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arXiv · 2606.28418

Metabolic scaling, von Bertalanffy growth and an exponent equation

Hana Krakovská·Klaus Stiefel·Rudolf Hanel
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Abstract

In this work, we interpret developmental growth as a metabolic energy allocation problem and link the von Bertalanffy growth model to metabolic energy investments into the growth channel. Using a framework that specifies how metabolic energy is allocated among baseline maintenance, growth, and other processes, we analyse the resulting growth allocation patterns and derive direct relationships between key scaling exponents: the mass-growth exponent, the length-based exponent, the metabolic scaling exponent, and the geometric exponent, which describes the mass-length relationship. These exponents determine the metabolic investment exponent, which controls the qualitative behaviour of the growth-allocation function. Requiring the inferred allocation fraction to remain biologically feasible, we derive constraints on developmental velocity and characteristic mass scales. This provides a physical, energy-based interpretation of phenomenological growth curves and clarifies how metabolic scaling, geometric scaling, and growth dynamics are interrelated within a single allocation framework.

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Hana Krakovská, Klaus Stiefel, Rudolf Hanel. 2026-06-25. Metabolic scaling, von Bertalanffy growth and an exponent equation. https://arxiv.org/abs/2606.28418

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