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Published on: October 1, 2011
A general basis for quarter-power scaling in animals
Jayanth R Banavar1, Melanie E Moses, James H Brown
1Department of Physics, Pennsylvania State University, University Park, 16802, USA.
Summary
Animal metabolic rate scales with body mass to the 3/4 power, explained by resource distribution network models. This quarter-power scaling emerges from flow velocity matching network dimensions, applicable to biological and engineered systems.
Area of Science:
- Biology
- Physics
- Engineering
Background:
- Metabolic rate in animals exhibits predictable scaling with body mass.
- A common scaling exponent is approximately 3/4, a value observed across diverse species.
Purpose of the Study:
- To explain the emergence of the 3/4 metabolic scaling exponent.
- To explore the underlying principles governing resource distribution networks.
Main Methods:
- Analysis of two resource distribution network models: radial explosion and hierarchically branched.
- Investigation of how flow velocity influences scaling exponents.
Main Results:
- Both models naturally yield a 2/3 exponent with constant flow velocity.
- A maximum exponent of 3/4 is achieved when flow velocity scales with a 1/12 exponent.
- Quarter-power scaling can occur without fractal network structures.
Conclusions:
- The 3/4 metabolic scaling exponent can be explained by matching flow velocity to network dimensions.
- These principles apply to the optimal design of systems distributing energy, materials, or information.
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