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  3. Metabolic Scaling From Fibonacci Dynamics.
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  3. Metabolic Scaling From Fibonacci Dynamics.

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Metabolic Scaling from Fibonacci Dynamics.

Dorilson Silva Cambui1

  • 1Governo de Mato Grosso, Secretaria de Estado de Educação de Mato Grosso - SEDUC/MT, Eng. Edgar Prado Arze, Cuiabá, 78049-909, Mato Grosso, Brazil. dcambui@fisica.ufmt.br.

Acta Biotheoretica
|May 14, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

We introduce a new discrete model for metabolic scaling based on geometric growth and Fibonacci recursion. This approach better explains stage-specific metabolic variations in mammals compared to continuous models.

Keywords:
Developmental allometryFibonacci growthMetabolic scaling

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Area of Science:

  • Metabolic scaling
  • Developmental biology
  • Allometry

Background:

  • Continuous fractal models like West-Brown-Enquist (WBE) theory are standard for metabolic scaling.
  • These models often assume a constant scaling exponent, which may not capture developmental variations.

Purpose of the Study:

  • To propose a discrete, stage-dependent model for metabolic scaling.
  • To offer an alternative to continuous models by incorporating geometric growth and Fibonacci recursion.
  • To explain stage-specific deviations from classical allometric scaling laws.

Main Methods:

  • Developed a discrete model where metabolism is the cumulative activity of structures from prior stages.
  • Used Fibonacci recursion as an archetype for geometric growth across developmental steps.
  • Derived a stage-dependent scaling exponent b(n) from a logarithmic relation between consecutive stages.

    • Main Results:

    • The discrete model shows improved agreement with empirical mammalian metabolic data compared to the WBE model.
    • Model-based scaling exponents b(n) were closer to intraspecific estimates across nine species.
    • Successfully inferred the developmental stage index n using birth mass and mass at stage n, linked to the golden ratio.

    Conclusions:

    • The proposed discrete model effectively captures systematic, stage-specific departures from constant metabolic scaling exponents.
    • This framework provides a mechanism linking recursive growth patterns to metabolic scaling.
    • Offers insights into the origins of deviations from classical allometric scaling in developing organisms.