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 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.

Using the Montgomery-Koyama-Smith equation to calculate the stomatal area per unit lamina area for 12 Magnoliaceae species.

BACKGROUND AND AIMS: The Montgomery-Koyama-Smith (MKS) equation predicts that total leaf area per shoot is proportional to the product of the sum of individual leaf widths and maximum individual leaf length, which has been validated for some herbaceous and woody plants. The equation is also predicted to be valid in describing the relationship between the total stomatal area per micrograph (AT) and the product of the sum of individual stomatal widths (denoted as LKS) and maximum individual stomatal length (denoted by WKS) in any particular micrograph. METHODS: To test the validity of the MKS equation, 69,931 stomata (from 720 stomatal micrographs from 12 Magnoliaceae species) were examined. The area of each stoma was calculated using empirical measurements of stomatal length and width multiplied by a constant. Six equations describing the relationships among AT, LKS, and WKS were compared. The root-mean-square (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 the structural complexity of each model, respectively. KEY RESULTS: Analyses supported the validity of the MKS equation and the power-law equation AT ∝ (LKS∙WKS)α, where a is a scaling exponent. The estimated values of α at the species level and for the pooled data were all statistically smaller than unity, which did not support the hypothesis that AT ∝ LTS∙WTS. The power-law equation had smaller RMSE and AIC values than the MKS equation for the data from the 12 individual species and the pooled data. CONCLUSIONS: These results indicate that AT tends to allometrically scale with LKS∙WKS, and that increases in AT do not keep pace with increases in LTS∙WTS. In addition, using the product of LKS and WKS is better than using only one of the two variables.

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.

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.

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.

Multiple Response Mechanisms of Plants to Drought Stress.

As climate change increasingly affects global ecosystems, understanding plant responses to drought stress has become essential for both conservation and agricultural productivity [...].

Comparison of four light-response models using relative curvature measures of nonlinearity.

Photosynthetic light response curves serve as powerful mathematical tools for quantitatively describing the rate of photosynthesis of plants in response to changes in irradiance. However, in practical applications, the daunting task of selecting an appropriate nonlinear model to accurately fit these curves persists as a significant challenge. Thus, there arises a need for a method to systematically evaluate the efficacy of such models. In the present study, four distinct nonlinear models, namely Exponential Model (EM), Rectangular Hyperbola Model (RHM), Nonrectangular Hyperbola Model (NHM), and Modified Rectangular Hyperbola Model (MRHM), were used to fit the relationship between light intensity and the rate of photosynthesis across 42 empirical datasets. The goodness of fit for each model was assessed using the root-mean-square error, and relative curvature measures of nonlinearity were employed to assess the nonlinear behavior of the models. In terms of goodness of fit, pairwise difference tests of the root-mean-square error revealed that there was little to choose among the four models, although RHM gave a marginally poorer fit. However, in terms of nonlinear behavior, EM not only provided the most favorable linear approximation performance at the global level, but also exhibited the best close-to-linear behavior at the individual parameter level among the four models across the 42 datasets. Consequently, the results strongly advocate for EM as the most suitable mathematical framework for fitting photosynthetic light response curves. These findings provide insights into the model assessment for nonlinear regression in describing the relationship between the photosynthetic rate and light intensity.

The "Leafing Intensity Premium" Hypothesis and the Scaling Relationships of the Functional Traits of Bamboo Species.

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.

Comparison of egg-shape equations using relative curvature measures of nonlinearity.

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.

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, 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.

Influence of tree size on the scaling relationships of lamina and petiole traits: A case study using Camptotheca acuminata Decne.

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.

Comparison of five equations in describing the variation of leaf area distributions of Alangium chinense (Lour.) Harms.

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.

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.

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.

Scaling relationships between the total number of leaves and the total leaf area per culm of two dwarf bamboo species.

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.

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.