Year: 2026
Type: preprint
Abstract: A “ fundamental but unanswered biological question” is how much energy life forms expend per unit mass and time to remain alive [1]. The West–Brown–Enquist (WBE) theory explains Kleiber’s 3 / 4-power law [2] through complex vascular networks [3–14], but assumes “size-invariant terminal units” and predicts neither absolute rates, small-organism linearity, nor group-specific levels. Yet capillary dimensions vary with body mass [15] and obey Murray’s optimization principle [16]. Furthermore, 3 / 4-power scaling occurs in planarians with a simple tubular metabolic system [17]. Here we extend Krogh’s capillary–tissue unit [18] to an optimized mesoscale oxygen-transport system, the Metabolic Holon (MH). Krogh’s geometry, Murray’s minimum-work principle, and optimal oxygen utilization determine its geometry and operating state. Kleiber’s asymptote thus emerges from an optimized Krogh unit, without requiring complex vascular-network architecture; repetition and within-group body-mass-invariant topology determine organismal metabolism. Without fitting metabolicrate data, MH predicts absolute rates across 18 orders of magnitude ( R 2 = 97.7 %), including linear scaling and group-specific Kleiber asymptotes. Independent dimensional analysis recovers these asymptotes. The theory also predicts absolute mammalian heart rates without calibration; absolute lifespan additionally requires an empirical lifetime-heartbeat constraint. By representing evolutionary selection and adaptation through mesoscale optimization, the theory explains why “mass-specific metabolic rates are strikingly similar across life’s major domains” [1].
Authors: Peter F. Pelz, Tobias Meck
Institution: Technische Universität Darmstadt
Language: English
Subfield: Ecology
Field: Environmental Science
Domain: Physical Sciences
Open Access status: green
Funder: Technische Universität Darmstadt
OpenAlex ID: W7211990744