Skip to main content
SpringerLink
Log in

Optimal information transfer and stochastic resonance in collective decision making

  • Published:
Swarm Intelligence Aims and scope Submit manuscript

Abstract

Self-organised collective decision making is one of the core components of swarm intelligence, and numerous swarm algorithms that are widely used in optimisation and optimal control have been inspired by the biological mechanisms driving it. Beyond the life sciences and bio-inspired engineering, collective decision making is important in a number of other disciplines, most prominently economics and the social sciences. A paradigmatic model system for collective decision making is the foraging behaviour of mass recruiting ant colonies. While this system has been investigated extensively, our knowledge about its function in dynamic environments is still incomplete at best. We show that the mathematical model of mass foraging is really just a specific instance of a very general class of rational group decision making processes. We analyse this general class using an information-theoretic framework, which allows us to abstract from the specific details of a fixed model system. We specifically investigate how noisy communication can enable groups to share information about changes in an environment more efficiently. In the present paper, we show that an optimal noise level exists and that this optimal level depends on the rate of change in the environment. We explain this on the basis of stochastic resonance theory and show why stochastic attractor switching is a suitable base mechanism for adaptive group decision making in dynamic environments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Notes

  1. This is true for purely mass foraging species (Hölldobler and Wilson 1990).

  2. Note that this figure gives the exact plot of a double-well potential function U that we will be defining later in Sect. 4.4.1 and Eq. 19. Here the only property of U that matters is that it is a double-well potential. The exact shape of the potential and thus the parameter values are not relevant at the present point.

  3. There are of course also other channels of communication, for example trophallaxis, but we focus the discussion on pheromone communication here.

  4. Since actual movements have no impact on the simulation outcomes they are not explicitly modelled.

  5. All calculations were performed using numerical integration in Mathematica 11.0 with parameters WorkingPrecision = 16, AccuracyGoal = 2, Method = {GlobalAdaptive, MaxErrorIncreases = 10000}.

  6. For a critical discussion of this claim see Pfeifer (2006).

  7. The sole exception is the approximation by adiabatic elimination, which is entirely dispensable in our approach, as we can rely on EFA instead.

References

  • Armitage, J. (1999). Bacterial tactic responses. Advances in Microbial Physiology, 41, 229–289.

    Article  Google Scholar 

  • Axelrod, R. (1997). The complexity of cooperation: Agent-based models of competition and collaboration. Princeton: Princeton University Press.

    Google Scholar 

  • Beckers, R., Deneubourg, J., & Goss, S. (1993). Modulation of trail laying in the ant Lasius niger and its role in the collective selection of a food source. Journal of Insect Behaviour, 6, 751–759.

    Article  Google Scholar 

  • Ben-Jacob, E., Cohen, I., & Levine, H. (2000). Cooperative self-organization of microorganisms. Advances in Physics, 49(4), 395–554.

    Article  Google Scholar 

  • Blum, C. (2005). Ant colony optimization: Introduction and recent trends. Physics of Life Reviews, 24(4), 353–373.

    Article  Google Scholar 

  • Bonabeau, E., Theraulaz, G., & Dorigo, M. (1999). Swarm intelligence: From natural to artificial systems. New York: Oxford University Press.

    MATH  Google Scholar 

  • Brambilla, M., Ferrante, E., Birattari, M., & Dorigo, M. (2013). Swarm robotics: A review from the swarm engineering perspective. Swarm Intelligence, 7, 1–41.

    Article  Google Scholar 

  • Britton, N., Franks, N., Pratt, S., & Seeley, T. (2002). Deciding on a new home: How do honeybees agree? Proceedings of the Royal Society of London Series B, 269, 1382–1388. doi:10.1098/rspb.2002.2001.

    Article  Google Scholar 

  • Camazine, S., Deneubourg, J., Franks, N. R., Sneyd, J., Theraulaz, G., & Bonabeau, E. (2001). Self-organization in biological systems. Princeton: Princeton University Press.

    MATH  Google Scholar 

  • Capasso, V., & Bakstein, D. (2005). An introduction to continuous-time stochastic processes. Basel: Birkhäuser.

    MATH  Google Scholar 

  • Collins, J. (1999). Fishing for function in noise. Nature, 402, 241–242.

    Article  Google Scholar 

  • Collins, J., Chow, C., Capela, A., & Imhoff, T. (1996). Aperiodic stochastic resonance. Physical Review E, 54(5), 5575–5584.

    Article  Google Scholar 

  • Corell, N. (2008). Social control of herd animals by integration of artificially controlled congeners. LNAI, 5040, 437–446.

    Google Scholar 

  • Cover, T., & Thomas, J. A. (2006). Elements of information theory. Hoboken: Wiley.

