COLLECTIVE VORTEX BEHAVIORS: DIVERSITY, PROXIMATE, AND ULTIMATE CAUSES OF CIRCULAR ANIMAL GROUP MOVEMENTS

Scale at the interface of spatial and social ecology

Animals simultaneously navigate spatial and social environments, and their decision-making with respect to those environments constitutes their spatial (e.g. habitat selection) and social (e.g. conspecific associations) phenotypes. The spatial-social interface is a recently introduced conceptual framework linking these components of spatial and social ecology. The spatial-social interface is inherently scale-dependent, yet it has not been integrated with the rich body of literature on ecological scale. Here, we develop a conceptual connection between the spatial-social interface and ecological scale. We propose three key innovations that incrementally build upon each other. First, the use-availability framework that underpins a large body of literature in behavioural ecology can be used in analogy to the phenotype-environment nomenclature and is transferable across the spatial and social realms. Second, both spatial and social phenotypes are hierarchical, with nested components that are linked via constraints-from the top down-or emergent properties-from the bottom up. Finally, in both the spatial and social realms, the definitions of environment and phenotype depend on the focal scale of inquiry. These conceptual innovations cast our understanding of the relationships between social and spatial dimensions of animal ecology in a new light, allowing a more holistic understanding and clearer hypothesis development for animal behaviour. This article is part of the theme issue 'The spatial-social interface: a theoretical and empirical integration'.

Collective foraging of active particles trained by reinforcement learning

Collective self-organization of animal groups is a recurring phenomenon in nature which has attracted a lot of attention in natural and social sciences. To understand how collective motion can be achieved without the presence of an external control, social interactions have been considered which regulate the motion and orientation of neighbors relative to each other. Here, we want to understand the motivation and possible reasons behind the emergence of such interaction rules using an experimental model system of light-responsive active colloidal particles (APs). Via reinforcement learning (RL), the motion of particles is optimized regarding their foraging behavior in presence of randomly appearing food sources. Although RL maximizes the rewards of single APs, we observe the emergence of collective behaviors within the particle group. The advantage of such collective strategy in context of foraging is to compensate lack of local information which strongly increases the robustness of the resulting policy. Our results demonstrate that collective behavior may not only result on the optimization of behaviors on the group level but may also arise from maximizing the benefit of individuals. Apart from a better understanding of collective behaviors in natural systems, these results may also be useful in context of the design of autonomous robotic systems.

Collective dynamics of dipolar self-propelled particles

We present a numerical study of the collective behavior of self-propelled particles for which dipolar interactions are considered. These are obtained by introducing pointlike magnetic dipoles in the particles. Various dynamical regimes are found depending on three major parameters: the density of particles, the ratio Γ defined as the competition between kinetic energy and potential magnetic energy, as well as the orientation of the magnetic dipoles inherent to the particles. Patterns such as chains, vortices, flocks, and strips have been obtained.

Dynamics and risk sharing in groups of selfish individuals

Understanding why animals organize in collective states is a central question of current research in, e.g., biology, physics, and psychology. More than 50 years ago, W.D. Hamilton postulated that the formation of animal herds may simply result from the individual's selfish motivation to minimize their predation risk. The latter is quantified by the domain of danger (DOD) which is given by the Voronoi area around each individual. In fact, simulations show that individuals aiming to reduce their DODs form compact groups similar to what is observed in many living systems. However, despite the apparent simplicity of this problem, it is not clear what motional strategy is required to find an optimal solution. Here, we use the framework of Multi Agent Reinforcement Learning (MARL) which gives the unbiased and optimal strategy of individuals to solve the selfish herd problem. We demonstrate that the motivation of individuals to reduce their predation risk naturally leads to pronounced collective behaviors including the formation of cohesive swirls. We reveal a previously unexplored rather complex intra-group motion which eventually leads to a evenly shared predation risk amongst selfish individuals.

Spontaneous vortex formation by microswimmers with retarded attractions

Collective states of inanimate particles self-assemble through physical interactions and thermal motion. Despite some phenomenological resemblance, including signatures of criticality, the autonomous dynamics that binds motile agents into flocks, herds, or swarms allows for much richer behavior. Low-dimensional models have hinted at the crucial role played in this respect by perceived information, decision-making, and feedback, implying that the corresponding interactions are inevitably retarded. Here we present experiments on spherical Brownian microswimmers with delayed self-propulsion toward a spatially fixed target. We observe a spontaneous symmetry breaking to a transiently chiral dynamical state and concomitant critical behavior that do not rely on many-particle cooperativity. By comparison with the stochastic delay differential equation of motion of a single swimmer, we pinpoint the delay-induced effective synchronization of the swimmers with their own past as the key mechanism. Increasing numbers of swimmers self-organize into layers with pro- and retrograde orbital motion, synchronized and stabilized by steric, phoretic, and hydrodynamic interactions. Our results demonstrate how even most simple retarded interactions can foster emergent complex adaptive behavior in small active-particle ensembles.

