A species-level model for metabolic scaling in trees I. Exploring boundaries to scaling space within and across 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.

Ecophysiological adaptations shape distributions of closely related trees along a climatic moisture gradient

Tradeoffs between the energetic benefits and costs of traits can shape species and trait distributions along environmental gradients. Here we test predictions based on such tradeoffs using survival, growth, and 50 photosynthetic, hydraulic, and allocational traits of ten Eucalyptus species grown in four common gardens along an 8-fold gradient in precipitation/pan evaporation (P/Ep) in Victoria, Australia. Phylogenetically structured tests show that most trait-environment relationships accord qualitatively with theory. Most traits appear adaptive across species within gardens (indicating fixed genetic differences) and within species across gardens (indicating plasticity). However, species from moister climates have lower stomatal conductance than others grown under the same conditions. Responses in stomatal conductance and five related traits appear to reflect greater mesophyll photosynthetic sensitivity of mesic species to lower leaf water potential. Our data support adaptive cross-over, with realized height growth of most species exceeding that of others in climates they dominate. Our findings show that pervasive physiological, hydraulic, and allocational adaptations shape the distributions of dominant Eucalyptus species along a subcontinental climatic moisture gradient, driven by rapid divergence in species P/Ep and associated adaptations.

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.

Dynamic Energy Budget models: fertile ground for understanding resource allocation in plants in a changing world

Climate change is having dramatic effects on the diversity and distribution of species. Many of these effects are mediated by how an organism's physiological patterns of resource allocation translate into fitness through effects on growth, survival and reproduction. Empirically, resource allocation is challenging to measure directly and so has often been approached using mathematical models, such as Dynamic Energy Budget (DEB) models. The fact that all plants require a very similar set of exogenous resources, namely light, water and nutrients, integrates well with the DEB framework in which a small number of variables and processes linked through pathways represent an organism's state as it changes through time. Most DEB theory has been developed in reference to animals and microorganisms. However, terrestrial vascular plants differ from these organisms in fundamental ways that make resource allocation, and the trade-offs and feedbacks arising from it, particularly fundamental to their life histories, but also challenging to represent using existing DEB theory. Here, we describe key features of the anatomy, morphology, physiology, biochemistry, and ecology of terrestrial vascular plants that should be considered in the development of a generic DEB model for plants. We then describe possible approaches to doing so using existing DEB theory and point out features that may require significant development for DEB theory to accommodate them. We end by presenting a generic DEB model for plants that accounts for many of these key features and describing gaps that would need to be addressed for DEB theory to predict the responses of plants to climate change. DEB models offer a powerful and generalizable framework for modelling resource allocation in terrestrial vascular plants, and our review contributes a framework for expansion and development of DEB theory to address how plants respond to anthropogenic change.

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.

Coupled whole-tree optimality and xylem hydraulics explain dynamic biomass partitioning

Trees partition biomass in response to resource limitation and physiological activity. It is presumed that these strategies evolved to optimize some measure of fitness. If the optimization criterion can be specified, then allometry can be modeled from first principles without prescribed parameterization. We present the Tree Hydraulics and Optimal Resource Partitioning (THORP) model, which optimizes allometry by estimating allocation fractions to organs as proportional to their ratio of marginal gain to marginal cost, where gain is net canopy photosynthesis rate, and costs are senescence rates. Root total biomass and profile shape are predicted simultaneously by a unified optimization. Optimal partitioning is solved by a numerically efficient analytical solution. THORP's predictions agree with reported tree biomass partitioning in response to size, water limitations, elevated CO₂ and pruning. Roots were sensitive to soil moisture profiles and grew down to the groundwater table when present. Groundwater buffered against water stress regardless of meteorology, stabilizing allometry and root profiles as deep as c. 30 m. Much of plant allometry can be explained by hydraulic considerations. However, nutrient limitations cannot be fully ignored. Rooting mass and profiles were synchronized with hydrological conditions and groundwater even at considerable depths, illustrating that the below ground shapes whole-tree allometry.

