Determining asymptotically large population sizes in insect swarms

Social animals commonly form aggregates that exhibit emergent collective behaviour, with group dynamics that are distinct from the behaviour of individuals. Simple models can qualitatively reproduce such behaviour, but only with large numbers of individuals. But how rapidly do the collective properties of animal aggregations in nature emerge with group size? Here, we study swarms of Chironomus riparius midges and measure how their statistical properties change as a function of the number of participating individuals. Once the swarms contain order 10 individuals, we find that all statistics saturate and the swarms enter an asymptotic regime. The influence of environmental cues on the swarm morphology decays on a similar scale. Our results provide a strong constraint on how rapidly swarm models must produce collective states. But our findings support the feasibility of using swarms as a design template for multi-agent systems, because self-organized states are possible even with few agents.     

The feeding dynamics of broiler chickens

Contrary to a commonly held belief that broiler chickens need more space, there is increasing evidence that these birds are attracted to other birds. Indeed, commercially farmed birds exhibit a range of socially facilitated behaviours, such as increased feeding and preening in response to the presence of other birds. Social facilitation can generate feedback loops, whereby the adoption of a particular behaviour can spread rapidly and suddenly through the population. Here, by measuring the rate at which broiler chickens join and leave a feeding trough as a function of the number of birds already there, we quantify social facilitation. We use these measurements to parameterize a simulation model of chicken feeding behaviour. This model predicts, and further observations of broiler chickens confirm, that social facilitation leads to excitatory and synchronized patterns of group feeding. Such models could prove a powerful tool in understanding how feeding patterns depend on broiler house design.     

A model comparison reveals dynamic social information drives the movements of humbug damselfish (Dascyllus aruanus)

Animals make use a range of social information to inform their movement decisions. One common movement rule, found across many different species, is that the probability that an individual moves to an area increases with the number of conspecifics there. However, in many cases, it remains unclear what social cues produce this and other similar movement rules. Here, we investigate what cues are used by damselfish (Dascyllus aruanus) when repeatedly crossing back and forth between two coral patches in an experimental arena. We find that an individual''s decision to move is best predicted by the recent movements of conspecifics either to or from that individual''s current habitat. Rather than actively seeking attachment to a larger group, individuals are instead prioritizing highly local and dynamic information with very limited spatial and temporal ranges. By reanalysing data in which the same species crossed for the first time to a new coral patch, we show that the individuals use static cues in this case. This suggests that these fish alter their information usage according to the structure and familiarity of their environment by using stable information when moving to a novel area and localized dynamic information when moving between familiar areas.     

Social information use and the evolution of unresponsiveness in collective systems

Animal groups in nature often display an enhanced collective information-processing capacity. It has been speculated that natural selection will tune this response to be optimal, ensuring that the group is reactive while also being robust to noise. Here, we show that this is unlikely to be the case. By using a simple model of decision-making in a dynamic environment, we find that when individuals behave rationally and are subject to selection based on their accuracy, optimality of collective decision-making is not attained. Instead, individuals overly rely on social information and evolve to be too readily influenced by their neighbours. This is due to a classic evolutionary conflict between individual and collective interest. The result is a sub-optimal system that is poised on the cusp of total unresponsiveness. Individuals in the evolved group exhibit delayed reactions to changes in the environment, before responding with rapid, socially reinforced transitions, reminiscent of familiar human and animal social systems (markets, stampedes, fashions, etc.). Our results demonstrate that behaviour of this type may not be pathological, but instead could represent an evolutionary attractor for such collective systems.     

Interaction rules underlying group decisions in homing pigeons

Travelling in groups gives animals opportunities to share route information by following cues from each other''s movement. The outcome of group navigation will depend on how individuals respond to each other within a flock, school, swarm or herd. Despite the abundance of modelling studies, only recently have researchers developed techniques to determine the interaction rules among real animals. Here, we use high-resolution GPS (global positioning system) tracking to study these interactions in pairs of pigeons flying home from a familiar site. Momentary changes in velocity indicate alignment with the neighbour''s direction, as well as attraction or avoidance depending on distance. Responses were stronger when the neighbour was in front. From the flocking behaviour, we develop a model to predict features of group navigation. Specifically, we show that the interactions between pigeons stabilize a side-by-side configuration, promoting bidirectional information transfer and reducing the risk of separation. However, if one bird gets in front it will lead directional choices. Our model further predicts, and observations confirm, that a faster bird (as measured from solo flights) will fly slightly in front and thus dominate the choice of homing route. Our results explain how group decisions emerge from individual differences in homing flight behaviour.     

