Testing metabolic theory with models of tree growth that include light competition

Variance in tree growth rates provides a key link for completing the theory of forest size structure formation

In natural forests at a demographic equilibrium state, the size frequency distribution (SFD) of trees is linked with their size-dependent growth and mortality rates. While the mean growth rate (MGR) of each size class is generally used for determining the SFD, the variance in the growth rate (VGR) has always been ignored. Here, based on the analyses with Kolmogorov forward equation, we show that in general, the VGR can flatten the slope of the SFD and, in particular, can address the contradiction between the size-dependent MGR and the -2 power-law SFD in the metabolic scaling theory. We traced the origin of the VGR to the intrinsic stochasticity in the allometric growth coefficients of trees and deduced its functional form based on variance propagation. Using the forest censuses data from Barro Colorado Island, we verified the prediction of the VGR and indicated its indispensability in the theory of forest size-structure formation.

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.

Are trait-growth models transferable? Predicting multi-species growth trajectories between ecosystems using plant functional traits

Plant functional traits are increasingly used to generalize across species, however few examples exist of predictions from trait-based models being evaluated in new species or new places. Can we use functional traits to predict growth of unknown species in different areas? We used three independently collected datasets, each containing data on heights of individuals from non-resprouting species over a chronosquence of time-since-fire sites from three ecosystems in south-eastern Australia. We examined the influence of specific leaf area, woody density, seed size and leaf nitrogen content on three aspects of plant growth; maximum relative growth rate, age at maximum growth and asymptotic height. We tested our capacity to perform out-of-sample prediction of growth trajectories between ecosystems using species functional traits. We found strong trait-growth relationships in one of the datasets; whereby species with low SLA achieved the greatest asymptotic heights, species with high leaf-nitrogen content achieved relatively fast growth rates, and species with low seed mass reached their time of maximum growth early. However these same growth-trait relationships did not hold across the two other datasets, making accurate prediction from one dataset to another unachievable. We believe there is evidence to suggest that growth trajectories themselves may be fundamentally different between ecosystems and that trait-height-growth relationships may change over environmental gradients.

Drivers of aboveground wood production in a lowland tropical forest of West Africa: teasing apart the roles of tree density, tree diversity, soil phosphorus, and historical logging

Tropical forests currently play a key role in regulating the terrestrial carbon cycle and abating climate change by storing carbon in wood. However, there remains considerable uncertainty as to whether tropical forests will continue to act as carbon sinks in the face of increased pressure from expanding human activities. Consequently, understanding what drives productivity in tropical forests is critical. We used permanent forest plot data from the Gola Rainforest National Park (Sierra Leone) – one of the largest tracts of intact tropical moist forest in West Africa – to explore how (1) stand basal area and tree diversity, (2) past disturbance associated with past logging, and (3) underlying soil nutrient gradients interact to determine rates of aboveground wood production (AWP). We started by statistically modeling the diameter growth of individual trees and used these models to estimate AWP for 142 permanent forest plots. We then used structural equation modeling to explore the direct and indirect pathways which shape rates of AWP. Across the plot network, stand basal area emerged as the strongest determinant of AWP, with densely packed stands exhibiting the fastest rates of AWP. In addition to stand packing density, both tree diversity and soil phosphorus content were also positively related to productivity. By contrast, historical logging activities negatively impacted AWP through the removal of large trees, which contributed disproportionately to productivity. Understanding what determines variation in wood production across tropical forest landscapes requires accounting for multiple interacting drivers – with stand structure, tree diversity, and soil nutrients all playing a key role. Importantly, our results also indicate that logging activities can have a long‐lasting impact on a forest's ability to sequester and store carbon, emphasizing the importance of safeguarding old‐growth tropical forests.

Tree-centric mapping of forest carbon density from airborne laser scanning and hyperspectral data

Forests are a major component of the global carbon cycle, and accurate estimation of forest carbon stocks and fluxes is important in the context of anthropogenic global change. Airborne laser scanning (ALS) data sets are increasingly recognized as outstanding data sources for high‐fidelity mapping of carbon stocks at regional scales.

