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Physical principles and laws determine the set of possible organismal phenotypes. Constraints arising from development, the environment, and evolutionary history then yield workable, integrated phenotypes. We propose a theoretical and practical framework that considers the role of changing environments. This 'ecomechanical approach' integrates functional organismal traits with the ecological variables. This approach informs our ability to predict species shifts in survival and distribution and provides critical insights into phenotypic diversity. We outline how to use the ecomechanical paradigm using drag-induced bending in trees as an example. Our approach can be incorporated into existing research and help build interdisciplinary bridges. Finally, we identify key factors needed for mass data collection, analysis, and the dissemination of models relevant to this framework.

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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) (AT) and the total number of leaves per plant (or per shoot) (NT) 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 AT 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 AT and NT for each species. For S. chinensis, the exponent of the AT versus NT 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 NT for each species. The data reconfirm that there is a strong positive power‐law relationship between AT and NT for each of the two species, which may reflect adaptations of plants in response to intra‐ and inter‐specific competition for light. [ABSTRACT FROM AUTHOR]

The Lorenz curve is used to describe the relationship between the cumulative proportion of household income and the number of households of an economy. The extent to which the Lorenz curve deviates from the line of equality (i.e., y = x) is quantified by the Gini coefficient. Prior models are based on the simulated and empirical data of income distributions. In biology, the Lorenz curves of cell or organ size distributions tend to have similar shapes. When the Lorenz curve is rotated by 135 degrees counterclockwise and shifted to the right by a distance of 2 , a three-parameter performance equation (PE), and its generalized version with five parameters (GPE), accurately describe this rotated and right-shifted curve. However, in prior studies, PE and GPE were not compared with the other Lorenz equations, and little is known about whether the skewness of the distribution could influence the validity of these equations. To address these two issues, simulation data from the beta distributions with different skewness values and six empirical datasets of plant (organ) size distributions were used to compare PE and GPE with three other Lorenz equations in describing the rotated and right-shifted plant (organ) size distributions. The root-mean-square error and Akaike information criterion were used to assess the validity of the two performance equations and the three other Lorenz equations. PE and GPE were both validated in describing the rotated and right-shifted simulation and empirical data of plant (organ) distributions. Nevertheless, GPE worked better than PE and the three other Lorenz equations from the perspectives of the goodness of fit, and the trade-off between the goodness of fit and the model structural complexity. Analyses indicate that GPE provides a powerful tool for quantifying size distributions across a broad spectrum of organic entities and can be used in a variety of ecological and evolutionary applications. Even for the simulation data from hypothetical extreme skewed distribution curves, GPE still worked well. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Summary: 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. [ABSTRACT FROM AUTHOR]