Search

Many natural radial symmetrical shapes (e.g., sea stars) follow the Gielis equation (GE) or its twin equation (TGE). A supertriangle (three triangles arranged around a central polygon) represents such a shape, but no study has tested whether natural shapes can be represented as/are supertriangles or whether the GE or TGE can describe their shape. We collected 100 pieces of Koelreuteria paniculata fruit, which have a supertriangular shape, extracted the boundary coordinates for their vertical projections, and then fitted them with the GE and TGE. The adjusted root mean square errors (RMSEadj) of the two equations were always less than 0.08, and >70% were less than 0.05. For 57/100 fruit projections, the GE had a lower RMSEadj than the TGE, although overall differences in the goodness of fit were non-significant. However, the TGE produces more symmetrical shapes than the GE as the two parameters controlling the extent of symmetry in it are approximately equal. This work demonstrates that natural supertriangles exist, validates the use of the GE and TGE to model their shapes, and suggests that different complex radially symmetrical shapes can be generated by the same equation, implying that different types of biological symmetry may result from the same biophysical mechanisms. [ABSTRACT FROM AUTHOR]

Abstract: The linear and Logan models are usually used to describe the effect of temperature on insect developmental rate. The linear model is often used to estimate the lower developmental threshold. However, it cannot be used to calculate the upper developmental threshold. Additionally, it fails to describe developmental rates near, at, and above the optimal developmental temperature. The Logan model can reflect temperature-dependent developmental rates from the lower to upper developmental thresholds. It is often used to compute the optimal developmental temperature and the upper developmental threshold, but it is not used to compute the lower developmental threshold. To avoid the disadvantages of these two models, we develop a new model, the ‘performance model’ on the basis of the impact of increasing temperature on enzyme activity and denaturation. The performance model was first used by Huey and Stevenson (Amer. Zool. 19, 357–366) to provide a statistical description of the impact of body temperature on performance, but they did not provide underlying physiological mechanisms. Few studies have used the performance model to analyze the temperature-dependent developmental rates of insects, perhaps because of the lack of a theoretical justification. Here, we provide a theoretical justification to use the model and we use the performance model to evaluate the developmental rate data of two insect species. We found that the performance model has advantages over the linear and Logan models, and that the lower and upper developmental thresholds can be simultaneously obtained from this model. [Copyright &y& Elsevier]

Leaf shape is closely related to economics of leaf support and leaf functions, including light interception, water use, and CO2 uptake, so correct quantification of leaf shape is helpful for studies of leaf structure/function relationships. There are some extant indices for quantifying leaf shape, including the leaf width/length ratio (W/L), leaf shape fractal dimension (FD), leaf dissection index, leaf roundness index, standardized bilateral symmetrical index, etc. W/L ratio is the simplest to calculate, and recent studies have shown the importance of the W/L ratio in explaining the scaling exponent of leaf dry mass vs. leaf surface area and that of leaf surface area vs. leaf length. Nevertheless, whether the W/L ratio could reflect sufficient geometrical information of leaf shape has been not tested. The FD might be the most accurate measure for the complexity of leaf shape because it can characterize the extent of the self-similarity and other planar geometrical features of leaf shape. However, it is unknown how strongly different indices of leaf shape complexity correlate with each other, especially whether W/L ratio and FD are highly correlated. In this study, the leaves of nine Magnoliaceae species (>140 leaves for each species) were chosen for the study. We calculated the FD value for each leaf using the box-counting approach, and measured leaf fresh mass, surface area, perimeter, length, and width. We found that FD is significantly correlated to the W/L ratio and leaf length. However, the correlation between FD and the W/L ratio was far stronger than that between FD and leaf length for each of the nine species. There were no strong correlations between FD and other leaf characteristics, including leaf area, ratio of leaf perimeter to area, fresh mass, ratio of leaf fresh mass to area, and leaf roundness index. Given the strong correlation between FD and W/L, we suggest that the simpler index, W/L ratio, can provide sufficient information of leaf shape for similarly-shaped leaves. Future studies are needed to characterize the relationships among FD and W/L in leaves with strongly varying shape, e.g., in highly dissected leaves. [ABSTRACT FROM AUTHOR]