We develop a tree‐centric approach to carbon mapping, based on identifying individual tree crowns (ITCs) and species from airborne remote sensing data, from which individual tree carbon stocks are calculated. We identify ITCs from the laser scanning point cloud using a region‐growing algorithm and identifying species from airborne hyperspectral data by machine learning. For each detected tree, we predict stem diameter from its height and crown‐width estimate. From that point on, we use well‐established approaches developed for field‐based inventories: above‐ground biomasses of trees are estimated using published allometries and summed within plots to estimate carbon density.

We show this approach is highly reliable: tests in the Italian Alps demonstrated a close relationship between field‐ and ALS‐based estimates of carbon stocks (r² = 0·98). Small trees are invisible from the air, and a correction factor is required to accommodate this effect.

An advantage of the tree‐centric approach over existing area‐based methods is that it can produce maps at any scale and is fundamentally based on field‐based inventory methods, making it intuitive and transparent. Airborne laser scanning, hyperspectral sensing and computational power are all advancing rapidly, making it increasingly feasible to use ITC approaches for effective mapping of forest carbon density also inside wider carbon mapping programs like REDD++.

How do size distributions relate to concurrently measured demographic rates? Evidence from over 150 tree species in Panama

In stable populations with constant demographic rates, size distributions reflect size-dependent patterns of growth and mortality. However, population growth can also affect size distributions, which may not be aligned with current growth and mortality. Using 25 y of demographic data from the 50-ha Barro Colorado Island plot, we examined how interspecific variation in diameter distributions of over 150 tropical trees relates to growth–diameter and mortality–diameter curves and to population growth rates. Diameter distributions were more skewed in species with faster increases/slower decreases in absolute growth and mortality with diameter and higher population growth rates. The strongest predictor of the diameter distribution shape was the exponent governing the scaling of growth with diameter (partial R2 = 0.20–0.34), which differed among growth forms, indicating a role of life history variation. However, interspecific variation in diameter distributions was also significantly related to population growth rates (partial R2 = 0.03–0.23), reinforcing that many populations are not at equilibrium. Consequently, although fitted size distribution parameters were positively related to theoretical predictions based on current size-dependent growth and mortality, there was considerable deviation. These analyses show that temporally variable demographic rates, probably related to cyclic climate variation, are important influences on forest structure.

Dominance of the suppressed: Power-law size structure in tropical forests

Tropical tree size distributions are remarkably consistent despite differences in the environments that support them. With data analysis and theory, we found a simple and biologically intuitive hypothesis to explain this property, which is the foundation of forest dynamics modeling and carbon storage estimates. After a disturbance, new individuals in the forest gap grow quickly in full sun until they begin to overtop one another. The two-dimensional space-filling of the growing crowns of the tallest individuals relegates a group of losing, slow-growing individuals to the understory. Those left in the understory follow a power-law size distribution, the scaling of which depends on only the crown area-to-diameter allometry exponent: a well-conserved value across tropical forests.

Functional traits explain light and size response of growth rates in tropical tree species

Relationships between functional traits and average or potential demographic rates have provided insight into the functional constraints and trade-offs underlying life-history strategies of tropical tree species. We have extended this framework by decomposing growth rates of -130 000 trees of 171 Neotropical tree species into intrinsic growth and the response of growth to light and size. We related these growth characteristics to multiple functional traits (wood density, adult stature, seed mass, leaf traits) in a hierarchical Bayesian model that accounted for measurement error and intraspecific variability of functional traits. Wood density was the most important trait determining all three growth characteristics. Intrinsic growth rates were additionally strongly related to adult stature, while all traits contributed to light response. Our analysis yielded a predictive model that allows estimation of growth characteristics for rare species on the basis of a few easily measurable morphological traits.

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.