehow determined before the movement itself. Here, we find similar results in lone T. albipennis ants exploring a large arena outside the nest, both when the arena is clean and when it contains chemical information left by previous nest-mates. This implies that these movement characteristics originate from the same individual neural and/or physiological mechanism(s), operating without immediate regard to social influences. However, the presence of pheromones and/or other cues was found to affect the inter-event speed correlations. Hence we suggest that ants' motor planning results in intermittent response to the social environment: movement duration is adjusted in response to social information only between movements, not during them. This environmentally flexible, intermittently responsive movement behaviour points towards a spatially allocated division of labour in this species. It also prompts more general questions on collective animal movement and the role of intermittent causation from higher to lower organizational levels in the stability of complex systems.

Locust Collective Motion and Its Modeling

Over the past decade, technological advances in experimental and animal tracking techniques have motivated a renewed theoretical interest in animal collective motion and, in particular, locust swarming. This review offers a comprehensive biological background followed by comparative analysis of recent models of locust collective motion, in particular locust marching, their settings, and underlying assumptions. We describe a wide range of recent modeling and simulation approaches, from discrete agent-based models of self-propelled particles to continuous models of integro-differential equations, aimed at describing and analyzing the fascinating phenomenon of locust collective motion. These modeling efforts have a dual role: The first views locusts as a quintessential example of animal collective motion. As such, they aim at abstraction and coarse-graining, often utilizing the tools of statistical physics. The second, which originates from a more biological perspective, views locust swarming as a scientific problem of its own exceptional merit. The main goal should, thus, be the analysis and prediction of natural swarm dynamics. We discuss the properties of swarm dynamics using the tools of statistical physics, as well as the implications for laboratory experiments and natural swarms. Finally, we stress the importance of a combined-interdisciplinary, biological-theoretical effort in successfully confronting the challenges that locusts pose at both the theoretical and practical levels.

Ultimate failure of the Lévy Foraging Hypothesis: Two-scale searching strategies outperform scale-free ones even when prey are scarce and cryptic

The "Lévy Foraging Hypothesis" promotes Lévy walk (LW) as the best strategy to forage for patchily but unpredictably located prey. This strategy mixes extensive and intensive searching phases in a mostly cue-free way through strange, scale-free kinetics. It is however less efficient than a cue-driven two-scale Composite Brownian walk (CBW) when the resources encountered are systematically detected. Nevertheless, it could be assumed that the intrinsic capacity of LW to trigger cue-free intensive searching at random locations might be advantageous when resources are not only scarcely encountered but also so cryptic that the probability to detect those encountered during movement is low. Surprisingly, this situation, which should be quite common in natural environments, has almost never been studied. Only a few studies have considered "saltatory" foragers, which are fully "blind" while moving and thus detect prey only during scanning pauses, but none of them compared the efficiency of LW vs. CBW in this context or in less extreme contexts where the detection probability during movement is not null but very low. In a study based on computer simulations, we filled the bridge between the concepts of "pure continuous" and "pure saltatory" foraging by considering that the probability to detect resources encountered while moving may range from 0 to 1. We showed that regularly stopping to scan the environment can indeed improve efficiency, but only at very low detection probabilities. Furthermore, the LW is then systematically outperformed by a mixed cue-driven/internally-driven CBW. It is thus more likely that evolution tends to favour strategies that rely on environmental feedbacks rather than on strange kinetics.

Inherent noise appears as a Lévy walk in fish schools

Recent experimental and observational data have revealed that the internal structures of collective animal groups are not fixed in time. Rather, individuals can produce noise continuously within their group. These individuals' movements on the inside of the group, which appear to collapse the global order and information transfer, can enable interactions with various neighbors. In this study, we show that noise generated inherently in a school of ayus (Plecoglossus altivelis) is characterized by various power-law behaviors. First, we show that individual fish move faster than Brownian walkers with respect to the center of the mass of the school as a super-diffusive behavior, as seen in starling flocks. Second, we assess neighbor shuffling by measuring the duration of pair-wise contact and find that this distribution obeys the power law. Finally, we show that an individual's movement in the center of a mass reference frame displays a Lévy walk pattern. Our findings suggest that inherent noise (i.e., movements and changes in the relations between neighbors in a directed group) is dynamically self-organized in both time and space. In particular, Lévy walk in schools can be regarded as a well-balanced movement to facilitate dynamic collective motion and information transfer throughout the group.

Topological data analysis of biological aggregation models

We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists of numerical simulation output from the models of Vicsek and D'Orsogna. These models are dynamical systems describing the movement of agents who interact via alignment, attraction, and/or repulsion. Each simulation time frame is a point cloud in position-velocity space. We analyze the topological structure of these point clouds, interpreting the persistent homology by calculating the first few Betti numbers. These Betti numbers count connected components, topological circles, and trapped volumes present in the data. To interpret our results, we introduce a visualization that displays Betti numbers over simulation time and topological persistence scale. We compare our topological results to order parameters typically used to quantify the global behavior of aggregations, such as polarization and angular momentum. The topological calculations reveal events and structure not captured by the order parameters.

Evidence for a pervasive 'idling-mode' activity template in flying and pedestrian insects

Understanding the complex movement patterns of animals in natural environments is a key objective of 'movement ecology'. Complexity results from behavioural responses to external stimuli but can also arise spontaneously in their absence. Drawing on theoretical arguments about decision-making circuitry, we predict that the spontaneous patterns will be scale-free and universal, being independent of taxon and mode of locomotion. To test this hypothesis, we examined the activity patterns of the European honeybee, and multiple species of noctuid moth, tethered to flight mills and exposed to minimal external cues. We also reanalysed pre-existing data for Drosophila flies walking in featureless environments. Across these species, we found evidence of common scale-invariant properties in their movement patterns; pause and movement durations were typically power law distributed over a range of scales and characterized by exponents close to 3/2. Our analyses are suggestive of the presence of a pervasive scale-invariant template for locomotion which, when acted on by environmental cues, produces the movements with characteristic scales observed in nature. Our results indicate that scale-finite complexity as embodied, for instance, in correlated random walk models, may be the result of environmental cues overriding innate behaviour, and that scale-free movements may be intrinsic and not limited to 'blind' foragers as previously thought.

Universality in ant behaviour

Prediction for social systems is a major challenge. Universality at the social level has inspired a unified theory for urban living but individual variation makes predicting relationships within societies difficult. Here, we show that in ant societies individual average speed is higher when event duration is longer. Expressed as a single scaling function, this relationship is universal because for any event duration an ant, on average, moves at the corresponding average speed except for a short acceleration and deceleration at the beginning and end. This establishes cause and effect within a social system and may inform engineering and control of artificial ones.