Leaf shape can reflect the survival and development of plants in different environments. In particular, leaf area, showing a scaling relationship with other leaf-shape indices, has been used to evaluate the extent of salt stress on plants. Based on the scaling relationships between leaf area and other leaf-shape indices in experiments at different levels of salt stress, we could examine which leaf-shape indices are also related to salt stress. In the present study, we explored the effects of different salt concentration treatments on leaf dry mass per unit area (LMA), the quotient of leaf perimeter and leaf area (QPA), the quotient of leaf width and length (QWL), the areal quotient (AQ) of left and right sides of a leaf and the standardized index (SI) for bilateral symmetry. We treated Pyrus betulifolia Bunge under NaCl salt solution of 2‰, 4‰ and 6‰, respectively, with fresh water with no salt as the control. The reduced major axis (RMA) was used to fit a linear relationship of the log-transformed data between any leaf trait measures and leaf area. We found that leaf fresh weight and dry weight decrease with salt concentration increasing, whereas the exponents of leaf dry weight versus leaf area exhibit an increasing trend, which implies that the leaves expanding in higher salt environments are prone to have a higher cost of dry mass investment to increase per unit leaf area than those in lower salt environments. Salt concentration has a significant influence on leaf shape especially QWL, and QWL under 6‰ concentration treatment is significantly greater than the other treatments. However, there is no a single increasing or decreasing trend for the extent of leaf bilateral symmetry with salt concentration increasing. In addition, we found that the scaling exponents of QPA versus leaf area for four treatments have no significant difference. It indicates that the scaling relationship of leaf perimeter versus leaf area did not change with salt concentration increasing. The present study suggests that salt stress can change leaf functional traits especially the scaling relationship of leaf dry weight versus leaf area and QWL, however, it does not significantly affect the scaling relationships between leaf morphological measures (including QPA and the extent of leaf bilateral symmetry) and leaf area. [ABSTRACT FROM AUTHOR]

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.

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 non-destructively measuring A for many broadleaved plants. At present, the methods used to compute L and W for the 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 previous 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. The 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 analysed 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 the two methods. This further validates that the ME is an effective method for estimating A in broadleaved 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 the ME to estimate A in the future., (© The Author(s) 2024. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved. For commercial re-use, please contact reprints@oup.com for reprints and translation rights for reprints. All other permissions can be obtained through our RightsLink service via the Permissions link on the article page on our site—for further information please contact journals.permissions@oup.com.)

Eutectic alloys (EAs) with superior fluidity are known to be the easiest to cast into high-quality ingots, making them the alloys of choice for making large-sized structural parts. However, conventional EAs (CEAs) have never reached strength-ductility combinations on par with the best in other alloy categories. Via thermomechanical processing of cast Ni-32.88wt%Fe-9.53wt%Al CEAs, a cocoon-like nano-meshed (as fine as 26 nm) network of dislocations (CNN-D) is produced via recovery annealing, through the rearrangement of cold-work-accumulated dislocations anchored by dense pre-existing nanoprecipitates. In lieu of traditional plasticity mechanisms, such as TWIP and TRIP, the CNN-D is particularly effective in eutectic lamellae with alternating phases, as it instigates nanometer-spaced planar slip bands that not only dynamically refine the microstructure but also transmit from the FCC (face-centered-cubic) layers into the otherwise brittle B2 layers. These additional mechanisms for strengthening and strain hardening sustain stable tensile flow, resulting in a striking elevation of both strength and ductility to outrank not only all previous CEAs, but also the state of the art-additively manufactured eutectic high-entropy alloys. The CNN-D thus adds a novel microstructural strategy for performance enhancement, especially for compositionally complex alloys that increasingly make use of nanoprecipitates or local chemical order., (© 2024 Wiley‐VCH GmbH.)

The proportions in the size of the avian egg albumen, yolk, and shell are crucial for understanding bird survival and reproductive success because their relationships with volume and surface area can affect ecological and life history strategies. Prior studies have focused on the relationship between the albumen and the yolk, but little is known about the scaling relationship between eggshell mass and shape and the mass of the albumen and the yolk. Toward this end, 691 eggs of six precocial species were examined, and their 2-D egg profiles were photographed and digitized. The explicit Preston equation, which assumes bilateral symmetrical geometry, was used to fit the 2-D egg profiles and to calculate surface areas and volumes based on the hypothesis that eggs can be treated as solids of profile revolution. The scaling relationships of eggshell mass (Ms), albumen mass (Ma), and yolk mass (My), as well as the surface area (S), volume (V), and total mass (Mt) were determined. The explicit Preston equation was validated in describing the 2-D egg profiles. The scaling exponents of Ma vs. Ms, My vs. Ms, and My vs. Ma were smaller than unity, indicating that increases in Ma and My fail to keep pace with increases in Ms, and that increases in My fail to keep pace with increases in Ma. Therefore, increases in unit nutrient contents (i.e., the yolk) involve disproportionately larger increases in eggshell mass and disproportionately larger increases in albumen mass. The data also revealed a 2/3-power scaling relationship between S and V for each species, that is, the simple Euclidean geometry is obeyed. These findings help to inform our understanding of avian egg construction and reveal evolutionary interspecific trends in the scaling of egg shape, volume, mass, and mass allocation., (© The Author(s) 2024. Published by Oxford University Press on behalf of the Society for Integrative and Comparative Biology.)

