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

Abstract

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.