Research

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

Hendrik Poorter1, Andrzej M. Jagodzinski2,3, Ricardo Ruiz-Peinado4,5, Shem Kuyah6, Yunjian Luo7,8, Jacek Oleksyn2,9, Vladimir A. Usoltsev10,11, Thomas N. Buckley12, Peter B. Reich9,13 and Lawren Sack14 1Plant Sciences (IBG-2), Forschungszentrum Julich€ GmbH, D-52425 Julich,€ Germany; 2Polish Academy of Sciences, Institute of Dendrology, Parkowa 5, Kornik PL-62-035, Poland; 3Department of Game Management and Forest Protection, Faculty of Forestry, Poznan University of Life Sciences, Wojska Polskiego 71c, Poznan PL-60-625, Poland; 4Departamento de Selvicultura y Gestion de Sistemas Forestales, INIA-CIFOR, Avda. A Coruna,~ km 7.5., Madrid 28040, Spain; 5Sustainable Forest Management Research Institute, University of Valladolid- INIA, Madrid, Spain; 6Jomo Kenyatta University of Agriculture and Technology (JKUAT), PO Box 62000, Nairobi 00200, Kenya; 7Department of Ecology, School of Horticulture and Plant Protection, Yangzhou University, 48 Wenhui East Road, Yangzhou 225009, China; 8State Key Laboratory of Urban and Regional Ecology, Research Centre for Eco-Environmental Sciences, Chinese Academy of Sciences, 18 Shuangqing Road, Haidian District, Beijing 100085, China; 9Department of Forest Resources, University of Minnesota, 1530 Cleveland Ave N, St Paul, MN 55108, USA; 10Ural State Forest Engineering University, Sibirskiy Trakt 37, Ekaterinburg 620100, Russia; 11Botanical Garden of Ural Branch of Russian Academy of Sciences, ul. Vos’mogo Marta 202a, Ekaterinburg 620144, Russia; 12IA Watson Grains Research Centre, Faculty of Agriculture and Environment, The University of Sydney, 12656 Newell Highway, Narrabri, NSW, Australia; 13Hawkesbury Institute for the Environment, University of Western Sydney, Locked Bag 1797, Penrith, NSW 2751, Australia; 14Department of Ecology and Evolution, University of California Los Angeles, 621 Charles E. Young Drive South, Los Angeles, CA 90095, USA

Summary Authors for correspondence: We compiled a global database for leaf, stem and root biomass representing c. 11 000 Hendrik Poorter records for c. 1200 herbaceous and woody species grown under either controlled or field con- Tel: +49 2461 61 8684 ditions. We used this data set to analyse allometric relationships and fractional biomass distri- Email: [email protected] bution to leaves, stems and roots. Yunjian Luo We tested whether allometric scaling exponents are generally constant across plant sizes as Tel: +86 514 8797 9344 predicted by metabolic scaling theory, or whether instead they change dynamically with plant Email: [email protected] size. We also quantified interspecific variation in biomass distribution among plant families Received: 29 April 2015 and functional groups. Accepted: 15 June 2015 Across all species combined, leaf vs stem and leaf vs root scaling exponents decreased from c. 1.00 for small plants to c. 0.60 for the largest trees considered. Evergreens had substantially New Phytologist (2015) higher leaf mass fractions (LMFs) than deciduous species, whereas graminoids maintained doi: 10.1111/nph.13571 higher root mass fractions (RMFs) than eudicotyledonous herbs. These patterns do not support the hypothesis of fixed allometric exponents. Rather, contin- uous shifts in allometric exponents with plant size during ontogeny and evolution are the Key words: allometry, biomass allocation, norm. Across seed plants, variation in biomass distribution among species is related more to biomass distribution, leaf mass fraction (LMF), leaf weight ratio, metabolic scaling function than phylogeny. We propose that the higher LMF of evergreens at least partly com- theory, shoot : root ratio. pensates for their relatively low leaf area : leaf mass ratio.