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.

Leveraging plant hydraulics to yield predictive and dynamic plant leaf allocation in vegetation models with climate change

Plant functional traits provide a link in process-based vegetation models between plant-level physiology and ecosystem-level responses. Recent advances in physiological understanding and computational efficiency have allowed for the incorporation of plant hydraulic processes in large-scale vegetation models. However, a more mechanistic representation of water limitation that determines ecosystem responses to plant water stress necessitates a re-evaluation of trait-based constraints for plant carbon allocation, particularly allocation to leaf area. In this review, we examine model representations of plant allocation to leaves, which is often empirically set by plant functional type-specific allometric relationships. We analyze the evolution of the representation of leaf allocation in models of different scales and complexities. We show the impacts of leaf allocation strategy on plant carbon uptake in the context of recent advancements in modeling hydraulic processes. Finally, we posit that deriving allometry from first principles using mechanistic hydraulic processes is possible and should become standard practice, rather than using prescribed allometries. The representation of allocation as an emergent property of scarce resource constraints is likely to be critical to representing how global change processes impact future ecosystem dynamics and carbon fluxes and may reduce the number of poorly constrained parameters in vegetation models.

Current-year shoot hydraulic structure in two boreal conifers-implications of growth habit on water potential

Metabolic scaling theory allows us to link plant hydraulic structure with metabolic rates in a quantitative framework. In this theoretical framework, we considered the hydraulic structure of current-year shoots in Pinus sylvestris and Picea abies, focusing on two properties unaccounted for by metabolic scaling theories: conifer needles are attached to the entire length of shoots, and the shoot as a terminal element does not display invariant properties. We measured shoot length and diameter as well as conduit diameter and density in two locations of 14 current-year non-leader shoots of pine and spruce saplings, and calculated conductivities of shoots from measured conduit properties. We evaluated scaling exponents for the hydraulic structure of shoots at the end of the water transport pathway from the data and applied the results to simulate water potential of shoots in the crown. Shoot shape was intermediate between cylindrical and paraboloid. Contrary to previous findings, we found that conduit diameter scaled with relative, not absolute, distance from the apex and absolute under-bark shoot diameter independently of species within the first-year shoots. Shoot hydraulic conductivity scaled with shoot diameter and hydraulic diameter. Larger shoots had higher hydraulic conductance. We further demonstrate by novel model calculations that ignoring foliage distribution along the hydraulic pathway overestimates water potential loss in shoots and branches and therefore overestimates related water stress effects. Scaling of hydraulic properties with shoot size enhances apical dominance and may contribute to the decline of whole-tree conductance in large trees.

Clothing the Emperor: Dynamic Root-Shoot Allocation Trajectories in Relation to Whole-Plant Growth Rate and in Response to Temperature

We quantified how root-shoot biomass allocation and whole-plant growth rate co-varied ontogenetically in contrasting species in response to cooling. Seven grass and four forb species were grown for 56 days in hydroponics. Growth was measured repeatedly before and after day/night temperatures were reduced at 28 days from 20 °C/15 °C to 10 °C/5 °C; controls remained unchanged. Sigmoid trajectories of root and shoot growth were reconstructed from the experimental data to derive continuous whole-plant relative growth rates (RGRs) and root mass fractions (RMFs). Root mass fractions in cooled plants generally increased, but this originated from unexpected and previously uncharacterised differences in response among species. Root mass fraction and RGR co-trajectories were idiosyncratic in controls and cooled plants. The RGR-RMF co-trajectories responded to cooling in grasses, but not forbs. The RMF responses of stress-tolerant grasses were predictably weak but projected to eventually out-respond faster-growing species. Sigmoid growth constrains biomass allocation. Only when neither root nor shoot biomass is near-maximal can biomass allocation respond to environmental drivers. Near maximum size, plants cannot adjust RMF, which then reflects net above- and belowground productivities. Ontogenetic biomass allocations are not equivalent to those based on interspecific surveys, especially in mature vegetation. This reinforces the importance of measuring temporal growth dynamics, and not relying on "snapshot" comparisons to infer the functional significance of root-shoot allocation.