Emergence of collective changes in travel direction of starling flocks from individual birds' fluctuations

One of the most impressive features of moving animal groups is their ability to perform sudden coherent changes in travel direction. While this collective decision can be a response to an external alarm cue, directional switching can also emerge from the intrinsic fluctuations in individual behaviour. However, the cause and the mechanism by which such collective changes of direction occur are not fully understood yet. Here, we present an experimental study of spontaneous collective turns in natural flocks of starlings. We employ a recently developed tracking algorithm to reconstruct three-dimensional trajectories of each individual bird in the flock for the whole duration of a turning event. Our approach enables us to analyse changes in the individual behaviour of every group member and reveal the emergent dynamics of turning. We show that spontaneous turns start from individuals located at the elongated tips of the flocks, and then propagate through the group. We find that birds on the tips deviate from the mean direction of motion much more frequently than other individuals, indicating that persistent localized fluctuations are the crucial ingredient for triggering a collective directional change. Finally, we quantitatively verify that birds follow equal-radius paths during turning, the effects of which are a change of the flock''s orientation and a redistribution of individual locations in the group.     

Collective sensing and collective responses in quorum-sensing bacteria

Bacteria often face fluctuating environments, and in response many species have evolved complex decision-making mechanisms to match their behaviour to the prevailing conditions. Some environmental cues provide direct and reliable information (such as nutrient concentrations) and can be responded to individually. Other environmental parameters are harder to infer and require a collective mechanism of sensing. In addition, some environmental challenges are best faced by a group of cells rather than an individual. In this review, we discuss how bacteria sense and overcome environmental challenges as a group using collective mechanisms of sensing, known as ‘quorum sensing’ (QS). QS is characterized by the release and detection of small molecules, potentially allowing individuals to infer environmental parameters such as density and mass transfer. While a great deal of the molecular mechanisms of QS have been described, there is still controversy over its functional role. We discuss what QS senses and how, what it controls and why, and how social dilemmas shape its evolution. Finally, there is a growing focus on the use of QS inhibitors as antibacterial chemotherapy. We discuss the claim that such a strategy could overcome the evolution of resistance. By linking existing theoretical approaches to data, we hope this review will spur greater collaboration between experimental and theoretical researchers.     

Collective response to perturbations in a data-driven fish school model

Fish schools are able to display a rich variety of collective states and behavioural responses when they are confronted by threats. However, a school''s response to perturbations may be different depending on the nature of its collective state. Here we use a previously developed data-driven fish school model to investigate how the school responds to perturbations depending on its different collective states, we measure its susceptibility to such perturbations, and exploit its relation with the intrinsic fluctuations in the school. In particular, we study how a single or a small number of perturbing individuals whose attraction and alignment parameters are different from those of the main population affect the long-term behaviour of a school. We find that the responsiveness of the school to the perturbations is maximum near the transition region between milling and schooling states where the school exhibits multistability and regularly shifts between these two states. It is also in this region that the susceptibility, and hence the fluctuations, of the polarization order parameter is maximal. We also find that a significant school''s response to a perturbation only happens below a certain threshold of the noise to social interactions ratio.     

Fish and robots swimming together: attraction towards the robot demands biomimetic locomotion

The integration of biomimetic robots in a fish school may enable a better understanding of collective behaviour, offering a new experimental method to test group feedback in response to behavioural modulations of its ‘engineered’ member. Here, we analyse a robotic fish and individual golden shiners (Notemigonus crysoleucas) swimming together in a water tunnel at different flow velocities. We determine the positional preference of fish with respect to the robot, and we study the flow structure using a digital particle image velocimetry system. We find that biomimetic locomotion is a determinant of fish preference as fish are more attracted towards the robot when its tail is beating rather than when it is statically immersed in the water as a ‘dummy’. At specific conditions, the fish hold station behind the robot, which may be due to the hydrodynamic advantage obtained by swimming in the robot''s wake. This work makes a compelling case for the need of biomimetic locomotion in promoting robot–animal interactions and it strengthens the hypothesis that biomimetic robots can be used to study and modulate collective animal behaviour.     

Automated,contour-based tracking and analysis of cell behaviour over long time scales in environments of varying complexity and cell density

Understanding single and collective cell motility in model environments is foundational to many current research efforts in biology and bioengineering. To elucidate subtle differences in cell behaviour despite cell-to-cell variability, we introduce an algorithm for tracking large numbers of cells for long time periods and present a set of physics-based metrics that quantify differences in cell trajectories. Our algorithm, termed automated contour-based tracking for in vitro environments (ACTIVE), was designed for adherent cell populations subject to nuclear staining or transfection. ACTIVE is distinct from existing tracking software because it accommodates both variability in image intensity and multi-cell interactions, such as divisions and occlusions. When applied to low-contrast images from live-cell experiments, ACTIVE reduced error in analysing cell occlusion events by as much as 43% compared with a benchmark-tracking program while simultaneously tracking cell divisions and resulting daughter–daughter cell relationships. The large dataset generated by ACTIVE allowed us to develop metrics that capture subtle differences between cell trajectories on different substrates. We present cell motility data for thousands of cells studied at varying densities on shape-memory-polymer-based nanotopographies and identify several quantitative differences, including an unanticipated difference between two ‘control’ substrates. We expect that ACTIVE will be immediately useful to researchers who require accurate, long-time-scale motility data for many cells.     

