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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.

Bacterial swarming is a collective mode of motion in which cells migrate rapidly over surfaces, forming dynamic patterns of whirls and jets. This review presents a physical point of view of swarming bacteria, with an emphasis on the statistical properties of the swarm dynamics as observed in experiments. The basic physical principles underlying the swarm and their relation to contemporary theories of collective motion and active matter are reviewed and discussed in the context of the biological properties of swarming cells. We suggest a paradigm according to which bacteria have optimized some of their physical properties as a strategy for rapid surface translocation. In other words, cells take advantage of favorable physics, enabling efficient expansion that enhances survival under harsh conditions.

One of the hallmarks of the collective movement of large schools of pelagic fish are waves of shimmering flashes that propagate across the school, usually following an attack by a predator. Such flashes arise when sunlight is reflected off the specular (mirror-like) skin that characterizes many pelagic fishes, where it is otherwise thought to offer a means for camouflage in open waters. While it has been suggested that these ‘shimmering waves’ are a visual manifestation of the synchronized escape response of the fish, the phenomenon has been regarded only as an artifact of esthetic curiosity. In this study we apply agent-based simulations and deep learning techniques to show that, in fact, shimmering waves contain information on the behavioral dynamics of the school. Our analyses are based on a model that combines basic rules of collective motion and the propagation of light beams in the ocean, as they hit and reflect off the moving fish. We use the resulting reflection patterns to infer the essential dynamics and inter-individual interactions which are necessary to generate shimmering waves. Moreover, we show that light flashes observed by the school members themselves may extend the range at which information can be communicated across the school. Assuming that fish pay heed to this information, for example by entering an apprehensive state of reduced response-time, our analysis suggests that it can speed up the propagation of information across the school. Further still, we use an artificial neural network to show that light flashes are, on their own, indicative of the state and dynamics of the school, and are sufficient to infer the direction of attack and the shape of the school with high accuracy.

Meso-scale turbulence was originally observed experimentally in various suspensions of swimming bacteria, as well as in the collective motion of active colloids. The corresponding large scale dynamical patterns were reproduced in a simple model of a polar fluid, assuming a constant density of active particles. Recent, more detailed studies in a variety of experimental realizations of active polar fluids revealed additional interesting aspects, such as anomalous velocity statistics and clustering phenomena. Those phenomena cannot be explained by currently available models for active polar fluids. Herein, we extend the continuum model suggested by Dunkel et al to include density variations and a local feedback between the local density and self-propulsion speed of the active polar particles. If the velocity decreases strong enough with the density, a linear stability analysis of the resulting model shows that, in addition to the short-wavelength instability of the original model, a long-wavelength instability occurs. This is typically observed for high densities of polar active particles and is analogous to the well-known phenomenon of motility-induced phase separation (MIPS) in scalar active matter. We determine a simple phase diagram indicating the linear instabilities and perform systematic numerical simulations for the various regions in the corresponding parameter space. The interplay between the well understood short-range instability (leading to meso-scale turbulence) and the long-range instability (associated with MIPS) leads to interesting dynamics and novel phenomena concerning nucleation and coarsening processes. Our simulation results display a rich variety of novel patterns, including phase separation into domains with dynamically changing irregularly shaped boundaries. Anomalous velocity statistics are observed in all phases where the system segregates into regions of high and low densities. This offers a simple explanation for their occurrence in recent experiments with bacterial suspensions.

Individual swimming bacteria are known to bias their random trajectories in search of food and to optimize survival. The motion of bacteria within a swarm, wherein they migrate as a collective group over a solid surface, is fundamentally different as typical bacterial swarms show large-scale swirling and streaming motions involving millions to billions of cells. Here by tracking trajectories of fluorescently labelled individuals within such dense swarms, we find that the bacteria are performing super-diffusion, consistent with Lévy walks. Lévy walks are characterized by trajectories that have straight stretches for extended lengths whose variance is infinite. The evidence of super-diffusion consistent with Lévy walks in bacteria suggests that this strategy may have evolved considerably earlier than previously thought. Lévy walks have been found in the motion of large animals such as birds and fish in search of sparsely and randomly distributed food. Here, Ariel et al . observe, by tracking long-duration trajectories of fluorescently labelled bacteria, similar walks in bacterial swarms for the first time.