There is a lack of research on whether tree size affects lamina and petiole biomass allocation patterns, whereas the trade-off between leaf biomass allocated to the lamina and the petiole is of significance when considering the hydraulic and mechanical function of the leaf as a whole. Here, Camptotheca acuminata Decne was selected for study because of the availability of trees differing in size growing under the same conditions. A total of 600 leaves for two tree size groups and 300 leaves per group differing in height and trunk diameter were collected. The lamina fresh mass (LFM), lamina dry mass (LDM), lamina area (LA), petiole fresh mass (PFM), and petiole length (PL) of each leaf was measured, and reduced major axis regression protocols were used to determine the scaling relationships among the five functional traits. The bootstrap percentile method was used to determine if the scaling exponents of the traits differed significantly between the two tree size groups. The results indicated that (i) there was a significant difference in the LFM, LDM, PFM, PL, LMA, LFMA and PFM/LFM between large and small trees, but no significant difference in LA; (ii) the LA versus LFM, LA versus LDM, LFM versus PFM, LA versus PFM, and PL versus PFM scaling relationships of the two groups were allometric (i.e., not isometric); (iii) there were significant differences in the scaling exponents of LA versus LFM, LA versus PFM, PL versus PFM between the two groups, but there was no significant difference in the LFM versus PFM scaling relationship between the two groups of trees. The data were also consistent with the phenomenon known as "diminishing returns". These data indicate that tree size influences leaf biomass allocation patterns in ways that can potentially influence overall plant growth, and therefore have an important bearing on life-history strategies., Competing Interests: The authors declare that they have no conflict of interest., (© 2024 The Author(s). Ecology and Evolution published by John Wiley & Sons Ltd.)

Total leaf area per plant is an important measure of the photosynthetic capacity of an individual plant that together with plant density drives the canopy leaf area index, that is, the total leaf area per unit ground area. Because the total number of leaves per plant (or per shoot) varies among conspecifics and among mixed species communities, this variation can affect the total leaf area per plant and per canopy but has been little studied. Previous studies have shown a strong linear relationship between the total leaf area per plant (or per shoot) ( A T ) and the total number of leaves per plant (or per shoot) ( N T ) on a log-log scale for several growth forms. However, little is known whether such a scaling relationship also holds true for bamboos, which are a group of Poaceae plants with great ecological and economic importance in tropical, subtropical, and warm temperate regions. To test whether the scaling relationship holds true in bamboos, two dwarf bamboo species ( Shibataea chinensis Nakai and Sasaella kongosanensis 'Aureostriatus') with a limited but large number of leaves per culm were examined. For the two species, the leaves from 480 and 500 culms, respectively, were sampled and A T was calculated by summing the areas of individual leaves per culm. Linear regression and correlation analyses reconfirmed that there was a significant log-log linear relationship between A T and N T for each species. For S. chinensis , the exponent of the A T versus N T scaling relationship was greater than unity, whereas that of S. kongosanensis 'Aureostriatus' was smaller than unity. The coefficient of variation in individual leaf area increased with increasing N T for each species. The data reconfirm that there is a strong positive power-law relationship between A T and N T for each of the two species, which may reflect adaptations of plants in response to intra- and inter-specific competition for light., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (© 2024 The Author(s). Ecology and Evolution published by John Wiley & Sons Ltd.)

