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      A Simple Iterative Model Accurately Captures Complex Trapline Formation by Bumblebees Across Spatial Scales and Flower Arrangements

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          Abstract

          Pollinating bees develop foraging circuits (traplines) to visit multiple flowers in a manner that minimizes overall travel distance, a task analogous to the travelling salesman problem. We report on an in-depth exploration of an iterative improvement heuristic model of bumblebee traplining previously found to accurately replicate the establishment of stable routes by bees between flowers distributed over several hectares. The critical test for a model is its predictive power for empirical data for which the model has not been specifically developed, and here the model is shown to be consistent with observations from different research groups made at several spatial scales and using multiple configurations of flowers. We refine the model to account for the spatial search strategy of bees exploring their environment, and test several previously unexplored predictions. We find that the model predicts accurately 1) the increasing propensity of bees to optimize their foraging routes with increasing spatial scale; 2) that bees cannot establish stable optimal traplines for all spatial configurations of rewarding flowers; 3) the observed trade-off between travel distance and prioritization of high-reward sites (with a slight modification of the model); 4) the temporal pattern with which bees acquire approximate solutions to travelling salesman-like problems over several dozen foraging bouts; 5) the instability of visitation schedules in some spatial configurations of flowers; 6) the observation that in some flower arrays, bees' visitation schedules are highly individually different; 7) the searching behaviour that leads to efficient location of flowers and routes between them. Our model constitutes a robust theoretical platform to generate novel hypotheses and refine our understanding about how small-brained insects develop a representation of space and use it to navigate in complex and dynamic environments.

          Author Summary

          Pollinating bees, along with bats, hummingbirds, rodents and primates, typically develop circuits (traplines) to visit multiple foraging sites in an efficient stable sequence. The question of how animals encode and process spatial information to develop these impressive foraging patterns remains poorly understood. Previously we showed that an iterative improvement heuristic model of bumblebee traplining can replicate the establishment of stable routes by bees between flowers distributed over several hectares. Here we tested the model against a variety of datasets with different configurations of flowers and found it to give good agreements with all these observations. We have thus shown how these complex dynamic routing problems can be solved by small-brained bees using simple learning heuristics and without acquiring a ‘map-like’ memory. The proposed heuristic shows how bees develop optimal routes simply by following multi-segment journeys composed of learnt flight routines (local vectors), each pointing towards target locations (flowers) and coupled to a visual context (landmarks or panoramas). Such a decentralized representation of space relying on learnt sensorimotor routines is akin to ‘route-based’ navigation as described in desert ants, where spatial information is thought to be processed by separate, potentially modular, guidance systems.

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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
          March 2013
          March 2013
          7 March 2013
          : 9
          : 3
          : e1002938
          Affiliations
          [1 ]Rothamsted Research, Harpenden, Hertfordshire, United Kingdom
          [2 ]School of Biological Sciences and the Charles Perkins Centre, The University of Sydney, Sydney, New South Wales, Australia
          [3 ]Psychology Division, School of Biological and Chemical Sciences, Queen Mary University of London, London, United Kingdom
          Northeastern University, United States of America
          Author notes

          The authors have declared that no competing interests exist.

          Conceived and designed the experiments: AMR ML LC. Performed the experiments: AMR ML LC. Analyzed the data: AMR ML LC. Contributed reagents/materials/analysis tools: AMR ML LC. Wrote the paper: AMR ML LC.

          Article
          PCOMPBIOL-D-12-01344
          10.1371/journal.pcbi.1002938
          3591286
          23505353
          7c9a9965-a792-43e0-a151-770b3e42b99d
          Copyright @ 2013

          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.

          History
          : 23 August 2012
          : 10 January 2013
          Page count
          Pages: 10
          Funding
          This research is funded by the Biotechnology and Biological Sciences Research Council (BBSRC)(UK). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
          Categories
          Research Article
          Biology
          Anatomy and Physiology
          Neurological System
          Neuroscience
          Animal Cognition
          Theoretical Biology
          Mathematics
          Mathematical Computing

          Quantitative & Systems biology
          Quantitative & Systems biology

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