Does the exception prove the rule?

Plant size-dependent influence of foliar fungal pathogens promotes diversity through allometric growth

The effect of pathogens on host diversity has attracted much attention in recent years, yet how the influence of pathogens on individual plants scales up to affect community-level host diversity remains unclear. Here, we assessed the effects of foliar fungal pathogens on plant growth and species richness using allometric growth theory in population-level and community-level foliar fungal pathogen exclusion experiments. We calculated growth scaling exponents of 24 species to reveal the intraspecific size-dependent effects of foliar fungal pathogens on plant growth. We also calculated the intercepts to infer the growth rates of relatively larger conspecific individuals. We found that foliar fungal pathogens inhibited the growth of small conspecific individuals more than large individuals, resulting in a positive allometric growth. After foliar fungal pathogen exclusion, species-specific growth scaling exponents and intercepts decreased, but became positively related to species' relative abundance, providing a growth advantage for individuals of abundant species with a higher growth scaling exponent and intercept compared with rare species, and thus reduced species diversity. By adopting allometric growth theory, we elucidate the size-dependent mechanisms through which pathogens regulate species diversity and provide a powerful framework to incorporate antagonistic size-dependent processes in understanding species coexistence.

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.

Seasonal variations in carbon, nitrogen, and phosphorus of Pinus yunnanenis at different stand ages

The seasonal variations in carbon (C), nitrogen (N), and phosphorus (P) at the organ level of Pinus yunnanenis during different season are poorly understood. In this study, the C, N, P, and their stoichiometric ratios in various organs of P. yunnanensis during the four seasons are discussed. The middle and young aged P. yunnanensis forests in central Yunnan province, China were chosen, and the contents of C, N, and P in fine roots (<2 mm), stems, needles, and branches were analyzed. The results showed that the C, N, P contents and their ratios in P. yunnanensis were significantly influenced by season and organ, less affected by age. The C content of the middle-aged and young forests decreased continuously from spring to winter, whereas N and P first decreased and then increased. No significant allometric growth relationships were observed between P-C of the branches or stems in the young and middle-aged forests, whereas a significant allometric growth relationship existed for N-P of needles in the young stands, indicating that the P-C and N-P nutrient distribution patterns shows different trends in the organ level in different age stands. The pattern of P allocation between organs shows differences in stand age, with more allocation to needles in middle-aged stands and more allocation to fine roots in young stands. The N:P ratio in needles was less than 14, indicating that P. yunnanensis was mainly limited by N and increasing the application of N fertilizer would be beneficial for the productivity of this stand. The results will be helpful to nutrient management in P. yunnanensis plantation.

Flow similarity, stochastic branching, and quarter-power scaling in plants

The origin of allometric scaling patterns that are multiples of one-fourth has long fascinated biologists. While not universal, quarter-power scaling relationships are common and have been described in all major clades. Several models have been advanced to explain the origin of such patterns, but questions regarding the discordance between model predictions and empirical data have limited their widespread acceptance. Notable among these is a fractal branching model that predicts power-law scaling of both metabolism and physical dimensions. While a power law is a useful first approximation to some data sets, nonlinear data compilations suggest the possibility of alternative mechanisms. Here, we show that quarter-power scaling can be derived using only the preservation of volume flow rate and velocity as model constraints. Applying our model to land plants, we show that incorporating biomechanical principles and allowing different parts of plant branching networks to be optimized to serve different functions predicts nonlinearity in allometric relationships and helps explain why interspecific scaling exponents covary along a fractal continuum. We also demonstrate that while branching may be a stochastic process, due to the conservation of volume, data may still be consistent with the expectations for a fractal network when one examines sub-trees within a tree. Data from numerous sources at the level of plant shoots, stems, and petioles show strong agreement with our model predictions. This theoretical framework provides an easily testable alternative to current general models of plant metabolic allometry.

Solving the grand challenge of phenotypic integration: allometry across scales

Phenotypic integration is a concept related to the cascade of trait relationships from the lowest organizational levels, i.e. genes, to the highest, i.e. whole-organism traits. However, the cause-and-effect linkages between traits are notoriously difficult to determine. In particular, we still lack a mathematical framework to model the relationships involved in the integration of phenotypic traits. Here, we argue that allometric models developed in ecology offer testable mathematical equations of trait relationships across scales. We first show that allometric relationships are pervasive in biology at different organizational scales and in different taxa. We then present mechanistic models that explain the origin of allometric relationships. In addition, we emphasized that recent studies showed that natural variation does exist for allometric parameters, suggesting a role for genetic variability, selection and evolution. Consequently, we advocate that it is time to examine the genetic determinism of allometries, as well as to question in more detail the role of genome size in subsequent scaling relationships. More broadly, a possible-but so far neglected-solution to understand phenotypic integration is to examine allometric relationships at different organizational levels (cell, tissue, organ, organism) and in contrasted species.

Towards 3D basic theories of plant forms

Allometric, metabolic, and biomechanical theories are the critical foundations for scientifically deciphering plant forms. Their concrete laws, however, are found to deviate for plenty of plant specimens. This phenomenon has not been extensively studied, due to technical restrictions. This bottleneck now can be overcome by the state-of-the-art three-dimensional (3D) mapping technologies, such as fine-scale terrestrial laser scanning. On these grounds, we proposed to reexamine the basic theories regarding plant forms, and then, we case validated the feasibility of upgrading them into 3D modes. As an in-time enlightening of 3D revolutionizing the related basic subject, our theoretical prospect further sorted out the potential challenges as the cutting points for advancing its future exploration, which may enable 3D reconstruction of the basic theories of plant forms and even boost life science.

