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In recent years, the impacts of climate change and human activities have intensified the loss and fragmentation of habitats for wild rare Magnoliaceae. Predicting the potential impacts of future climate change on the suitable habitat distribution of wild and endangered Magnoliaceae species is of great significance for their conservation and application. This study employs the optimized MaxEnt model to investigate current and future potential suitable habitats of three rare Magnoliaceae species (Michelia crassipes, Lirianthe coco, and Manglietia insignis). The dominant environmental variables influencing the distribution of three species were also explored. The results showed the following: (1) The potential habitat range of three Magnoliaceae species currently span from 92–122° N and 19–36° E. Variables associated with temperature (bio2, bio9, bio4) and altitude (Ele) significantly influence the distribution of these species, with precipitation (bio17) and ultraviolet radiation (UVB4) playing a minor role. The warm and humid climate in central and southern China is highly conducive to their growth. (2) Under the SSP126 scenario, after the mid-21st century, the suitable habitat area of Michelia crassipes has undergone a fluctuating trend of initial increase followed by decrease, reducing to 51.84 × 104 km2 in 2090. On the other hand, both the suitable habitat areas of Lirianthe coco and Manglietia insignis show an upward trend. Under the SSP245 and SSP585 scenarios, the total suitable habitat areas of these three rare Magnoliaceae species gradually decrease. (3) We compared the priority protection areas with existing Protected Areas (PAs) in gap analysis; 96.84% of priority conservation areas are lacking effective protection. (4) The distribution centroid is constantly moving to western China. In order to address habitat fragmentation, it is recommended that the range of natural reserves be expanded and ecological corridors be established in the future, preferably according to the predicted suitable climate for protected areas and refuges or habitats for these species. Overall, these findings provide valuable insights for the preservation, stewardship, and utilization of the endangered species of Magnoliaceae under the circumstances of projected global climate change.

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 (AT; 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 AT 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.

Total leaf area per shoot (AT) can reflect the photosynthetic capacity of a shoot. A prior study hypothesized that AT is proportional to the product of the sum of the individual leaf widths per shoot (LKS) and the maximum individual leaf length per shoot (WKS), referred to as the Montgomery–Koyama–Smith equation (MKSE). However, empirical evidence does not support such a proportional relationship hypothesis, as AT was found to allometrically scale with LKSWKS, i.e., AT∝LKSWKSα, where α≠1, referred to as the power law equation (PLE). Given that there is variation in the total number of leaves per shoot (n), little is known about whether the leaf area distribution has an explicit mathematical link with the sorted leaf area sequence per shoot, and it is unknown whether the mathematical link can affect the prediction accuracy of the MKSE and PLE. In the present study, the leaves of 500 shoots of a dwarf bamboo (Sasaella kongosanensis ‘Aureostriatus’) were scanned, and the leaf area, length, and width values were obtained by digitizing the leaf images. We selected the shoots with n ranging from 3 to 10, which accounted for 76.6% of the totally sampled shoots (388 out of 500 shoots). We used the formula for the sum of the first j terms (j ranging from 1 to n) of a geometric series (GS), with the mean of the quotients of any adjacent two terms (denoted as q¯A) per shoot as the common ratio of the GS, to fit the cumulative leaf area observations. Mean absolute percentage error (MAPE) was used to measure the goodness of fit of the GS. We found that there were 367 out of 388 shoots (94.6%) where 1 < q¯A < 1.618 and MAPE < 15%, and these 367 shoots were defined as valid samples. The GS hypothesis for leaf area distribution was supported by the result that the MAPE values for most valid samples (349 out of 367, i.e., 95.1%) were smaller than 5%. Here, we provide a theoretical basis using the GS hypothesis to demonstrate the validity of the MKSE and PLE. The MAPE values for the two equations to predict AT were smaller than 5%. This work demonstrates that the leaf area sequence per shoot follows a GS and provides a useful tool for the calculation of total leaf area per shoot, which is helpful to assess the photosynthetic capacity of plants.

