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      The modelling cycle for collective animal behaviour

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          Abstract

          Collective animal behaviour is the study of how interactions between individuals produce group level patterns, and why these interactions have evolved. This study has proved itself uniquely interdisciplinary, involving physicists, mathematicians, engineers as well as biologists. Almost all experimental work in this area is related directly or indirectly to mathematical models, with regular movement back and forth between models, experimental data and statistical fitting. In this paper, we describe how the modelling cycle works in the study of collective animal behaviour. We classify studies as addressing questions at different levels or linking different levels, i.e. as local, local to global, global to local or global. We also describe three distinct approaches—theory-driven, data-driven and model selection—to these questions. We show, with reference to our own research on species across different taxa, how we move between these different levels of description and how these various approaches can be applied to link levels together.

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          Most cited references61

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

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            Collective motion

            We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the various facets of this highly multidisciplinary field, including experiments, mathematical methods and models for simulations, so that readers with a variety of background could get both the basics and a broader, more detailed picture of the field. The observations we report on include systems consisting of units ranging from macromolecules through metallic rods and robots to groups of animals and people. Some emphasis is put on models that are simple and realistic enough to reproduce the numerous related observations and are useful for developing concepts for a better understanding of the complexity of systems consisting of many simultaneously moving entities. As such, these models allow the establishing of a few fundamental principles of flocking. In particular, it is demonstrated, that in spite of considerable differences, a number of deep analogies exist between equilibrium statistical physics systems and those made of self-propelled (in most cases living) units. In both cases only a few well defined macroscopic/collective states occur and the transitions between these states follow a similar scenario, involving discontinuity and algebraic divergences.
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              Inferring the structure and dynamics of interactions in schooling fish.

              Determining individual-level interactions that govern highly coordinated motion in animal groups or cellular aggregates has been a long-standing challenge, central to understanding the mechanisms and evolution of collective behavior. Numerous models have been proposed, many of which display realistic-looking dynamics, but nonetheless rely on untested assumptions about how individuals integrate information to guide movement. Here we infer behavioral rules directly from experimental data. We begin by analyzing trajectories of golden shiners (Notemigonus crysoleucas) swimming in two-fish and three-fish shoals to map the mean effective forces as a function of fish positions and velocities. Speeding and turning responses are dynamically modulated and clearly delineated. Speed regulation is a dominant component of how fish interact, and changes in speed are transmitted to those both behind and ahead. Alignment emerges from attraction and repulsion, and fish tend to copy directional changes made by those ahead. We find no evidence for explicit matching of body orientation. By comparing data from two-fish and three-fish shoals, we challenge the standard assumption, ubiquitous in physics-inspired models of collective behavior, that individual motion results from averaging responses to each neighbor considered separately; three-body interactions make a substantial contribution to fish dynamics. However, pairwise interactions qualitatively capture the correct spatial interaction structure in small groups, and this structure persists in larger groups of 10 and 30 fish. The interactions revealed here may help account for the rapid changes in speed and direction that enable real animal groups to stay cohesive and amplify important social information.
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                Author and article information

                Journal
                Interface Focus
                Interface Focus
                RSFS
                royfocus
                Interface Focus
                The Royal Society
                2042-8898
                2042-8901
                6 December 2012
                15 August 2012
                15 August 2012
                : 2
                : 6 , Collective motion in biological systems: experimental approaches joint with particle and continuum models Andreas Deutsch, Guy Theraulaz and Tamas Vicsek
                : 764-773
                Affiliations
                Mathematics Department, Uppsala University, Uppsala, Sweden
                Author notes
                Article
                rsfs20120031
                10.1098/rsfs.2012.0031
                3499127
                23173077
                d7366a28-58fd-4082-8e23-316d7c6d56a8
                This journal is © 2012 The Royal Society

                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 work is properly cited.

                History
                : 28 May 2012
                : 23 July 2012
                Categories
                1004
                16
                181
                44
                Articles
                Review Article

                Life sciences
                collective animal behaviour,theoretical modelling,collective motion
                Life sciences
                collective animal behaviour, theoretical modelling, collective motion

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