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.

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.

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.

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.

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.

Insect root feeders incur negative density-dependent damage across plant species in an alpine meadow.

Although herbivores are well known to incur positive density-dependent damage and mortality, thereby likely shaping plant community assembly, the response of belowground root feeders to changes in plant density has seldom been addressed. Locally rare plant species (with lower plant biomass per area) are often smaller with shallower roots than common species (with higher plant biomass per area) in competition-intensive grasslands. Likewise, root feeders are often distributed in the upper soil layers. We hypothesized, therefore, that root feeders would incur negative density (biomass)-dependent damage across plant species. To test this hypothesis, we investigated the diversity and abundance of plant and root feeder species in an alpine meadow and determined the diet of the root feeders using metabarcoding. Across all species, root feeder load decreased with increasing aboveground plant biomass, root biomass, and total plant biomass per area, indicating a negative density dependence of damage across plant species. Aboveground plant biomass per area increased with increasing individual plant biomass and root depth per area across species, suggesting that rare plant species were smaller in size and had shallower root systems compared to common plant species. Both root biomass per area and root feeder biomass per area decreased with soil depth, but the root feeder biomass decreased disproportionately faster compared to root biomass with increasing root depth. Root feeder load decreased with increasing root depth but was not correlated with the feeding preference of root feeder species. Moreover, the prediction derived from a random process incorporating vertical distributions of root biomass and root feeder biomass significantly accounted for interspecific variation in root feeder load. In conclusion, the data indicate that root feeders incur negative density-dependent damage across plant species. On this basis, we suggest that manipulative experiments should be conducted to determine the effect of the negative density-dependent damage on plant community structure and that different types of plant-animal interactions should be concurrently examined to fully understand the effect of plant density on overall herbivore damage across plant 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, 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 scaling of elemental stoichiometry and growth rate over the course of bamboo ontogeny.

Stoichiometric rules may explain the allometric scaling among biological traits and body size, a fundamental law of nature. However, testing the scaling of elemental stoichiometry and growth to size over the course of plant ontogeny is challenging. Here, we used a fast-growing bamboo species to examine how the concentrations and contents of carbon (C), nitrogen (N) and phosphorus (P), relative growth rate (G), and nutrient productivity scale with whole-plant mass (M) at the culm elongation and maturation stages. The whole-plant C content vs M and N content vs P content scaled isometrically, and the N or P content vs M scaled as a general 3/4 power function across both growth stages. The scaling exponents of G vs M and N (and P) productivity in newly grown mass vs M relationships across the whole growth stages decreased as a -1 power function. These findings reveal the previously undocumented generality of stoichiometric allometries over the course of plant ontogeny and provide new insights for understanding the origin of ubiquitous quarter-power scaling laws in the biosphere.

The allocation of anatomical traits determines the trade-off between fine root resource acquisition-transport function.

Cortex radius (CR) and stele radius (SR) are important functional traits associated with the nutrient acquisition and transport functions of fine roots, respectively. However, for developmental and anatomical reasons, the resource acquisition-transport relationship of fine roots is expected to be different for different root orders. To address this issue, critical fine root anatomical traits were examined for the first three orders of roots of 59 subtropical woody plants. Designating the most distal fine roots as order one, SR scaled isometrically with respect to root radius (RR) (i.e., SR ∝ RR1.0) in the three root orders, whereas CR scaled allometrically with respect to RR (i.e., CR ∝ RR>1.0) with the numerical values of scaling exponents increasing significantly with increasing root orders thereby indicating a disproportional increase in CR with increasing root orders. There were also differences between normalized root tissue (CR/RR and SR/RR) and RR in different root orders. A negative isometric relationship (i.e., SR/RR ∝ RR-1.0) existed between SR/RR and RR in three order roots, whereas the allometric exponent between CR/RR and RR increased with root order (from 0.88 to 1.55). Collectively, the data indicate that root anatomical and functional traits change as a function of RR and that these changes need to be considered when modeling fine root resource acquisition-transport functions.

Moderate Grazing Promotes Arthropod Species Diversity in an Alpine Meadow.

