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Costs of task allocation with local feedback: Effects of colony size and extra workers in social insects and other multi-agent systems

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      Abstract

      Adaptive collective systems are common in biology and beyond. Typically, such systems require a task allocation algorithm: a mechanism or rule-set by which individuals select particular roles. Here we study the performance of such task allocation mechanisms measured in terms of the time for individuals to allocate to tasks. We ask: (1) Is task allocation fundamentally difficult, and thus costly? (2) Does the performance of task allocation mechanisms depend on the number of individuals? And (3) what other parameters may affect their efficiency? We use techniques from distributed computing theory to develop a model of a social insect colony, where workers have to be allocated to a set of tasks; however, our model is generalizable to other systems. We show, first, that the ability of workers to quickly assess demand for work in tasks they are not currently engaged in crucially affects whether task allocation is quickly achieved or not. This indicates that in social insect tasks such as thermoregulation, where temperature may provide a global and near instantaneous stimulus to measure the need for cooling, for example, it should be easy to match the number of workers to the need for work. In other tasks, such as nest repair, it may be impossible for workers not directly at the work site to know that this task needs more workers. We argue that this affects whether task allocation mechanisms are under strong selection. Second, we show that colony size does not affect task allocation performance under our assumptions. This implies that when effects of colony size are found, they are not inherent in the process of task allocation itself, but due to processes not modeled here, such as higher variation in task demand for smaller colonies, benefits of specialized workers, or constant overhead costs. Third, we show that the ratio of the number of available workers to the workload crucially affects performance. Thus, workers in excess of those needed to complete all tasks improve task allocation performance. This provides a potential explanation for the phenomenon that social insect colonies commonly contain inactive workers: these may be a ‘surplus’ set of workers that improves colony function by speeding up optimal allocation of workers to tasks. Overall our study shows how limitations at the individual level can affect group level outcomes, and suggests new hypotheses that can be explored empirically.

      Author summary

      Many complex systems have to allocate their units to different functions: cells in an embryo develop into different tissues, servers in a computer cluster perform different calculations, and insect workers choose particular tasks, such as brood care or foraging. Here we demonstrate that this process does not automatically become easier or harder with system size. If more workers are present than needed to complete the work available, some workers will always be idle; despite this, having surplus workers makes redistributing them across the tasks that need work much faster. Thus, unexpectedly, such surplus, idle workers may potentially significantly improve system performance. Our work suggests that interdisciplinary studies between biology and distributed computing can yield novel insights for both fields.

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            Author and article information

            Affiliations
            [1 ] Electrical Engineering and Computer Science Department, Massachusetts Institute of Technology, Cambridge, MA, USA
            [2 ] Department of Ecology and Evolutionary Biology, The University of Arizona, Tucson, AZ, USA
            [3 ] School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
            University of California Irvine, UNITED STATES
            Author notes

            The authors have declared that no competing interests exist.

            ‡ These authors are joint senior authors on this work.

            Contributors
            ORCID: http://orcid.org/0000-0001-7179-0706, Role: Conceptualization, Role: Formal analysis, Role: Methodology, Role: Writing – original draft
            Role: Conceptualization, Role: Funding acquisition, Role: Methodology, Role: Project administration, Role: Supervision, Role: Writing – review & editing
            ORCID: http://orcid.org/0000-0003-3045-265X, Role: Conceptualization, Role: Formal analysis, Role: Funding acquisition, Role: Methodology, Role: Project administration, Role: Supervision, Role: Writing – review & editing
            ORCID: http://orcid.org/0000-0001-9756-0167, Role: Conceptualization, Role: Funding acquisition, Role: Methodology
            Role: Conceptualization, Role: Formal analysis, Role: Methodology
            Role: Editor
            Journal
            PLoS Comput Biol
            PLoS Comput. Biol
            plos
            ploscomp
            PLoS Computational Biology
            Public Library of Science (San Francisco, CA USA )
            1553-734X
            1553-7358
            December 2017
            14 December 2017
            : 13
            : 12
            29240763
            5746283
            PCOMPBIOL-D-17-00494
            10.1371/journal.pcbi.1005904
            (Editor)
            © 2017 Radeva 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.

            Counts
            Figures: 2, Tables: 4, Pages: 29
            Product
            Funding
            Funded by: Wyss Institute for Biologically Inspired Engineering, Harvard University
            Award Recipient : ORCID: http://orcid.org/0000-0001-9756-0167
            Funded by: funder-id http://dx.doi.org/10.13039/100000001, National Science Foundation;
            Award ID: CCF-0939370
            Award Recipient : ORCID: http://orcid.org/0000-0003-3045-265X
            Funded by: funder-id http://dx.doi.org/10.13039/100000001, National Science Foundation;
            Award ID: CCF-1461559
            Award Recipient : ORCID: http://orcid.org/0000-0003-3045-265X
            Funded by: funder-id http://dx.doi.org/10.13039/100006831, U.S. Air Force;
            Award ID: FA9550-13-1-0042
            Award Recipient : ORCID: http://orcid.org/0000-0003-3045-265X
            Funded by: funder-id http://dx.doi.org/10.13039/100000001, National Science Foundation;
            Award ID: IOS-3014230
            Award Recipient :
            RN is funded by the Wyss Institute for Biologically Inspired Engineering, Harvard University ( https://wyss.harvard.edu/). AD is funded by the National Science Foundation ( https://www.nsf.gov/) Awards number IOS-3014230. NL, TR, and HS are funded by the National Science Foundation ( https://www.nsf.gov/) Awards numbers CCF-0939370 and CCF-1461559, and by the Air Force Office of Scientific Research ( http://www.wpafb.af.mil/afrl/afosr) Contract Number: FA9550-13-1-0042. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
            Categories
            Research Article
            Biology and Life Sciences
            Organisms
            Eukaryota
            Animals
            Invertebrates
            Arthropoda
            Insects
            Social Sciences
            Sociology
            Social Systems
            Physical Sciences
            Mathematics
            Applied Mathematics
            Algorithms
            Research and Analysis Methods
            Simulation and Modeling
            Algorithms
            Physical Sciences
            Mathematics
            Numerical Analysis
            Biology and Life Sciences
            Behavior
            Animal Behavior
            Foraging
            Biology and Life Sciences
            Zoology
            Animal Behavior
            Foraging
            Computer and Information Sciences
            Systems Science
            Complex Systems
            Physical Sciences
            Mathematics
            Systems Science
            Complex Systems
            Biology and Life Sciences
            Organisms
            Eukaryota
            Animals
            Invertebrates
            Arthropoda
            Insects
            Hymenoptera
            Bees
            Honey Bees
            Physical Sciences
            Mathematics
            Probability Theory
            Probability Distribution
            Custom metadata
            vor-update-to-uncorrected-proof
            2017-12-28
            All relevant data are within the paper and its Supporting Information files.

            Quantitative & Systems biology

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