Comparison between computer recognition and manual measurement methods for the estimation of leaf area.

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.

Scaling relationships of leaf vein and areole traits versus leaf size for nine Magnoliaceae species differing in venation density.

PREMISE: Across species, main leaf vein density scales inversely with leaf area (A). Yet, minor vein density manifests no clear relationship with respect to A, despite having the potential to provide important insights into the trade-off among the investments in leaf mechanical support, hydraulics, and light interception. METHODS: To examine this phenomenon, the leaves of nine Magnoliaceae leaves were sampled, and the scaling relationships among A and midrib length (ML), total vein length (TVL), total vein area (TVA), total areole area (TAA), and mean areole area (MAA) were determined. The scaling relationships between MAA and areole density (the number of areoles per unit leaf area) and between MAA and A were also analyzed. RESULTS: For five of the nine species, A was proportional to ML2 . For eight of the nine species, TVL and TVA were both proportional to A. The numerical values of the scaling exponents for TAA vs. A were between 1.0 and 1.07 for eight species; i.e., as expected, TAA was isometrically proportional to A. There was no correlation between MAA and A, but MAA scaled inversely with respect to areole density for each species. CONCLUSIONS: The correlation between midrib "density" (i.e., ML/A) and A, and the lack of correlation between total leaf vein density and A result from the A ∝$\propto $ ML2 scaling relationship and the proportional relationship between TVL and A, respectively. Leaves with the same size can have widely varying MAA. Thus, leaf size itself does not directly constrain leaf hydraulic efficiency and redundancy.

Diminishing returns among lamina fresh and dry mass, surface area, and petiole fresh mass among nine Lauraceae species.

PREMISE: The phenomenon called "diminishing returns" refers to a scaling relationship between lamina mass (M) vs. lamina area (A) in many species, i.e., M ∝ Aα>1 , where α is the scaling exponent exceeding unity. Prior studies have focused on the scaling relationships between lamina dry mass (DM) and A, or between fresh mass (FM) and A. However, the scaling between petiole mass and M and A has seldom been investigated. Here, we examine the scaling relationships among FM, DM, A, and petiole fresh mass (PFM). METHODS: For each of 3268 leaves from nine Lauraceae species, FM, DM, A, and PFM were measured, and their scaling relationships were fitted using reduced major axis regression protocols. The bootstrap percentile method was used to test the significance of the difference in α-values between any two species. RESULTS: The phenomenon of diminishing returns was verified between FM vs. A and DM vs. A. The FM vs. A scaling relationship was statistically more robust than the DM vs. A scaling relationship based on bivariate regression r2 -values. Diminishing returns were also observed for the PFM vs. FM and PFM vs. A scaling relationships. The PFM vs. FM scaling relationship was statistically more robust than the PFM vs. A scaling relationship. CONCLUSIONS: "Diminishing returns" was confirmed among the FM, DM, A, and PFM scaling relationships. The data collectively indicate that the petiole scales mechanically more strongly with lamina mass than with area, suggesting that static (self) loading takes precedence over dynamic (wind) loading.

Spatial distribution characteristics of stomata at the areole level in Michelia cavaleriei var. platypetala (Magnoliaceae).

BACKGROUND AND AIMS: In hierarchically reticulate venation patterns, smaller orders of veins form areoles in which stomata are located. This study aimed to quantify the spatial relationship among stomata at the areole level. METHODS: For each of 12 leaves of M. cavaleriei var. platypetala, we assumed that stomatal characteristics were symmetrical on either side of the midrib, and divided the leaf surface on one side of the midrib into six layers equidistantly spaced along the apical-basal axis. We then further divided each layer into three positions equidistantly spaced from midrib to leaf margin, resulting in a total of 18 sampling locations. In addition, for 60 leaves, we sampled three positions from midrib to margin within only the widest layer of the leaf. Stomatal density and mean nearest neighbour distance (MNND) were calculated for each section. A replicated spatial point pattern approach quantified stomatal spatial relationships at different distances (0-300 µm). KEY RESULTS: A tendency towards regular arrangement (inhibition as opposed to attraction or clustering) was observed between stomatal centres at distances <100 µm. Leaf layer (leaf length dimension) had no significant effect on local stomatal density, MNND or the spatial distribution characteristics of stomatal centres. In addition, we did not find greater inhibition at the centre of areoles, and in positions farther from the midrib. CONCLUSIONS: Spatial inhibition might be caused by the one-cell-spacing rule, resulting in more regular arrangement of stomata, and it was found to exist at distances up to ~100 µm. This work implies that leaf hydraulic architecture, consisting of both vascular and mesophyll properties, is sufficient to prevent important spatial variability in water supply at the areole level.

Leaf size estimation based on leaf length, width and shape.