Livestock grazing is an important tool used in grassland land management practices. Studies have substantially addressed the effect of grazing on plant species diversity, revealing that moderate grazing increases plant species diversity. However, few studies have dealt with the relationship between grazing and arthropod species diversity, which remains unclear. Here, we hypothesize that moderate grazing promotes arthropod species diversity because arthropods are directly or indirectly dependent on plant diversity. In this study, we conducted a two-year plant and arthropod survey from 2020 to 2021 at four levels of grazing intensity, i.e., nongrazing (as a control), light grazing, moderate grazing, and heavy grazing, of the long-term grazing experiment starting in 2016. The data show that plant species diversity peaked in the moderate grazing treatment, and herbivore species diversity was positively correlated with plant species diversity (and hence peaked in the moderate grazing treatment). Moderate grazing promoted parasitoid species diversity, which was positively correlated with herbivore species diversity. However, predator species diversity did not significantly differ among the four treatments. In addition, saprophage species diversity decreased, whereas coprophages increased with increasing grazing levels, such that species richness (but not species diversity of detritivores statistically) was highest in the moderate grazing treatment. Consequently, the species diversity of arthropods as a whole peaked at the moderate grazing level, a phenomenology that is consistent with the intermediate disturbance hypothesis. Considering that moderate grazing has been found to increase plant species diversity, facilitate soil carbon accumulation, and prevent soil erosion, we suggest that moderate grazing would maximize multi-functional ecosystem services.

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.

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.

Diminishing returns: A comparison between fresh mass vs. area and dry mass vs. area in deciduous species.

"Diminishing returns" in leaf economics occurs when increases in lamina mass (M), which can either be represented by lamina dry mass (DM) or fresh mass (FM), fail to produce proportional increases in leaf surface area (A), such that the scaling exponent (α) for the M vs. A scaling relationship exceeds unity (i.e., α > 1.0). Prior studies have shown that FM vs. A is better than DM vs A in assessing diminishing returns in evergreen species. However, the superiority of FM vs. A over DM vs. A has been less well examined for deciduous species. Here, we applied reduced major axis protocols to test whether FM vs. A is better than DM vs. A to describe the M vs. A scaling relationship, using a total of 4271 leaves from ten deciduous and two evergreen tree species in the Fagaceae and Ulmaceae for comparison. The significance of the difference between the scaling exponents of FM vs. A and DM vs. A was tested using the bootstrap percentile method. Further, we tested the non-linearity of the FM (DM) vs. A data on a log-log scale using ordinary least squares. We found that (i) the majority of scaling exponents of FM vs. A and DM vs. A were >1 thereby confirming diminishing returns for all 12 species, (ii) FM vs. A was more robust than DM vs. A to identify the M vs. A scaling relationship, (iii) the non-linearity of the allometric model was significant for both DM vs. A and FM vs. A., and (iv) the evergreen species of Fagaceae had significantly higher DM and FM per unit area than other deciduous species. In summary, FM vs. A is a more reliable measure than DM vs. A when dealing with diminishing returns, and deciduous species tend to invest less biomass in unit leaf light harvesting area than evergreen species.

Viridiplantae Body Plans Viewed Through the Lens of the Fossil Record and Molecular Biology.

A review of the fossil record coupled with insights gained from molecular and developmental biology reveal a series of body plan transformations that gave rise to the first land plants. Across diverse algal clades, including the green algae and their descendants, the plant body plan underwent a unicellul ar $\to$ colonial $\to$ simple multicellular $\to \,\,$complex multicellular transformation series. The colonization of land involved increasing body size and associated cell specialization, including cells capable of hydraulic transport. The evolution of the life-cycle that characterizes all known land plant species involved a divergence in body plan phenotypes between the haploid and diploid generations, one adapted to facilitate sexual reproduction (a free-water dependent gametophyte), and another adapted to the dissemination of spores (a more water-independent sporophyte). The amplification of this phenotypic divergence, combined with indeterminate growth in body size, resulted in a desiccation-adapted branched sporophyte with a cuticularized epidermis, stomates, and vascular tissues. Throughout the evolution of the land plants, the body plans of the sporophyte generation involved "axiation," i.e., the acquisition of a cylindrical geometry and subsequent organographic specializations.