Changes in species’ habitats provide important insights into the effects of climate change. Woonyoungia septentrionalis, a critically endangered species endemic to karst ecosystems, has a highly restricted distribution and is a key biological resource. Despite its ecological importance, the factors influencing its habitat suitability and distribution remain poorly understood. This study employed ecological niche modeling to predict the potential distribution of Woonyoungia septentrionalis across China and analyzed shifts in centroid location to explore migration pathways under current and future climate scenarios. The model exhibited high predictive accuracy (AUC = 0.988), indicating its robustness in assessing habitat suitability. Under current climatic conditions, Woonyoungia septentrionalis is predominantly found in the Guizhou–Guangxi border region, southeastern Yunnan, eastern Sichuan, southeastern Tibet, and parts of Chongqing, Hunan, and Hubei. Among these, the Guizhou-Guangxi border represents the primary suitable habitat. Temperature factors, particularly bio6 (minimum temperature of the coldest month) and bio7 (annual temperature range), were the most significant determinants of habitat suitability, contributing 43.29% and 12.65%, respectively. Soil cation exchange capacity (CEC) accounted for 15.82%, while precipitation had a relatively minor impact. Under future climate scenarios, suitable habitats for Woonyoungia septentrionalis are projected to shrink and shift toward higher altitudes and latitudes, increasing the risk of extinction due to the “mountain trap” effect, where migration is constrained by limited habitat at higher elevations. Stable habitats, particularly in Libo (Guizhou) and Huanjiang (Guangxi), are identified as critical refugia. We recommend prioritizing shrinking and stable habitats in Guizhou, Guangxi, and Yunnan for in situ conservation. Ex situ conservation efforts should focus on areas identified based on key environmental factors and predicted migration pathways to ensure the species’ long-term survival. This study provides both theoretical and practical guidance for the conservation of this species and its vulnerable habitat.

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.

The formation process of membrane fouling is complex and diverse, which is an important problem that needs to be overcome in membrane applications. In this paper, three foulant systems consisting of humic acid, humic acid plus Ca2+ and humic acid plus Ca2+ plus yeast were selected to compare membrane fouling processes with different aeration intensities. The aim was to establish the quantitative relationship between membrane fouling rate and shear stress, respectively, in a large-scale flat sheet MBR (FSMBR). The shear stress values at different aeration intensities were obtained using computational fluid dynamics (CFD). The membrane fouling rate during the filtration of different substances was measured by performing experiments. The comparison results showed that the membrane fouling rate varied greatly during the filtration of different substances. With the help of particle size distribution, the effect of different shear forces on floc size was further explored. Using the dual control of fouling rate and floc size, the recommended aeration intensity was 6~8 L/(m2·min).

Stomata are involved in transpiration and CO2 uptake by mediating gas exchange between internal plant tissues and the atmosphere. The capacity for gas exchange depends on stomatal density (SD), stomatal size, and pore dimensions. Most published work on stomatal quantification has assumed that stomatal distribution and stomatal density are spatially homogeneous across the leaf, but this assumption has been seldom tested. We selected 32 leaves from a Photinia hybrid, Photinia × fraseri ‘Red Robin’, and one of its parents, P. serratifolia. For each leaf, the leaf surface was divided into three or four equidistant layers along the apical–basal axis, and, in each layer, two positions, one closer to the midrib and the other closer to the leaf margin, were further selected. We calculated SD and mean nearest neighbor distance (MNND) for each lamina section and tested the scaling relationship between SD and MNND of the sampled stomatal centers using reduced major axis protocols. In addition, we calculated the stomatal aggregation index (SAI) for each lamina section to examine the spatial arrangement of stomata at the given size of field of view of 1.2 mm × 0.9 mm. We observed that SD decreased from the lamina apex towards the base for central lamina areas but varied little at leaf margins. An inverse scaling relationship between SD and MNND was observed for both species. This relationship could be used for SD estimation using the rapidly estimated trait, MNND. SAI did not vary significantly throughout leaf lamina, and the numerical values of SAI for all fields of view were greater than one, which indicates significant spatial repulsion between stomata. The study suggests that SD varies across leaf lamina to fine-tune plant water use and maximize carbon gain. However, spatial structures of stomata from different lamina sections exhibit similar patterns (i.e., spatial inhibition between stomata at small scales), probably due to hierarchical leaf vein patterns.

