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Scaling relations in food webs.

L A Barbosa1, A Castro e Silva, J Kamphorst Leal da Silva

  • 1Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, C.P. 702, 30123-970, Belo Horizonte, MG, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 23, 2006
PubMed
Summary

This study reveals that the energy transport efficiency exponent in food webs is not universal. Its value depends on the food web

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Area of Science:

  • Ecology
  • Network Theory
  • Theoretical Biology

Background:

  • Researchers have sought universal patterns in food web structures for decades.
  • A recent proposal suggested a universal value for the energy transport efficiency exponent (eta = 1.13).

Purpose of the Study:

  • To establish bounds for the energy transport efficiency exponent (eta) in general spanning trees.
  • To investigate the dependence of eta on food web size and structure.

Main Methods:

  • Analytical derivation of lower and upper bounds for eta.
  • Numerical evaluation of eta for hierarchical and random networks.
  • Analysis of eta's behavior with varying numbers of trophic species (K) and levels (M).

Main Results:

  • Lower and upper bounds for eta converge to 1 as the number of species (K) increases.
  • The previously proposed universal value (eta = 1.13) is attributed to finite-size effects.
  • The exponent eta is demonstrably dependent on the size (K) of the food web, approaching 1 for large K.
  • This finding holds true for any fixed number of trophic levels (M).

Conclusions:

  • The energy transport efficiency exponent in food webs is not a universal constant.
  • Food web size significantly influences the value of the eta exponent.
  • The universal value of eta = 1.13 is an artifact of small food web sizes.

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