In this Perspective, the authors discuss how state-of-the-art three-dimensional mapping technologies such as fine-scale terrestrial laser scanning can help us understand the theories of plant forms.

Competitive performance of Pinus massoniana is related to scaling relationships at the individual plant and branch levels

PREMISE

Competition is an important driver of tree mortality and thus affects forest structure and dynamics. Tree architectural traits, such as height-to-diameter (H-D) and branch length-to-diameter (L-d) relationships are thought to influence species competitiveness by affecting light capture. Unfortunately, little is known about how the H vs. D and L vs. d scaling exponents are related to tree performance (defined in the context of growth vigor) in competition.

METHODS

Using data from field surveys of 1547 individuals and destructive sampling of 51 trees with 1086 first-order branches from a high-density Pinus massoniana forest, we explored whether the H vs. D and the L vs. d scaling exponents respectively differed numerically across tree performance and branch vertical position in crowns.

RESULTS

The results indicated that (1) the H vs. D scaling exponent decreased as tree performance declined; (2) the L vs. d scaling exponent differed across tree performance classes (i.e., the scaling exponent of "inferior" trees was significantly larger than that of "moderate" and "superior" trees); (3) the L vs. d scaling exponent decreased as branch position approached ground level; and (4) overall, the branch scaling exponent decreased as tree performance improved in each crown layer, but decreased significantly in the intermediate layer.

CONCLUSIONS

This study highlights the variation within (and linkage among) length-to-diameter scaling relationships across tree performance at the individual and branch levels. This linkage provides new insights into potential mechanisms of tree growth variation (and even further mortality) under competition in subtropical forests.

Toward a general theory of plant carbon economics

Plant life-history variation reflects different outcomes of natural selection given the strictures of resource allocation trade-offs. However, there is limited theory of selection predicting how leaves, stems, roots, and reproductive organs should evolve in concert across environments. Here, we synthesize two optimality theories to offer a general theory of plant carbon economics, named as Gmax theory, that shows how life-history variation is limited to phenotypes that have an approximately similar lifetime net carbon gain per body mass. In consequence, fast-slow economics spectra are the result of trait combinations obtaining similar lifetime net carbon gains from leaves and similar net carbon investment costs in stems, roots, and reproductive organs. Gmax theory also helps explain ecosystem and crop productivity and even helps guide carbon conservation strategies.

Effects of biotic and abiotic factors on forest biomass fractions

The extent to which key factors at the global scale influence plant biomass allocation patterns remains unclear. Here, we provide a theory about how biotic and abiotic factors influence plant biomass allocation and evaluate its predictions using a large global database for forested communities. Our analyses confirm theoretical predictions that temperature, precipitation, and plant height and density jointly regulate the quotient of leaf biomass and total biomass, and that they have a much weaker effect on shoot (leaf plus stem) biomass fractions at a global scale. Moreover, biotic factors have larger effects than abiotic factors. Climatic variables act equally on shoot and root growth, and differences in plant body size and age, as well as community species composition, which vary with climate in ways that drown out the variations in biomass fractions. The theory and data presented here provide mechanistic explanations of why climate has little effect on biomass fractions.

Scaling of joint mass and metabolism fluctuations in in silico cell-laden spheroids

Allometric scaling has many applications, from the prediction of pharmacokinetics in animals and humans to the probing of ecosystem dynamics. Most studies have neglected to account for variations and fluctuations, although they are intrinsic features of all biological systems. To understand how metabolic scaling emerges in the presence of variations, we developed computer-generated models of cell-laden spheroids to define the experimental size range of cell cultures with quantifiable similitudes in terms of fluctuations and metabolic scaling with living organisms. We show that the estimates of scaling exponents may change with increasing variability in both mass and metabolic rate. The computational pipeline described underpins the sound design of statistically meaningful cell-based models, with impacts in both biomedical science and ecology.

Variations and fluctuations are characteristic features of biological systems and are also manifested in cell cultures. Here, we describe a computational pipeline for identifying the range of three-dimensional (3D) cell-aggregate sizes in which nonisometric scaling emerges in the presence of joint mass and metabolic rate fluctuations. The 3D cell-laden spheroids with size and single-cell metabolic rates described by probability density functions were randomly generated in silico. The distributions of the resulting metabolic rates of the spheroids were computed by modeling oxygen diffusion and reaction. Then, a method for estimating scaling exponents of correlated variables through statistically significant data collapse of joint probability distributions was developed. The method was used to identify a physiologically relevant range of spheroid sizes, where both nonisometric scaling and a minimum oxygen concentration (0.04 mol⋅m⁻³) is maintained. The in silico pipeline described enables the prediction of the number of experiments needed for an acceptable collapse and, thus, a consistent estimate of scaling parameters. Using the pipeline, we also show that scaling exponents may be significantly different in the presence of joint mass and metabolic-rate variations typically found in cells. Our study highlights the importance of incorporating fluctuations and variability in size and metabolic rates when estimating scaling exponents. It also suggests the need for taking into account their covariations for better understanding and interpreting experimental observations both in vitro and in vivo and brings insights for the design of more predictive and physiologically relevant in vitro models.

