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A fundamental question in complex systems is how to relate interactions between individual components ("microscopic description") to the global properties of the system ("macroscopic description"). Another fundamental question is whether such a macroscopic description exists at all and how well it describes the large-scale properties. Here, we address these questions using as a canonical example of a self-organizing complex system - the collective motion of desert locusts. One of the world's most devastating insect plagues begins when flightless juvenile locusts form "marching bands". Moving through semiarid habitats in the search for food, these bands display remarkable coordinated motion. We investigated how well physical models can describe the flow of locusts within a band. For this, we filmed locusts within marching bands during an outbreak in Kenya and automatically tracked all individuals passing through the camera frame. We first analysed the spatial topology of nearest neighbors and found individuals to be isotropically distributed. Despite this apparent randomness, a local order was observed in regions of high density with a clear second neighbor peak in the radial distribution function, akin to an ordered fluid. Furthermore, reconstructing individual locust trajectories revealed a highly-aligned movement, consistent with the one-dimensional version of the Toner-Tu equations, which are a generalization of the Navier-Stokes equations for fluids, used to describe the equivalent macroscopic fluid properties of active particles. Using this effective Toner-Tu equation, which relates the gradient of the pressure to the acceleration, we show that the effective "pressure" of locusts increases as a linear function of density in segments with highest polarization. Our study thus demonstrates an effective hydrodynamic description of flow dynamics in plague locust swarms., Comment: 21 pages, 13 figures

Markerless methods for animal posture tracking have been rapidly developing recently, but frameworks and benchmarks for tracking large animal groups in 3D are still lacking. To overcome this gap in the literature, we present 3D-MuPPET, a framework to estimate and track 3D poses of up to 10 pigeons at interactive speed using multiple camera views. We train a pose estimator to infer 2D keypoints and bounding boxes of multiple pigeons, then triangulate the keypoints to 3D. For identity matching of individuals in all views, we first dynamically match 2D detections to global identities in the first frame, then use a 2D tracker to maintain IDs across views in subsequent frames. We achieve comparable accuracy to a state of the art 3D pose estimator in terms of median error and Percentage of Correct Keypoints. Additionally, we benchmark the inference speed of 3D-MuPPET, with up to 9.45 fps in 2D and 1.89 fps in 3D, and perform quantitative tracking evaluation, which yields encouraging results. Finally, we showcase two novel applications for 3D-MuPPET. First, we train a model with data of single pigeons and achieve comparable results in 2D and 3D posture estimation for up to 5 pigeons. Second, we show that 3D-MuPPET also works in outdoors without additional annotations from natural environments. Both use cases simplify the domain shift to new species and environments, largely reducing annotation effort needed for 3D posture tracking. To the best of our knowledge we are the first to present a framework for 2D/3D animal posture and trajectory tracking that works in both indoor and outdoor environments for up to 10 individuals. We hope that the framework can open up new opportunities in studying animal collective behaviour and encourages further developments in 3D multi-animal posture tracking.

Collective motion is ubiquitous in nature; groups of animals, such as fish, birds, and ungulates appear to move as a whole, exhibiting a rich behavioral repertoire that ranges from directed movement to milling to disordered swarming. Typically, such macroscopic patterns arise from decentralized, local interactions among constituent components (e.g., individual fish in a school). Preeminent models of this process describe individuals as self-propelled particles, subject to self-generated motion and 'social forces' such as short-range repulsion and long-range attraction or alignment. However, organisms are not particles; they are probabilistic decision-makers. Here, we introduce an approach to modelling collective behavior based on active inference. This cognitive framework casts behavior as the consequence of a single imperative: to minimize surprise. We demonstrate that many empirically-observed collective phenomena, including cohesion, milling and directed motion, emerge naturally when considering behavior as driven by active Bayesian inference -- without explicitly building behavioral rules or goals into individual agents. Furthermore, we show that active inference can recover and generalize the classical notion of social forces as agents attempt to suppress prediction errors that conflict with their expectations. By exploring the parameter space of the belief-based model, we reveal non-trivial relationships between the individual beliefs and group properties like polarization and the tendency to visit different collective states. We also explore how individual beliefs about uncertainty determine collective decision-making accuracy. Finally, we show how agents can update their generative model over time, resulting in groups that are collectively more sensitive to external fluctuations and encode information more robustly., Comment: 29 pages (main text), 29 pages (supplemental appendices), 4 figures, 1 supplemental figure, 5 movies

