ABSTRACT
Previous studies have validated a performance equation (PE) and its generalized version (GPE) in describing the rotated and right-shifted Lorenz curves of organ size (e.g., leaf area and fruit volume) distributions of herbaceous plants. Nevertheless, there are still two questions that have not been adequately addressed by prior work: (i) whether the PE and GPE apply to woody plant species and (ii) how do the PE and GPE perform in comparison with other Lorenz equations when fitting data. To address these deficiencies, we measured the lamina length and width of each leaf on 60 Alangium chinense saplings to compare the performance of the PE and GPE with three other Lorenz equations in quantifying the inequality of leaf area distributions across individual trees. Leaf area is shown to be the product of a proportionality coefficient (k) and leaf length and width. To determine the numerical value of k, we scanned 540 leaves to obtain the leaf area empirically. Using the estimated k, the leaf areas of 60 A. chinense saplings were calculated. Using these data, the two performance equations and three other Lorenz equations were then compared and assessed using the root-mean-square error (RMSE) and Akaike information criterion (AIC). The PE and GPE were found to be valid in describing the rotated and right-shifted Lorenz curves of the A. chinense leaf area distributions, and GPE has the lowest RMSE and AIC values. This work validates the GPE as the best model in gauging variations in leaf area of the woody species.
ABSTRACT
BACKGROUND AND AIMS: Leaf area (A) is a crucial indicator of the photosynthetic capacity of plants. The Montgomery equation (ME), which hypothesizes that A is proportional to the product of leaf length (L) and width (W), is a valid tool for nondestructively measuring A for many broad-leaved plants. At present, the methods used to compute L and W for ME can be broadly divided into two kinds: using computer recognition, and measuring manually. However, the potential difference in the prediction accuracy using either method has not been thoroughly examined in prior studies. METHODS: In the present study, we measured 540 Alangium chinense leaves, 489 Liquidambar formosana leaves, and 215 Liriodendron × sinoamericanum leaves, utilizing computer recognition and manual measurement methods to determine L and W. ME was used to fit the data determined by the two methods, and the goodness of fits were compared. The prediction errors of A were analyzed by examining the correlations with two leaf symmetry indices (areal ratio of the left side to the right side, and standardized index for bilateral asymmetry), as well as the leaf shape complexity index (the leaf dissection index). KEY RESULTS: The results indicate that there is a neglectable difference in the estimation of A between both methods. This further validates that ME is an effective method for estimating A in broad-leaved tree species, including those with lobes. Additionally, leaf shape complexity significantly influenced the estimation of A. CONCLUSIONS: These results show that the use of computer recognition and manual measurement in the field are both effective and feasible, although the influence of leaf shape complexity should be considered when applying ME to estimate A in the future.