Lignin composition is related to xylem embolism resistance and leaf life span in trees in a tropical semiarid climate

Wood properties influence the leaf life span (LL) of tree crowns. As lignin is an important component of wood and the water transport system, we investigated its relationship with embolism resistance and the LL of several tree species in a seasonally dry tropical ecosystem. We determined total lignin and the monomer contents of guaiacyl (G) and syringyl (S) and related them to wood traits and xylem vulnerability to embolism (Ψ₅₀ ) for the most common species of the Brazilian semiarid, locally known as Caatinga. Leaf life span was negatively related to Ψ₅₀ and positively related to S : G, which was negatively related to Ψ₅₀ . This means that greater S : G increases LL by reducing Ψ₅₀ . Lignin content was not correlated with any variable. We found two apparently unrelated axes of drought resistance. One axis, associated with lignin monomeric composition, increases LL in the dry season as a result of lower xylem embolism vulnerability. The other, associated with wood density and stem water content, helps leafless trees to withstand drought and allows them to resprout at the end of the dry season. The monomeric composition of lignin (S : G) is therefore an important functional wood attribute affecting several key functional aspects of tropical tree species in a semiarid climate.

Why size matters: the interactive influences of tree diameter distribution and sap flow parameters on upscaled transpiration

In stands with a broad range of diameters, a small number of very large trees can disproportionately influence stand basal area and transpiration (Et). Sap flow-based Et estimates may be particularly sensitive to large trees due to nonlinear relationships between tree-level water use (Q) and tree diameter at breast height (DBH). Because Q is typically predicted on the basis of DBH and sap flow rates measured in a subset of trees and then summed to obtain Et, we assessed the relative importance of DBH and sap flow variables (sap velocity, Vs, and sapwood depth, Rs) in determining the magnitude of Et and its dependence on large trees in a tropical montane forest ecosystem. Specifically, we developed a data-driven simulation framework to vary the relationship between DBH and Vs and stand DBH distribution and then calculate Q, Et and the proportion of Et contributed by the largest tree in each stand. Our results demonstrate that variation in how Rs is determined in the largest trees can alter estimates up to 26% of Et while variation in how Vs is determined can vary results by up to 132%. Taken together, these results highlight a great need to expand our understanding of water transport in large trees as this hinders our ability to predict water fluxes accurately from stand to catchment scales.

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.

High-Resolution Laser Scanning Reveals Plant Architectures that Reflect Universal Network Design Principles

Transport networks serve critical functions in biological and engineered systems, and yet their design requires trade-offs between competing objectives. Due to their sessile lifestyle, plants need to optimize their architecture to efficiently acquire and distribute resources while also minimizing costs in building infrastructure. To understand how plants resolve this design trade-off, we used high-precision three-dimensional laser scanning to map the architectures of tomato, tobacco, or sorghum plants grown in several environmental conditions and through multiple developmental time points, scanning in total 505 architectures from 37 plants. Using a graph-theoretic algorithm that we developed to evaluate design strategies, we find that plant architectures lie along the Pareto front between two simple length-based objectives-minimizing total branch length and minimizing nutrient transport distance-thereby conferring a selective fitness advantage for plant transport processes. The location along the Pareto front can distinguish among species and conditions, suggesting that during evolution, natural selection may employ common network design principles despite different optimization trade-offs.

Growing larger with domestication: a matter of physiology, morphology or allocation?

