A species-level model for metabolic scaling of trees II. Testing in a ring- and diffuse-porous species

Stretched sapwood, ultra-widening permeability and ditching da Vinci: revising models of plant form and function

BACKGROUND

The mechanisms leading to dieback and death of trees under drought remain unclear. To gain an understanding of these mechanisms, addressing major empirical gaps regarding tree structure-function relations remains essential.

SCOPE

We give reasons to think that a central factor shaping plant form and function is selection simultaneously favouring constant leaf-specific conductance with height growth and isometric (1:1) scaling between leaf area and the volume of metabolically active sink tissues ('sapwood'). Sapwood volume-leaf area isometry implies that per-leaf area sapwood volumes become transversely narrower with height growth; we call this 'stretching'. Stretching means that selection must favour increases in permeability above and beyond that afforded by tip-to-base conduit widening ("ultra-widening permeability"), via fewer and wider vessels or tracheids with larger pits or larger margo openings. Leaf area-metabolically active sink tissue isometry would mean that it is unlikely that larger trees die during drought because of carbon starvation due to greater sink-source relationships as compared to shorter plants. Instead, an increase in permeability is most plausibly associated with greater risk of embolism, and this seems a more probable explanation of the preferential vulnerability of larger trees to climate change-induced drought. Other implications of selection favouring constant per-leaf area sapwood construction and maintenance costs are departure from the da Vinci rule expectation of similar sapwood areas across branching orders, and that extensive conduit furcation in the stem seems unlikely.

CONCLUSIONS

Because all these considerations impact the likelihood of vulnerability to hydraulic failure versus carbon starvation, both implicated as key suspects in forest mortality, we suggest that these predictions represent essential priorities for empirical testing.

Vascular optimality dictates plant morphology away from Leonardo's rule

Metabolic scaling theory (MST) provides an understanding of scaling in organismal morphology. Empirical data on the apparently universal pattern of tip-to-base conduit widening across vascular plants motivate a set of generalized MST (gMST) relationships allowing for variable rates of conduit coalescence and taper and a transition between transport and diffusive domains. Our model, with coalescence limited to the distalmost part of the conductive system, reconciles previous MST-based models and extends their applicability to the entire plant. We derive an inverse relationship between stem volume taper and conduit widening, which implies that plant morphology is dictated by vascular optimality and not the assumption of constant sapwood area across all branching levels, contradicting Leonardo's rule. Thus, energy efficiency controls conduit coalescence rate, lowering the carbon cost needed to sustain the vascular network. Our model shows that as a plant grows taller, it must increase conduit widening and coalescence, which may make it more vulnerable to drought. We calculated how our gMST model implies a lower carbon cost to sustain a similar network compared to previous MST-based models. We also show that gMST predicts the cross-sectional area of vessels and their frequency along the relative length better than previous MST models for a range of plant types. We encourage further research obtaining data that would allow testing other gMST predictions that remain unconfirmed empirically, such as conduit coalescence rate in stems. The premise of energy efficiency can potentially become instrumental to our understanding of plant carbon allocation.

Do stomata optimize turgor-driven growth? A new framework for integrating stomata response with whole-plant hydraulics and carbon balance

Every existing optimal stomatal model uses photosynthetic carbon assimilation as a proxy for plant evolutionary fitness. However, assimilation and growth are often decoupled, making assimilation less ideal for representing fitness when optimizing stomatal conductance to water vapor and carbon dioxide. Instead, growth should be considered a closer proxy for fitness. We hypothesize stomata have evolved to maximize turgor-driven growth, instead of assimilation, over entire plants' lifetimes, improving their abilities to compete and reproduce. We develop a stomata model that dynamically maximizes whole-stem growth following principles from turgor-driven growth models. Stomata open to assimilate carbohydrates that supply growth and osmotically generate turgor, while stomata close to prevent losses of turgor and growth due to negative water potentials. In steady state, the growth optimization model captures realistic stomatal, growth, and carbohydrate responses to environmental cues, reconciles conflicting interpretations within existing stomatal optimization theories, and explains patterns of carbohydrate storage and xylem conductance observed during and after drought. Our growth optimization hypothesis introduces a new paradigm for stomatal optimization models, elevates the role of whole-plant carbon use and carbon storage in stomatal functioning, and has the potential to simultaneously predict gross productivity, net productivity, and plant mortality through a single, consistent modeling framework.