Consistent scaling of whole-shoot respiration between Moso bamboo (Phyllostachys pubescens) and trees

Both Moso bamboo (Phyllostachys pubescens) and tree forests have a large biomass; they are considered to play an important role in ecosystem carbon budgets. The scaling relationship between individual whole-shoot (i.e., aboveground parts) respiration and whole-shoot mass provides a clue for comparing the carbon budgets of Moso bamboo and tree forests. However, nobody has empirically demonstrated whether there is a difference between these forest types in the whole-shoot scaling relationship. We developed whole-shoot chambers and measured the shoot respiration of 58 individual mature bamboo shoots from the smallest to the largest in a Moso bamboo forest, and then compared them with that of 254 tree shoots previously measured. For 30 bamboo shoots, we measured the respiration rate of leaves, branches, and culms. We found that the scaling exponent of whole-shoot respiration of bamboo fitted by a simple power function on a log-log scale was 0.843 (95 % CI 0.797-0.885), which was consistent with that of trees, 0.826 (95 % CI 0.799-0.851), but higher than 3/4, the value typifying the Kleiber's rule. The respiration rates of leaves, branches, and culms at the whole-shoot level were proportional to their mass, revealing a constant mean mass-specific respiration of 1.19, 0.224, and 0.0978 µmol CO₂ kg^- 1 s^- 1, respectively. These constant values suggest common traits of organs among physiologically integrated ramets within a genet. Additionally, the larger the shoots, the smaller the allocation of organ mass to the metabolically active leaves, and the larger the allocation to the metabolically inactive culms. Therefore, these shifts in shoot-mass partitioning to leaves and culms caused a negative metabolic scaling of Moso bamboo shoots. The observed convergent metabolic scaling of Moso bamboo and trees may facilitate comparisons of the ecosystem carbon budgets of Moso bamboo and tree forests.

Growth, death, and resource competition in sessile organisms

Population-level scaling in ecological systems arises from individual growth and death with competitive constraints. We build on a minimal dynamical model of metabolic growth where the tension between individual growth and mortality determines population size distribution. We then separately include resource competition based on shared capture area. By varying rates of growth, death, and competitive attrition, we connect regular and random spatial patterns across sessile organisms from forests to ants, termites, and fairy circles. Then, we consider transient temporal dynamics in the context of asymmetric competition, such as canopy shading or large colony dominance, whose effects primarily weaken the smaller of two competitors. When such competition couples slow timescales of growth to fast competitive death, it generates population shocks and demographic oscillations similar to those observed in forest data. Our minimal quantitative theory unifies spatiotemporal patterns across sessile organisms through local competition mediated by the laws of metabolic growth, which in turn, are the result of long-term evolutionary dynamics.

The allometry of plant height explains species loss under nitrogen addition

Light asymmetry, with a higher light acquisition per unit biomass for larger plants, has been proposed as a major mechanism of species loss after nitrogen addition. However, solid evidence for this has been scarce. We measured the allometric size-height relationships of 25 plant species along a nitrogen addition gradient manipulated annually for eight years in a speciose alpine meadow and found that the positive relationship between species relative abundance and the height scaling exponent in natural conditions disappeared after nitrogen addition. Those species with lower height scaling exponents increased in relative abundance after nitrogen addition, thereby decreasing the community weighted mean and dispersion of the height scaling exponent and ultimately the species richness. Our results provided some unique evidence for light asymmetry induced species loss after nitrogen addition and a new insight from the perspective of allometric scaling to explain biodiversity maintenance in the face of global changes.

Water content quantitatively affects metabolic rates over the course of plant ontogeny

Plant metabolism determines the structure and dynamics of ecological systems across many different scales. The metabolic theory of ecology quantitatively predicts the scaling of metabolic rate as a function of body size and temperature. However, the role of tissue water content has been neglected even though hydration significantly affects metabolism, and thus ecosystem structure and functioning. Here, we use a general model based on biochemical kinetics to quantify the combined effects of water content, body size and temperature on plant metabolic rates. The model was tested using a comprehensive dataset from 205 species across 10 orders of magnitude in body size from seeds to mature large trees. We show that water content significantly influences mass-specific metabolic rates as predicted by the model. The scaling exponents of whole-plant metabolic rate vs body size numerically converge onto 1.0 after water content is corrected regardless of body size or ontogenetic stage. The model provides novel insights into how water content together with body size and temperature quantitatively influence plant growth and metabolism, community dynamics and ecosystem energetics.

Universal scaling laws rule explosive growth in human cancers

Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a measure of the size of the system. Here we describe the discovery of universal superlinear metabolic scaling laws in human cancers. This dependence underpins increasing tumour aggressiveness, due to evolutionary dynamics, which leads to an explosive growth as the disease progresses. We validated this dynamic using longitudinal volumetric data of different histologies from large cohorts of cancer patients. To explain our observations we put forward increasingly-complex biologically-inspired mathematical models that captured the key processes governing tumor growth. Our models predicted that the emergence of superlinear allometric scaling laws is an inherently three-dimensional phenomenon. Moreover, the scaling laws thereby identified allowed us to define a set of metabolic metrics with prognostic value, thus providing added clinical utility to the base findings.

From Dendrochronology to Allometry

The contribution of tree-ring analysis to other fields of scientific inquiry with overlapping interests, such as forestry and plant population biology, is often hampered by the different parameters and methods that are used for measuring growth. Here I present relatively simple graphical, numerical, and mathematical considerations aimed at bridging these fields, highlighting the value of crossdating. Lack of temporal control prevents accurate identification of factors that drive wood formation, thus crossdating becomes crucial for any type of tree growth study at inter-annual and longer time scales. In particular, exactly dated tree rings, and their measurements, are crucial contributors to the testing and betterment of allometric relationships.

