Collective Animal Motion Research Articles

Energetics of collective movement in vertebrates.

The collective directional movement of animals occurs over both short distances and longer migrations, and is a critical aspect of feeding, reproduction and the ecology of many species. Despite the implications of collective motion for lifetime fitness, we know remarkably little about its energetics. It is commonly thought that collective animal motion saves energy: moving alone against fluid flow is expected to be more energetically expensive than moving in a group. Energetic conservation resulting from collective movement is most often inferred from kinematic metrics or from computational models. However, the direct measurement of total metabolic energy savings during collective motion compared with solitary movement over a range of speeds has yet to be documented. In particular, longer duration and higher speed collective motion must involve both aerobic and non-aerobic (high-energy phosphate stores and substrate-level phosphorylation) metabolic energy contributions, and yet no study to date has quantified both types of metabolic contribution in comparison to locomotion by solitary individuals. There are multiple challenging questions regarding the energetics of collective motion in aquatic, aerial and terrestrial environments that remain to be answered. We focus on aquatic locomotion as a model system to demonstrate that understanding the energetics and total cost of collective movement requires the integration of biomechanics, fluid dynamics and bioenergetics to unveil the hydrodynamic and physiological phenomena involved and their underlying mechanisms.

Nearest Neighbour Node Deployment Algorithm for Mobile Sensor Networks.

Many animal aggregations display remarkable collective coordinated movements on a large scale, which emerge as a result of distributed local decision-making by individuals. The recent advances in modelling the collective motion of animals through the utilisation of Nearest Neighbour rules, without the need for centralised coordination, resulted in the development of self-deployment algorithms in Mobile Sensor Networks (MSNs) to achieve various types of coverage essential for different applications. However, the energy consumption associated with sensor movement to achieve the desired coverage remains a significant concern for the majority of algorithms reported in the literature. In this paper, the Nearest Neighbour Node Deployment (NNND) algorithm is proposed to efficiently provide blanket coverage across a given area while minimising energy consumption and enhancing fault tolerance. In contrast to other algorithms that sequentially move sensors, NNND leverages the power of parallelism by employing multiple streams of sensor motions, each directed towards a distinct section of the area. The cohesion of each stream is maintained by adaptively choosing a leader for each stream while collision avoidance is also ensured. These properties contribute to minimising the travel distance within each stream, resulting in decreased energy consumption. Additionally, the utilisation of multiple leaders in NNND eliminates the presence of a single point of failure, hence enhancing the fault tolerance of the area coverage. The results of our extensive simulation study demonstrate that NNND not only achieves lower energy consumption but also a higher percentage of k-coverage.

Actin self-organization in gliding parasitic cells.

Following a playful introduction to the Toner-Tu flocking theory first inspired by the collective motion of animals, we will move down a million-fold in length scale to focus on “molecular flocks”: collectively moving actin filaments at the surface of the single-celled parasite Toxoplasma gondii. During host infection, apicomplexan parasites like Plasmodium and Toxoplasma use these myosin-powered surface actin movements to drive a form of cell locomotion called gliding, which differs fundamentally from the swim-or-crawl paradigm of eukaryotic cell motility. How does the collective motion of surface actin filaments emerge, and how does it drive the varied parasite gliding movements that we observe experimentally? I will present findings based on single-molecule imaging in live parasites and use continuum flocking theory to predict emergent filament flows in the unusual confines provided by parasite geometry. This molecular filament flocking model enables the exploration of distinct self-organized states tuned by filament lifetime, which can account for the diversity of observed Toxoplasma gliding motions. This theory-experiment interplay will illustrate how different forms of gliding motility can arise as an intrinsic consequence of emergent active filament flows on a complex surface.

Ideal free flows of optimal foragers: Vertical migrations in the ocean

We consider the collective motion of animals in time-varying environments, using as a case the diel vertical migration of marine copepods. The animals are distributed in space such that each animal moves optimally, seeking regions which offer high growth rates and low mortalities, subject to costs on excessive movements as well as being in regions with high densities of conspecifics. The model applies to repeated scenarios such as diel or seasonal patterns, where the animals are aware of both current and future environmental conditions. We show that this problem can be viewed as a differential game of mean field type, and that the evolutionary stable solution, i.e., the Nash equilibrium, is characterized by partial differential equations, which govern the distributions and migration velocities of animals. These equations have similarities to equations that appear in the fluid dynamics, specifically the Euler equations for compressible inviscid fluids. If the environment is constant, the ideal free distribution emerges as an equilibrium. We illustrate the theory with a numerical example of vertical migrations of oceanic copepods, where animals are attracted to nutrient-rich surface waters while repulsed from light during daytime due to the presence of visual predators, aiming to reduce both proximity to conspecifics and swimming efforts. For this case, we show that optimal movements are diel vertical migrations in qualitative agreement with observations of copepods.

Coordination of movement via complementary interactions of leaders and followers in termite mating pairs.