Animals must constantly make decisions on the move, such as when choosing among multiple options, or "targets", in space. Recent evidence suggests that this results from a recursive feedback between the (vectorial) neural representation of the targets and the resulting motion defined by this consensus, which then changes the egocentric neural representation of the the options, and so on. Here we employ a simple model of this process to both explore how its dynamics account for the experimentally-observed abruptly-branching trajectories exhibited by animals during spatial decision-making, and to provide new insights into spatiotemporal computation. Essential neural dynamics, notably local excitation and long-range inhibition, are captured in our model via spin-system dynamics, with groups of Ising-spins representing neural "activity bumps" corresponding to target directions. Analysis, employing a novel "mean-field trajectory" approach, reveals the nature of the spontaneous symmetry breaking - bifurcations in the model that result in literal bifurcations in trajectory space and how it results in new geometric principles for spatiotemporal decision-making. We find that all bifurcation points, beyond the very first, fall on a small number of "bifurcation curves". It is the spatial organization of these curves that is shown to be key to determining the shape of the trajectories, such as self-similar or space filling, exhibited during decision-making, irrespective of the trajectory's starting point. Furthermore, we find that a non-Euclidean representation of space considerably reduces the number of bifurcation points in many geometrical configurations, preventing endless indecision and promoting effective spatial decision-making. This suggests that a non-Euclidean neural representation of space may be expected to have evolved across species in order to facilitate spatial decision-making., Comment: 19 pages, 10 figures

Recent advances in machine learning and computer vision are revolutionizing the field of animal behavior by enabling researchers to track the poses and locations of freely moving animals without any marker attachment. However, large datasets of annotated images of animals for markerless pose tracking, especially high-resolution images taken from multiple angles with accurate 3D annotations, are still scant. Here, we propose a method that uses a motion capture (mo-cap) system to obtain a large amount of annotated data on animal movement and posture (2D and 3D) in a semi-automatic manner. Our method is novel in that it extracts the 3D positions of morphological keypoints (e.g eyes, beak, tail) in reference to the positions of markers attached to the animals. Using this method, we obtained, and offer here, a new dataset - 3D-POP with approximately 300k annotated frames (4 million instances) in the form of videos having groups of one to ten freely moving birds from 4 different camera views in a 3.6m x 4.2m area. 3D-POP is the first dataset of flocking birds with accurate keypoint annotations in 2D and 3D along with bounding box and individual identities and will facilitate the development of solutions for problems of 2D to 3D markerless pose, trajectory tracking, and identification in birds.

While moving, animals must frequently make decisions about their future travel direction, whether they are alone or in a group. Here we investigate this process for zebrafish (Danio rerio), which naturally move in cohesive groups. Employing state-of-the-art virtual reality, we study how real fish follow one or several moving, virtual conspecifics. These data are used to inform, and test, a model of social response that includes a process of explicit decision-making, whereby the fish can decide which of the virtual conspecifics to follow, or to follow some average direction. This approach is in contrast with previous models where the direction of motion was based on a continuous computation, such as directional averaging. Building upon a simplified version of this model [Sridhar et al. 2021], which was limited to a one-dimensional projection of the fish motion, we present here a model that describes the motion of the real fish as it swims freely in two-dimensions. Motivated by experimental observations, the swim speed of the fish in this model uses a burst-and-coast swimming pattern, with the burst frequency being dependent on the distance of the fish from the followed conspecific(s). We demonstrate that this model is able to explain the observed spatial distribution of the real fish behind the virtual conspecifics in the experiments. In particular, the model naturally explains the observed critical bifurcations for a freely swimming fish, whenever the fish makes a decision to follow only one of the virtual conspecifics, instead of following them as an averaged group. This model can provide the foundation for modeling a cohesive shoal of swimming fish, while explicitly describing their directional decision-making process at the individual level, Comment: 32 pages,22 figures (6 in the main text), supplementary material link https://drive.google.com/drive/folders/1H76yOawtv9zuou84VY2HrxOjO-2jXu-w?usp=sharing