Turgor-limited predictions of tree growth, height and metabolic scaling over tree lifespans

Increasing evidence suggests that tree growth is sink-limited by environmental and internal controls rather than by carbon availability. However, the mechanisms underlying sink-limitations are not fully understood and thus not represented in large-scale vegetation models. We develop a simple, analytically solved, mechanistic, turgor-driven growth model (TDGM) and a phloem transport model (PTM) to explore the mechanics of phloem transport and evaluate three hypotheses. First, phloem transport must be explicitly considered to accurately predict turgor distributions and thus growth. Second, turgor-limitations can explain growth-scaling with size (metabolic scaling). Third, turgor can explain realistic growth rates and increments. We show that mechanistic, sink-limited growth schemes based on plant turgor limitations are feasible for large-scale model implementations with minimal computational demands. Our PTM predicted nearly uniform sugar concentrations along the phloem transport path regardless of phloem conductance, stem water potential gradients and the strength of sink-demands contrary to our first hypothesis, suggesting that phloem transport is not limited generally by phloem transport capacity per se but rather by carbon demand for growth and respiration. These results enabled TDGM implementation without explicit coupling to the PTM, further simplifying computation. We test the TDGM by comparing predictions of whole-tree growth rate to well-established observations (site indices) and allometric theory. Our simple TDGM predicts realistic tree heights, growth rates and metabolic scaling over decadal to centurial timescales, suggesting that tree growth is generally sink and turgor limited. Like observed trees, our TDGM captures tree-size- and resource-based deviations from the classical ¾ power-law metabolic scaling for which turgor is responsible.

The Widened Pipe Model of plant hydraulic evolution

Shaping global water and carbon cycles, plants lift water from roots to leaves through xylem conduits. The importance of xylem water conduction makes it crucial to understand how natural selection deploys conduit diameters within and across plants. Wider conduits transport more water but are likely more vulnerable to conduction-blocking gas embolisms and cost more for a plant to build, a tension necessarily shaping xylem conduit diameters along plant stems. We build on this expectation to present the Widened Pipe Model (WPM) of plant hydraulic evolution, testing it against a global dataset. The WPM predicts that xylem conduits should be narrowest at the stem tips, widening quickly before plateauing toward the stem base. This universal profile emerges from Pareto modeling of a trade-off between just two competing vectors of natural selection: one favoring rapid widening of conduits tip to base, minimizing hydraulic resistance, and another favoring slow widening of conduits, minimizing carbon cost and embolism risk. Our data spanning terrestrial plant orders, life forms, habitats, and sizes conform closely to WPM predictions. The WPM highlights carbon economy as a powerful vector of natural selection shaping plant function. It further implies that factors that cause resistance in plant conductive systems, such as conduit pit membrane resistance, should scale in exact harmony with tip-to-base conduit widening. Furthermore, the WPM implies that alterations in the environments of individual plants should lead to changes in plant height, for example, shedding terminal branches and resprouting at lower height under drier climates, thus achieving narrower and potentially more embolism-resistant conduits.

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.

Predictive models for radial sap flux variation in coniferous, diffuse-porous and ring-porous temperate trees

Accurately scaling sap flux observations to tree or stand levels requires accounting for variation in sap flux between wood types and by depth into the tree. However, existing models for radial variation in axial sap flux are rarely used because they are difficult to implement, there is uncertainty about their predictive ability and calibration measurements are often unavailable. Here we compare different models with a diverse sap flux data set to test the hypotheses that radial profiles differ by wood type and tree size. We show that radial variation in sap flux is dependent on wood type but independent of tree size for a range of temperate trees. The best-fitting model predicted out-of-sample sap flux observations and independent estimates of sapwood area with small errors, suggesting robustness in the new settings. We develop a method for predicting whole-tree water use with this model and include computer code for simple implementation in other studies.