A General Model for Seed and Seedling Respiratory Metabolism

The ontogeny of seed plants usually involves a dormant dehydrated state and the breaking of dormancy and germination, which distinguishes it from that of most organisms. Seed germination and seedling establishment are critical ontogenetic stages in the plant life cycle, and both are fueled by respiratory metabolism. However, the scaling of metabolic rate with respect to individual traits remains poorly understood. Here, we tested metabolic scaling theory during seed germination and early establishment growth using a recently developed model and empirical data collected from 41 species. The results show that (i) the mass-specific respiration rate (R_m) was weakly correlated with body mass, mass-specific N content, and mass-specific C content; (ii) R_m conformed to a single Michaelis-Menten curve as a function of tissue water content; and (iii) the central parameters in the model were highly correlated with DNA content and critical enzyme activities. The model offers new insights and a more integrative scaling theory that quantifies the combined effects of tissue water content and body mass on respiratory metabolism during early plant ontogeny.

The effect of allometric partitioning on herbivory tolerance in four species in South China

Herbivory tolerance can offset the negative effects of herbivory on plants and plays an important role in both immigration and population establishment. Biomass reallocation is an important potential mechanism of herbivory tolerance. To understand how biomass allocation affects plant herbivory tolerance, it is necessary to distinguish the biomass allocations resulting from environmental gradients or plant growth. There is generally a tight balance between the amounts of biomass invested in different organs, which must be analyzed by means of an allometric model. The allometric exponent is not affected by individual growth and can reflect the changes in biomass allocation patterns of different parts. Therefore, the allometric exponent was chosen to study the relationship between biomass allocation pattern and herbivory tolerance. We selected four species (Wedelia chinensis, Wedelia trilobata, Merremia hederacea, and Mikania micrantha), two of which are invasive species and two of which are accompanying native species, and established three herbivory levels (0%, 25% and 50%) to compare differences in allometry. The biomass allocation in stems was negatively correlated with herbivory tolerance, while that in leaves was positively correlated with herbivory tolerance. Furthermore, the stability of the allometric exponent was related to tolerance, indicating that plants with the ability to maintain their biomass allocation patterns are more tolerant than those without this ability, and the tendency to allocate biomass to leaves rather than to stems or roots helps increase this tolerance. The allometric exponent was used to remove the effects of individual development on allocation pattern, allowing the relationship between biomass allocation and herbivory tolerance to be more accurately explored. This research used an allometric model to fit the nonlinear process of biomass partitioning during the growth and development of plants and provides a new understanding of the relationship between biomass allocation and herbivory tolerance.

Biomass Allocation in Response to Nitrogen and Phosphorus Availability: Insight From Experimental Manipulations of Arabidopsis thaliana

Allocation of biomass to different organs is a fundamental aspect of plant responses and adaptations to changing environmental conditions, but how it responds to nitrogen (N) and phosphorus (P) availability remains poorly addressed. Here we conducted greenhouse fertilization experiments using Arabidopsis thaliana, with five levels of N and P additions and eight repeat experiments, to ascertain the effects of N and P availability on biomass allocation patterns. N addition increased leaf and stem allocation, but decreased root and fruit allocation. P addition increased stem and fruit allocation, but decreased root and leaf allocation. Pooled data of the five levels of N addition relative to P addition resulted in lower scaling exponents of stem mass against leaf mass (0.983 vs. 1.226; p = 0.000), fruit mass against vegetative mass (0.875 vs. 1.028; p = 0.000), and shoot mass against root mass (1.069 vs. 1.324; p = 0.001). This suggested that N addition relative to P addition induced slower increase in stem mass with increasing leaf mass, slower increase in reproductive mass with increasing vegetative mass, and slower increase in shoot mass with increasing root mass. Further, the levels of N or P addition did not significantly affect the allometric relationships of stem mass vs. leaf mass, and fruit mass vs. vegetative mass. In contrast, increasing levels of N addition increased the scaling exponent of shoot to root mass, whereas increasing levels of P addition exerted the opposite influence on the scaling exponent. This result suggests that increasing levels of N addition promote allocation to shoot mass, whereas the increasing levels of P addition promote allocation to root mass. Our findings highlight that biomass allocation of A. thaliana exhibits a contrasting response to N and P availability, which has profound implications for forecasting the biomass allocation strategies in plants to human-induced nutrient enrichment.

Nonlinear phenotypic variation uncovers the emergence of heterosis in Arabidopsis thaliana

Heterosis describes the phenotypic superiority of hybrids over their parents in traits related to agronomic performance and fitness. Understanding and predicting nonadditive inheritance such as heterosis is crucial for evolutionary biology as well as for plant and animal breeding. However, the physiological bases of heterosis remain debated. Moreover, empirical data in various species have shown that diverse genetic and molecular mechanisms are likely to explain heterosis, making it difficult to predict its emergence and amplitude from parental genotypes alone. In this study, we examined a model of physiological dominance initially proposed by Sewall Wright to explain the nonadditive inheritance of traits like metabolic fluxes at the cellular level. We evaluated Wright's model for two fitness-related traits at the whole-plant level, growth rate and fruit number, using 450 hybrids derived from crosses among natural accessions of A. thaliana. We found that allometric relationships between traits constrain phenotypic variation in a nonlinear and similar manner in hybrids and accessions. These allometric relationships behave predictably, explaining up to 75% of heterosis amplitude, while genetic distance among parents at best explains 7%. Thus, our findings are consistent with Wright's model of physiological dominance and suggest that the emergence of heterosis on plant performance is an intrinsic property of nonlinear relationships between traits. Furthermore, our study highlights the potential of a geometric approach of phenotypic relationships for predicting heterosis of major components of crop productivity and yield.