Domestication might affect plant size. We investigated whether herbaceous crops are larger than their wild progenitors, and the traits that influence size variation. We grew six crop plants and their wild progenitors under common garden conditions. We measured the aboveground biomass gain by individual plants during the vegetative stage. We then tested whether photosynthesis rate, biomass allocation to leaves, leaf size and specific leaf area (SLA) accounted for variations in whole-plant photosynthesis, and ultimately in aboveground biomass. Despite variations among crops, domestication generally increased the aboveground biomass (average effect +1.38, Cohen's d effect size). Domesticated plants invested less in leaves and more in stems than their wild progenitors. Photosynthesis rates remained similar after domestication. Variations in whole-plant C gains could not be explained by changes in leaf photosynthesis. Leaves were larger after domestication, which provided the main contribution to increases in leaf area per plant and plant-level C gain, and ultimately to larger aboveground biomass. In general, cultivated plants have become larger since domestication. In our six crops, this occurred despite lower investment in leaves, comparable leaf-level photosynthesis and similar biomass costs of leaf area (i.e. SLA) than their wild progenitors. Increased leaf size was the main driver of increases in aboveground size. Thus, we suggest that large seeds, which are also typical of crops, might produce individuals with larger organs (i.e. leaves) via cascading effects throughout ontogeny. Larger leaves would then scale into larger whole plants, which might partly explain the increases in size that accompanied domestication.

Relationships between individual-tree mortality and water-balance variables indicate positive trends in water stress-induced tree mortality across North America

Accounting for water stress-induced tree mortality in forest productivity models remains a challenge due to uncertainty in stress tolerance of tree populations. In this study, logistic regression models were developed to assess species-specific relationships between probability of mortality (P_m ) and drought, drawing on 8.1 million observations of change in vital status (m) of individual trees across North America. Drought was defined by standardized (relative) values of soil water content (W_s,z ) and reference evapotranspiration (ET_r,z ) at each field plot. The models additionally tested for interactions between the water-balance variables, aridity class of the site (AC), and estimated tree height (h). Considering drought improved model performance in 95 (80) per cent of the 64 tested species during calibration (cross-validation). On average, sensitivity to relative drought increased with site AC (i.e. aridity). Interaction between water-balance variables and estimated tree height indicated that drought sensitivity commonly decreased during early height development and increased during late height development, which may reflect expansion of the root system and decreasing whole-plant, leaf-specific hydraulic conductance, respectively. Across North America, predictions suggested that changes in the water balance caused mortality to increase from 1.1% yr^-1 in 1951 to 2.0% yr^-1 in 2014 (a net change of 0.9 ± 0.3% yr^-1 ). Interannual variation in mortality also increased, driven by increasingly severe droughts in 1988, 1998, 2006, 2007 and 2012. With strong confidence, this study indicates that water stress is a common cause of tree mortality. With weak-to-moderate confidence, this study strengthens previous claims attributing positive trends in mortality to increasing levels of water stress. This 'learn-as-we-go' approach - defined by sampling rare drought events as they continue to intensify - will help to constrain the hydraulic limits of dominant tree species and the viability of boreal and temperate forest biomes under continued climate change.

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.

Bark thickness across the angiosperms: more than just fire

Global variation in total bark thickness (TBT) is traditionally attributed to fire. However, bark is multifunctional, as reflected by its inner living and outer dead regions, meaning that, in addition to fire protection, other factors probably contribute to TBT variation. To address how fire, climate, and plant size contribute to variation in TBT, inner bark thickness (IBT) and outer bark thickness (OBT), I sampled 640 species spanning all major angiosperm clades and 18 sites with contrasting precipitation, temperature, and fire regime. Stem size was by far the main driver of variation in thickness, with environment being less important. IBT was closely correlated with stem diameter, probably for metabolic reasons, and, controlling for size, was thicker in drier and hotter environments, even fire-free ones, probably reflecting its water and photosynthate storage role. OBT was less closely correlated with size, and was thicker in drier, seasonal sites experiencing frequent fires. IBT and OBT covaried loosely and both contributed to overall TBT variation. Thickness variation was higher within than across sites and was evolutionarily labile. Given high within-site diversity and the multiple selective factors acting on TBT, continued study of the different drivers of variation in bark thickness is crucial to understand bark ecology.