Emergent behavioural phenotypes of swarming models revealed by mimicking a frustrated anti-ferromagnet

Self-propelled particle (SPP) models are often compared with animal swarms. However, the collective animal behaviour observed in experiments often leaves considerable unconstrained freedom in the structure of a proposed model. Essentially, multiple models can describe the observed behaviour of animal swarms in simple environments. To tackle this degeneracy, we study swarms of SPPs in non-trivial environments as a new approach to distinguish between candidate models. We restrict swarms of SPPs to circular (periodic) channels where they polarize in one of two directions (like spins) and permit information to pass through windows between neighbouring channels. Co-alignment between particles then couples the channels (anti-ferromagnetically) so that they tend to counter-rotate. We study channels arranged to mimic a geometrically frustrated anti-ferromagnet and show how the effects of this frustration allow us to better distinguish between SPP models. Similar experiments could therefore improve our understanding of collective motion in animals. Finally, we discuss how the spin analogy can be exploited to construct universal logic gates, and therefore swarming systems that can function as Turing machines.     

Animal transportation networks

Many group-living animals construct transportation networks of trails, galleries and burrows by modifying the environment to facilitate faster, safer or more efficient movement. Animal transportation networks can have direct influences on the fitness of individuals, whereas the shape and structure of transportation networks can influence community dynamics by facilitating contacts between different individuals and species. In this review, we discuss three key areas in the study of animal transportation networks: the topological properties of networks, network morphogenesis and growth, and the behaviour of network users. We present a brief primer on elements of network theory, and then discuss the different ways in which animal groups deal with the fundamental trade-off between the competing network properties of travel efficiency, robustness and infrastructure cost. We consider how the behaviour of network users can impact network efficiency, and call for studies that integrate both network topology and user behaviour. We finish with a prospectus for future research.     

Real-time synchronization of batch trajectories for on-line multivariate statistical process control using Dynamic Time Warping

This paper addresses the real-time monitoring of batch processes with multiple different local time trajectories of variables measured during the process run. For Unfold Principal Component Analysis (U-PCA)—or Unfold Partial Least Squares (U-PLS)-based on-line monitoring of batch processes, batch runs need to be synchronized, not only to have the same time length, but also such that key events happen at the same time. An adaptation from Kassidas et al.'s approach [1] will be introduced to achieve the on-line synchronization of batch trajectories using the Dynamic Time Warping (DTW) algorithm. In the proposed adaptation, a new boundaries definition is presented for accurate on-line synchronization of an ongoing batch, together with a way to adapt mapping boundaries to batch length. A relaxed greedy strategy is introduced to avoid assessing the optimal path each time a new sample is available. The key advantages of the proposed strategy are its computational speed and accuracy for the batch process context. Data from realistic simulations of a fermentation process of the Saccharomyces cerevisae cultivation are used to illustrate the performance of the proposed strategy.     

A unifying framework for quantifying the nature of animal interactions

Collective phenomena, whereby agent–agent interactions determine spatial patterns, are ubiquitous in the animal kingdom. On the other hand, movement and space use are also greatly influenced by the interactions between animals and their environment. Despite both types of interaction fundamentally influencing animal behaviour, there has hitherto been no unifying framework for the models proposed in both areas. Here, we construct a general method for inferring population-level spatial patterns from underlying individual movement and interaction processes, a key ingredient in building a statistical mechanics for ecological systems. We show that resource selection functions, as well as several examples of collective motion models, arise as special cases of our framework, thus bringing together resource selection analysis and collective animal behaviour into a single theory. In particular, we focus on combining the various mechanistic models of territorial interactions in the literature with step selection functions, by incorporating interactions into the step selection framework and demonstrating how to derive territorial patterns from the resulting models. We demonstrate the efficacy of our model by application to a population of insectivore birds in the Amazon rainforest.     

A novel statistical tolerance analysis method for assembled parts

Tolerance analysis of an assembly is an important issue for mechanical design. Among various tolerance analysis methods, statistical analysis is the most commonly employed method. However, the conventional statistical tolerance method is often based on the normal distribution. It fails to predict the resultant tolerance of an assembly of parts with non-normal distributions. In this paper, a novel method based on statistical moments is proposed. Tolerance distributions of parts are first transferred into statistical moments that are then used for computing tolerance stack-up. The computed moments, particularly the variance, the skewness and the kurtosis, are then mapped back to probability distributions in order to calculate the resultant tolerance of the assembly. The proposed method can be used to analyse the resultant tolerance specification for non-normal distributions with different skewness and kurtosis. Simulated results showed that tail coefficients of different distributions with the same kurtosis are close to each other for normalised probabilities between ?3 and 3. That is, the tail coefficients of a statistical distribution can be predicted by the coefficients of skewness and kurtosis. Two examples are illustrated in the paper to demonstrate the proposed method. The predicted resultant tolerances of the two examples are only 0.5% and 1.5% differences compared with that by the Monte Carlo simulation for 1,000,000 samples. The proposed method is much faster in computation with higher accuracy than conventional statistical tolerance methods. The merit of the proposed method is that the computation is fast and comparatively accurate for both symmetrical and unsymmetrical distributions, particularly when the required probability is between ±2σ and ±3σ.