Stem Diameter (and Not Length) Limits Twig Leaf Biomass

The relationship between leaf and stem biomass as well as the relationship between leaf biomass and stem length and diameter are important to our understanding of a broad range of important plant scaling relationship because of their relationship to photosynthesis and thus growth. To understand how twig architecture (i.e., current year leaves, and stem diameter and length) affects stem diameter and length, and leaf number and biomass, we examined the twigs of 64 woody species collected from three forest types along an elevational gradient in the Wuyi Mountains, Jiangxi Province, China. We also compared the scaling relationships we observed with biomass allocation patterns reported at the whole tree level. Our results revealed isometric relationship between leaf and stem biomass on twigs despite differences in forest communities and despite changes in environmental factors along an elevational gradient. Across the 64 species, from twigs to individual trees, leaf biomass scaled approximately as the 2.0-power of stem diameter (but not for stem length or leaf number). These results help to identify a general rule that operates at two different levels of biological organization (twigs and whole trees). The scaling relationship between leaf biomass and stem diameter in twigs is insensitive to differences in species composition, elevation, or forest type. We speculate that this rule emerges because stem diameter serves as a proxy for the amount of resources supplied per unit cross section to developing leaves and for the flow of photosynthates from mature leaves to the rest of the plant body.

Process-based allometry describes the influence of management on orchard tree aboveground architecture

We evaluated allometric relationships in length, diameter, and mass of branches for two variably managed orchard tree species (tart cherry, Prunus cerasus; apple, Malus spp.). The empirically estimated allometric exponents (a) of the orchard trees were described in the context of two processed-based allometry models that make predictions for a: the West, Brown and Enquist fractal branching model (WBE) and the recently introduced Flow Similarity model (FS). These allometric models make predictions about relationships in plant morphology (e.g., branch mass, diameter, length, volume, surface area) based on constraints imposed on plant growth by physical and physiological processes. We compared our empirical estimates of a to the model predictions to interpret the physiological implications of pruning and management in orchard systems. Our study found strong allometric relationships among the species and individuals studied with limited agreement with the expectations of either model. The 8/3-power law prediction of the mass ∼ diameter relationship by the WBE, indicative of biomechanical limitations, was marginally supported by this study. Length-including allometric relationships deviated from predictions of both models, but shift toward the expectation of flow similarity. In this way, managed orchard trees deviated from strict adherence to the idealized expectations of the models, but still fall within the range of model expectations in many cases despite intensive management.

Adaptive diversification of growth allometry in the plant Arabidopsis thaliana

Seed plants vary tremendously in size and morphology; however, variation and covariation in plant traits may be governed, at least in part, by universal biophysical laws and biological constants. Metabolic scaling theory (MST) posits that whole-organismal metabolism and growth rate are under stabilizing selection that minimizes the scaling of hydrodynamic resistance and maximizes the scaling of resource uptake. This constrains variation in physiological traits and in the rate of biomass accumulation, so that they can be expressed as mathematical functions of plant size with near-constant allometric scaling exponents across species. However, the observed variation in scaling exponents calls into question the evolutionary drivers and the universality of allometric equations. We have measured growth scaling and fitness traits of 451 Arabidopsis thaliana accessions with sequenced genomes. Variation among accessions around the scaling exponent predicted by MST was correlated with relative growth rate, seed production, and stress resistance. Genomic analyses indicate that growth allometry is affected by many genes associated with local climate and abiotic stress response. The gene with the strongest effect, PUB4, has molecular signatures of balancing selection, suggesting that intraspecific variation in growth scaling is maintained by opposing selection on the trade-off between seed production and abiotic stress resistance. Our findings suggest that variation in allometry contributes to local adaptation to contrasting environments. Our results help reconcile past debates on the origin of allometric scaling in biology and begin to link adaptive variation in allometric scaling to specific genes.

Divergent scaling of respiration rates to nitrogen and phosphorus across four woody seedlings between different growing seasons

Empirical studies indicate that the exponents governing the scaling of plant respiration rates (R) with respect to biomass (M) numerically vary between three-fourth for adult plants and 1.0 for seedlings and saplings and are affected by nitrogen (N) and phosphorus (P) content. However, whether the scaling of R with respect to M (or N and P) varies among different phylogenetic groups (e.g., gymnosperms vs. angiosperms) or during the growing and dormant seasons remains unclear. We measured the whole-plant R and M, and N and P content of the seedlings of four woody species during the growing season (early October) and the dormant season (January). The data show that (i) the scaling exponents of R versus M, R versus N, and R versus P differed significantly among the four species, but (ii), not between the growing and dormant seasons for each of the four species, although (iii) the normalization constants governing the scaling relationships were numerically greater for the growing season compared to the dormant season. In addition, (iv) the scaling exponents of R versus M, R versus N, and R versus P were numerically larger for the two angiosperm species compared to those of the two gymnosperm species, (v) the interspecific scaling exponents for the four species were greater during the growing season than in the dormant season, and (vi), interspecifically, P scaled nearly isometric with N content. Those findings indicate that the metabolic scaling relationships among R, M, N, and P manifest seasonal variation and differ between angiosperm and gymnosperm species, that is, there is no single, canonical scaling exponent for the seedlings of woody species.

