Metabolic Scaling Theory Prediction Research Articles

Genetic variability and plasticity of plant allometry

Abstract The metabolic scaling theory (MST) predicts quasi‐universal trait–size relationships in plants, characterised by a unique allometric exponent within and across large taxonomic scales. However, recent studies have identified variability in allometric relationships, without a clear understanding of the modulating role played by genetic variation and environment. Here, we investigated (1) the allometric relationships for two central traits of MST, namely total leaf area and plant growth rate, in the model species Arabidopsis thaliana, (2) the variability of plant allometries between genotypes and (3) the plastic responses of plant allometries under water deficit, high temperature and their interaction. Using a population of 120 genotypes, we found that intraspecific allometries adhered on average with MST predictions. However, a broad variability but a moderate plasticity in the allometric exponents was observed across genotypes and environments. Allometric exponents were impacted significantly, yet weakly, by water deficit, but not by high temperature. Moreover, genotypes that deviated from MST predictions exhibited more plasticity in trait–size relationships than genotypes that followed MST predictions. Our study suggests that plant allometry is genetically variable and might be related to different adaptive strategies to cope with stressing conditions. Thus, our results highlights the need of assessing trait–size relationships within species to understand the mechanisms of plant adaptation to contrasted environments. Read the free Plain Language Summary for this article on the Journal blog.

Tallo: A global tree allometry and crown architecture database.

Data capturing multiple axes of tree size and shape, such as a tree's stem diameter, height and crown size, underpin a wide range of ecological research—from developing and testing theory on forest structure and dynamics, to estimating forest carbon stocks and their uncertainties, and integrating remote sensing imagery into forest monitoring programmes. However, these data can be surprisingly hard to come by, particularly for certain regions of the world and for specific taxonomic groups, posing a real barrier to progress in these fields. To overcome this challenge, we developed the Tallo database, a collection of 498,838 georeferenced and taxonomically standardized records of individual trees for which stem diameter, height and/or crown radius have been measured. These data were collected at 61,856 globally distributed sites, spanning all major forested and non‐forested biomes. The majority of trees in the database are identified to species (88%), and collectively Tallo includes data for 5163 species distributed across 1453 genera and 187 plant families. The database is publicly archived under a CC‐BY 4.0 licence and can be access from: https://doi.org/10.5281/zenodo.6637599. To demonstrate its value, here we present three case studies that highlight how the Tallo database can be used to address a range of theoretical and applied questions in ecology—from testing the predictions of metabolic scaling theory, to exploring the limits of tree allometric plasticity along environmental gradients and modelling global variation in maximum attainable tree height. In doing so, we provide a key resource for field ecologists, remote sensing researchers and the modelling community working together to better understand the role that trees play in regulating the terrestrial carbon cycle.

Biological scaling in green algae: the role of cell size and geometry

The Metabolic Scaling Theory (MST), hypothesizes limitations of resource-transport networks in organisms and predicts their optimization into fractal-like structures. As a result, the relationship between population growth rate and body size should follow a cross-species universal quarter-power scaling. However, the universality of metabolic scaling has been challenged, particularly across transitions from bacteria to protists to multicellulars. The population growth rate of unicellulars should be constrained by external diffusion, ruling nutrient uptake, and internal diffusion, operating nutrient distribution. Both constraints intensify with increasing size possibly leading to shifting in the scaling exponent. We focused on unicellular algae Micrasterias. Large size and fractal-like morphology make this species a transitional group between unicellular and multicellular organisms in the evolution of allometry. We tested MST predictions using measurements of growth rate, size, and morphology-related traits. We showed that growth scaling of Micrasterias follows MST predictions, reflecting constraints by internal diffusion transport. Cell fractality and density decrease led to a proportional increase in surface area with body mass relaxing external constraints. Complex allometric optimization enables to maintain quarter-power scaling of population growth rate even with a large unicellular plan. Overall, our findings support fractality as a key factor in the evolution of biological scaling.

