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      Multi-scale Inference of Interaction Rules in Animal Groups Using Bayesian Model Selection

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          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns ( Paratya australiensis). We show that these exhibit a stereotypical ‘phase transition’, whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have ‘memory’ of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture fine scale rules of interaction, which are primarily mediated by physical contact. Conversely, the Markovian self-propelled particle model captures the fine scale rules of interaction but fails to reproduce global dynamics. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects.

          Author Summary

          The collective movement of animals in a group is an impressive phenomenon whereby large scale spatio-temporal patterns emerge from simple interactions between individuals. Theoretically, much of our understanding of animal group motion comes from models inspired by statistical physics. In these models, animals are treated as moving (self-propelled) particles that interact with each other according to simple rules. Recently, researchers have shown greater interest in using experimental data to verify which rules are actually implemented by a particular animal species. In our study, we present a rigorous selection between alternative models inspired by the literature for a system of glass prawns. We find that the classic theoretical models can accurately capture either the fine-scale behaviour or the large-scale collective patterns of movement of the prawns. However, none are able to reproduce both levels of description at the same time. To resolve this conflict we introduce a new class of models wherein prawns ‘remember’, their previous interactions, integrating their experiences over time when deciding to change behaviour. These outperform the traditional models in predicting when individual prawns will change their direction of motion and restore consistency between the fine-scale rules of interaction and the global behaviour of the group.

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          Most cited references 42

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

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            Probability Theory

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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

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                1553-734X
                1553-7358
                January 2012
                January 2012
                5 January 2012
                : 8
                : 1
                Affiliations
                [1 ]Department of Mathematics, Uppsala University, Uppsala, Sweden
                [2 ]Robotics Institute, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
                [3 ]School of Biological Sciences, University of Sydney, Sydney, Australia
                Indiana University, United States of America
                Author notes

                Conceived and designed the experiments: AJWW. Performed the experiments: AJWW JEH-R. Analyzed the data: RPM AP DJTS DS RG AJWW. Contributed reagents/materials/analysis tools: RPM AP DS DJTS. Wrote the paper: RPM DJTS AP.

                Article
                PCOMPBIOL-D-11-01272
                10.1371/journal.pcbi.1002308
                3252267
                22241970
                Mann et al. 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: 12
                Categories
                Research Article
                Biology
                Computational Biology
                Ecology
                Behavioral Ecology
                Theoretical Ecology
                Theoretical Biology
                Zoology
                Animal Behavior
                Mathematics
                Applied Mathematics
                Complex Systems
                Probability Theory
                Bayes Theorem
                Markov Model
                Probability Density
                Probability Distribution
                Stochastic Processes
                Physics
                Statistical Mechanics

                Quantitative & Systems biology

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