BACKGROUND AND AIMS: Leaf size has considerable ecological relevance, making it desirable to obtain leaf size estimations for as many species worldwide as possible. Current global databases, such as TRY, contain leaf size data for ~30 000 species, which is only ~8% of known species worldwide. Yet, taxonomic descriptions exist for the large majority of the remainder. Here we propose a simple method to exploit information on leaf length, width and shape from species descriptions to robustly estimate leaf areas, thus closing this considerable knowledge gap for this important plant functional trait. METHODS: Using a global dataset of all major leaf shapes measured on 3125 leaves from 780 taxa, we quantified scaling functions that estimate leaf size as a product of leaf length, width and a leaf shape-specific correction factor. We validated our method by comparing leaf size estimates with those obtained from image recognition software and compared our approach with the widely used correction factor of 2/3. KEY RESULTS: Correction factors ranged from 0.39 for highly dissected, lobed leaves to 0.79 for oblate leaves. Leaf size estimation using leaf shape-specific correction factors was more accurate and precise than estimates obtained from the correction factor of 2/3. CONCLUSION: Our method presents a tractable solution to accurately estimate leaf size when only information on leaf length, width and shape is available or when labour and time constraints prevent usage of image recognition software. We see promise in applying our method to data from species descriptions (including from fossils), databases, field work and on herbarium vouchers, especially when non-destructive in situ measurements are needed.

"Diminishing returns" for leaves of five age-groups of Phyllostachys edulis culms.

PREMISE: Leaf mass (M) and lamina surface area (A) are important functional traits reported to obey a scaling relationship called "diminishing returns" (i.e., M ∝ Aα>1 ). Previous studies have focused primarily on eudicots and ignored whether the age of leaves affects the numerical value of the scaling exponent (i.e., α). METHODS: The effect of age was examined using 1623 Phyllostachys edulis leaves from culms differing in age collected in Nanjing, China. The scaling relationships among leaf A, fresh mass (FM), and dry mass (DM) were evaluated using reduced major axis protocols. The bootstrap percentile method was used to test the significance of differences in α-values. RESULTS: Overall, the numerical values of α exceeded 1.0. The scaling relationship between FM and A was statistically more robust than that between DM and A. The scaling exponents of FM vs. A exhibited a "high-low-high-low-high" numerical trend from the oldest to the youngest age-group. FM increased linearly as culm age decreased; the leaf DM per unit area (LMA) exhibited a parabolic trend across the age-groups. CONCLUSIONS: "Diminishing returns" is confirmed for all but one age-group of an important monocot species. The relationship between FM and A was statistically more robust than that between DM and A for each age-group. The FM per unit A decreased with increasing age-groups, whereas the middle age-groups had a greater LMA than the oldest and youngest age-groups. These data are the first to show that the age of shoots affects the scaling relationship between leaf mass and area.

Nondestructive estimation of leaf area for 15 species of vines with different leaf shapes.

PREMISE: The nondestructive measurement of leaf area is important for expediting data acquisition in the field. The Montgomery equation (ME) assumes that leaf area (A) is a proportional function of the product of leaf length (L) and width (W), i.e., A = cLW, where c is called the Montgomery parameter. The ME has been successfully applied to calculate the surface area of many broad-leaved species with simple leaf shapes. However, whether this equation is valid for more complex leaf shapes has not been verified. METHODS: Leaf A, L, and W were measured directly for each of 5601 leaves of 15 vine species, and ME and three other models were used to fit the data. All four models were compared based on their root mean square errors (RMSEs) to determine whether ME provided the best fit. RESULTS: The ME was a reliable method for estimating the A of all 15 species. In addition, the numerical values of 13 of the 15 values of c fell within a previously predicted numerical range (i.e., between 1/2 and π/4). The data show that the numerical values of c are largely affected by the value of W/L, the concavity of the leaf base, and the number of lobes on the lamina. CONCLUSIONS: The Montgomery parameter can reflect the influence of leaf shape on leaf-area calculations and can serve as an important tool for nondestructive measurements of leaf area for many broad-leaved species and for the investigation of leaf morphology.

Exploring key cellular processes and candidate genes regulating the primary thickening growth of Moso underground shoots.

The primary thickening growth of Moso (Phyllostachys edulis) underground shoots largely determines the culm circumference. However, its developmental mechanisms remain largely unknown. Using an integrated anatomy, mathematics and genomics approach, we systematically studied cellular and molecular mechanisms underlying the growth of Moso underground shoots. We discovered that the growth displayed a spiral pattern and pith played an important role in promoting the primary thickening process of Moso underground shoots and driving the evolution of culms with different sizes among different bamboo species. Different with model plants, the shoot apical meristem (SAM) of Moso is composed of six layers of cells. Comparative transcriptome analysis identified a large number of genes related to the vascular tissue formation that were significantly upregulated in a thick wall variant with narrow pith cavity, mildly spiral growth, and flat and enlarged SAM, including those related to plant hormones and those involved in cell wall development. These results provide a systematic perspective on the primary thickening growth of Moso underground shoots, and support a plausible mechanism resulting in the narrow pith cavity, weak spiral growth but increased vascular bundle of the thick wall Moso.