The Influence of Ecosystem and Phylogeny on Tropical Tree Crown Size and Shape

The sizes and shapes of tree crowns are of fundamental importance in ecology, yet understanding the forces that determine them remains elusive. A cardinal question facing ecologists is the degree to which general and non-specific versus ecological and context-dependent processes are responsible for shaping tree crowns. Here, we test this question for the first time across diverse tropical ecosystems. Using trees from 20 plots varying in elevation, precipitation, and ecosystem type (savanna-forest transitions) across the paleo- and neo-tropics, we test the relationship between crown dimensions and tree size. By analyzing these scaling relationships across environmental gradients, biogeographic regions, and phylogenetic distance, we extend Metabolic Scaling Theory (MST) predictions to include how local selective pressures shape variation in crown dimensions. Across all sites, we find strong agreement between mean trends and MST predictions for the scaling of crown size and shape, but large variation around the mean. While MST explained approximately half of the observed variation in tree crown dimensions, we find that local, ecosystem, and phylogenetic predictors account for the half of the residual variation. Crown scaling does not change significantly across regions, but does change across ecosystem types, where savanna tree crowns grow more quickly with tree girth than forest tree crowns. Crowns of legumes were wider and more voluminous than those of other taxa. Thus, while MST can accurately describe the central tendency of tree crown size, local ecological conditions and evolutionary history appear to modify the scaling of crown shape. Importantly, our extension of MST incorporating these differences accounts for the mechanisms driving variation in the scaling of crown dimensions across the tropics. We present allometric equations for the prediction of crown dimensions across tropical ecosystems. These results are critical when scaling the function of individual trees to larger spatial scales or incorporating the size and shape of tree crowns in global biogeochemical models.

Equilibrium forest demography explains the distribution of tree sizes across North America

The distribution of tree sizes within a forest strongly influences how it will respond to disturbances and environmental changes such as future climate change and increases in atmospheric CO2. This means that global vegetation models must include variation in tree size to accurately represent carbon sinks, such as that seen in North America. Here we use an analytical model of large-scale forest demography which assumes tree growth varies as a power of tree diameter whilst tree mortality is independent of size. The equilibrium solutions of this model are able to accurately reproduce the tree-size distributions, for 61 species and four plant functional types, measured across North America, using just a single species-specific fitting parameter, μ, which determines the ratio of mortality to growth. The predictions of metabolic scaling theory for tree-size distributions are also tested and found to deviate significantly from observations and that maybe explained by the assumptions made about how individual trees fill the available space. We show that equilibrium forest demography implies a single curve that relates mean tree diameter to μ, and that this can be used to make reasonable estimates of the whole dataset mean trunk diameter by fitting only to the larger trees. Our analysis suggests that analytical solutions such as those in this paper may have a role in aiding the understanding and development of next-generation Dynamic Global Vegetation Models based on ecosystem demography.

What causes greater deviations from predictions of metabolic scaling theory in earlier successional forests?

Abstract Metabolic scaling theory (MST) is frequently criticized because its predictions do not match many observations that allometric relationships change with climate and species. Understanding why observations deviate from theory predictions is critical for better forest carbon accounting and management in a rapid warming world. Here we used forest plots across successional and latitudinal gradients to test the predictions that: (1) observed exponents should deviate more from MST predictions at earlier successional stages; (2) the deviations may be related to changes in competition, recruitment limitation and tree size across successional stages and climate gradient. We sampled forest plots (each 1000 m 2 ) from four successional stages (early to late) in four sites along a latitudinal gradient (42–50°N) in Northeast China, and examined the scaling relationship between tree diameter and height ( D-H ) and plot-level tree size distribution ( D-N scaling). We related the scaling exponents for each plot to successional stage, climate, local topographic factors, and proxies for tree size, light competition and recruitment limitation. We used mixed-effect structural equation model to examine the major factors causing the deviations from MST predictions. The results showed that both D-H and D-N scaling exponents conformed to MST predictions in late-successional forests, but D-H exponent deceased while D-N exponent increased regularly towards later-successional stages. Both exponents were little correlated with climate and local topographic factors, but were significantly correlated to tree size, and proxies for competition (stem density) and recruitment limitation (skewness of tree size distribution). D-H scaling was mainly affected by stem density and successional stage, while D-N scaling mainly affected by skewness and succession. Both scaling relationships were not significantly affected by tree size, and were indirectly influenced by climate through stem density or skewness. Our results provide clear evidence that MST predictions are only supported in the late successional forests, while forests at an earlier successional stage reveal greater deviations. These deviations may be caused by processes not considered in MST, including light competition, demography dynamics and successional status. Future MST need to incorporate these ecological processes to better predict the allometries for disturbed forests, which are widespread across the world and have important roles in carbon sequestration.

Tree Morphologic Plasticity Explains Deviation from Metabolic Scaling Theory in Semi-Arid Conifer Forests, Southwestern USA.