Introduction paper to describe how the biomass of one organ relates to that of another or of the whole is ‘biomass distribution’. Note that this A plant’s organs serve multiple distinct functions. For example, should not be confused with dynamic allocation of newly fixed leaves provide sugars, stems and branches position the leaves in photosynthates to different organ systems, as the realized biomass an advantageous light environment and transport water as well as distribution at any moment is the cumulative result of dynamic nutrients, and roots acquire water and nutrients and anchor the carbon (C) allocation over time and loss rates of mass among plant. For a species to achieve optimal performance at the whole- organs throughout its life. In this study, we focus on the relation- plant level, there has to be a certain proportionality among these ship of biomass distribution to plant size and its variation among functions, as all are essential for growth and reproduction. This species. proportionality depends in part on the relative amounts of mass Biomass distribution has been studied using two basic present in these organs. Although various terminology has been approaches. The first approach employs an allometric analysis. It used (Reich, 2002), the generic term we will use throughout this focuses on how the absolute size of an organ (or its physiological

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rate) relates to the total size of the organism or another organ, as explanation of the acronyms used). This theory suggested a cen- these sizes or rates may change during development or across tral role for the vascular transport system of water in the case of species. These relationships are often well described by a power plants and of blood or air in the case of animals. It involved a law of the form: number of assumptions, of which the optimization of the fractal- like design of the vascular transport system is the most impor- Y ¼ aX b Eqn 1 tant, and predicted constant scaling exponents (such as ¾ for metabolic rate vs size) across large ranges of plant size, often with where X could be, for example, the mass of an individual of a quarter-powers. Niklas, Enquist and co-workers further devel- given species, and Y the mass of a specific organ. Parameter a is oped the MST to include relationships between plant parts in the ‘allometric constant’ and b the ‘scaling exponent’. Early across-species comparisons, again predicting fixed exponents researchers including Snell (1892) and Dubois (1897) observed with quarter-powers (e.g. Enquist & Niklas, 2002a; Niklas, that across species the relationship between brain mass and 2004; McCarthy et al., 2007). Combining MST with a number whole-organism mass was characterized by a scaling exponent of of assumptions regarding the lengths, diameters and mass densi- ⅔. Pearsall (1927) applied Eqn 1 to analyse relationships ties of stems and roots, these authors predicted that the scaling of between different plant organs during development, and showed leaf vs stem, leaf vs root and stem vs root mass would follow con- the scaling exponent b to be mathematically equivalent to the stant scaling exponents of ¾, ¾ and 1.0, respectively (Enquist & ratio of the relative growth rates of organs X and Y (Huxley, Niklas, 2002a). We will refer to this model as the MST1 model. 