A large variety of motile bacterial species exhibit collective motions while inhabiting liquids or colonizing surfaces. These collective motions are often characterized by coherent dynamic clusters, where hundreds of cells move in correlated whirls and jets. Previously, all species that were known to form such motion had a rod-shaped structure, which enhances the order through steric and hydrodynamic interactions. Here we show that the spherical motile bacteria Serratia marcescens exhibit robust collective dynamics and correlated coherent motion while grown in suspensions. As cells migrate to the upper surface of a drop, they form a monolayer, and move collectively in whirls and jets. At all concentrations, the distribution of the bacterial speed was approximately Rayleigh with an average that depends on concentration in a non-monotonic way. Other dynamical parameters such as vorticity and correlation functions are also analyzed and compared to rod-shaped bacteria from the same strain. Our results demonstrate that self-propelled spherical objects do form complex ordered collective motion. This opens a door for a new perspective on the role of cell aspect ratio and alignment of cells with regards to collective motion in nature.

Recent experiments with the bacteria Paenibacillus vortex reveal a remarkable strategy enabling it to cope with antibiotics by cooperating with a different bacterium-Escherichia coli. While P. vortex is a highly effective swarmer, it is sensitive to the antibiotic ampicillin. On the other hand, E. coli can degrade ampicillin but is non-motile when grown on high agar percentages. The two bacterial species form a shared colony in which E. coli is transported by P. vortex and E. coli detoxifies the ampicillin. The paper presents a simplified model, consisting of coupled reaction-diffusion equations, describing the development of ring patterns in the shared colony. Our results demonstrate some of the possible cooperative movement strategies bacteria utilize in order to survive harsh conditions. In addition, we explore the behavior of mixed colonies under new conditions such as antibiotic gradients, synchronization between colonies and possible dynamics of a 3-species system including P. vortex, E. coli and a carbon producing algae that provides nutrients under illuminated, nutrient poor conditions. The derived model was able to simulate an asymmetric relationship between two or three micro-organisms where cooperation is required for survival. Computationally, in order to avoid numerical artifacts due to symmetries within the discretizing grid, the model was solved using a second order Vectorizable Random Lattices method, which is developed as a finite volume scheme on a random grid.

Bacterial swarming is a rapid mass-migration, in which thousands of cells spread collectively to colonize surfaces. Physically, swarming is a natural example for active particles that use energy to generate motion. Accordingly, understanding the constraints physics imposes on these dynamics is essential for understanding the mechanisms underlying swarming. We present new experiments of swarming Bacillus subtilis mutants with different aspect ratios and at different densities; two physical quantities known to be associated with collective behavior. Analyzing the dynamics reveals a rich phase diagram of qualitatively distinct swarming regimes, describing how cell shape and population density govern the dynamical characteristics of the swarm. In particular, we show that under standard conditions, bacteria inhabit a region of phase space that is associated with rapid mixing and robust dynamics, with homogeneous density and no preferred direction of motion. The results suggest that bacteria have adapted their physical properties to optimize the principle functions assumed for swarming. Swarming is a ubiquitous behaviour in living systems, emerging from local interactions. Here, the authors exploit genetic mutations to experimentally characterize how distinct swarming phases of Bacillus subtilis emerge as a function of the shape and density of these bacteria.

The principal interactions leading to the emergence of order in swarms of marching locust nymphs was studied both experimentally, using small groups of marching locusts in the lab, and using computer simulations. We utilized a custom tracking algorithm to reveal fundamental animal-animal interactions leading to collective motion. Uncovering this behavior introduced a new agent-based modeling approach in which pause-and-go motion is pivotal. The behavioral and modeling findings are largely based on motion-related visual sensory inputs obtained by the individual locust. Results suggest a generic principle, in which intermittent animal motion can be considered as a sequence of individual decisions as animals repeatedly reassess their situation and decide whether or not to swarm. This interpretation implies, among other things, some generic characteristics regarding the build-up and emergence of collective order in swarms: in particular, that order and disorder are generic meta-stable states of the system, suggesting that the emergence of order is kinetic and does not necessarily require external environmental changes. This work calls for further experimental as well as theoretical investigation of the neural mechanisms underlying locust coordinative behavior.

A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of marginal distributions and joint dependency, also known as the copula. The entropy of marginals is estimated using one-dimensional methods. The entropy of the copula, which always has a compact support, is estimated recursively by splitting the data along statistically dependent dimensions. The method can be applied both for distributions with compact and non-compact supports, which is imperative when the support is not known or of a mixed type (in different dimensions). At high dimensions (larger than 20), numerical examples demonstrate that our method is not only more accurate, but also significantly more efficient than existing approaches.