Testing Foundations of Biological Scaling Theory Using Automated Measurements of Vascular Networks

Scientists have long sought to understand how vascular networks supply blood and oxygen to cells throughout the body. Recent work focuses on principles that constrain how vessel size changes through branching generations from the aorta to capillaries and uses scaling exponents to quantify these changes. Prominent scaling theories predict that combinations of these exponents explain how metabolic, growth, and other biological rates vary with body size. Nevertheless, direct measurements of individual vessel segments have been limited because existing techniques for measuring vasculature are invasive, time consuming, and technically difficult. We developed software that extracts the length, radius, and connectivity of in vivo vessels from contrast-enhanced 3D Magnetic Resonance Angiography. Using data from 20 human subjects, we calculated scaling exponents by four methods—two derived from local properties of branching junctions and two from whole-network properties. Although these methods are often used interchangeably in the literature, we do not find general agreement between these methods, particularly for vessel lengths. Measurements for length of vessels also diverge from theoretical values, but those for radius show stronger agreement. Our results demonstrate that vascular network models cannot ignore certain complexities of real vascular systems and indicate the need to discover new principles regarding vessel lengths.

Vascular networks distribute resources and constrain metabolic rate. Founded on a few key principles, biological scaling theories predict characteristic patterns for vascular networks as they branch from large to small vessels. These theories also predict seemingly unrelated phenomena, such as size limits on mammals. However, vascular networks are difficult to measure because there are billions of vessels that range in size from meters to micrometers. To test the foundations of biological scaling theories, we developed software that quickly measures thousands of in vivo vessels based on MRI. Data for vessel radii match predicted patterns but lengths do not. Our work suggests the need for new theoretical principles and should facilitate comparisons across organisms, spatial scales, and healthy and diseased tissue.

Isometric partitioning of hydraulic conductance between leaves and stems: balancing safety and efficiency in different growth forms and habitats

Recent advances in modelling the architecture and function of the plant hydraulic network have led to improvements in predicting and interpreting the consequences of functional trait variation on CO2 uptake and water loss. We build upon one such model to make novel predictions for scaling of the total specific hydraulic conductance of leaves and shoots (kL and kSH , respectively) and variation in the partitioning of hydraulic conductance. Consistent with theory, we observed isometric (slope = 1) scaling between kL and kSH across several independently collected datasets and a lower ratio of kL and kSH , termed the leaf-to-shoot conductance ratio (CLSCR ), in arid environments and in woody species. Isometric scaling of kL and kSH supports the concept that hydraulic design is coordinated across the plant. We propose that CLSCR is an important adaptive trait that represents the trade-off between efficiency and safety at the scale of the whole plant.

Distilling allometric and environmental information from time series of conduit size: the standardization issue and its relationship to tree hydraulic architecture

Trees are among the best natural archives of past environmental information. Xylem anatomy preserves information related to tree allometry and ecophysiological performance, which is not available from the more customary ring-width or wood-density proxy parameters. Recent technological advances make tree-ring anatomy very attractive because time frames of many centuries can now be covered. This calls for the proper treatment of time series of xylem anatomical attributes. In this article, we synthesize current knowledge on the biophysical and physiological mechanisms influencing the short- to long-term variation in the most widely used wood-anatomical feature, namely conduit size. We also clarify the strong mechanistic link between conduit-lumen size, tree hydraulic architecture and height growth. Among the key consequences of these biophysical constraints is the pervasive, increasing trend of conduit size during ontogeny. Such knowledge is required to process time series of anatomical parameters correctly in order to obtain the information of interest. An appropriate standardization procedure is fundamental when analysing long tree-ring-related chronologies. When dealing with wood-anatomical parameters, this is even more critical. Only an interdisciplinary approach involving ecophysiology, wood anatomy and dendrochronology will help to distill the valuable information about tree height growth and past environmental variability correctly.