Active inference is an account of cognition and behavior in complex systems which brings together action, perception, and learning under the theoretical mantle of Bayesian inference. Active inference has seen growing applications in academic research, especially in fields that seek to model human or animal behavior. While in recent years, some of the code arising from the active inference literature has been written in open source languages like Python and Julia, to-date, the most popular software for simulating active inference agents is the DEM toolbox of SPM, a MATLAB library originally developed for the statistical analysis and modelling of neuroimaging data. Increasing interest in active inference, manifested both in terms of sheer number as well as diversifying applications across scientific disciplines, has thus created a need for generic, widely-available, and user-friendly code for simulating active inference in open-source scientific computing languages like Python. The Python package we present here, pymdp (see https://github.com/infer-actively/pymdp), represents a significant step in this direction: namely, we provide the first open-source package for simulating active inference with partially-observable Markov Decision Processes or POMDPs. We review the package's structure and explain its advantages like modular design and customizability, while providing in-text code blocks along the way to demonstrate how it can be used to build and run active inference processes with ease. We developed pymdp to increase the accessibility and exposure of the active inference framework to researchers, engineers, and developers with diverse disciplinary backgrounds. In the spirit of open-source software, we also hope that it spurs new innovation, development, and collaboration in the growing active inference community.

Data acquisition in animal ecology is rapidly accelerating due to inexpensive and accessible sensors such as smartphones, drones, satellites, audio recorders and bio-logging devices. These new technologies and the data they generate hold great potential for large-scale environmental monitoring and understanding, but are limited by current data processing approaches which are inefficient in how they ingest, digest, and distill data into relevant information. We argue that machine learning, and especially deep learning approaches, can meet this analytic challenge to enhance our understanding, monitoring capacity, and conservation of wildlife species. Incorporating machine learning into ecological workflows could improve inputs for population and behavior models and eventually lead to integrated hybrid modeling tools, with ecological models acting as constraints for machine learning models and the latter providing data-supported insights. In essence, by combining new machine learning approaches with ecological domain knowledge, animal ecologists can capitalize on the abundance of data generated by modern sensor technologies in order to reliably estimate population abundances, study animal behavior and mitigate human/wildlife conflicts. To succeed, this approach will require close collaboration and cross-disciplinary education between the computer science and animal ecology communities in order to ensure the quality of machine learning approaches and train a new generation of data scientists in ecology and conservation.

Living systems such as neuronal networks and animal groups process information about their environment via the dynamics of interacting units. These can transition between distinct macroscopic behaviors. Near such a transition (or critical point) collective computation is generally thought to be optimized, due to the associated maximal sensitivity to perturbations and fast dissemination of information. For biological systems, however, optimality depends on environmental context, making the flexible, context-dependent adoption of different distances to a critical point potentially more beneficial than its unique properties. Here, studying escape waves in schooling fish at two levels of perceived environmental risk, we investigate a) if and how distance to criticality is regulated in response to environmental changes and b) how the individual level benefits derived from special properties of the critical point compare to those achieved via regulation of the group's distance to it. We find that the observed fish schools are subcritical (not maximally responsive and sensitive to environmental cues), but decrease their distance to criticality with increased perceived risk. Considering an individual's hypothetical costs of two detection error types, we find that optimal distance to criticality depends on the riskiness and noisiness of the environment, which may explain the observed behavior. Our results highlight the benefit of evaluating biological consequences of different distances to criticality for individuals within animal collectives. This provides insights into the adaptive function of a collective system and motivates future questions about the evolutionary forces that brought the system to make this particular trade-off.

The core idea in an XR (VR/MR/AR) application is to digitally stimulate one or more sensory systems (e.g. visual, auditory, olfactory) of the human user in an interactive way to achieve an immersive experience. Since the early 2000s biologists have been using Virtual Environments (VE) to investigate the mechanisms of behavior in non-human animals including insect, fish, and mammals. VEs have become reliable tools for studying vision, cognition, and sensory-motor control in animals. In turn, the knowledge gained from studying such behaviors can be harnessed by researchers designing biologically inspired robots, smart sensors, and multi-agent artificial intelligence. VE for animals is becoming a widely used application of XR technology but such applications have not previously been reported in the technical literature related to XR. Biologists and computer scientists can benefit greatly from deepening interdisciplinary research in this emerging field and together we can develop new methods for conducting fundamental research in behavioral sciences and engineering. To support our argument we present this review which provides an overview of animal behavior experiments conducted in virtual environments., Comment: Conditional acceptance in IEEE TVCG

Soaring migrants exploit columns of rising air (thermals) to cover large distances with minimal energy. Employing social information while locating thermals may be beneficial, but examining collective movements in wild migrants has been a major challenge. We investigated the group movements of a flock of 27 naturally migrating, juvenile white storks using high-resolution GPS and accelerometers. Analyzing individual and group movements on multiple scales reveals that birds ahead navigate to and explore thermals, while followers benefit from their movements. Despite this benefit, followers often leave thermals earlier and at lower height, and consequently must flap considerably more. Followers also migrated less far annually than did leaders. We provide insights into the interactions between freely-flying social migrants and the costs and benefits of collective movement in natural populations., Comment: The first two authors contributed equally to this work. 9 pages, 4 figures