A significant concern about Metabolic Scaling Theory (MST) in real forests relates to consistent differences between the values of power law scaling exponents of tree primary size measures used to estimate mass and those predicted by MST. Here we consider why observed scaling exponents for diameter and height relationships deviate from MST predictions across three semi-arid conifer forests in relation to: (1) tree condition and physical form, (2) the level of inter-tree competition (e.g. open vs closed stand structure), (3) increasing tree age, and (4) differences in site productivity. Scaling exponent values derived from non-linear least-squares regression for trees in excellent condition (n = 381) were above the MST prediction at the 95% confidence level, while the exponent for trees in good condition were no different than MST (n = 926). Trees that were in fair or poor condition, characterized as diseased, leaning, or sparsely crowned had exponent values below MST predictions (n = 2,058), as did recently dead standing trees (n = 375). Exponent value of the mean-tree model that disregarded tree condition (n = 3,740) was consistent with other studies that reject MST scaling. Ostensibly, as stand density and competition increase trees exhibited greater morphological plasticity whereby the majority had characteristically fair or poor growth forms. Fitting by least-squares regression biases the mean-tree model scaling exponent toward values that are below MST idealized predictions. For 368 trees from Arizona with known establishment dates, increasing age had no significant impact on expected scaling. We further suggest height to diameter ratios below MST relate to vertical truncation caused by limitation in plant water availability. Even with environmentally imposed height limitation, proportionality between height and diameter scaling exponents were consistent with the predictions of MST.

Application of Metabolic Scaling Theory to reduce error in local maxima tree segmentation from aerial LiDAR

Identifying individual trees across large forested landscapes is an important benefit of an aerial LiDAR collection. However, current approaches toward individual tree segmentation of aerial LiDAR data do not always reflect how the allometry of tree canopies change with height, age, or competition for limiting space and resources. We developed a variable-area local maxima (VLM) algorithm that incorporates predictions of the Metabolic Scaling Theory (MST) to reduce the frequency of commission error in a local maxima individual tree inventory derived from aerial LiDAR. By comparing the MST prediction to 663 species of North American champion-sized trees (which include the tallest and the largest trees on the planet), and 610 measured trees in semi-arid conifer forests in Arizona and New Mexico we show the MST canopy radius model rcan=βhα where β is the normalization constant, h is height, and α is a dynamic exponent predicted by MST to be α=1, can be applied as a general model in many water-limited conifer forests. MST also informs the estimate of individual tree bole diameter dbole (which aerial LiDAR does not measure directly) based on two primary size measures easily obtained from the aerial LiDAR: height h and canopy diameter dcan. A two parameter model βh√dcan is shown to better predict bole diameter (r2=0.811, RMSE=7.66cm) than a single parameter model of either canopy diameter or height alone: βdcanα (r2=0.51 RMSE=12. 4cm) or βhα (r2=0.753, RMSE=8.94cm). By improving methods to identify individual trees and more accurately predict bole diameter, estimates of total forest stand density, structural diversity, above ground biomass and carbon over large landscapes will likewise be improved.

The role of belowground competition and plastic biomass allocation in altering plant mass–density relationships

Metabolic scaling theory (MST) predicts a ‘universal scaling law’ for plant mass–density relationships, but empirical observations are more variable. Possible explanations of this variability include plasticity in biomass allocation between the above‐ and belowground compartment and different modes of competition, which can be asymmetric or symmetric. Although complex interactions of these factors are likely to occur, so far the majority of modelling and empirical studies has focussed on mono‐factorial explanations. We here present a generic individual‐based model, which allows exploring the plant mass–density relationship in realistic settings by representing plasticity of biomass allocation and different modes of competition in the above‐ and belowground compartment. Plants grew according to an ontogenetic growth model derived from MST. To evaluate the behavior of the simulated plants related to the allocation patterns and to validate model predictions, we conducted greenhouse experiments with tree seedlings. The model reproduced empirical patterns both at the individual and population level. Without belowground resource limitation, aboveground processes dominated and the slopes of mass–density relationships followed the predictions of MST. In contrast, resource limitation led to an increased allocation of biomass to belowground parts of the plants. The subsequent dominance of symmetric belowground competition caused significantly shallower slopes of the mass–density relationship, even though the growth of individual plants followed MST. We conclude that changes in biomass allocation induced by belowground resource limitation explain the deviations from the mass–density relationship predicted by MST. Taking into account the plasticity of biomass allocation and its linkage to the above‐ and belowground competition is critical for fully representing plant communities, in particular for correctly predicting their response of carbon storage and sequestration to changing environmental conditions.

