Stomatal area estimation based on stomatal length and width of four Magnoliaceae species: even “kidney”-shaped stomata are not elliptical

Zhang, Liuyue; Niklas, Karl J.; Niinemets, Ülo; Li, Qiying; Yu, Kexin; Li, J. M.; Chen, Lei; Shi, Peijian

doi:10.1007/s00468-023-02425-1

Cited by 3 publications

(2 citation statements)

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“…The stomatal length (L) and width (W) were directly measured using ImageJ software (version 1.54g; https://imagej.nih.gov/ij/index.html (accessed on 1 March 2024)), and stomatal area (i.e., the area profile formed by two guard cells) was estimated as 0.811 × LW. The site and sampling information are provided in [15], and the validity of the estimation method on the stomatal area is provided in [16].…”

Section: Data Of Plant (Organ) Size Distributionsmentioning

confidence: 99%

“…It is based on the Lorenz curve (LC), which is a graphical representation of the cumulative proportion (or percentage) of household income plotted against the cumulative proportion (or percentage) of the number of households in the economy [1]. The Gini coefficient is equal to the area formed by the LC and the line of absolute equality Symmetry 2024, 16, 565 2 of 14 (i.e., y = x) divided by one half of the area of the unit square. Botanists have used the Gini coefficient to quantify the variation in tree and seed size [2,3], but few studies have checked the validity of the LC in describing the size distributions of other organic structures.…”

Section: Introductionmentioning

confidence: 99%

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Rotated Lorenz Curves of Biological Size Distributions Follow Two Performance Equations

Shi,

Deng,

Niklas

2024

Symmetry

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The Lorenz curve is used to describe the relationship between the cumulative proportion of household income and the number of households of an economy. The extent to which the Lorenz curve deviates from the line of equality (i.e., y = x) is quantified by the Gini coefficient. Prior models are based on the simulated and empirical data of income distributions. In biology, the Lorenz curves of cell or organ size distributions tend to have similar shapes. When the Lorenz curve is rotated by 135 degrees counterclockwise and shifted to the right by a distance of 2, a three-parameter performance equation (PE), and its generalized version with five parameters (GPE), accurately describe this rotated and right-shifted curve. However, in prior studies, PE and GPE were not compared with the other Lorenz equations, and little is known about whether the skewness of the distribution could influence the validity of these equations. To address these two issues, simulation data from the beta distributions with different skewness values and six empirical datasets of plant (organ) size distributions were used to compare PE and GPE with three other Lorenz equations in describing the rotated and right-shifted plant (organ) size distributions. The root-mean-square error and Akaike information criterion were used to assess the validity of the two performance equations and the three other Lorenz equations. PE and GPE were both validated in describing the rotated and right-shifted simulation and empirical data of plant (organ) distributions. Nevertheless, GPE worked better than PE and the three other Lorenz equations from the perspectives of the goodness of fit, and the trade-off between the goodness of fit and the model structural complexity. Analyses indicate that GPE provides a powerful tool for quantifying size distributions across a broad spectrum of organic entities and can be used in a variety of ecological and evolutionary applications. Even for the simulation data from hypothetical extreme skewed distribution curves, GPE still worked well.

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Section: Data Of Plant (Organ) Size Distributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Rotated Lorenz Curves of Biological Size Distributions Follow Two Performance Equations

Shi,

Deng,

Niklas

2024

Symmetry

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Using the Montgomery–Koyama–Smith equation to calculate the stomatal area per unit lamina area for 12 Magnoliaceae species

Yan,

Shi,

et al. 2024

Annals of Botany

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Background and aims The Montgomery-Koyama-Smith (MKS) equation predicts that total leaf area per shoot is proportional to the product of the sum of individual leaf widths and maximum individual leaf length, which has been validated for some herbaceous and woody plants. The equation is also predicted to be valid in describing the relationship between the total stomatal area per micrograph (AT) and the product of the sum of individual stomatal widths (denoted as LKS) and maximum individual stomatal length (denoted by WKS) in any particular micrograph. Methods To test the validity of the MKS equation, 69,931 stomata (from 720 stomatal micrographs from 12 Magnoliaceae species) were examined. The area of each stoma was calculated using empirical measurements of stomatal length and width multiplied by a constant. Six equations describing the relationships among AT, LKS, and WKS were compared. The root-mean-square (RMSE) and the Akaike information criterion (AIC) were used to measure the goodness of fit, and the trade-off between the goodness of fit and the structural complexity of each model, respectively. Key Results Analyses supported the validity of the MKS equation and the power-law equation AT ∝ (LKS∙WKS)α, where a is a scaling exponent. The estimated values of α at the species level and for the pooled data were all statistically smaller than unity, which did not support the hypothesis that AT ∝ LTS∙WTS. The power-law equation had smaller RMSE and AIC values than the MKS equation for the data from the 12 individual species and the pooled data. Conclusions These results indicate that AT tends to allometrically scale with LKS∙WKS, and that increases in AT do not keep pace with increases in LTS∙WTS. In addition, using the product of LKS and WKS is better than using only one of the two variables.

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Testing the Validity of the Montgomery–Koyama–Smith Equation for Calculating the Total Petal Area per Flower Using Two Rosaceae Species

Zhao,

Wang,

et al. 2024

Plants

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The size of floral organs is closely related to the successful reproduction of plants, and corolla size is, to some extent, indicative of the size of floral organs. Petals are considered homologous to leaves, so we also attempted to estimate the area of a single petal using a method (i.e., the Montgomery equation) that is typically employed for estimating single leaf area. Additionally, we estimated the total petal area per flower (AT; i.e., the whole corolla area) using a method (i.e., the Montgomery–Koyama–Smith equation) designed for estimating the total leaf area per shoot. The Montgomery equation (ME) estimates the leaf area by assuming that the leaf area is proportional to the product of leaf length and width. The Montgomery–Koyama–Smith equation (MKSE) assumes that the total leaf area per shoot is proportional to the product of the sum of individual leaf widths and the maximum individual leaf length. To test the validity of the ME for predicting petal area, a total of 1005 petals from 123 flowers of two Rosaceae species, which exhibit a certain variation in petal shape, were used to fit the relationship between the petal area (A) and the product of petal length (L) and width (W). Two equations, including the MKSE and a power-law equation (PLE), were used to describe the relationship between the total petal area per flower and the product of the sum of individual petal widths and the maximum individual petal length. The RMSE and the Akaike information criterion (AIC) were used to measure the goodness of fit and the structural complexity of each equation. The results show that the ME has a low RMSE value and a high correlation coefficient when fitting the relationship between A and LW for either of the two species. Additionally, the MKSE and the PLE exhibit low RMSEs and AICs for estimating the AT of both Rosaceae species. These results indicate that the ME, MKSE, and PLE are effective in predicting petal area and corolla area, respectively. The use of these models will significantly reduce the time, labor, and financial costs of future petal area and corolla area measurements.

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Stomatal area estimation based on stomatal length and width of four Magnoliaceae species: even “kidney”-shaped stomata are not elliptical

Cited by 3 publications

References 39 publications

Rotated Lorenz Curves of Biological Size Distributions Follow Two Performance Equations

Rotated Lorenz Curves of Biological Size Distributions Follow Two Performance Equations

Using the Montgomery–Koyama–Smith equation to calculate the stomatal area per unit lamina area for 12 Magnoliaceae species

Testing the Validity of the Montgomery–Koyama–Smith Equation for Calculating the Total Petal Area per Flower Using Two Rosaceae Species

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