Daisyworld in Two Dimensional Small-World Networks

  • Dharani Punithan
  • Dong-Kyun Kim
  • RI (Bob) McKay
Part of the Communications in Computer and Information Science book series (CCIS, volume 258)

Abstract

Daisyworld was initially proposed as an abstract model of the self-regulation of planetary ecosystems. The original one-point model has also been extended to one- and two-dimensional worlds. The latter are especially interesting, in that they not only demonstrate the emergence of spatially-stabilised homeostasis but also emphasise dynamics of heterogeneity within a system, in which individual locations in the world experience booms and busts, yet the overall behaviour is stabilised as patches of white and black daisies migrate around the world. We extend the model further, to small-world networks, more realistic for social interaction – and even for some forms of ecological interaction – using the Watts-Strogatz (WS) and Newman-Watts (NW) models. We find that spatially-stabilised homeostasis is able to persist in small-world networks. In the WS model, as the rewiring probabilities increase even far beyond normal small-world limits, there is only a small loss of effectiveness. However as the average number of connections increases in the NW model, we see a gradual breakdown of heterogeneity in patch dynamics, leading to less interesting – more homogenised – worlds.

Keywords

Small World Regular Lattice Regular Network Connectivity Topology Rewire Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Watson, A.J., Lovelock, J.E.: Biological homeostasis of the global environment: the parable of daisyworld. Tellus B 35(4), 284–289 (1983)CrossRefGoogle Scholar
  2. 2.
    Adams, B., Carr, J., Lenton, T.M., White, A.: One-dimensional daisyworld: Spatial interactions and pattern formation. Journal of Theoretical Biology 223(4), 505–513 (2003)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Von Bloh, W., Block, A., Schellnhuber, H.J.: Self-stabilization of the biosphere under global change: a tutorial geophysiological approach. Tellus B 49(3), 249–262 (1997)CrossRefGoogle Scholar
  4. 4.
    Ackland, G., Clark, M., Lenton, T.: Catastrophic desert formation in daisyworld. Journal of Theoretical Biology 223(1), 39–44 (2003)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Saunders, P.T., Koeslag, J.H., Wessels, J.A.: Integral rein control in physiology ii: a general model. Journal of Theoretical Biology 206(2), 211–220 (2000)CrossRefGoogle Scholar
  6. 6.
    Dyke, J.G., Harvey, I.R.: Pushing up the daisies. In: Artificial Life X, Proceedings of the Tenth International Conference on the Simulation and Synthesis of Living Systems, pp. 426–431. MIT Press (2006)Google Scholar
  7. 7.
    Nuño, J.C., De Vicente, J., Olarrea, J., López, P., Lahoz-Beltrá, R.: Evolutionary daisyworld models: A new approach to studying complex adaptive systems. Ecological Informatics 5(4), 231–240 (2010)CrossRefGoogle Scholar
  8. 8.
    Leskovec, J., Horvitz, E.: Planetary-scale views on a large instant-messaging network. In: Proceeding of the 17th International Conference on World Wide Web, pp. 915–924. Association for Computing Machinery (2008)Google Scholar
  9. 9.
    Perera, L., Russell, J.R., Provan, J., Powell, W.: Use of microsatellite dna markers to investigate the level of genetic diversity and population genetic structure of coconut (Cocos nucifera L.). Genome 43(1), 15–21 (2000)CrossRefGoogle Scholar
  10. 10.
    White, C., Selkoe, K.A., Watson, J., Siegel, D.A., Zacherl, D.C., Toonen, R.J.: Ocean currents help explain population genetic structure. Proceedings of the Royal Society B: Biological Sciences 277(1688), 1685 (2010)CrossRefGoogle Scholar
  11. 11.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393(6684), 440–442 (1998)CrossRefGoogle Scholar
  12. 12.
    Watts, D.J.: Small Worlds: the Dynamics of Networks between Order and Randomness. Princeton University Press, Princeton (2003)MATHGoogle Scholar
  13. 13.
    Newman, M., Watts, D.: Renormalization group analysis of the small-world network model. Physics Letters A 263(4-6), 341–346 (1999)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Krebs, J.R., Davies, N.B.: An Introduction to Behavioural Ecology. Wiley-Blackwell (1993)Google Scholar
  15. 15.
    Kleinberg, J.M.: Navigation in a small world. Nature 406(6798), 845 (2000)CrossRefGoogle Scholar
  16. 16.
    McGuffie, K., Henderson-Sellers, A.: A Climate Modelling Primer, vol. 1. Wiley, Chichester (2005)CrossRefGoogle Scholar
  17. 17.
    Kanamaru, T., Aihara, K.: Roles of inhibitory neurons in rewiring-induced synchronization in pulse-coupled neural networks. Neural Computation 22(5), 1383–1398 (2010)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Kitano, K., Fukai, T.: Variability vs synchronicity of neuronal activity in local cortical network models with different wiring topologies. Journal of Computational Neuroscience 23(2), 237–250 (2007)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Moore, C., Newman, M.E.J.: Epidemics and percolation in small-world networks. Physical Reviews E 61(5), 5678–5682 (2000)CrossRefGoogle Scholar
  20. 20.
    Lago-Fernández, L., Huerta, R., Corbacho, F., Sigüenza, J.: Fast response and temporal coherent oscillations in small-world networks. Physical Review Letters 84(12), 2758–2761 (2000)CrossRefGoogle Scholar
  21. 21.
    Latora, V., Marchiori, M.: Efficient behavior of small-world networks. Physical Review Letters 87(19), 198701 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dharani Punithan
    • 1
  • Dong-Kyun Kim
    • 1
  • RI (Bob) McKay
    • 1
  1. 1.Structural Complexity LaboratorySeoul National UniversitySouth Korea

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