In collective animal motion, coordination is often achieved by feedback between leaders and followers. For stable coordination, a leader's signals and a follower's responses are hypothesized to be attuned to each other. However, their roles are difficult to disentangle in species with highly coordinated movements, hiding potential diversity of behavioural mechanisms for collective behaviour. Here, we show that two Coptotermes termite species achieve a similar level of coordination via distinct sets of complementary leader-follower interactions. Even though C. gestroi females produce less pheromone than C. formosanus, tandem runs of both species were stable. Heterospecific pairs with C. gestroi males were also stable, but not those with C. formosanus males. We attributed this to the males' adaptation to the conspecific females; C. gestroi males have a unique capacity to follow females with small amounts of pheromone, while C. formosanus males reject C. gestroi females as unsuitable but are competitive over females with large amounts of pheromone. An information-theoretic analysis supported this conclusion by detecting information flow from female to male only in stable tandems. Our study highlights cryptic interspecific variation in movement coordination, a source of novelty for the evolution of social interactions.

Deep attention networks reveal the rules of collective motion in zebrafish.

A variety of simple models has been proposed to understand the collective motion of animals. These models can be insightful but may lack important elements necessary to predict the motion of each individual in the collective. Adding more detail increases predictability but can make models too complex to be insightful. Here we report that deep attention networks can obtain a model of collective behavior that is simultaneously predictive and insightful thanks to an organization in modules. When using simulated trajectories, the model recovers the ground-truth interaction rule used to generate them, as well as the number of interacting neighbours. For experimental trajectories of large groups of 60-100 zebrafish, Danio rerio, the model obtains that interactions between pairs can approximately be described as repulsive, attractive or as alignment, but only when moving slowly. At high velocities, interactions correspond only to alignment or alignment mixed with repulsion at close distances. The model also shows that each zebrafish decides where to move by aggregating information from the group as a weighted average over neighbours. Weights are higher for neighbours that are close, in a collision path or moving faster in frontal and lateral locations. The network also extracts that the number of interacting individuals is dynamical and typically in the range 8–22, with 1–10 more important ones. Our results suggest that each animal decides by dynamically selecting information from the collective.

Effects of Heterogeneous Social Interactions on Flocking Dynamics.

Social relationships characterize the interactions that occur within social species and may have an important impact on collective animal motion. Here, we consider a variation of the standard Vicsek model for collective motion in which interactions are mediated by an empirically motivated scale-free topology that represents a heterogeneous pattern of social contacts. We observe that the degree of order of the model is strongly affected by network heterogeneity: more heterogeneous networks show a more resilient ordered state, while less heterogeneity leads to a more fragile ordered state that can be destroyed by sufficient external noise. Our results challenge the previously accepted equivalence between the static Vicsek model and the equilibrium XY model on the network of connections, and point towards a possible equivalence with models exhibiting a different symmetry.

An efficient method for sorting and quantifying individual social traits based on group‐level behaviour

Abstract In social contexts, animal behaviour is often studied in terms of group‐level characteristics. One clear example of this is the collective motion of animals in decentralized structures, such as bird flocks and fish schools. A major goal of research is to identify how group‐level behaviours are shaped by the traits of individuals within them. Few methods exist to make these connections. Individual assessment is often limited, forcing alternatives such as fitting agent‐based models to experimental data. We provide a systematic experimental method for sorting animals according to socially relevant traits, without assaying them or even tagging them individually. Instead, they are repeatedly subjected to behavioural assays in groups, between which the group memberships are rearranged, in order to test the effect of many different combinations of individuals on a group‐level property or feature. We analyse this method using a general model for the group feature, and simulate a variety of specific cases to track how individuals are sorted in each case. We find that in the case where the members of a group contribute equally to the group feature, the sorting procedure increases the between‐group behavioural variation well above what is expected for groups randomly sampled from a population. For a wide class of group feature models, the individual phenotypes are efficiently sorted across the groups and thus become available for further analysis on how individual properties affect group behaviour. We also show that the experimental data can be used to estimate the individual‐level repeatability of the underlying traits. Our method allows experimenters to find repeatable variation in social behaviours that cannot be assessed in solitary individuals. Furthermore, experiments in animal behaviour often focus on comparisons between groups randomly sampled from a population. Increasing the behavioural variation between groups increases statistical power for testing whether a group feature is related to other properties of groups or to their phenotypic composition. Sorting according to socially relevant traits is also beneficial in artificial selection experiments, and for testing correlations with other traits. Overall, the method provides a useful tool to study how individual properties influence social behaviour.

Flow instability originating from particle configurations using the two-dimensional optimal velocity model.

The two-dimensional optimal velocity model has potential applications to pedestrian dynamics and the collective motion of animals. In this paper, we extend the linear stability analysis presented in a previous paper [A Nakayama et al., Phys. Rev. E. 77, 016105 (2008)] and investigate the effects of particle configuration on the stability of several wave modes of collective oscillations of moving particles. We find that, when a particle moves without interacting with particles that are positioned in a diagonally forward or backward direction, the stable region of the particle flow is completely removed by the elliptically polarized mode.