Significant correlation between leaf vein length per unit area and stomatal density: evidence from Red Tip and Chinese photinias.

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.

Scaling relationships among the mass of eggshell, albumen, and yolk in six precocial birds.

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, i.e., 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.

Comparison of four performance models in quantifying the inequality of leaf and fruit size distribution.

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.

Strong-Yet-Ductile Eutectic Alloys Employing Cocoon-Like Nanometer-Sized Dislocation Cells.

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.

Effect of temperature on the development of Laodelphax striatellus (Homoptera: Delphacidae).

Temperature has a significant influence on the development of Laodelphax striatellus (Fallén), an important rice pest insect in east Asia. We set eight constant temperatures from 18 to 32 degrees C in 2 degrees C-increments to check the effect of temperature on the developmental rate of this insect species. The developmental durations of eggs and nymphs were observed daily. To ensure the accuracy of developmental durations, 500 initial samples were taken for the nymphal stage at each temperature. Performance-2 model was used to fit these data because this model can provide the lower and upper developmental thresholds simultaneously. The estimate of lower developmental thresholds of eggs (10.0 degrees C) was different from that of nymphs (7.5 degrees C). And the estimate of upper developmental thresholds of eggs (35.5 degrees C) was also different from that of nymphs (30.2 degrees C). However, for male and female nymphs, the difference in the lower developmental threshold is nonsignificant, and the difference in the upper developmental thresholds is very small (95% confidence interval of the difference: [0.007 degrees C, 0.043 degrees C]). The rate isomorphy hypothesis considers that the lower developmental thresholds of different stages for the same insect might be constant. However, the current study provides a counterexample of this hypothesis that the lower developmental threshold of eggs is different from that of nymphs. Thus, we demonstrate that the rate isomorphy hypothesis does not apply all insects. In addition, we used a popular nonlinear model, Lactin model, to fit the developmental rate data of our experiment. And we found that the estimates of lower and upper developmental thresholds by using Performance-2 model were very approximate to those by using Lactin model. The current study provides reliable estimates of thermal parameters for L. striatellus by using large experimental samples at different temperatures. It would be useful for exploring the relationship of climate change and the outbreak of this insect on rice.

Effects of Plant Coverage on the Abundance of Adult Mosquitos at an Urban Park.

People who take a walk in urban parks, including or adjacent to a water body such as a river, a pond, or a lake, usually suffer from mosquito bites in summer and early autumn. The insects can negatively affect the health and mood of these visitors. Prior studies about the effects of landscape composition on the abundance of mosquitos have usually taken stepwise multiple linear regression protocols to look for the landscape variables that can significantly affect the abundance of mosquitos. However, those studies have largely overlooked the nonlinear effects of landscape plants on the abundance of mosquitos. In the present study, we compared the multiple linear regression (MLR) with the generalized additive model (GAM) based on the trapped mosquito abundance data obtained by using photo-catalytic CO2-baited lamps placed at the Xuanwu Lake Park, a representative subtropical urban scenic spot. We measured the coverage of trees, shrubs, forbs, proportion of hard paving, proportion of water body, and coverage of aquatic plants within a distance of 5 m from each lamp's location. We found that MLR and GAM both detected the significant influences of the coverage of terrestrial plants on the abundance of mosquitos, but GAM provided a better fit to the observations by relaxing the limitation of the linear relationship hypothesis by MLR. The coverage of trees, shrubs, and forbs accounted for 55.2% of deviance, and the coverage of shrubs had the greatest contribution rate among the three predictors, accounting for 22.6% of the deviance. The addition of the interaction between the coverage of trees and that of shrubs largely enhanced the goodness of fit, and it increased the explained deviance of the GAM from 55.2% to 65.7%. The information in this work can be valuable for the planning and design of landscape plants to reduce the abundance of mosquitos at special urban scenic points.

Plant Morphology and Function, Geometric Morphometrics, and Modelling: Decoding the Mathematical Secrets of Plants.

Functional plant traits include a plant's phenotypic morphology, nutrient element characteristics, and physiological and biochemical features, reflecting the survival strategies of plants in response to environmental changes [...].

An Inverse Scaling Relationship between Stomatal Density and Mean Nearest Neighbor Distance: Evidence from a Photinia Hybrid and One of Its Parents.

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.

Evidence That Field Muskmelon (Cucumis melo L. var. agrestis Naud.) Fruits Are Solids of Revolution.

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.

Leaf-age and petiole biomass play significant roles in leaf scaling theory.

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.

A simple way to calculate the volume and surface area of avian eggs.

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 (LW2 )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.

Inequality Measure of Leaf Area Distribution for a Drought-Tolerant Landscape Plant.

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.