Measuring the inequality of leaf area distribution per plant (ILAD) can provide a useful tool for quantifying the influences of intra- and interspecific competition, foraging behavior of herbivores, and environmental stress on plants’ above-ground architectural structures and survival strategies. Despite its importance, there has been limited research on this issue. This paper aims to fill this gap by comparing four inequality indices to measure ILAD, using indices for quantifying household income that are commonly used in economics, including the Gini index (which is based on the Lorenz curve), the coefficient of variation, the Theil index, and the mean log deviation index. We measured the area of all leaves for 240 individual plants of the species Shibataea chinensis Nakai, a drought-tolerant landscape plant found in southern China. A three-parameter performance equation was fitted to observations of the cumulative proportion of leaf area vs. the cumulative proportion of leaves per plant to calculate the Gini index for each individual specimen of S. chinensis. The performance equation was demonstrated to be valid in describing the rotated and right shifted Lorenz curve, given that >96% of root-mean-square error values were smaller than 0.004 for 240 individual plants. By examining the correlation between any of the six possible pairs of indices among the Gini index, the coefficient of variation, the Theil index, and the mean log deviation index, the data show that these indices are closely related and can be used interchangeably to quantify ILAD.

Bamboo is an important component in subtropical and tropical forest communities. The plant has characteristic long lanceolate leaves with parallel venation. Prior studies have shown that the leaf shapes of this plant group can be well described by a simplified version (referred to as SGE-1) of the Gielis equation, a polar coordinate equation extended from the superellipse equation. SGE-1 with only two model parameters is less complex than the original Gielis equation with six parameters. Previous studies have seldom tested whether other simplified versions of the Gielis equation are superior to SGE-1 in fitting empirical leaf shape data. In the present study, we compared a three-parameter Gielis equation (referred to as SGE-2) with the two-parameter SGE-1 using the leaf boundary coordinate data of six bamboo species within the same genus that have representative long lanceolate leaves, with >300 leaves for each species. We sampled 2000 data points at approximately equidistant locations on the boundary of each leaf, and estimated the parameters for the two models. The root–mean–square error (RMSE) between the observed and predicted radii from the polar point to data points on the boundary of each leaf was used as a measure of the model goodness of fit, and the mean percent error between the RMSEs from fitting SGE-1 and SGE-2 was used to examine whether the introduction of an additional parameter in SGE-1 remarkably improves the model’s fitting. We found that the RMSE value of SGE-2 was always smaller than that of SGE-1. The mean percent errors among the two models ranged from 7.5% to 20% across the six species. These results indicate that SGE-2 is superior to SGE-1 and should be used in fitting leaf shapes. We argue that the results of the current study can be potentially extended to other lanceolate leaf shapes.

This study investigated the effects of an aqueous acidic solution at typical concentrations on polymeric polyvinylidene fluoride (PVDF)-based membranes. Flat-sheet PVDF-based membranes were completely embedded in sulfuric acid at varying concentrations. The effect of the acid concentration after a prolonged exposure time on the chemical, mechanical and physical properties of the membrane were checked via FE-SEM, EDX (Energy-Dispersive Spectrometer), FTIR, XRD, tensile strength, zeta potential, contact angle, porosity, pure water flux measurement and visual observation. The result reveals prompt initiation of reaction between the PVDF membrane and sulfuric acid, even at a mild concentration. As the exposure time extends with increasing concentration, the change in chemical and mechanical properties become more pronounced, especially in the morphology, although this was not really noticeable in either the crystalline phase or the functional group analyses. The ultimate mechanical strength decreased from 46.18 ± 0.65 to 32.39 ± 0.22 MPa, while the hydrophilicity was enhanced due to enlargement of the pores. The flux at the highest concentration and exposure period increased by 2.3 times that of the neat membrane, while the BSA (Bovine Serum Albumin) rejection dropped by 55%. Similar to in an alkaline environment, the stability and performance of the PVDF-based membrane analyzed in this study manifested general deterioration.