Effects of biophysical constraints, climate and phylogeny on forest shrub allometries along an altitudinal gradient in Northeast China

Whether there is a general allometry law across plant species with different sizes and under different environment has long been controversial and shrubs are particularly useful to examine these questions. Here we sampled 939 individuals from 50 forest shrub species along a large altitudinal gradient. We tested several allometry models with four relationships simultaneously (between stem diameter, height, leaf, stem and aboveground biomass), including geometric, elastic and stress similarity, and metabolic scaling theory's predictions on small plants (MSTs) and trees (MSTt). We also tested if allometric exponents change markedly with climate and phylogeny. The predicted exponents of MSTt, elastic similarity and stress similarity (models for trees) were not supported by our data, while MSTs and geometric similarity gained more support, suggesting the finite size effect is more important for shrub allometries than being a woody plant. The influence of climate and phylogeny on allometric exponents were not significant or very weak, again suggesting strong biophysical constraints on shrub allometries. Our results reveal clear differences of shrub allometries from previous findings on trees (e.g. much weaker climatic and phylogenic control). Comparisons of herbs, shrubs and trees along a same climatic gradient are needed for better understanding of plant allometries.

An empirical test of 'universal' biomass scaling relationships in kelps: evidence of convergence with seed plants

Biomass allocation patterns have received substantial consideration, leading to the recognition of several 'universal' interspecific trends. Despite efforts to understand biomass partitioning among embryophytes, few studies have examined macroalgae that evolved independently, yet function ecologically in much the same ways as plants. Kelps allocate photosynthate among three organs (the blade(s), stipe(s) and holdfast) that are superficially convergent with organs of land plants, providing a unique opportunity to test the limits of 'universal' trends. In this study, we used an allometric approach to quantify interspecific biomass partitioning patterns in kelps and assess whether embryophyte-based predictions of biomass scaling can be applied to marine macrophytes that lack root-to-leaf hydraulic transport. Photosynthetic area and dry mass were found to scale to approximately the ¾ power and kelp biomass allocation patterns were shown to match closely to empirical measures of allometric scaling among woody plants. Larger kelp species were found to have increased relative stipe and holdfast mass than smaller species, highlighting important consequences of size for marine macroalgae. Our study provides insights into the evolution of size in the largest marine macrophytes and corroborates previous work suggesting that the morphology of divergent lineages of photoautotrophs may reflect similar selective pressures.

A predictive nondestructive model for the covariation of tree height, diameter, and stem volume scaling relationships

Metabolic scaling theory (MST) posits that the scaling exponents among plant height H, diameter D, and biomass M will covary across phyletically diverse species. However, the relationships between scaling exponents and normalization constants remain unclear. Therefore, we developed a predictive model for the covariation of H, D, and stem volume V scaling relationships and used data from Chinese fir (Cunninghamia lanceolata) in Jiangxi province, China to test it. As predicted by the model and supported by the data, normalization constants are positively correlated with their associated scaling exponents for D vs. V and H vs. V, whereas normalization constants are negatively correlated with the scaling exponents of H vs. D. The prediction model also yielded reliable estimations of V (mean absolute percentage error = 10.5 ± 0.32 SE across 12 model calibrated sites). These results (1) support a totally new covariation scaling model, (2) indicate that differences in stem volume scaling relationships at the intra-specific level are driven by anatomical or ecophysiological responses to site quality and/or management practices, and (3) provide an accurate non-destructive method for predicting Chinese fir stem volume.

Evaluating general allometric models: interspecific and intraspecific data tell different stories due to interspecific variation in stem tissue density and leaf size

The ability of general scaling models to capture the central tendency or dispersion in biological data has been questioned. In fact, the appropriate domain of such models has never been clearly articulated and they have been supported and challenged using both interspecific and/or intraspecific data. Here, we evaluate several simplifying assumptions and predictions of two prominent scaling models: West, Brown and Enquist's fractal model (WBE) and a null model of geometric similarity (GEOM). Using data for 53 herbaceous angiosperm species from the Songnen Grasslands of Northern China, we compared both the interspecific and intraspecific scaling relationships for plant geometry and biomass partitioning. Specifically, we considered biomass investment in shoots and leaves as well as related several traits not commonly collected in plant allometric analyses: shoot volume, leaf number, and mean leaf mass. At the interspecific level, we find substantial variation in regression slopes, and the simplifying assumptions of WBE and predictions of both the WBE and GEOM models do not hold. In contrast, we find substantial support for the WBE model at the intraspecific level, and to a lesser extent for GEOM. The differences between our results at interspecific and intraspecific levels are due to the fact that leaf size and stem tissue density vary considerably across species in contrast to the simplifying assumptions of WBE. These results highlight the domain within which simplifying model assumptions might be most appropriate, and suggest allometric models may be useful points of departure within some species, growth forms or taxonomic groups.

Scaling the respiratory metabolism to phosphorus relationship in plant seedlings

There are empirical indications of an isometric scaling relationship between plants' respiratory metabolism rates and nitrogen contents. To test the hypothesis that there may be a similar relationship between plants' respiratory metabolism and phosphorus contents we used data obtained from 150 laboratory and field-grown seedlings representing 30 herbaceous species and 20 woody deciduous species. Our results show that whole-plant respiration rates strongly scaled to the 0.81-power of the whole-plant phosphorus content, across wide ranges of growth conditions and functional classifications. Moreover, we also found a similar scaling exponent between whole-plant respiration rates and total nitrogen contents for the same set of samples. The similarities of the metabolic scaling relationships suggest that similar mechanisms may be involved in the transport and storage of phosphorus and nitrogen in plants.

