Chaos–order transition in foraging behavior of ants

Contributed by Hans Joachim Schellnhuber, April 24, 2014 (sent for review February 5, 2014)
May 27, 2014
111 (23) 8392-8397

Significance

We have studied the foraging behavior of group animals that live in fixed colonies (especially ants) as an important problem in ecology. Building on former findings on deterministic chaotic activities of single ants, we uncovered that the transition from chaotic to periodic regimes results from an optimization scheme of the self-organization of such an animal colony. We found that an effective foraging of ants mainly depends on their nest as well as their physical abilities and knowledge due to experience. As an important outcome, the foraging behavior of ants is not represented by random, but rather by deterministic walks, in a random environment: Ants use their intelligence and experience to navigate.

Abstract

The study of the foraging behavior of group animals (especially ants) is of practical ecological importance, but it also contributes to the development of widely applicable optimization problem-solving techniques. Biologists have discovered that single ants exhibit low-dimensional deterministic-chaotic activities. However, the influences of the nest, ants’ physical abilities, and ants’ knowledge (or experience) on foraging behavior have received relatively little attention in studies of the collective behavior of ants. This paper provides new insights into basic mechanisms of effective foraging for social insects or group animals that have a home. We propose that the whole foraging process of ants is controlled by three successive strategies: hunting, homing, and path building. A mathematical model is developed to study this complex scheme. We show that the transition from chaotic to periodic regimes observed in our model results from an optimization scheme for group animals with a home. According to our investigation, the behavior of such insects is not represented by random but rather deterministic walks (as generated by deterministic dynamical systems, e.g., by maps) in a random environment: the animals use their intelligence and experience to guide them. The more knowledge an ant has, the higher its foraging efficiency is. When young insects join the collective to forage with old and middle-aged ants, it benefits the whole colony in the long run. The resulting strategy can even be optimal.

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Acknowledgments

This work was partially supported by International Research Training Group 1740 (Deutsche Forschungsgemeinschaft and Fundação de Amparo à Pesquisa do Estado de São Paulo), the Government of the Russian Federation (Grant 14.Z50.31.0033), the Beijing Center for Mathematics and Information Interdisciplinary Sciences, and the National Natural Science Foundation of China (Grants 61100204 and 61121061).

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Information & Authors

Information

Published in

Go to Proceedings of the National Academy of Sciences
Go to Proceedings of the National Academy of Sciences
Proceedings of the National Academy of Sciences
Vol. 111 | No. 23
June 10, 2014
PubMed: 24912159

Classifications

Submission history

Published online: May 27, 2014
Published in issue: June 10, 2014

Keywords

  1. foraging dynamics
  2. learning process
  3. low-dimensional chaos
  4. mathematical modeling
  5. synchronization

Acknowledgments

This work was partially supported by International Research Training Group 1740 (Deutsche Forschungsgemeinschaft and Fundação de Amparo à Pesquisa do Estado de São Paulo), the Government of the Russian Federation (Grant 14.Z50.31.0033), the Beijing Center for Mathematics and Information Interdisciplinary Sciences, and the National Natural Science Foundation of China (Grants 61100204 and 61121061).

Authors

Affiliations

Lixiang Li
Information Security Center, State Key Laboratory of Networking and Switching Technology, and
Potsdam Institute for Climate Impact Research, D14473 Potsdam, Germany; and
Haipeng Peng1 [email protected]
Information Security Center, State Key Laboratory of Networking and Switching Technology, and
Jürgen Kurths1 [email protected]
Potsdam Institute for Climate Impact Research, D14473 Potsdam, Germany; and
Yixian Yang
Information Security Center, State Key Laboratory of Networking and Switching Technology, and
National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876, China;
Hans Joachim Schellnhuber1 [email protected]
Potsdam Institute for Climate Impact Research, D14473 Potsdam, Germany; and
Santa Fe Institute, Santa Fe, NM 87501

Notes

1
To whom correspondence may be addressed. E-mail: [email protected], [email protected], or [email protected].
Author contributions: L.L., H.P., and J.K. designed research; L.L., H.P., and Y.Y. performed research; H.P. analyzed data; and L.L., J.K., and H.J.S. wrote the paper.

Competing Interests

The authors declare no conflict of interest.

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    Chaos–order transition in foraging behavior of ants
    Proceedings of the National Academy of Sciences
    • Vol. 111
    • No. 23
    • pp. 8313-8696

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