Cauchy--Schwarz inequality predicts biomass allocation and tree size-shape allometry

Cauchy--Schwarz inequality predicts biomass allocation and tree size-shape allometry | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 25 November 2025 V1 Latest version Share on Cauchy--Schwarz inequality predicts biomass allocation and tree size-shape allometry Author : Dimitris ZIANIS 0000-0002-6005-4129 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176405243.35631960/v1 120 views 56 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Biomass scaling with size and partitioning of organic matter among tree components, are critical to linking plant form, function, and carbon dynamics. Here, the Cauchy–Schwarz inequality—a fundamental relation in mathematics— is introduced as a general geometrical framework for predicting biomass allocation and size–shape allometry in trees. Using two independent datasets (288 trees from the BAAD database (Falster et al ., 2015) and 1,430 diameter–biomass pairs from 35 studies), the hypothesis that this inequality captures universal constraints governing biomass distribution, was tested. The inequality-based model explained 75% of the variance in root biomass and reproduced empirical diameter–biomass scaling with accuracy comparable to classical allometries, despite requiring only two trees for calibration. These findings reveal that the Cauchy–Schwarz inequality provides a simple yet powerful expression of proportionality and constraint in living systems, offering a unifying bridge between mathematical symmetry and biological organization across forest ecosystems. Supplementary Material File (ms_16_mathmeth.docx) Download 189.79 KB Information & Authors Information Version history V1 Version 1 25 November 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords allometry biomass allocation carbon estimation cauchy–schwarz inequality scaling size–shape relationships trees Authors Affiliations Dimitris ZIANIS 0000-0002-6005-4129 [email protected] Agricultural University of Athens View all articles by this author Metrics & Citations Metrics Article Usage 120 views 56 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Dimitris ZIANIS. Cauchy--Schwarz inequality predicts biomass allocation and tree size-shape allometry. Authorea . 25 November 2025. DOI: https://doi.org/10.22541/au.176405243.35631960/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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