How does biomass distribution change with size and differ among species? An analysis for 1200 plant species from five continents

We compiled a global database for leaf, stem and root biomass representing c. 11 000 records for c. 1200 herbaceous and woody species grown under either controlled or field conditions. We used this data set to analyse allometric relationships and fractional biomass distribution to leaves, stems and roots. We tested whether allometric scaling exponents are generally constant across plant sizes as predicted by metabolic scaling theory, or whether instead they change dynamically with plant size. We also quantified interspecific variation in biomass distribution among plant families and functional groups. Across all species combined, leaf vs stem and leaf vs root scaling exponents decreased from c. 1.00 for small plants to c. 0.60 for the largest trees considered. Evergreens had substantially higher leaf mass fractions (LMFs) than deciduous species, whereas graminoids maintained higher root mass fractions (RMFs) than eudicotyledonous herbs. These patterns do not support the hypothesis of fixed allometric exponents. Rather, continuous shifts in allometric exponents with plant size during ontogeny and evolution are the norm. Across seed plants, variation in biomass distribution among species is related more to function than phylogeny. We propose that the higher LMF of evergreens at least partly compensates for their relatively low leaf area : leaf mass ratio.

Constraint around Quarter-Power Allometric Scaling in Wild Tomatoes (Solanum sect. Lycopersicon; Solanaceae)

The West-Brown-Enquist (WBE) metabolic scaling theory posits that many organismal features scale predictably with body size because of selection to minimize transport costs in resource distribution networks. Many scaling exponents are quarter-powers, as predicted by WBE, but there are also biologically significant deviations that could reflect adaptation to different environments. A central but untested prediction of the WBE model is that wide deviation from optimal scaling is penalized, leading to a pattern of constraint on scaling exponents. Here, we demonstrate, using phylogenetic comparative methods, that variation in allometric scaling between mass and leaf area across 17 wild tomato taxa is constrained around a value indistinguishable from that predicted by WBE but significantly greater than 2/3 (geometric-similarity model). The allometric-scaling exponent was highly correlated with fecundity, water use, and drought response, suggesting that it is functionally significant and therefore could be under selective constraints. However, scaling was not strictly log-log linear but rather declined during ontogeny in all species, as has been observed in many plant species. We caution that although our results supported one prediction of the WBE model, it did not strongly test the model in other important respects. Nevertheless, phylogenetic comparative methods such as those used here are powerful but underutilized tools for metabolic ecology that complement existing methods to adjudicate between models.

A theoretical framework for whole-plant carbon assimilation efficiency based on metabolic scaling theory: a test case using Picea seedlings

Simultaneous and accurate measurements of whole-plant instantaneous carbon-use efficiency (ICUE) and annual total carbon-use efficiency (TCUE) are difficult to make, especially for trees. One usually estimates ICUE based on the net photosynthetic rate or the assumed proportional relationship between growth efficiency and ICUE. However, thus far, protocols for easily estimating annual TCUE remain problematic. Here, we present a theoretical framework (based on the metabolic scaling theory) to predict whole-plant annual TCUE by directly measuring instantaneous net photosynthetic and respiratory rates. This framework makes four predictions, which were evaluated empirically using seedlings of nine Picea taxa: (i) the flux rates of CO(2) and energy will scale isometrically as a function of plant size, (ii) whole-plant net and gross photosynthetic rates and the net primary productivity will scale isometrically with respect to total leaf mass, (iii) these scaling relationships will be independent of ambient temperature and humidity fluctuations (as measured within an experimental chamber) regardless of the instantaneous net photosynthetic rate or dark respiratory rate, or overall growth rate and (iv) TCUE will scale isometrically with respect to instantaneous efficiency of carbon use (i.e., the latter can be used to predict the former) across diverse species. These predictions were experimentally verified. We also found that the ranking of the nine taxa based on net photosynthetic rates differed from ranking based on either ICUE or TCUE. In addition, the absolute values of ICUE and TCUE significantly differed among the nine taxa, with both ICUE and temperature-corrected ICUE being highest for Picea abies and lowest for Picea schrenkiana. Nevertheless, the data are consistent with the predictions of our general theoretical framework, which can be used to access annual carbon-use efficiency of different species at the level of an individual plant based on simple, direct measurements. Moreover, we believe that our approach provides a way to cope with the complexities of different ecosystems, provided that sufficient measurements are taken to calibrate our approach to that of the system being studied.

Fundamental origins and limits for scaling a maternal morphogen gradient

Tissue expansion and patterning are integral to development, but it is unknown quantitatively how a mother accumulates molecular resources to invest in the future of instructing robust embryonic patterning. Here we develop a model, Tissue Expansion-Modulated Maternal Morphogen Scaling (TEM³S), to study scaled anterior-posterior patterning in Drosophila embryos. Using both ovaries and embryos, we measure a core quantity of the model, the scaling power of the Bicoid (Bcd) morphogen gradient’s amplitude n_A. We also evaluate directly model-derived predictions about Bcd gradient and patterning properties. Our results show that scaling of the Bcd gradient in the embryo originates from, and is constrained fundamentally by, a dynamic relationship between maternal tissue expansion and bcd gene copy number expansion in the ovary. This delicate connection between the two transitioning stages of a life cycle, stemming from a finite value of n_A ~ 3, underscores a key feature of developmental systems depicted by TEM³S.