1932). Further work showed strong allometric trends in animals The predicted relationships were apparently supported by the for metabolic rate (e.g. whole-organism respiration rate) against high r2 of fixed power laws fitted to compiled data sets of c. body mass, with an apparently stable scaling exponent of ¾ 400–700 records (the number depending on the publication), (Kleiber, 1932; but see Makarieva et al., 2008). Although correla- combining data for c. 250–300 vascular plant species ranging tion coefficients or r2 values were not commonly reported in the from small herbs grown in the laboratory to adult trees from var- time of Kleiber, it was already obvious that Eqn 1 explained a ious forests and plantations around the world (Enquist & Niklas, great deal of the variation in the biological traits considered. 2002a; Niklas, 2004). Niklas & Enquist (2002) therefore con- West et al. (1997) proposed an intriguing biological model cluded that ‘a single biomass allocation pattern for leaf stem and unifying allometric observations in plants and animals in what is root construction appears to hold sway across all extant seed now called ‘metabolic scaling theory’ (MST; see Table 1 for an plants.’ In a deviation from the MST1 model, Enquist & Niklas (2002a,b), Niklas (2004) and Enquist et al. (2007) suggested that Table 1 List of abbreviations of concepts and variables used here ¾ scaling does not apply to ‘small’ plants, and that isometric scal- = Abbreviation Full name Elucidation Units ing was expected for such plants (i.e. b 1.0). Various biological reasons were proposed for this change, including a disappearing MST Metabolic A model explaining scaling effect of seed mass (Enquist & Niklas, 2002a,b), stem photosyn- scaling relationships between thesis being only present in young plants (Enquist & Niklas, theory biological variables among (groups of) 2002b), the onset of secondary thickening in plants older than plants or animals 1 yr (Niklas, 2004) and changes in gravity and volume-filling FEM Functional The concept that architecture with age (Enquist et al., 2007), although these effects equilibrium plants invest relatively more were not verified. In their series of papers, these authors argued model biomass in the organ for a binary contrast with an abrupt shift of the scaling exponent that limits growth most ¾ LMF Leaf mass Leaf dry mass/total gg 1 from 1.0 to , at a transition point that was variously defined as fraction plant dry mass 1 yr of age (Enquist & Niklas, 2002a), or of 1 g (Enquist et al., SMF Stem mass Stem dry mass/total gg 1 2007) or 64 g of total dry mass (Niklas, 2004). We refer to this fraction plant dry mass 1 model as the MST2 model. RMF Root mass Root dry mass/total gg A second way to analyse biomass distribution is to express the fraction plant dry mass pLMF Percentile The percentile rank % biomass of individual organs as a fraction or proportion of the rank of LMF of an LMF observation total organismal biomass present at a given time (leaf mass frac- relative to all data in tion (LMF); stem mass fraction (SMF); root mass fraction the database, after (RMF)). These proportional biomass distribution patterns have correction for been used to analyse responses of given genotypes to a range of size-related differences pSMF Percentile As pLMF, but for an % environmental conditions, to examine ontogenetic trends over rank of SMF SMF observation time and to compare performance across species, and they are pRMF Percentile As pLMF, but for a % fundamental to models that analyse growth rates of plants to rank of RMF RMF observation reveal the underlying components (e.g. Evans, 1972; Poorter SLA Specific leaf area Leaf area/leaf dry mass m2 kg 1 et al., 2013). We will refer to this method as ‘clasmometry’ (mea- LAI Leaf area index Total leaf area/total m2 m 2 ground area suring fractions) to distinguish it from allometry. Clasmometry is simpler than allometric analyses because biomass fractions can be