A 2-dimensional (2D) egg-shape equation can be used to construct a 3D egg geometry based on the hypothesis that an egg is a solid of revolution, which helps to calculate egg volume and surface area. The parameters in the 2D egg-shape equation are potentially valuable for providing a clue to the ecology and evolution of avian eggs. In this study, the 5-parameter Preston equation (PE), the 4-parameter Troscianko equation (TE), and another 2 egg-shape equations, were compared in describing real 2D egg-shape data of 300 Gallus gallus domesticus eggs and additional 50 eggs that represented the variation in avian egg geometries. Adjusted root-mean-square error was used to quantify each equation's prediction error. Given that the 4 equations are nonlinear, relative curvature measures of nonlinearity were used to assess the extent of nonlinearity in each equation. PE was found to be the best among the 4 equations in terms of adjusted root-mean-square error and minimizing nonlinearity. The empirically determined egg volumes using a graduated cylinder were compared with the predicted egg volumes using the formula for a solid of revolution based on 2D predictions from the 4 egg-shape equations. There were negligible differences in the predicted egg volumes and surface areas among the 4 equations, indicating that these equations are all valid in calculating egg volume and surface area. In addition, we proposed a 5-parameter TE and found that it outperformed the above 4 equations in describing the 2D egg shape of G. gallus, but was less general than PE for other egg shapes. This work provides statistical evidence to show which equation is the best for describing the geometry of avian eggs and nondestructively calculating their volume and surface area, helping to classify poultry eggs into different grades according to the morphological characteristics of the eggs., Competing Interests: DISCLOSURES The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier Inc. All rights reserved.)

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., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The handling editor JG declared a past co-authorship with the author(s) KN and PS., (Copyright © 2024 Deng, He, Niklas, Shi, Mu and Shi.)

The vascular veins in photosynthetic leaves play an important role in transporting water and sugars throughout the plant body, and their venation pattern and vein density determine the hydraulic efficiency of the leaf. Likewise, stomatal density (SD) can influence photosynthetic gas exchange. However, the correlation between leaf vein density and SD is seldom reported. Herein, we examined 16 leaves from the hybrid Photinia × fraseri and 16 leaves from one of its parents, P. serratifolia , to explore the correlation between leaf vein density and SD. For each leaf, equidistant lamina quadrats were excised along two longitudinal transects (one along the midrib and another along the leaf margin). For each quadrat, micrographs of 1.2 mm × 0.9 mm stomatal imprints, and 2.51 mm × 1.88 mm micrographs of leaf veins were used to measure total vein area per leaf unit area (VAA) and total vein length per unit area (VLA), as indicators of leaf vein density, to determine the correlation between SD and leaf vein density. For each taxon, there was no significant correlation between SD and VAA, but there was a significant correlation between SD and VLA. The data indicate that SD is not positively correlated with VAA but positively correlated with VLA for both the hybrid and the parent species. This study indicates that future work should focus on the relationships between SD and total vein length per unit area rather than on total leaf vein area per unit area within and across species., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 He, Niklas, Niinemets, Wang, Jiao and Shi.)

The inequality in leaf and fruit size distribution per plant can be quantified using the Gini index, which is linked to the Lorenz curve depicting the cumulative proportion of leaf (or fruit) size against the cumulative proportion of the number of leaves (or fruits). Prior researches have predominantly employed empirical models-specifically the original performance equation (PE-1) and its generalized counterpart (GPE-1)-to fit rotated and right-shifted Lorenz curves. Notably, another potential performance equation (PE-2), capable of generating similar curves to PE-1, has been overlooked and not systematically compared with PE-1 and GPE-1. Furthermore, PE-2 has been extended into a generalized version (GPE-2). In the present study, we conducted a comparative analysis of these four performance equations, evaluating their applicability in describing Lorenz curves related to plant organ (leaf and fruit) size. Leaf area was measured on 240 culms of dwarf bamboo ( Shibataea chinensis Nakai), and fruit volume was measured on 31 field muskmelon plants ( Cucumis melo L. var. agrestis Naud.). Across both datasets, the root-mean-square errors of all four performance models were consistently smaller than 0.05. Paired t -tests indicated that GPE-1 exhibited the lowest root-mean-square error and Akaike information criterion value among the four performance equations. However, PE-2 gave the best close-to-linear behavior based on relative curvature measures. This study presents a valuable tool for assessing the inequality of plant organ size distribution., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd.)

