Letter | Published:

Effects of topology on network evolution

Nature Physics volume 2, pages 532536 (2006) | Download Citation

Subjects

Abstract

The ubiquity of scale-free topology in nature raises the question of whether this particular network design confers an evolutionary advantage1. A series of studies has identified key principles controlling the growth and the dynamics of scale-free networks2,3,4. Here, we use neuron-based networks of boolean components as a framework for modelling a large class of dynamical behaviours in both natural and artificial systems5,6,7. Applying a training algorithm, we characterize how networks with distinct topologies evolve towards a pre-established target function through a process of random mutations and selection8,9,10. We find that homogeneous random networks and scale-free networks exhibit drastically different evolutionary paths. Whereas homogeneous random networks accumulate neutral mutations and evolve by sparse punctuated steps11,12, scale-free networks evolve rapidly and continuously. Remarkably, this latter property is robust to variations of the degree exponent. In contrast, homogeneous random networks require a specific tuning of their connectivity to optimize their ability to evolve. These results highlight an organizing principle that governs the evolution of complex networks and that can improve the design of engineered systems.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    , & Error and attack tolerance of complex networks. Nature 406, 378–382 (2000).

  2. 2.

    , & Weighted evolving networks: Coupling topology and weight dynamics. Phys. Rev. Lett. 92, 228701 (2004).

  3. 3.

    & Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002).

  4. 4.

    & Response of complex networks to stimuli. Proc. Natl Acad. Sci. USA 101, 4341–4345 (2004).

  5. 5.

    & The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. J. Theor. Biol. 223, 1–18 (2003).

  6. 6.

    , , , & The yeast cell-cycle network is robustly designed. Proc. Natl Acad. Sci. USA 101, 4781–4786 (2004).

  7. 7.

    Neural networks and physical systems with emergent collective computational abilities. Proc. Natl Acad. Sci. USA 79, 2554–2558 (1982).

  8. 8.

    & Spontaneous evolution of modularity and network motifs. Proc. Natl Acad. Sci. USA 102, 13773–13778 (2005).

  9. 9.

    Emergence of homeostasis and ‘noise imprinting’ in an evolution model. Proc. Natl Acad. Sci. USA 96, 10746–10751 (1999).

  10. 10.

    & Continuity in evolution: On the nature of transitions. Science 280, 1451–1455 (1998).

  11. 11.

    & Neutral mutations and punctuated equilibrium in evolving genetic networks. Phys. Rev. Lett. 81, 236–239 (1998).

  12. 12.

    & in Models in Paleobiology (ed. Schopf, T. J. M.) 82–115 (Cooper & Co, San Francisco, 1972).

  13. 13.

    Protein molecules as computational elements in living cells. Nature 376, 307–312 (1995) ibid. 378, 419 (1995).

  14. 14.

    & Network studies of social-influence. Sociol. Methods Res. 22, 127–151 (1993).

  15. 15.

    Threshold models of collective behavior. Am. J. Sociol. 83, 1420–1443 (1978).

  16. 16.

    Does evolutionary plasticity evolve? Evolution 50, 1008–1023 (1996).

  17. 17.

    Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence (MIT Press, Cambridge, Massachusetts, 1992).

  18. 18.

    & Analytic solution of a static scale-free network model. Eur. Phys. J. B 44, 241–248 (2005).

  19. 19.

    , & VLSI implementations of threshold logic—A comprehensive survey. IEEE Trans. Neural Netw. 14, 1217–1243 (2003).

  20. 20.

    An Introduction to Genetic Algorithms (MIT Press, Cambridge, Massachusetts, 1996).

  21. 21.

    , & Networks, dynamics, and modularity. Phys. Rev. Lett. 92, 188701 (2004).

  22. 22.

    Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22, 437–467 (1969).

  23. 23.

    Correspondence between neural threshold networks and Kauffman boolean cellular automata. J. Phys. A 21, L615–L619 (1988).

  24. 24.

    Parameter sensitivity as a criterion for evaluating and comparing performance of biochemical systems. Nature 229, 542–544 (1971).

  25. 25.

    & A natural class of robust networks. Proc. Natl Acad. Sci. USA 100, 8710–8714 (2003).

  26. 26.

    & Towards a general-theory of adaptive walks on rugged landscapes. J. Theor. Biol. 128, 11–45 (1987).

  27. 27.

    & Evolvability. Proc. Natl Acad. Sci. USA 95, 8420–8427 (1998).

  28. 28.

    & Random networks of automata—A simple annealed approximation. Europhys. Lett. 1, 45–49 (1986).

  29. 29.

    & Criticality in random threshold networks: annealed approximation and beyond. Physica A 310, 245–259 (2002).

  30. 30.

    The Origins of Order: Self Organization and Selection in Evolution (Oxford Univ. Press, New York, 1993).

Download references

Acknowledgements

We thank L. P. Kadanoff for stimulating discussions and we are also thankful to M. Aldana, C. Guet and T. Emonet for useful comments. This work was supported by the Materials Research Science and Engineering Center program of the National Science Foundation under NSF DMR-0213745. We gratefully acknowledge use of the ‘Jazz’ cluster operated by the Mathematics and Computer Science Division at Argonne National Laboratory.

Author information

Affiliations

  1. The James Franck Institute and Institute for Biophysical Dynamics, Department of Physics, University of Chicago, Gordon Center for Integrative Science, 929 E. 57th St, Chicago, Illinois 60637, USA

    • Panos Oikonomou
    •  & Philippe Cluzel

Authors

  1. Search for Panos Oikonomou in:

  2. Search for Philippe Cluzel in:

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Panos Oikonomou or Philippe Cluzel.

Supplementary information

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nphys359

Further reading