    MATH  Google Scholar 

  • Czaczkes, T., Grüter, C., Jones, S., & Ratnieks, F. (2011). Synergy between social and private information increases foraging efficiency in ants. Biology Letters. Published online before print February 16, 2011. doi:10.1098/rsbl.2011.0067.

  • Detrain, C., & Deneubourg, J. (2006). Self-organized structures in a superorganism: Do ants behave like molecules? Physics of Life Reviews, 3, 162–187.

    Article  Google Scholar 

  • Dorigo, M., Birattari, M., & Brambilla, M. (2014). Swarm robotics. Scholarpedia, 9(1), 1463.

    Article  Google Scholar 

  • Dressler, F. (2007). Self-organization in sensor and actor networks. Hoboken: Wiley.

    Book  Google Scholar 

  • Dussutour, A., Beekman, M., Nicolis, S. C., & Meyer, B. (2009). Noise improves collective decision-making by ants in dynamic environments. Proceedings of the Royal Society London B, 276, 4353–4361. doi:10.1098/rspb.2009.1235.

    Article  Google Scholar 

  • Edelstein-Keshet, L., Watmough, J., & Ermentrout, G. (1995). Trail following in ants: Individual properties determine population behaviour. Behavioral Ecology and Sociobiology, 36, 119–133.

    Article  Google Scholar 

  • Fewell, J. (2003). Social insect networks. Science, 301, 1867–1870.

    Article  Google Scholar 

  • Gammaitoni, L., Hänggi, P., Jung, P., & Marchesoni, F. (1998). Stochastic resonance. Reviews of Modern Physics, 70(1), 223–287.

    Article  Google Scholar 

  • Gardiner, C. (2004). Handbook of stochastic methods (3rd ed.). Berlin: Springer.

    Book  MATH  Google Scholar 

  • Garnier, S., Gautrais, J., & Theraulaz, G. (2007). The biological principles of swarm intelligence. Swarm Intelligence, 1, 3–31.

    Article  Google Scholar 

  • Gillespie, D. (1992). Markov processes: An introduction for physical scientists. Cambridge: Academic.

    MATH  Google Scholar 

  • Haken, H. (2006). Information and self-organization–A macroscopic approach to complex systems. Berlin: Springer.

    MATH  Google Scholar 

  • Helbing, D., Buzna, L., Johansson, A., & Werner, T. (2005). Self-organized pedestrian crowd dynamics. Transportation Science, 39(1), 1–24.

    Article  Google Scholar 

  • Heneghan, C., Chow, C., Collins, J., Imhoff, T., Lowen, S., & Teich, M. (1996). Information measures quantifying aperiodic stochastic resonance. Physical Review E, 54(3), 2228–2231.

    Article  Google Scholar 

  • Hölldobler, B., & Wilson, E. (1990). The ants. Cambridge: Harvard University Press.

    Book  Google Scholar 

  • Jaynes, E. (1963). Information theory and statistical mechanics. In K. Ford (Ed.), Statistical physics. Amsterdam: Benjamin.

    Google Scholar 

  • Longtin, A. (1993). Stochastic resonance in neuron models. Journal of Statistical Physics, 70(1/2), 309–327.

    Article  MATH  Google Scholar 

  • Meyer, B. (2008). On the deterministic convergence dynamics of ant colony search. Complexity International, 12, 1–15. msid05.

    Google Scholar 

  • Meyer, B., Ansorge, C., & Nakagaki, T. (2017). The role of noise in self-organized decision making by the true slime mold Physarum polycephalum. PLoS ONE, 12(3), e0172933.

    Article  Google Scholar 

  • Moss, F., Ward, L., & Sannita, W. G. (2004). Stochastic resonance and sensory information processing. Clinical Neurophysiology, 115(2), 267–281.

    Article  Google Scholar 

  • Nadal, J., Weisbuch, G., Chenevez, O., & Kirman, A. (1998). A formal approach to market organization: Choice functions, mean field approximation and maximum entropy principle. In J. Lesourne & A. Orlean (Eds.), Advances in selforganization and evolutionary economics (pp. 149–159). Paris: Economica.

    Google Scholar 

  • Nakagaki, T., Iima, M., Ueda, T., Nishiura, Y., Saigusa, T., Tero, A., et al. (2007). Minimum-risk path finding by an adaptive amoebal network. Physical Review Letters, 99, 068104.

    Article  Google Scholar 

  • Nakagaki, T., Yamada, H., & Toth, A. (2000). Maze-solving by an amoeboid organism. Nature, 407, 470.

    Article  Google Scholar 

  • Neiman, A., Shulgin, B., Anishchenko, V., Ebeling, W., Schimansky-Geier, L., & Freund, J. (1996). Dynamical entropies applied to stochastic resonance. Physical Review Letters, 76(23), 4299–4302.