Comparison of Leaf Shape between a Photinia Hybrid and One of Its Parents.

Leaf shape and size can vary between hybrids and their parents. However, this has seldom been quantitatively tested. Photinia × fraseri is an important landscaping plant in East Asia as a hybrid between evergreen shrubs P. glabra and P. serratifolia. Its leaf shape looks like that of P. serratifolia. To investigate leaf shape, we used a general equation for calculating the leaf area (A) of broad-leaved plants, which assumes a proportional relationship between A and product of lamina length (L) and width (W). The proportionality coefficient (which is referred to as the Montgomery parameter) serves as a quantitative indicator of leaf shape, because it reflects the proportion of leaf area A to the area of a rectangle with L and W as its side lengths. The ratio of L to W, and the ellipticalness index were also used to quantify the complexity of leaf shape for elliptical leaves. A total of >4000 leaves from P. × fraseri and P. serratifolia (with >2000 leaves for each taxon) collected on a monthly basis was used to examine: (i) whether there is a significant difference in leaf shape between the two taxa, and (ii) whether there is a monotonic or parabolic trend in leaf shape across leaf ages. There was a significant difference in leaf shape between the two taxa (p < 0.05). Although there were significant differences in leaf shape on a monthly basis, the variation in leaf shape over time was not large, i.e., leaf shape was relatively stable over time for both taxa. However, the leaf shape of the hybrid was significantly different from its parent P. serratifolia, which has wider and more elliptical leaves than the hybrid. This work demonstrates that variations in leaf shape resulting from hybridization can be rigorously quantified and compared among species and their hybrids. In addition, this work shows that leaf shape does not changes as a function of age either before or after the full expansion of the lamina.

Leaf water content contributes to global leaf trait relationships.

Leaf functional traits are important indicators of plant growth and ecosystem dynamics. Despite a wealth of knowledge about leaf trait relationships, a mechanistic understanding of how biotic and abiotic factors quantitatively influence leaf trait variation and scaling is still incomplete. We propose that leaf water content (LWC) inherently affects other leaf traits, although its role has been largely neglected. Here, we present a modification of a previously validated model based on metabolic theory and use an extensive global leaf trait dataset to test it. Analyses show that mass-based photosynthetic capacity and specific leaf area increase nonlinearly with LWC, as predicted by the model. When the effects of temperature and LWC are controlled, the numerical values for the leaf area-mass scaling exponents converge onto 1.0 across plant functional groups, ecosystem types, and latitudinal zones. The data also indicate that leaf water mass is a better predictor of whole-leaf photosynthesis and leaf area than whole-leaf nitrogen and phosphorus masses. Our findings highlight a comprehensive theory that can quantitatively predict some global patterns from the leaf economics spectrum.

The fern economics spectrum is unaffected by the environment.

The plant economics spectrum describes the trade-off between plant resource acquisition and storage, and sheds light on plant responses to environmental changes. However, the data used to construct the plant economics spectrum comes mainly from seed plants, thereby neglecting vascular non-seed plant lineages such as the ferns. To address this omission, we evaluated whether a fern economics spectrum exists using leaf and root traits of 23 fern species living under three subtropical forest conditions differing in light intensity and nutrient gradients. The fern leaf and root traits were found to be highly correlated and formed a plant economics spectrum. Specific leaf mass and root tissue density were found to be on one side of the spectrum (conservative strategy), whereas photosynthesis rate, specific root area, and specific root length were on the other side of the spectrum (acquisitive strategy). Ferns had higher photosynthesis and respiration rates, and photosynthetic nitrogen-use efficiency under high light conditions and higher specific root area and lower root tissue density in high nutrient environments. However, environmental changes did not significantly affect their resource acquisition strategies. Thus, the plant economics spectrum can be broadened to include ferns, which expands its phylogenetic and ecological implications and utility.

'biogeom': An R package for simulating and fitting natural shapes.

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.