Coordination between water transport capacity, biomass growth, metabolic scaling and species stature in co-occurring shrub and tree species

The significance of xylem function and metabolic scaling theory begins from the idea that water transport is strongly coupled to growth rate. At the same time, coordination of water transport and growth seemingly should differ between plant functional types. We evaluated the relationships between water transport, growth and species stature in six species of co-occurring trees and shrubs. Within species, a strong proportionality between plant hydraulic conductance (K), sap flow (Q) and shoot biomass growth (G) was generally supported. Across species, however, trees grew more for a given K or Q than shrubs, indicating greater growth-based water-use efficiency (WUE) in trees. Trees also showed slower decline in relative growth rate (RGR) than shrubs, equivalent to a steeper G by mass (M) scaling exponent in trees (0.77-0.98). The K and Q by M scaling exponents were common across all species (0.80, 0.82), suggesting that the steeper G scaling in trees reflects a size-dependent increase in their growth-based WUE. The common K and Q by M exponents were statistically consistent with the 0.75 of ideal scaling theory. A model based upon xylem anatomy and branching architecture consistently predicted the observed K by M scaling exponents but only when deviations from ideal symmetric branching were incorporated.

Investigating water transport through the xylem network in vascular plants

Our understanding of physical and physiological mechanisms depends on the development of advanced technologies and tools to prove or re-evaluate established theories, and test new hypotheses. Water flow in land plants is a fascinating phenomenon, a vital component of the water cycle, and essential for life on Earth. The cohesion-tension theory (CTT), formulated more than a century ago and based on the physical properties of water, laid the foundation for our understanding of water transport in vascular plants. Numerous experimental tools have since been developed to evaluate various aspects of the CTT, such as the existence of negative hydrostatic pressure. This review focuses on the evolution of the experimental methods used to study water transport in plants, and summarizes the different ways to investigate the diversity of the xylem network structure and sap flow dynamics in various species. As water transport is documented at different scales, from the level of single conduits to entire plants, it is critical that new results be subjected to systematic cross-validation and that findings based on different organs be integrated at the whole-plant level. We also discuss the functional trade-offs between optimizing hydraulic efficiency and maintaining the safety of the entire transport system. Furthermore, we evaluate future directions in sap flow research and highlight the importance of integrating the combined effects of various levels of hydraulic regulation.

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.

Deviation from symmetrically self-similar branching in trees predicts altered hydraulics, mechanics, light interception and metabolic scaling

The West, Brown, Enquist (WBE) model derives symmetrically self-similar branching to predict metabolic scaling from hydraulic conductance, K, (a metabolism proxy) and tree mass (or volume, V). The original prediction was Kα V(0.75). We ask whether trees differ from WBE symmetry and if it matters for plant function and scaling. We measure tree branching and model how architecture influences K, V, mechanical stability, light interception and metabolic scaling. We quantified branching architecture by measuring the path fraction, Pf : mean/maximum trunk-to-twig pathlength. WBE symmetry produces the maximum, Pf = 1.0. We explored tree morphospace using a probability-based numerical model constrained only by biomechanical principles. Real tree Pf ranged from 0.930 (nearly symmetric) to 0.357 (very asymmetric). At each modeled tree size, a reduction in Pf led to: increased K; decreased V; increased mechanical stability; and decreased light absorption. When Pf was ontogenetically constant, strong asymmetry only slightly steepened metabolic scaling. The Pf ontogeny of real trees, however, was 'U' shaped, resulting in size-dependent metabolic scaling that exceeded 0.75 in small trees before falling below 0.65. Architectural diversity appears to matter considerably for whole-tree hydraulics, mechanics, photosynthesis and potentially metabolic scaling. Optimal architectures likely exist that maximize carbon gain per structural investment.

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.