Asymmetries arising from the space-filling nature of vascular networks

Cardiovascular networks span the body by branching across many generations of vessels. The resulting structure delivers blood over long distances to supply all cells with oxygen via the relatively short-range process of diffusion at the capillary level. The structural features of the network that accomplish this density and ubiquity of capillaries are often called space-filling. There are multiple strategies to fill a space, but some strategies do not lead to biologically adaptive structures by requiring too much construction material or space, delivering resources too slowly, or using too much power to move blood through the system. We empirically measure the structure of real networks (18 humans and 1 mouse) and compare these observations with predictions of model networks that are space-filling and constrained by a few guiding biological principles. We devise a numerical method that enables the investigation of space-filling strategies and determination of which biological principles influence network structure. Optimization for only a single principle creates unrealistic networks that represent an extreme limit of the possible structures that could be observed in nature. We first study these extreme limits for two competing principles, minimal total material and minimal path lengths. We combine these two principles and enforce various thresholds for balance in the network hierarchy, which provides a novel approach that highlights the tradeoffs faced by biological networks and yields predictions that better match our empirical data.

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.

What plant hydraulics can tell us about responses to climate-change droughts

Climate change exposes vegetation to unusual drought, causing declines in productivity and increased mortality. Drought responses are hard to anticipate because canopy transpiration and diffusive conductance (G) respond to drying soil and vapor pressure deficit (D) in complex ways. A growing database of hydraulic traits, combined with a parsimonious theory of tree water transport and its regulation, may improve predictions of at-risk vegetation. The theory uses the physics of flow through soil and xylem to quantify how canopy water supply declines with drought and ceases by hydraulic failure. This transpiration 'supply function' is used to predict a water 'loss function' by assuming that stomatal regulation exploits transport capacity while avoiding failure. Supply-loss theory incorporates root distribution, hydraulic redistribution, cavitation vulnerability, and cavitation reversal. The theory efficiently defines stomatal responses to D, drying soil, and hydraulic vulnerability. Driving the theory with climate predicts drought-induced loss of plant hydraulic conductance (k), canopy G, carbon assimilation, and productivity. Data lead to the 'chronic stress hypothesis' wherein > 60% loss of k increases mortality by multiple mechanisms. Supply-loss theory predicts the climatic conditions that push vegetation over this risk threshold. The theory's simplicity and predictive power encourage testing and application in large-scale modeling.

Is the WBE model appropriate for semi-arid shrubs subjected to clear cutting?

It is crucial to understand the adaptive mechanisms of woody plants facing periodic drought to assess their vulnerability to the increasing climate variability predicted in the Sahel. Guiera senegalensis J.F.Gmel is a semi-evergreen Combretaceae commonly found in Sahelian rangelands, fallows and crop fields because of its value as an agroforestry species. We compared canopy leafing, and allometric measurements of leaf area, stem area and stem length and their relationships with leaf water potential, stomatal conductance (gs) and soil-to-leaf hydraulic conductance (KS-L), in mature and current-year resprouts of G. senegalensis in Sahelian Niger. In mature shrubs, seasonal drought reduced the ratio of leaf area to cross-sectional stem area (AL : AS), mainly due to leaf shedding. The canopy of the current-year resprouts remained permanently leafed as the shrubs produced leaves and stems continuously, and their AL : AS ratio increased throughout the dry season. Their KS-L increased, whereas gs decreased. West, Brown and Enquist's (WBE) model can thus describe allometric trends in the seasonal life cycle of undisturbed mature shrubs, but not that of resprouts. Annual clear cutting drives allometric scaling relationships away from theoretical WBE predictions in the current-year resprouts, with scaling exponents 2.5 times greater than those of mature shrubs. High KS-L (twice that of mature shrubs) supports this intensive regeneration process. The adaptive strategy described here is probably common to many woody species that have to cope with both severe seasonal drought and regular disturbance over the long term.

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.

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.