Leadership emergence in a data-driven model of zebrafish shoals with speed modulation

Models of collective animal motion can greatly aid in the design and interpretation of behavioural experiments that seek to unravel, isolate, and manipulate the determinants of leader-follower relationships. Here, we develop an initial model of zebrafish social behaviour, which accounts for both speed and angular velocity regulatory interactions among conspecifics. Using this model, we analyse the macroscopic observables of small shoals influenced by an “informed” agent, showing that leaders which actively modulate their speed with respect to their neighbours can entrain and stabilise collective dynamics of the naive shoal.

A new interaction potential for swarming models

We consider a self-propelled particle system which has been used to describe certain types of collective motion of animals, such as fish schools and bird flocks. Interactions between particles are specified by means of a pairwise potential, repulsive at short ranges and attractive at longer ranges. The exponentially decaying Morse potential is a typical choice, and is known to reproduce certain types of collective motion observed in nature, particularly aligned flocks and rotating mills. We introduce a class of interaction potentials, that we call Quasi-Morse, for which flock and rotating mills states are also observed numerically, however in that case the corresponding macroscopic equations allow for explicit solutions in terms of special functions, with coefficients that can be obtained numerically without solving the particle evolution. We compare the obtained solutions with long-time dynamics of the particle systems and find a close agreement for several types of flock and mill solutions.

Inferring the rules of interaction of shoaling fish

Collective motion, where large numbers of individuals move synchronously together, is achieved when individuals adopt interaction rules that determine how they respond to their neighbors' movements and positions. These rules determine how group-living animals move, make decisions, and transmit information between individuals. Nonetheless, few studies have explicitly determined these interaction rules in moving groups, and very little is known about the interaction rules of fish. Here, we identify three key rules for the social interactions of mosquitofish (Gambusia holbrooki): (i) Attraction forces are important in maintaining group cohesion, while we find only weak evidence that fish align with their neighbor's orientation; (ii) repulsion is mediated principally by changes in speed; (iii) although the positions and directions of all shoal members are highly correlated, individuals only respond to their single nearest neighbor. The last two of these rules are different from the classical models of collective animal motion, raising new questions about how fish and other animals self-organize on the move.

The impact of social networks on animal collective motion

Many group-living animals show social preferences for relatives, familiar conspecifics or individuals of similar attributes such as size, personality or sex. How such preferences could affect the collective motion of animal groups has been rather unexplored. We present a general model of collective animal motion that includes social connections as preferential reactions between individuals. Our conceptual examples illustrate the possible impact of underlying social networks on the collective motion of animals. Our approach shows that the structure of these networks could influence: (1) the cohesion of groups; (2) the spatial position of individuals within groups; and (3) the hierarchical dynamics within such groups. We argue that the position of individuals within a social network and the social network structure of populations could have important fitness implications for individual animals. Counterintuitive results from our conceptual examples show that social structures can result in unexpected group dynamics. This sharpens our understanding of the way in which collective movement can be interpreted as a result of social interactions.

Limited interactions in flocks: relating model simulations to empirical data

The mechanism of self-organization resulting in coordinated collective motion has received wide attention from a range of scientists interested in both its technical and biological relevance. Models have been highly influential in highlighting how collective motion can be produced from purely local interactions between individuals. Typical models in this field are termed 'metric' because each individual only reacts to conspecifics within a fixed distance. A recent large-scale study has, however, provided evidence that interactions ruling collective behaviour occur between a fixed number of nearest neighbours ('topological' framework). Despite their importance in clarifying the nature of the mechanism underlying animal interactions, these findings have yet to be produced by either metric or topological models. Here, we present an original individual-based model of collective animal motion that reproduces the previous findings. Our approach bridges the current gap between previous model analysis and recent evidence, and presents a framework for further study.

Two-species-coagulation approach to consensus by group level interactions

We explore the self-organization dynamics of a set of entities by considering the interactions that affect the different subgroups conforming the whole. To this end, we employ the widespread example of coagulation kinetics, and characterize which interaction types lead to consensus formation and which do not, as well as the corresponding different macroscopic patterns. The crucial technical point is extending the usual one species coagulation dynamics to the two species one. This is achieved by means of introducing explicitly solvable kernels which have a clear physical meaning. The corresponding solutions are calculated in the long time limit, in which consensus may or may not be reached. The lack of consensus is characterized by means of scaling limits of the solutions. The possible applications of our results to some topics in which consensus reaching is fundamental, such as collective animal motion and opinion spreading dynamics, are also outlined.

Collective motion in animal groups from a neurobiological perspective: The adaptive benefits of dynamic sensory loads and selective attention

We explore mechanisms associated with collective animal motion by drawing on the neurobiological bases of sensory information processing and decision-making. The model uses simplified retinal processes to translate neighbor movement patterns into information through spatial signal integration and threshold responses. The structure provides a mechanism by which individuals can vary their sets of influential neighbors, a measure of an individual's sensory load. Sensory loads are correlated with group order and density, and we discuss their adaptive values in an ecological context. The model also provides a mechanism by which group members can identify, and rapidly respond to, novel visual stimuli.