A fellow-following-principle based group model and its application to fish school analysis

Group models based on simple rules are viewed as a bridge to clarifying animal group movements. The more similar a model to real-world observations, the closer it is to the essence of such movements. Inspired by the fish school, this study suggests a principle called fellow-following for group movements. More specifically, a simple-rules-based model was proposed and extended into a set of concrete rules, and two- and three-dimensional group models were established. The model results are intuitively similar to the fish school, and when the group size increases, the milling phase of both the model and fish school tends from unstable to stable. Further, we proposed a novel order parameter and a similarity measurement framework for group structures. The proposed model indicates the intuition similarity, consistency of dynamic characteristics, and static structure similarity with fish schools, which suggests that the principle of fellow-following may reveal the essence of fish school movements. Our work suggests a different approach for the self-organized formation of a swarm robotic system based on local information.

Categories, Quantum Computing, and Swarm Robotics: A Case Study

The swarms of robots are examples of artificial collective intelligence, with simple individual autonomous behavior and emerging swarm effect to accomplish even complex tasks. Modeling approaches for robotic swarm development is one of the main challenges in this field of research. Here, we present a robot-instantiated theoretical framework and a quantitative worked-out example. Aiming to build up a general model, we first sketch a diagrammatic classification of swarms relating ideal swarms to existing implementations, inspired by category theory. Then, we propose a matrix representation to relate local and global behaviors in a swarm, with diagonal sub-matrices describing individual features and off-diagonal sub-matrices as pairwise interaction terms. Thus, we attempt to shape the structure of such an interaction term, using language and tools of quantum computing for a quantitative simulation of a toy model. We choose quantum computing because of its computational efficiency. This case study can shed light on potentialities of quantum computing in the realm of swarm robotics, leaving room for progressive enrichment and refinement.

Why Do Hens Pile? Hypothesizing the Causes and Consequences

Piling is a behavior in laying hens whereby individuals aggregate in larger densities than would be normally expected. When piling behavior leads to mortalities it is known as smothering and its frequent but unpredictable occurrence is a major concern for many egg producers. There are generally considered to be three types of piling: panic, nest box and recurring piling. Whilst nest box and panic piling have apparent triggers, recurring piling does not, making it an enigmatic and ethologically intriguing behavior. The repetitive nature of recurring piling may result in a higher incidence of smothering and could have unconsidered, sub-lethal consequences. Here, we consider the possible causes of recurring piling from an ethological perspective and outline the potential welfare and production consequences. Drawing on a wide range of literature, we consider different timescales of causes from immediate triggers to ontogeny and domestication processes, and finally consider the evolution of collective behavior. By considering different timescales of influence, we built four hypotheses relevant to the causes of piling, which state that the behavior: (i) is caused by hens moving toward or away from an attractant/repellent; (ii) is socially influenced; (iii) is influenced by early life experiences and; (iv) can be described as a maladaptive collective behavior. We further propose that the following could be welfare consequences of piling behavior: Heat stress, physical injury (such as keel bone damage), and behavioral and physiological stress effects. Production consequences include direct and indirect mortality (smothering and knock-on effects of piling, respectively), potential negative impacts on egg quality and on worker welfare. In future studies the causes of piling and smothering should be considered according to the different timescales on which causes might occur. Here, both epidemiological and modeling approaches could support further study of piling behavior, where empirical studies can be challenging.

Spatial structure arising from chase-escape interactions with crowding

Movement of individuals, mediated by localised interactions, plays a key role in numerous processes including cell biology and ecology. In this work, we investigate an individual-based model accounting for various intraspecies and interspecies interactions in a community consisting of two distinct species. In this framework we consider one species to be chasers and the other species to be escapees, and we focus on chase-escape dynamics where the chasers are biased to move towards the escapees, and the escapees are biased to move away from the chasers. This framework allows us to explore how individual-level directional interactions scale up to influence spatial structure at the macroscale. To focus exclusively on the role of motility and directional bias in determining spatial structure, we consider conservative communities where the number of individuals in each species remains constant. To provide additional information about the individual-based model, we also present a mathematically tractable deterministic approximation based on describing the evolution of the spatial moments. We explore how different features of interactions including interaction strength, spatial extent of interaction, and relative density of species influence the formation of the macroscale spatial patterns.