Allometric Convergence in Savanna Trees and Implications for the Use of Plant Scaling Models in Variable Ecosystems

Theoretical models of allometric scaling provide frameworks for understanding and predicting how and why the morphology and function of organisms vary with scale. It remains unclear, however, if the predictions of ‘universal’ scaling models for vascular plants hold across diverse species in variable environments. Phenomena such as competition and disturbance may drive allometric scaling relationships away from theoretical predictions based on an optimized tree. Here, we use a hierarchical Bayesian approach to calculate tree-specific, species-specific, and ‘global’ (i.e. interspecific) scaling exponents for several allometric relationships using tree- and branch-level data harvested from three savanna sites across a rainfall gradient in Mali, West Africa. We use these exponents to provide a rigorous test of three plant scaling models (Metabolic Scaling Theory (MST), Geometric Similarity, and Stress Similarity) in savanna systems. For the allometric relationships we evaluated (diameter vs. length, aboveground mass, stem mass, and leaf mass) the empirically calculated exponents broadly overlapped among species from diverse environments, except for the scaling exponents for length, which increased with tree cover and density. When we compare empirical scaling exponents to the theoretical predictions from the three models we find MST predictions are most consistent with our observed allometries. In those situations where observations are inconsistent with MST we find that departure from theory corresponds with expected tradeoffs related to disturbance and competitive interactions. We hypothesize savanna trees have greater length-scaling exponents than predicted by MST due to an evolutionary tradeoff between fire escape and optimization of mechanical stability and internal resource transport. Future research on the drivers of systematic allometric variation could reconcile the differences between observed scaling relationships in variable ecosystems and those predicted by ideal models such as MST.

Plant Interactions Alter the Predictions of Metabolic Scaling Theory

Metabolic scaling theory (MST) is an attempt to link physiological processes of individual organisms with macroecology. It predicts a power law relationship with an exponent of −4/3 between mean individual biomass and density during density-dependent mortality (self-thinning). Empirical tests have produced variable results, and the validity of MST is intensely debated. MST focuses on organisms’ internal physiological mechanisms but we hypothesize that ecological interactions can be more important in determining plant mass-density relationships induced by density. We employ an individual-based model of plant stand development that includes three elements: a model of individual plant growth based on MST, different modes of local competition (size-symmetric vs. -asymmetric), and different resource levels. Our model is consistent with the observed variation in the slopes of self-thinning trajectories. Slopes were significantly shallower than −4/3 if competition was size-symmetric. We conclude that when the size of survivors is influenced by strong ecological interactions, these can override predictions of MST, whereas when surviving plants are less affected by interactions, individual-level metabolic processes can scale up to the population level. MST, like thermodynamics or biomechanics, sets limits within which organisms can live and function, but there may be stronger limits determined by ecological interactions. In such cases MST will not be predictive.

Initial density affects biomass–density and allometric relationships in self‐thinning populations of Fagopyrum esculentum

Summary The form and generality of the biomass–density relationship, especially during self‐thinning of crowded stands, have been intensively debated in recent years. All models of self‐thinning assume that the trajectory is independent of the initial pre‐thinning density, so populations differing in initial density can be analysed together. As plant allometry is a determinant of the self‐thinning trajectory, and competition alters plants' allometric growth, initial density may have consequences for the self‐thinning trajectory. To ask whether initial density can influence allometric relationships and the biomass–density trajectory, we grew Fagopyrum esculentum populations at three high densities and measured shoot biomass, density and the height and diameter of individual plants at six harvests. Initial density did not affect the slope of the log biomass–log density relationship, but there was a clear and significant effect on the intercept. Populations sown at higher densities had significantly more biomass at a given density of survivors. If the data for all densities and harvests are analysed together, the log biomass–log density relationship is linear with a slope of −0.377, which is consistent with the predictions of Metabolic Scaling Theory. If the independent variable initial density is included as a factor, the estimated slope of the log B–log N relationship is much steeper and consistent with the classical ‘Self‐thinning Rule’. The position of the self‐thinning trajectory is determined in part by the biomass density: the relationship between mass and volume. Initial density could affect this by altering allometric growth in a way that influences architectural compactness. An alternative hypothesis is that competition at higher initial density is more size symmetric, which has been shown to reduce growth and mortality. Synthesis. The self‐thinning trajectory is not always independent of initial population density. Interpopulation scaling patterns, even within one species, do not reflect processes within populations, and this conflation lies behind much of the current debate about size–density relationships in plant populations and communities. Interactions among plants and allometry are more important than internal physiological scaling mechanisms in determining the self‐thinning trajectory of crowded stands.

