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The common patterns of nature.

S A Frank1

  • 1Department of Ecology and Evolutionary Biology, University of California, Irvine, CA 92697-2525, USA. safrank@uci.edu

Journal of Evolutionary Biology
|June 23, 2009
PubMed
Summary

Neutral generative models explain natural patterns by assuming random processes. This study reveals these models succeed due to information constraints, linking patterns like Gaussian and power law to specific information preservation rules.

Area of Science:

  • Complex systems
  • Statistical modeling
  • Information theory

Background:

  • Large-scale natural phenomena often emerge from numerous small-scale interactions.
  • Neutral generative models, assuming random microscopic processes, frequently replicate observed macroscopic patterns.
  • Examples include disease onset, molecular evolution, and ecological community dynamics.

Purpose of the Study:

  • To explain the success of neutral generative models in describing natural patterns.
  • To elucidate the theoretical basis connecting classic statistical patterns (e.g., Poisson, Gaussian) to neutral processes.
  • To introduce an informational framework for understanding these patterns and their underlying constraints.

Main Methods:

  • Theoretical analysis of neutral generative models.

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  • Investigation of information constraints associated with common statistical patterns.
  • Application of the maximum entropy principle to develop a unified informational framework.

    • Main Results:

    • Demonstrated that neutral generative models align with patterns arising from specific information constraints.
    • Showcased how preserving information about the mean leads to exponential patterns, mean/variance to Gaussian, and geometric mean to power law.
    • Established a framework where neutral models are special cases of broader non-neutral processes defined by information constraints.

    Conclusions:

    • The success of neutral generative models is rooted in underlying information-theoretic principles.
    • Common natural patterns are explained by the way information is constrained or preserved during aggregation of processes.
    • The maximum entropy framework unifies diverse neutral patterns under a single informational perspective, applicable to non-neutral processes as well.