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<p>We propose a discrete, stage-dependent model for metabolic scaling grounded in approximately geometric growth across successive developmental steps, using Fibonacci recursion as an archetype. In contrast to continuous fractal models such as the West-Brown-Enquist (WBE) theory, our framework treats metabolism as the cumulative activity of structures formed in prior stages. The scaling exponent <i>b</i>(<i>n</i>) emerges from a logarithmic relation between consecutive stages and varies with the growth stage <i>n</i>. A refined logarithmic expression improves descriptive agreement with empirical mammalian data relative to the WBE baseline. Across nine species, model-based <i>b</i>(<i>n</i>) values are on average closer (mean deviation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(&lt;\!9\%\)</EquationSource> </InlineEquation>, with improvements up to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\sim \!12\%\)</EquationSource> </InlineEquation>) to intraspecific estimates. The stage index <i>n</i> is inferred deterministically as <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(n=\log _{\phi }(M(n)/M_0)\)</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\phi =(1+\sqrt{5})/2\)</EquationSource> </InlineEquation> is the golden ratio, from reported birth mass <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(M_0\)</EquationSource> </InlineEquation> and mass at stage <i>n</i>, <i>M</i>(<i>n</i>). The model is intended for moderate developmental stages under basal conditions and complements classical 2/3 and 3/4 baselines by capturing systematic, stage-specific departures from a single constant exponent. This discrete perspective clarifies when and why deviations from classical allometries arise and offers a compact mechanism linking recursive growth to metabolic scaling.</p>

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Metabolic Scaling from Fibonacci Dynamics

  • 期刊论文

  • 发表日期：

    2026年5月14日

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  • Dorilson Silva Cambui

摘要

We propose a discrete, stage-dependent model for metabolic scaling grounded in approximately geometric growth across successive developmental steps, using Fibonacci recursion as an archetype. In contrast to continuous fractal models such as the West-Brown-Enquist (WBE) theory, our framework treats metabolism as the cumulative activity of structures formed in prior stages. The scaling exponent b(n) emerges from a logarithmic relation between consecutive stages and varies with the growth stage n. A refined logarithmic expression improves descriptive agreement with empirical mammalian data relative to the WBE baseline. Across nine species, model-based b(n) values are on average closer (mean deviation \(<\!9\%\) , with improvements up to \(\sim \!12\%\) ) to intraspecific estimates. The stage index n is inferred deterministically as \(n=\log _{\phi }(M(n)/M_0)\) , where \(\phi =(1+\sqrt{5})/2\) is the golden ratio, from reported birth mass \(M_0\) and mass at stage n, M(n). The model is intended for moderate developmental stages under basal conditions and complements classical 2/3 and 3/4 baselines by capturing systematic, stage-specific departures from a single constant exponent. This discrete perspective clarifies when and why deviations from classical allometries arise and offers a compact mechanism linking recursive growth to metabolic scaling.