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Looplessness in networks is linked to trophic coherence.

Samuel Johnson1,2, Nick S Jones3

  • 1Warwick Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom; S.Johnson.2@warwick.ac.uk.

Proceedings of the National Academy of Sciences of the United States of America
|May 18, 2017
PubMed
Summary
This summary is machine-generated.

Natural systems often lack feedback loops for stability. This study reveals that trophic coherence, a measure of distinct levels in networks, determines feedback loop presence and network stability, suggesting coherence mechanisms drive looplessness.

Keywords:
feedbackfood websnetworksstabilitytrophic coherence

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Area of Science:

  • Complex systems analysis
  • Network theory
  • Systems biology

Background:

  • Many natural systems exhibit remarkable stability due to a lack of feedback loops.
  • Network representations of these systems show few or no cycles and small leading eigenvalues.
  • The architectural advantage of loopless structures, such as
  • qualitative stability,
  • remains unexplained.

Purpose of the Study:

  • To elucidate the structural properties determining feedback loops in complex systems.
  • To explain the origin of loopless network structures observed in nature.
  • To link network feedback to a quantifiable structural property.

Main Methods:

  • Introduced trophic coherence as a measure of how neatly nodes fall into distinct levels within a network.
  • Analyzed the relationship between trophic coherence and the number of feedback loops.
  • Examined eigenvalues of associated matrices in relation to network structure.
  • Developed a null model to assess the significance of feedback magnitudes.

Main Results:

  • Trophic coherence determines the number of feedback loops and network eigenvalues.
  • Networks were classified into high and low feedback regimes based on trophic coherence.
  • The theory successfully classified diverse networks, including those from biological, computational, and economic systems.
  • Coherence was found to suppress feedback, but feedback absence does not inherently lead to coherence.

Conclusions:

  • Trophic coherence is the key structural property governing feedback loops in complex networks.
  • The prevalence of loopless structures in nature is likely driven by coherence-inducing mechanisms.
  • Understanding trophic coherence offers insights into the stability and organization of natural systems.