Search bioRxiv⌕ Search
Home/Archive/bioRxiv

bioRxiv · 10.1101/2025.01.08.632031

The Existence and Uniqueness of Solutions in the Leaf Photosynthesis-Transpiration-Stomatal Conductance Model

Masutomi, Y.·Kobayashi, K.
View original source ↗Export metadata ↓

Abstract

The An-E-gs model, which consistently describes leaf photosynthesis (An), transpiration (E), and stomatal conductance (gs), is widely recognized and utilized as a "standard model" for quantifying these processes in terrestrial plants. However, since its proposal over 30 years ago, the model has faced a longstanding challenge: the "solution selection" problem, arising from the existence of multiple solutions with no guarantee that the obtained solution is correct. In this study, we mathematically proved that the An-E-gs model always has a unique solution satisfying the criteria gs > 0 and Ci > 0, where Ci represents the CO2 concentration inside the leaf. This result establishes a rigorous mathematical theorem on the existence and uniqueness of solutions in the model. The theorem resolves the longstanding "solution selection" problem by enabling the unambiguous identification of the correct solution through selecting the unique solution that satisfies these criteria. Furthermore, the theorem ensures the validity of past estimations that satisfy these criteria and guarantees that future studies applying these criteria will yield correct estimations. These findings provide a robust mathematical foundation for the An-E-gs model, reinforcing its role as the standard model for estimating leaf photosynthesis, transpiration, and stomatal conductance across diverse disciplines, from plant biology to climate science and beyond.

Explore related subjects

plant biologyPreprint

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Masutomi, Y., Kobayashi, K.. 2025-01-13. The Existence and Uniqueness of Solutions in the Leaf Photosynthesis-Transpiration-Stomatal Conductance Model. https://doi.org/10.1101/2025.01.08.632031

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related preprints

bioRxiv2026

Seeding paradise: germination ecophysiology of Xyris paradisiaca Wand. (Xyridaceae), an endangered endemic species from Central Brazil

Seed ecophysiology is essential for understanding plant regeneration and developing effective conservation and ecological restoration strategies, yet knowledge remains scarce for most threatened Cerrado species. We characterised the germination niche, desiccation tolerance and storage behaviour of Xyris paradisiaca (Xyridaceae), an Endangered species endemic to Central Brazil, to assess whether its restricted distribution is associated with narrow germination requirements and to inform seed-based conservation. Germination was tested across light regimes, constant temperatures, decreasing water potentials and short-duration heat shocks, while thermal- and hydro-time models were used to quantify thermal and hydric thresholds. Seeds exhibited an absolute light requirement but broad abiotic tolerances. Germination remained >87% between 15 and 40 {degrees}C, with estimated cardinal temperatures of Tb = 8.94 {degrees}C, To = 33.13 {degrees}C and Tc = 45.53 {degrees}C. Germination remained similar to the control down to -0.6 MPa and exceeded 40% at -1.0 MPa, with a median base water potential of {Psi}b = -1.03 MPa. Germination also remained high after 1-min heat shocks up to 200 {degrees}C. Seeds were desiccation tolerant, with 100% germination after drying and a viability loss index of -0.04, and germination remained >90% after 24 months of ambient storage. Thus, the highly restricted distribution of X. paradisiaca is not driven by a narrow physiological germination niche. Its broad environmental tolerances, desiccation tolerance and favourable storage behaviour also highlight its unexplored potential for seed-based restoration, propagation and ex situ conservation.

plant biology↗
bioRxiv2026

Planted origin of shade trees: a robust determinant of cocoa yield among smallholder farmers in Cote d'Ivoire

CONTEXT: While the agroeconomic literature on the determinants of cocoa yield among West African smallholders is abundant, it remains dominated by descriptive studies or work conducted at an aggregated regional scale, leaving open the question of the role of shade-tree management practices at the scale of the individual plantation. OBJECTIVE: This study tests whether shade-tree management practices and the farmer's socio-demographic profile explain variation in cocoa yield, using a nationwide sample of 409 plantations covering, for the first time, the three major Ivorian production zones (loops) (98, 151 and 160 plantations for loops 1, 2 and 3, respectively). METHODS: A univariate screening of 27 variables, a mixed model with a random intercept by village, a production-function specification, LASSO variable selection, and a random forest were applied, all evaluated by 5-fold cross-validation. RESULTS AND CONCLUSIONS: The five approaches converge on a robust result: the deliberately planted origin of shade trees (as opposed to a residual or spontaneous origin) is the strongest and most stable determinant of yield, with a mean gap of 332 versus 183 kg/ha/year. This effect withstands four successive robustness checks: it remains significant after simultaneous adjustment for age, plantation size, production zone, technical extension, and farmer education; it is not driven by a handful of extreme plantations; it holds within each of the three production zones taken separately rather than in only one of them; and, taken in isolation, it retains a positive out-of-sample predictive power (cross-validated R2=8776; 0.05). A second group of robust determinants of more modest magnitude emerges for agricultural technical extension (ANADER/CNRA/SATMACI) and farmer education level; shade-tree alignment shows a signal in the same direction, consistent with recent independent work in Cote d'Ivoire, but becomes statistically marginal once adjusted for these other factors. The full multivariate model reaches a cross-validated R2 of around 0.07-0.08. SIGNIFICANCE: This signal, undetectable in an analysis restricted to loop 1 alone (n=98) for lack of statistical power, confirms the value of nationwide sampling for detecting modest but real agronomic determinants, and argues for integrating shade-tree origin into agroforestry extension programmes.

plant biology↗
bioRxiv2026

Parental Genome Assemblies of Suyunuo1 Reveal Structural Variation Underlying Edible Waxy Maize Evolution, Superior Hybrid Performance and Yield - Flavor Balance

Edible waxy maize is a unique domesticated cereal valued for its superior sensory and nutritional properties, yet high quality gap free genomes remain lacking, hindering the exploration of structural variations (SVs) and domestication related divergence. Here, we assembled two chromosome level, gap free genomes of the elite waxy maize inbred lines Tongxi 5 and Hengbai 522, the parents of the widely cultivated hybrid Suyunuo 1. Comparative genomic analysis revealed substantial genome size variation, prominent megabase scale SVs, and extensive knob repeat expansion in Tongxi 5. We identified widespread gene presence absence variation and hyperdivergent regions enriched in transposable elements, which largely underpin genomic differentiation between waxy and field maize. Population genomic analyses further demonstrated asymmetric introgression from field maize into the two parents, whereas the conserved waxy haplotype supports a shared ancestral origin. Integrative GWAS based on SNPs, InDels and SVs revealed that SVs substantially contribute to phenotypic diversity and mediate the co-regulation of yield traits and flavor-related metabolites. Our results uncover key genomic events underlying post-domestication divergence and highlight the essential roles of SVs in heterosis and flavor-yield balance, providing valuable genomic resources for waxy maize improvement.

plant biology↗