Collective motion of cells is critical to some of the most vital tasks including wound healing, development, and immune response [Friedl and Gilmour 2009; Tokarski et al. 2012; Lee et al. 2012; Beltman et al. 2009], and is common to many pathological processes including cancer cell invasion and teratogenesis [Khalil and Friedl 2010]. The extensive understanding of movement by single cells [R{\o}rth 2011; Insall and Machesky 2011; Houk et al. 2012] is insufficient to predict the behavior of cellular groups [Theveneau et al. 2013; Trepat, X. and Fredberg 2011], and identifying underlying rules of coordination in collective cell migration is still evasive. Few of the supposed benefits of collective motion have ever been tested at the cellular scale. As an example, though collective sensing allows for larger groups to exhibit greater accuracy in navigation [Simons 2004; Berdahl et al. 2013] and group taxis is possible through the leadership of only a few individuals [Couzin et al. 2005], such effects have never been investigated in collective cell migration. We will investigate collective motion and decision-making in a primitive multicellular animal, Trichoplax adhaerens to understand how intercellular coordination affects animal behavior and how migration accuracy scales with cellular group size.

Understanding the organization of collective motion in biological systems is an ongoing challenge. In this Paper we consider a minimal model of self-propelled particles with variable speed. Inspired by experimental data from schooling fish, we introduce a power-law dependency of the speed of each particle on the degree of polarization order in its neighborhood. We derive analytically a coarse-grained continuous approximation for this model and find that, while the variable speed rule does not change the details of the ordering transition leading to collective motion, it induces an inverse power-law correlation between the speed or the local polarization order and the local density. Using numerical simulations, we verify the range of validity of this continuous description and explore regimes beyond it. We discover, in disordered states close to the transition, a phase-segregated regime where most particles cluster into almost static groups surrounded by isolated high-speed particles. We argue that the mechanism responsible for this regime could be present in a wide range of collective motion dynamics., Comment: 12 pages, 9 figures

We obtain a Fokker-Planck equation describing experimental data on the collective motion of locusts. The noise is of internal origin and due to the discrete character and finite number of constituents of the swarm. The stationary probability distribution shows a rich phenomenology including non-monotonic behavior of several order/disorder transition indicators in noise intensity. This complex behavior arises naturally as a result of the randomness in the system. Its counterintuitive character challenges standard interpretations of noise induced transitions and calls for an extension of this theory in order to capture the behavior of certain classes of biologically motivated models. Our results suggest that the collective switches of the group's direction of motion might be due to a random ergodic effect and, as such, they are inherent to group formation., Comment: Physical Review Focus 26, July 2010

Locating the source of an advected chemical signal is a common challenge facing many living organisms. When the advecting medium is characterized by either high Reynolds number or high Peclet number the task becomes highly non-trivial due to the generation of heterogenous, dynamically changing filamental concentrations which do not decrease monotonically with distance to the source. Defining search strategies which are effective in these environments has important implications for the understanding of animal behavior and for the design of biologically inspired technology. Here we present a strategy which is able to solve this task without the higher intelligence required to assess spatial gradient direction, measure the diffusive properties of the flow field or perform complex calculations. Instead our method is based on the collective behavior of autonomous individuals following simple social interaction rules which are modified according to the local conditions they are experiencing. Through these context-dependent interactions the group is able to locate the source of a chemical signal and in doing so displays an awareness of the environment not present at the individual level. Our model demonstrates the ability of decentralized information processing systems to solve real world problems and also illustrates an alternative pathway to the evolution of higher cognitive capacity via the emergent, group level intelligence which can result from local interactions., Comment: 3 figures

Recent studies suggest that non-cooperative behavior such as cannibalism may also be a driving mechanism of collective motion. Motivated by these novel results we introduce a simple model of Brownian particles interacting by pursuit and escape interactions. We show the onset of collective motion due to escape and pursuit response of individuals and demonstrate how experimentally accessible macroscopic observables depend strongly on the ratio of the escape and pursuit strength. We analyze the different impact of the escape and pursuit response on the motion statistics and determine the scaling of the migration speed with model parameters.