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      Deciphering Interactions in Moving Animal Groups

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          Abstract

          Collective motion phenomena in large groups of social organisms have long fascinated the observer, especially in cases, such as bird flocks or fish schools, where large-scale highly coordinated actions emerge in the absence of obvious leaders. However, the mechanisms involved in this self-organized behavior are still poorly understood, because the individual-level interactions underlying them remain elusive. Here, we demonstrate the power of a bottom-up methodology to build models for animal group motion from data gathered at the individual scale. Using video tracks of fish shoal in a tank, we show how a careful, incremental analysis at the local scale allows for the determination of the stimulus/response function governing an individual's moving decisions. We find in particular that both positional and orientational effects are present, act upon the fish turning speed, and depend on the swimming speed, yielding a novel schooling model whose parameters are all estimated from data. Our approach also leads to identify a density-dependent effect that results in a behavioral change for the largest groups considered. This suggests that, in confined environment, the behavioral state of fish and their reaction patterns change with group size. We debate the applicability, beyond the particular case studied here, of this novel framework for deciphering interactions in moving animal groups.

          Author Summary

          Swarms of insects, schools of fish and flocks of birds display an impressive variety of collective patterns that emerge from local interactions among group members. These puzzling phenomena raise a variety of questions about the behavioral rules that govern the coordination of individuals' motions and the emergence of large-scale patterns. While numerous models have been proposed, there is still a strong need for detailed experimental studies to foster the biological understanding of such collective motion. Here, we use data recorded on fish barred flagtails moving in groups of increasing sizes in a water tank to demonstrate the power of an incremental methodology for building a fish behavior model completely based on interactions with the physical environment and neighboring fish. In contrast to previous works, our model revealed an implicit balancing of neighbors position and orientation on the turning speed of fish, an unexpected transition between shoaling and schooling induced by a change in the swimming speed, and a group-size effect which results in a decrease of social interactions among fish as density increases. An important feature of this model lies in its ability to allow a large palette of adaptive patterns with a great economy of means.

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          Most cited references 19

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          Novel Type of Phase Transition in a System of Self-Driven Particles

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            Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study

            Numerical models indicate that collective animal behaviour may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely on aprioristic assumptions. By reconstructing the three-dimensional position of individual birds in airborne flocks of few thousands members, we prove that the interaction does not depend on the metric distance, as most current models and theories assume, but rather on the topological distance. In fact, we discover that each bird interacts on average with a fixed number of neighbours (six-seven), rather than with all neighbours within a fixed metric distance. We argue that a topological interaction is indispensable to maintain flock's cohesion against the large density changes caused by external perturbations, typically predation. We support this hypothesis by numerical simulations, showing that a topological interaction grants significantly higher cohesion of the aggregation compared to a standard metric one.
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              Large-scale vortex lattice emerging from collectively moving microtubules.

              Spontaneous collective motion, as in some flocks of bird and schools of fish, is an example of an emergent phenomenon. Such phenomena are at present of great interest and physicists have put forward a number of theoretical results that so far lack experimental verification. In animal behaviour studies, large-scale data collection is now technologically possible, but data are still scarce and arise from observations rather than controlled experiments. Multicellular biological systems, such as bacterial colonies or tissues, allow more control, but may have many hidden variables and interactions, hindering proper tests of theoretical ideas. However, in systems on the subcellular scale such tests may be possible, particularly in in vitro experiments with only few purified components. Motility assays, in which protein filaments are driven by molecular motors grafted to a substrate in the presence of ATP, can show collective motion for high densities of motors and attached filaments. This was demonstrated recently for the actomyosin system, but a complete understanding of the mechanisms at work is still lacking. Here we report experiments in which microtubules are propelled by surface-bound dyneins. In this system it is possible to study the local interaction: we find that colliding microtubules align with each other with high probability. At high densities, this alignment results in self-organization of the microtubules, which are on average 15 µm long, into vortices with diameters of around 400 µm. Inside the vortices, the microtubules circulate both clockwise and anticlockwise. On longer timescales, the vortices form a lattice structure. The emergence of these structures, as verified by a mathematical model, is the result of the smooth, reptation-like motion of single microtubules in combination with local interactions (the nematic alignment due to collisions)--there is no need for long-range interactions. Apart from its potential relevance to cortical arrays in plant cells and other biological situations, our study provides evidence for the existence of previously unsuspected universality classes of collective motion phenomena.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                PLoS Comput. Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                1553-734X
                1553-7358
                September 2012
                September 2012
                13 September 2012
                : 8
                : 9
                Affiliations
                [1 ]Centre de Recherches sur la Cognition Animale, UMR-CNRS 5169, Université Paul Sabatier, Toulouse, France
                [2 ]CNRS, Centre de Recherches sur la Cognition Animale, Toulouse, France
                [3 ]Service de Physique de l'État Condensé, CEA-Saclay, Gif-sur-Yvette, France
                [4 ]Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Roma, Italy
                [5 ]Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen, United Kingdom
                [6 ]Laboratoire Plasma et Conversion d'Energie, UMR-CNRS 5213, Université Paul Sabatier, Toulouse, France
                [7 ]CNRS, Laboratoire Plasma et Conversion d'Energie, Toulouse, France
                [8 ]Institut de Recherche pour le Développement (IRD), UMR EME, La Réunion, France
                Princeton University, United States of America
                Author notes

                The authors have declared that no competing interests exist.

                Conceived and designed the experiments: MS GT. Performed the experiments: MS GT. Analyzed the data: JG FG RF SB HC. Wrote the paper: JG FG RF SB HC GT. Designed the software used in analysis: JG RF SB.

                Article
                PCOMPBIOL-D-12-00112
                10.1371/journal.pcbi.1002678
                3441504
                23028277

                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                Page count
                Pages: 11
                Funding
                This study was supported by grants from the CNRS, IRD and the ANR PANURGE project (ANR-08-SYSC-015). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Agriculture
                Animal Management
                Animal Behavior
                Biology
                Computational Biology
                Biophysic Al Simulations
                Systems Biology
                Ecology
                Behavioral Ecology
                Neuroscience
                Animal Cognition
                Computer Science
                Computer Modeling
                Physics
                Condensed-Matter Physics
                Phase Transformation
                Interdisciplinary Physics
                Statistical Mechanics

                Quantitative & Systems biology

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