Heterogeneity of cells may explain allometric scaling of metabolic rate

The origin of allometric scaling of metabolic rate is a long-standing question in biology. Several models have been proposed for explaining the origin; however, they have advantages and disadvantages. In particular, previous models only demonstrate either two important observations for the allometric scaling: the variability of scaling exponents and predominance of 3/4-power law. Thus, these models have a dispute over their validity. In this study, we propose a simple geometry model, and show that a hypothesis that total surface area of cells determines metabolic rate can reproduce these two observations by combining two concepts: the impact of cell sizes on metabolic rate and fractal-like (hierarchical) organization. The proposed model both theoretically and numerically demonstrates the approximately 3/4-power law although several different biological strategies are considered. The model validity is confirmed using empirical data. Furthermore, the model suggests the importance of heterogeneity of cell size for the emergence of the allometric scaling. The proposed model provides intuitive and unique insights into the origin of allometric scaling laws in biology, despite several limitations of the model.

Allometric scaling relationship between above- and below-ground biomass within and across five woody seedlings

Allometric biomass allocation theory predicts that leaf biomass (M L ) scaled isometrically with stem (M S ) and root (M R ) biomass, and thus above-ground biomass (leaf and stem) (M A ) and root (M R ) scaled nearly isometrically with below-ground biomass (root) for tree seedlings across a wide diversity of taxa. Furthermore, prior studies also imply that scaling constant should vary with species. However, litter is known about whether such invariant isometric scaling exponents hold for intraspecific biomass allocation, and how variation in scaling constants influences the interspecific scaling relationship between above- and below-ground biomass. Biomass data of seedlings from five evergreen species were examined to test scaling relationships among biomass components across and within species. Model Type II regression was used to compare the numerical values of scaling exponents and constants among leaf, stem, root, and above- to below-ground biomass. The results indicated that M L and M S scaled in an isometric or a nearly isometric manner with M R , as well as M A to M R for five woody species. Significant variation was observed in the Y-intercepts of the biomass scaling curves, resulting in the divergence for intraspecific scaling and interspecific scaling relationships for M L versus M S and M L versus M R , but not for M S versus M R and M A versus M R . We conclude, therefore, that a nearly isometric scaling relationship of M A versus M R holds true within each of the studied woody species and across them irrespective the negative scaling relationship between leaf and stem.

Interspecific differences in whole-plant respiration vs. biomass scaling relationships: a case study using evergreen conifer and angiosperm tree seedlings

PREMISE OF THE STUDY

Empirical studies and theory indicate that respiration rates (R) of small plants scale nearly isometrically with both leaf biomass (ML) and total plant biomass (MT). These predictions are based on angiosperm species and apply only across a small range of body mass. Whether these relationships hold true for different plants, such as conifers, remains unclear.

METHODS

We tested these predictions using the whole-plant maintenance respiration rates and the biomass allocation patterns of the seedlings of two conifer tree species and two angiosperm tree species. Model Type II regression protocols were used to compare the scaling exponents (α) and normalization constants (β) across all four species and within each of the four species.

KEY RESULTS

The data show that the scaling exponents varied among the four species and that all differed significantly from isometry. For conifers, scaling exponents for R vs. MT, and R and ML were numerically smaller than those of the broadleaved angiosperm species. However, across the entire data set, R scaled isometrically with ML and with MT as predicted by the West, Brown, and Enquist (WBE) theory. We also observed higher respiration rates for small conifer seedlings compared to comparably sized angiosperm seedlings.

CONCLUSIONS

Our data add credence to the view that the R vs. M scaling relationship differs among species, and that in general, the numerical values of this interspecific scaling relationship will depend on the species pooled in the analysis and on the range of body sizes within the data set.

Form, function, and evolution of living organisms

Despite the vast diversity of sizes and shapes of living organisms, life's organization across scales exhibits remarkable commonalities, most notably through the approximate validity of Kleiber's law, the power law scaling of metabolic rates with the mass of an organism. Here, we present a derivation of Kleiber's law that is independent of the specificity of the myriads of organism species. Specifically, we account for the distinct geometries of trees and mammals as well as deviations from the pure power law behavior of Kleiber's law, and predict the possibility of life forms with geometries intermediate between trees and mammals. We also make several predictions in excellent accord with empirical data. Our theory relates the separate evolutionary histories of plants and animals through the fundamental physics underlying their distinct overall forms and physiologies.

Oxygen consumption rates of bacteria under nutrient-limited conditions

Many environments on Earth experience nutrient limitation and as a result have nongrowing or very slowly growing bacterial populations. To better understand bacterial respiration under environmentally relevant conditions, the effect of nutrient limitation on respiration rates of heterotrophic bacteria was measured. The oxygen consumption and population density of batch cultures of Escherichia coli K-12, Shewanella oneidensis MR-1, and Marinobacter aquaeolei VT8 were tracked for up to 200 days. The oxygen consumption per CFU (QO2) declined by more than 2 orders of magnitude for all three strains as they transitioned from nutrient-abundant log-phase growth to the nutrient-limited early stationary phase. The large reduction in QO2 from growth to stationary phase suggests that nutrient availability is an important factor in considering environmental respiration rates. Following the death phase, during the long-term stationary phase (LTSP), QO2 values of the surviving population increased with time and more cells were respiring than formed colonies. Within the respiring population, a subpopulation of highly respiring cells increased in abundance with time. Apparently, as cells enter LTSP, there is a viable but not culturable population whose bulk community and per cell respiration rates are dynamic. This result has a bearing on how minimal energy requirements are met, especially in nutrient-limited environments. The minimal QO2 rates support the extension of Kleiber's law to the mass of a bacterium (100-fg range).