Youying Mu

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.

The production and operation of corporates have a significant impact on the environment, and it is crucial for corporates to operate in an environmentally friendly manner, especially in the context of the China double carbon target. Corporate environmental performance refers to the degree of impact on the environment and the degree of contribution to environmental protection by corporates in their business activities. Our study conducted an assessment and early warning system for corporate environmental performance by monitoring seven typical corporate environmental performance variables, including the green asset ratio (Gra), the proportion of environmentally friendly products (Pefp), and cash flow for environmental protection to total assets ratio (ECF), of 2718 non-financial listed corporates in China’s A-share market. The dataset comprised empirical data from the CSMAR database and multi-scale measurements collected by us. Among data-driven monitoring methods, deep learning is widely applied due to its powerful automatic feature extraction abilities. However, multi-time scale data is often encountered in industrial ecology-related data, as the different underlying physical quantities of various data result in inconsistent sampling rates. Multi-time scale data are incomplete and asymmetrical, making it difficult for traditional models to use directly for corporate ecological monitoring. In this article, an improved CNN-LSTM monitoring model based on data fusion is proposed to address this issue. This method employs unified vectorization processing to transform incomplete multi-time scale data into uniform complete data. An end-to-end diagnostic model is constructed to simultaneously optimize feature extraction and monitoring. In a multi-time scale corporate monitoring model, CNN can mine hidden features of data, while LSTM can further capture the time dependence of underlying time series. Compared to manual feature extraction that relies on prior knowledge, the proposed model can learn more effective data features. The effectiveness of the method has been demonstrated through empirical data experiments, which is beneficial for corporates in the context of double carbon emissions, providing a method for regulating corporate ecological indicators.