Jinfeng Wang

Leaf size and the total number of leaves per shoot (N_T) reflect plant resource allocation strategies. Although studies often focus on single leaves, the leaf scaling relationships at the whole-shoot level are less known, especially in species with vertical leaf arrangements. This study investigates how total leaf area (A_T), total leaf dry mass per shoot (M_T), and N_T scale with each other in the bamboo Semiarundinaria densiflora, which has a near-vertical foliage structure. We sampled 121 culms with over 9200 leaves and measured A_T, M_T, N_T, and maximum individual leaf area per culm (A_max). The scaling relationships were examined using reduced major axis regression protocols. The distribution of N_T was modeled with a negative binomial distribution. N_T fit a negative binomial distribution. A_T and M_T scaled allometrically with N_T, with scaling exponents > 1. A_T scaled isometrically with both the product of N_T and A_max, and with M_T. The vertical foliage in S. densiflora leads to self-shading, promoting larger, thinner basipetal shade leaves. This results in a disproportionate increase in A_T with N_T and an isometric A_T vs. M_T relationship, which contrasts with the “diminishing returns” pattern seen in individual leaves. Canopy architecture therefore is key in shaping biomass allocation.

Distinctions between plant perianths are often defined by structural variations, which makes it critical to understand species evolution through the lens of morphological differentiation. Additionally, the size of the perianth is often closely related to the successful reproduction of plants, and the perianth area is generally considered one of the indicators of perianth size. The Montgomery equation (ME) hypothesizes that the individual leaf area is proportional to the product of leaf length and width, with the proportionality coefficient referred to as the Montgomery parameter (MP). To test the validity of the ME for calculating the tepal area, a total of 541 tepals (including petaloid and sepaloid tepals, which have similar shapes but different colors) from 60 Liriodendron × sinoamericanum P.C. Yieh ex C.B. Shang & Z.R. Wang flowers were used to fit the relationship between the tepal area (A) and the product of the tepal length (L) and width (W). Furthermore, this study compared whether there were significant differences in MPs between the two types of tepals, as well as differences in the fitting performance of the ME for each type. The root-mean-square error (RMSE) and mean absolute percentage error (MAPE) were used to assess the goodness of fit. The results revealed that the ME had low RMSE values (A and LW for either of the two different types of tepals. These findings indicate that the ME is effective in predicting the tepal area. Furthermore, there was a difference between the MPs of the two types of tepals. However, since the ME fitting of the data for each tepal type individually, as well as the combined data, all yielded a good fitting performance, the difference between the two types of tepals can be considered negligible in terms of its impact on the fitting results. Therefore, based on the combined morphology and ME fitting results of the two types of tepals, the tepals in L. × sinoamericanum do not show obvious differentiation. This study provides new insights into the understanding of the differentiation of similar organs during the evolution of angiosperms.

The concept of a geometric series (GS) plays an important role in mathematics. However, it has been neglected in describing biological size series. Herein, we show that a GS describes the nonreproductive (perianth) parts of the flowers of four Magnoliaceae species and two Rosaceae species and the leaves of 60 Alangium chinense and 60 Shibataea chinensis shoots. The sorted areas of floral parts and leaves formed a sequence that was fitted by a GS with the mean of the quotients of two adjacent members in the sequence as the common ratio of a GS. The mean absolute percent error (MAPE) was used to measure the goodness of fit of each GS. Over 99.7% of the MAPE values (371 out of the 372 tested flowers) were less than 10%, and over 97.8% of the MAPE values were less than 5%. Likewise, over 77.5% of the MAPE values (93 out of the 120 tested shoots) were less than 10%, and over 35% of the MAPE values were less than 5%. These analyses provide empirical evidence that the GS exists in nature, and confirm the usefulness of a classical algebraic formula for the study of plant developmental biology.

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 to be homologous to leaves, so we also attempted to estimate the area of a single petal using the method that is typically employed for estimating single leaf area (i.e., the Montgomery equation). Additionally, we estimated the total petal area per flower (A_T; i.e., the whole corolla area) using the method designed for estimating the total leaf area per shoot (i.e., the Montgomery–Koyama–Smith equation). 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 root-mean-square error (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 model’s structural complexity for 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 A_T of both Rosaceae species. These results indicate that the ME, MKSE, and PLE are effective in predicting individual petal area and total corolla area, respectively.

The “leafing intensity premium” hypothesis proposes that leaf size results from natural selection acting on different leafing intensities, i.e., the number of leaves per unit shoot volume or mass. The scaling relationships among various above-ground functional traits in the context of this hypothesis are important for understanding plant growth and ecology. Yet, they have not been sufficiently studied. In this study, we selected four bamboo species of the genus Indocalamus Nakai and measured the total leaf fresh mass per culm, total non-leaf above-ground fresh mass, total number of leaves per culm, and above-ground culm height of 90 culms from each species. These data were used to calculate leafing intensity (i.e., the total number of leaves per culm divided by the total non-leaf above-ground fresh mass) and mean leaf fresh mass per culm (i.e., the total leaf fresh mass per culm divided by the total number of leaves per culm). Reduced major axis regression protocols were then used to determine the scaling relationships among the various above-ground functional traits and leafing intensity. Among the four species, three exhibited an isometric (one-to-one) relationship between the total leaf fresh mass per culm and the total non-leaf above-ground fresh mass, whereas one species (Indocalamus pumilus) exhibited an allometric (not one-to-one) relationship. A negative isometric relationship was found between the mean leaf fresh mass per culm and the leafing intensity for one species (Indocalamus pedalis), whereas three negative allometric relationships between mean leaf fresh mass per culm and leafing intensity were observed for the other three species and the pooled data. An exploration of the alternative definitions of “leafing intensity” showed that the total number of leaves per culm divided by the above-ground culm height is superior because it facilitates the non-destructive calculation of leafing intensity for Indocalamus species. These results not only confirm the leafing intensity premium hypothesis for bamboo species but also highlight the interconnected scaling relationships among different functional traits, thereby contributing to our understanding of the ecological and evolutionary significance of leaf size variation and biomass investment strategies.

In nature, the fruit shapes of many plants resemble avian eggs, a form extensively studied as solids of revolution. Despite this, the hypothesis that egg-shaped fruits are themselves solids of revolution remains unvalidated. To address this, 751 Cucumis melo L. var. agrestis Naud. fruits were photographed, and the two-dimensional (2D) boundary coordinates of each fruit profile were digitized. Then, the explicit Preston equation (EPE), a universal egg-shape model, was used to fit the 2D boundary coordinates to obtain the estimates of the EPE’s parameters of each fruit. Under the hypothesis that egg-shaped fruits are solids of revolution, the fruit volumes were estimated using the solid of revolution formula based on the estimated EPE’s parameters. To test whether the fruits are solids of revolution, the fruit volumes were measured by using a graduated cylinder and compared with the estimated volumes using the solid of revolution formula. The EPE was demonstrated to be valid in describing the 2D profiles of C. melo var. agrestis fruits. There was a significant correlation between the measured fruit volumes using the graduated cylinder and the estimated fruit volumes using the solid of revolution formula based on the estimated EPE’s parameters. Acknowledging potential measurement errors, particularly fruit fuzz causing air bubbles during volume measurements, we recognize slight deviations between measured volumes and estimated values. Despite this, our findings strongly suggest that C. melo var. agrestis fruits are solids of revolution. This study contributes insights into the evolutionary aspects of fruit geometries in plants with egg-shaped fruits and introduces a practical tool for non-destructively calculating fruit volume and surface area based on photographed 2D fruit profiles.