Foliage leaves are essential for plant survival and growth, and how plants allocate biomass to their leaves reveals their economic and ecological strategies. Prior studies have shown that leaf-age significantly influences leaf biomass allocation patterns. However, unravelling the effects of ontogeny on partitioning biomass remains a challenge because it is confounded by the effects of environmental factors. Here, we aim to elucidate whether leaf-age affects the allocation to the lamina and petiole by examining leaves of known age growing in the same general environmental context. We sampled 2698 Photinia serratifolia leaves developing in the same environment from April to November 2021, representing eight leaf-ages ( n > 300 for each leaf-age). Petiole and lamina biomass, and lamina area were measured to evaluate the scaling relationships using reduced major axis regression protocols. The bootstrap percentile method was used to determine the differences in scaling exponents among the different leaf-ages. ANOVA with Tukey's HSD was used to compare the ratios of petiole and lamina biomass to lamina area across the leaf-ages. Correlation tests were used to determine if exponents, intercepts, and ratios differed significantly across the different leaf-ages. The data indicated that (i) the ratio of petiole and lamina biomass to lamina area and the scaling exponent of lamina biomass versus lamina area correlate positively with leaf-age, and (ii) the scaling exponent of petiole biomass versus lamina area correlates negatively with leaf-age. Leaf maturation process involves an inverse proportional allocation between lamina and petiole biomass for expanding photosynthetic area. This phenomenon underscores the effect of leaf-age on biomass allocation and the importance of adopting an ontogenetic perspective when entertaining plant scaling theories and unravelling the principles governing shifts in biomass allocation throughout the leaf lifespan., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Guo, Schrader, Shi, Jiao, Miao, Xue and Niklas.)

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.

Stomata are involved in transpiration and CO 2 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., Competing Interests: The authors declare no conflict of interest.

Egg geometry can be described using Preston's equation, which has seldom been used to calculate egg volume (V) and surface area (S) to explore S versus V scaling relationships. Herein, we provide an explicit re-expression of Preston's equation (designated as EPE) to calculate V and S, assuming that an egg is a solid of revolution. The side (longitudinal) profiles of 2221 eggs of six avian species were digitized, and the EPE was used to describe each egg profile. The volumes of 486 eggs from two avian species predicted by the EPE were compared with those obtained using water displacement in graduated cylinders. There was no significant difference in V using the two methods, which verified the utility of the EPE and the hypothesis that eggs are solids of revolution. The data also indicated that V is proportional to the product of egg length (L) and maximum width (W) squared. A 2/3-power scaling relationship between S and V for each species was observed, that is, S is proportional to (LW 2 ) 2/3 . These results can be extended to describe the shapes of the eggs of other species to study the evolution of avian (and perhaps reptilian) eggs., (© 2023 New York Academy of Sciences.)

Many natural objects exhibit radial or axial symmetry in a single plane. However, a universal tool for simulating and fitting the shapes of such objects is lacking. Herein, we present an R package called 'biogeom' that simulates and fits many shapes found in nature. The package incorporates novel universal parametric equations that generate the profiles of bird eggs, flowers, linear and lanceolate leaves, seeds, starfish, and tree-rings, and three growth-rate equations that generate the profiles of ovate leaves and the ontogenetic growth curves of animals and plants. 'biogeom' includes several empirical datasets comprising the boundary coordinates of bird eggs, fruits, lanceolate and ovate leaves, tree rings, seeds, and sea stars. The package can also be applied to other kinds of natural shapes similar to those in the datasets. In addition, the package includes sigmoid curves derived from the three growth-rate equations, which can be used to model animal and plant growth trajectories and predict the times associated with maximum growth rate. 'biogeom' can quantify the intra- or interspecific similarity of natural outlines, and it provides quantitative information of shape and ontogenetic modification of shape with important ecological and evolutionary implications for the growth and form of the living world., (© 2022 The Authors. Annals of the New York Academy of Sciences published by Wiley Periodicals LLC on behalf of New York Academy of Sciences.)

Scirpophaga incertulas Walker is an important agricultural pest in Asia. Only few studies are available on its long-term population dynamics under climate warming. In this study, we used the linear and generalized additive models (GAMs) to analyze the historical dataset of >50 years on this pest at Xinfeng County of Jiangxi Province, China. The main objective of this study was to explore the effects of density (delayed) dependence and minimum annual temperature (MAT), which indirectly reflects climate warming, on the population dynamics of this pest. We found that both density dependence and MAT have significant influence on the annual population growth rate. The GAMs had relatively better applicability to the dataset than the linear models. Nonparametric model provided satisfactory goodness-of-fit (R(2) > 0.5). At Xinfeng County, the MAT had a significant effect on the annual population growth rate of S. incertulas. The annual population growth rate of S. incertulas decreased with increase in MAT. Therefore, S. incertulas population becomes smaller and smaller in Southern China due to climate warming. The current study has two contributions: (1) providing a suitable method for predicting the annual population growth rate of S. incertulas, and (2) demonstrating that climate warming could decrease the S. incertulas population.