    Article  Google Scholar 

  • Nicolis, S. (2004). Fluctuation-induced symmetry breaking in a bistable system: A generic mechanism of selection between competing options. International Journal of Bifurcation and Chaos, 14(7), 2399–2405.

    Article  MATH  Google Scholar 

  • Nicolis, S., & Deneubourg, J. (1999). Emerging patterns and food recruitment in ants: An analytical study. Journal of Theoretical Biology, 198, 575–592.

    Article  Google Scholar 

  • Okubo, A. (1986). Dynamical aspects of animal grouping: Swarms, flocks and herds. Advances in Biophysics, 22, 1–94.

    Article  Google Scholar 

  • Pfeifer, J. (2006). The use of information theory in biology. Biological Theory, 1(3), 317–330.

    Article  Google Scholar 

  • Pratt, S., Mallon, E., Sumpter, D., & Franks, N. (2002). Quorum sensing, recruitment, and collective decision-making during colony emigration by the ant leptothorax albipennis. Behavioral Ecology and Sociobiology, 52, 117–127. doi:10.1007/s00265-002-0487-x.

    Article  Google Scholar 

  • Risken, H. (1989). The Fokker–Planck equation. Berlin: Springer.

    Book  MATH  Google Scholar 

  • Shannon, C. (1948). A mathematical theory of communication. The Bell System Technical Journal, 27, 379-423–623-656.

    Article  MathSciNet  MATH  Google Scholar 

  • Sole, R., & Miramontes, O. (1995). Information at the edge of chaos in fluid neural networks. Physica D, 80(1–2), 171–180.

    Article  MATH  Google Scholar 

  • Strogatz, S. H. (1994). Nonlinear dynamics and chaos. Boulder: Westview Press.

    Google Scholar 

  • Sumpter, D. (2010). Collective animal behavior. Princeton: Princeton University Press.

    Book  MATH  Google Scholar 

  • Tero, A., Kobayashi, R., & Nakagaki, T. (2007). A mathematical model for adaptive transport network in path finding by true slime mold. Journal of Theoretical Biology, 244, 553–564.

    Article  MathSciNet  Google Scholar 

  • Tindall, M., Porter, S., Maini, P., Gaglia, G., & Armitage, J. (2008). Overview of mathematical approaches used to model bacterial chemotaxis ii: Bacterial populations. Bulletin of Mathematical Biology, 70(6), 1570–1607.

    Article  MathSciNet  MATH  Google Scholar 

  • Tomforde, S., Prothmann, H., Rochner, F., Branke, J., Hähner, J., Müller-Schloer, C., & Schmeck, H. (2008). Decentralised progressive signal systems for organic traffic control. In Proceedings of the 2008 second IEEE international conference on self-adaptive and self-organizing systems, pp. 413–422, Venice: IEEE Press.

  • Vicsek, T. (2001). A question of scale. Nature, 411, 421.

    Article  Google Scholar 

  • Vigelius, M., Meyer, B., & Pascoe, G. (2014). Multiscale modelling and analysis of collective decision making in swarm robotics—The case of majority voting. PLoS ONE, 11(9), e111542.

    Article  Google Scholar 

  • Weisbuch, G., Kirman, A., & Herreiner, D. (2000). Market organisation and trading relationships. The Economic Journal, 110, 411–436. doi:10.1111/1468-0297.00531.

    Article  Google Scholar 

  • Weisbuch, G., & Stauffer, D. (2000). Hits and flops dynamics. Physica A, 287, 563–576.

    Article  MathSciNet  Google Scholar 

  • Wiesenfeld, K., & Moss, F. (1995). Stochastic resonance and the benefits of noise: From ice ages to crayfish and squids. Nature, 373, 33–36.

    Article  Google Scholar 

  • Williams, P., & Beer, R. (2010). Information dynamics of evolved agents. In From animals to animats , (SAB 2010), Vol. 11, pp. 38–49. Paris: Springer.

  • Wilson, E. (1962). Chemical communication among workers of the fire ant Solenopsis saevissima (Fr. Smith): 2. An information analysis of the odour trail. Animal Behavior, 10, 148–158.

    Article  Google Scholar 

  • Yates, C., Erban, R., Escuderoc, C., Couzin, I., Buhle, J., Kevrekidis, I., et al. (2009). Inherent noise can facilitate coherence in collective swarm motion. Proceedings of the National Academy of Science, 106, 5464–5469.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Australian Research Council under DP0879239 and DP110101413.

Author information

Authors and Affiliations

  1. Monash University, Caulfield East, Melbourne, VIC, Australia

    Bernd Meyer

Authors
  1. Bernd Meyer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bernd Meyer.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Meyer, B. Optimal information transfer and stochastic resonance in collective decision making. Swarm Intell 11, 131–154 (2017). https://doi.org/10.1007/s11721-017-0136-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11721-017-0136-7

Keywords

Search

Navigation