Local optimization of oxygen transport gives rise to Kleiber's law
- 1Fluidsystemtechnik, TU Darmstadt
Abstract
A fundamental but unanswered biological question is how much energy life forms expend per unit mass and time to remain alive (Makarieva et al., 2008). The West-Brown-Enquist (WBE) theory explains Kleiber's 3/4-power law (Kleiber, 1932) through complex vascular networks (West et al., 1997; Banavar et al., 1999; West et al., 1999; Dodds et al., 2001; Gillooly et al., 2001; West et al., 2002; Banavar et al., 2002; Kozowski & Konarzewski, 2004; Brown et al., 2005; White et al., 2007; Savage et al., 2008; Apol et al., 2008), 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 (Dawson, 2003) and obey Murray's optimization principle (Murray, 1926). Furthermore, 3/4-power scaling occurs in planarians with a simple tubular metabolic system (Thommen et al., 2019). Here we extend Krogh's capillary--tissue unit (Krogh, 1919) 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 metabolic-rate 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" (Makarieva et al., 2008).
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BibTeX
@misc{pelz2026local,
title = {{Local optimization of oxygen transport gives rise to Kleiber's law}},
author = {P. F. Pelz and T. C. Meck},
howpublished = {bioRxiv},
year = {2026},
month = sep,
doi = {10.64898/2026.09.03.749078},
url = {https://www.biorxiv.org/content/10.64898/2026.09.03.749078v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Local optimization of oxygen transport gives rise to Kleiber's law
AU - P. F. Pelz
AU - T. C. Meck
PY - 2026
DA - 2026/09/03
PB - bioRxiv
DO - 10.64898/2026.09.03.749078
UR - https://www.biorxiv.org/content/10.64898/2026.09.03.749078v1
AB - A fundamental but unanswered biological question is how much energy life forms expend per unit mass and time to remain alive (Makarieva et al., 2008). The West-Brown-Enquist (WBE) theory explains Kleiber's 3/4-power law (Kleiber, 1932) through complex vascular networks (West et al., 1997; Banavar et al., 1999; West et al., 1999; Dodds et al., 2001; Gillooly et al., 2001; West et al., 2002; Banavar et al., 2002; Kozowski & Konarzewski, 2004; Brown et al., 2005; White et al., 2007; Savage et al., 2008; Apol et al., 2008), 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 (Dawson, 2003) and obey Murray's optimization principle (Murray, 1926). Furthermore, 3/4-power scaling occurs in planarians with a simple tubular metabolic system (Thommen et al., 2019). Here we extend Krogh's capillary--tissue unit (Krogh, 1919) 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 metabolic-rate 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" (Makarieva et al., 2008).
ER -