Predictable changes in aboveground allometry of trees along gradients of temperature, aridity and competition

ABSTRACTAim Trees are often observed to get shorter and more narrowly crowned in dry regions and at high elevations. We explore how this pattern is driven by two opposing factors: competition for light makes it advantageous to extend branches to their biomechanical limit, whereas under cold or arid conditions it is advantageous to have shorter branches, thereby reducing the length of the hydraulic transport system and embolism risk. Using data from 700,000 trees of 26 species, we quantify how environmental conditions influence the scaling of height and crown diameter (CD) with stem diameter (d.b.h.). We compare our predictions with those of metabolic scaling theory (MST), which suggests that allometry is invariant of environment.Location 48,000 inventory plots that systematically sample mainland Spain, a region in which climate varies strongly.Methods We fit d.b.h.–height and d.b.h.–CD functions using Bayesian methods, allowing comparison of within‐ and across‐species trends in allometry along gradients of temperature, precipitation, drought and competition for light (i.e. the basal area of taller trees).Results The competitive environment had a strong influence on aboveground allometry, but all trees were far shorter than predicted by biomechanical models, suggesting that factors other than biomechanics are important. Species that dominate in arid and cold habitats were much shorter (for a given diameter) than those from benign conditions; but within‐species heights did not vary strongly across climatic gradients.Main conclusions Our results do not support the MST prediction that d.b.h.–height and d.b.h.–CD allometries are invariant, or that biomechanical constraints determine height allometry. Rather, we highlight the role of hydraulic limitations in this region. The fact that intra‐specific adjustment in d.b.h.–CD – height allometry along environmental gradients was far weaker than across‐species changes may indicate genetic constraints on allometry which might contribute to niche differentiation among species.

Testing the Metabolic Scaling Theory of tree growth

Summary 1. Metabolic Scaling Theory (MST) predicts a ‘universal scaling law’ of tree growth. Proponents claim that MST has strong empirical support: the size‐dependent growth curves of 40 out of 45 species in a Costa Rican forest have scaling exponents indistinguishable from the MST prediction. 2. Here, we show that the Costa Rican study has been misinterpreted. Using Standardized Major Axis (SMA) line‐fitting to estimate scaling exponents, we find that four out of five species represented by more than 100 stems have scaling exponents that deviate significantly from the MST prediction. On the other hand, sample sizes were too small to make strong inferences in the cases of 33 species represented by fewer than 50 stems. 3. Recently, it has been argued that MST is useful for predicting average scaling exponents, even if individual species do not conform to the theory. We find that the mean scaling exponent of the Costa Rican trees is greater than predicted (across‐species mean = 0.44), and hypothesize that scaling exponents in natural forests will generally be greater than predicted, because the theory fails to model asymmetric competition for light. 4. Synthesis. We highlight shortcomings in the interpretation of data used in support of a key MST prediction. We recommend that future research into biological scaling should compare the merits of alternative models rather than focusing attention on tests of a single theory.

Revisiting a Model of Ontogenetic Growth: Estimating Model Parameters from Theory and Data

The ontogenetic growth model (OGM) of West et al. provides a general description of how metabolic energy is allocated between production of new biomass and maintenance of existing biomass during ontogeny. Here, we reexamine the OGM, make some minor modifications and corrections, and further evaluate its ability to account for empirical variation on rates of metabolism and biomass in vertebrates both during ontogeny and across species of varying adult body size. We show that the updated version of the model is internally consistent and is consistent with other predictions of metabolic scaling theory and empirical data. The OGM predicts not only the near universal sigmoidal form of growth curves but also the M(1/4) scaling of the characteristic times of ontogenetic stages in addition to the curvilinear decline in growth efficiency described by Brody. Additionally, the OGM relates the M(3/4) scaling across adults of different species to the scaling of metabolic rate across ontogeny within species. In providing a simple, quantitative description of how energy is allocated to growth, the OGM calls attention to unexplained variation, unanswered questions, and opportunities for future research.

Revisiting a Model of Ontogenetic Growth: Estimating Model Parameters from Theory and Data

The ontogenetic growth model (OGM) of West et al. provides a general description of how metabolic energy is allocated between production of new biomass and maintenance of existing biomass during ontogeny. Here, we reexamine the OGM, make some minor modifications and corrections, and further evaluate its ability to account for empirical variation on rates of metabolism and biomass in vertebrates both during ontogeny and across species of varying adult body size. We show that the updated version of the model is internally consistent and is consistent with other predictions of metabolic scaling theory and empirical data. The OGM predicts not only the near universal sigmoidal form of growth curves but also the $$M^{1/ 4}$$ scaling of the characteristic times of ontogenetic stages in addition to the curvilinear decline in growth efficiency described by Brody. Additionally, the OGM relates the $$M^{3/ 4}$$ scaling across adults of different species to the scaling of metabolic rate across ontogeny within species. In providing a simple, quantitative description of how energy is allocated to growth, the OGM calls attention to unexplained variation, unanswered questions, and opportunities for future research.