Analysis of aligning active local searchers orbiting around their common home position

We discuss effects of pairwise aligning interactions in an ensemble of central place foragers or of searchers that are connected to a common home. In a wider sense, we also consider self-moving entities that are attracted to a central place such as, for instance, the zooplankton Daphnia being attracted to a beam of light. Single foragers move with constant speed due to some propulsive mechanism. They explore at random loops the space around and return rhytmically to their home. In the ensemble, the direction of the velocity of a searcher is aligned to the motion of its neighbors. At first, we perform simulations of this ensemble and find a cooperative behavior of the entities. Above an overcritical interaction strength the trajectories of the searcher qualitatively changes and searchers start to move along circles around the home position. Thereby, all searchers rotate either clockwise or anticlockwise around the central home position as it was reported for the zooplankton Daphnia. At second, the computational findings are analytically explained by the formulation of transport equations outgoing from the nonlinear mean field Fokker-Planck equation of the considered situation. In the asymptotic stationary limit, we find expressions for the critical interaction strength, the mean radial and orbital velocities of the searchers and their velocity variances. We also obtain the marginal spatial and angular densities in the undercritical regime where the foragers behave like individuals as well as in the overcritical regime where they rotate collectively around the considered home. We additionally elaborate the overdamped Smoluchowski-limit for the ensemble.

Bottom-level motion control for robotic fish to swim in groups: modeling and experiments

Moving in groups is an amazing spectacle of collective behaviour in fish and has attracted considerable interest from many fields, including biology, physics and engineering. Although robotic fish have been well studied, including algorithms to simulate group swimming, experiments that demonstrate multiple robotic fish as a stable group are yet to be achieved. One of the challenges is the lack of a robust bottom-level motion control system for robotic fish platforms. Here we seek to overcome this challenge by focusing on the design and implementation of a motion controller for robotic fish that allows multiple individuals to swim in groups. As direction control is essential in motion control, we first propose a high-accuracy controller which can control a sub-carangiform robotic fish from one arbitrary position/pose (position and direction) to another. We then develop a hydrodynamic-model-based simulation platform to expedite the process of the parameter tuning of the controller. The accuracy of the simulation platform was assessed by comparing the results from experiments on a robotic fish using speeding and turning tests. Subsequently, extensive simulations and experiments with robotic fish were used to verify the accuracy and robustness of the bottom-level motion control. Finally, we demonstrate the efficacy of our controller by implementing group swimming using three robotic fish swimming freely in prescribed trajectories. Although the fluid environment can be complex during group swimming, our bottom-level motion control remained nominally accurate and robust. This motion control strategy lays a solid foundation for further studies of group swimming with multiple robotic fish.

Methods for the effective study of collective behavior in a radial arm maze

Collective behaviors are observed throughout nature, from bacterial colonies to human societies. Important theoretical breakthroughs have recently been made in understanding why animals produce group behaviors and how they coordinate their activities, build collective structures, and make decisions. However, standardized experimental methods to test these findings have been lacking. Notably, easily and unambiguously determining the membership of a group and the responses of an individual within that group is still a challenge. The radial arm maze is presented here as a new standardized method to investigate collective exploration and decision-making in animal groups. This paradigm gives individuals within animal groups the opportunity to make choices among a set of discrete alternatives, and these choices can easily be tracked over long periods of time. We demonstrate the usefulness of this paradigm by performing a set of refuge-site selection experiments with groups of fish. Using an open-source, robust custom image-processing algorithm, we automatically counted the number of animals in each arm of the maze to identify the majority choice. We also propose a new index to quantify the degree of group cohesion in this context. The radial arm maze paradigm provides an easy way to categorize and quantify the choices made by animals. It makes it possible to readily apply the traditional uses of the radial arm maze with single animals to the study of animal groups. Moreover, it opens up the possibility of studying questions specifically related to collective behaviors.

On-board communication-based relative localization for collision avoidance in Micro Air Vehicle teams

To avoid collisions, Micro Air Vehicles (MAVs) flying in teams require estimates of their relative locations, preferably with minimal mass and processing burden. We present a relative localization method where MAVs need only to communicate with each other using their wireless transceiver. The MAVs exchange on-board states (velocity, height, orientation) while the signal strength indicates range. Fusing these quantities provides a relative location estimate. We used this for collision avoidance in tight areas, testing with up to three AR.Drones in a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\,\mathrm{m}~\mathbf {\times }~4\,\mathrm{m}$$\end{document}4m×4m area and with two miniature drones (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx 50\,\mathrm{g}$$\end{document}≈50g) in a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2~\mathrm{m}~\mathbf {\times }~2~\mathrm{m}$$\end{document}2m×2m area. The MAVs could localize each other and fly several minutes without collisions. In our implementation, MAVs communicated using Bluetooth antennas. The results were robust to the high noise and disturbances in signal strength. They could improve further by using transceivers with more accurate signal strength readings.