New Phytologist (2015) Ó 2015 The Authors www.newphytologist.com New Phytologist Ó 2015 New Phytologist Trust New Phytologist Research 3 computed directly for each plant, which avoids the assumptions objective of this study, therefore, was to determine how these inherent in fitting Eqn 1 to data for all plants combined. shifts in biomass fractions during plant growth are reflected in Although the resulting biomass fractions do not account directly the allometric scaling exponents. for variation in body size (Packard & Boardman, 1988), it is Our second question is how does biomass distribution vary straightforward to do so, by plotting biomass fractions against across species groups, independently of the overall trends with plant size, in effect achieving a similar goal as in an allometric plant size? While biomass fractions might shift greatly with plant analysis of biomass distribution (Poorter & Sack, 2012). Espe- size, there is also large variation among species at a given plant cially for trees, where individuals may grow through 10 orders of mass, and our aim was to quantify the major patterns underlying biomass, size is thought to be an important determinant of that variation. Although this question has received much less biomass fractions, as proportionally more biomass has to be attention in the plant literature so far, previous analyses have invested in support tissue as plants grow larger (Coleman et al., shown that woody gymnosperms invest relatively more in leaves 1994). Biomass fractions are often interpreted in terms of the and less in stems than woody angiosperms (K€orner, 1994; functional equilibrium model (FEM; sometimes referred to as McCarthy et al., 2007; Reich et al., 2014) and herbaceous eudi- optimal partitioning theory), which states that plants change the cots have higher LMFs and lower RMFs than herbaceous mono- proportion of leaves, stems and roots depending on the relative cots (Poorter et al., 2012). Hui et al. (2014) showed that, in limitations of light, CO2, water and nutrients on the physiologi- Chinese forests, RMFs differed among families, with low values cal activity of the various organs (Brouwer, 1963; Davidson, for Cupressaceae and high values for Ulmaceae. However, no 1969; Bloom et al., 1985). The FEM principles have been explic- previous study has made a systematic, phylogenetically ordinated itly represented within teleonomic (goal-directed) models in analysis across the plant kingdom. As size has such a strong effect which biomass distribution among organs is adjusted during on biomass distribution patterns (Poorter et al., 2012), rather growth such that growth rate is maximized (Thornley & Parsons, than considering the variation among species in their absolute 2014). Although the FEM was specifically designed to explain values for biomass fractions per se, we determined the deviations the response of plants to their environment, it can also be applied of biomass fractions from the main size-related trends. We subse- to plants during ontogeny (Brouwer, 1963; Buckley & Roberts, quently used allometry to analyse more specifically which of the 2006a), or to the comparison of species with different physiologi- organ relationships are affected. cal activities (Buckley & Roberts, 2006b). To answer these questions, we compiled a database of unprece- Most previous papers on biomass distribution focused on dented size and generality, with > 11 000 records on leaf, stem either allometric or clasmometric analyses, but not on both. and root dry mass for c. 1200 species from all five continents. We However, these provide two essential and complementary per- analysed the relationships between individual plant parts as well spectives on the same phenomenon (Poorter & Sack, 2012), and as differences in biomass fractions, and tested specifically whether in this paper we take both approaches. We focus on two related allometric exponents are fixed in relation to plant size across questions. First, combining all data within and across species for ontogeny and evolution, or whether there is evidence for dynamic a ‘general’ allometry, how does plant biomass distribution shift scaling, and how biomass fractions vary among lineages and func- with increasing plant size? Coordinated changes of organ sizes are tional groups, and which organ allometries can explain these dif- reflected in the value of the scaling exponents. If MST is correct ferences. and the scaling exponents are fixed over the entirety (MST1) or a large part (MST2) of the size trajectory, this implies that the Materials and Methods development and evolution of plant form and function are remarkably constrained. A constant scaling exponent of ¾ for leaf Data collection vs stem and leaf vs root scaling, as predicted by MST, means that, for every 1.0% increase in stem and root biomass, leaf biomass We compiled an extensive database of biomass values for leaves, will increase by 0.75% across the whole plant size range consid- stems, and roots for a broad range of species and conditions, for ered. According to that theory, the relative growth rates of leaves, gymnosperm and angiosperm species grown in growth chambers stems and roots would remain strictly proportional both during and glasshouses, outside in an agricultural setting or under natu- development across plant size and during evolution across a wide ral conditions. Data from experiments where plants were sub- range of lineages. An alternative hypothesis is that plants adjust jected to various environmental conditions were taken from the their biomass distribution more flexibly, so that scaling exponents MetaPhenomics database (Poorter et al., 2010), and supple- change dynamically with plant size to improve performance. For mented with a range of literature data focused on species compar- animals, variation in the scaling exponent b has been reported by isons (e.g. Swanborough & Westoby, 1996; Taylor et al., 2010) Makarieva et al. (2008) and Kolokotrones et al. (2010), for exam- or from any other experiment we found in the literature where ple, who showed that, even for Kleiber’s law (the well-recognized plants were grown and where leaf, stem, and root mass values relationship between metabolic rate and body size), b was not a were reported separately. We did not include genetically modi- constant, but varied with animal type and generally decreased fied organisms or plants treated with herbicides, hormones, and/ with size. It is clear that with increasing size plants generally show or heavy metals, which may have led to substantial deviations continuously increasing SMF and decreasing LMF, and less pro- from typical physiology and biomass distribution. To avoid nounced changes in RMF (Poorter et al., 2012). A further ambiguous interpretations of individual plant size, we excluded

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clonal plants for which the biomass of all ramets together was smoothing the resulting data with a polynomial (Poorter, 1989). reported. Finally, because biomass distribution patterns in herbs Hence, we divided all data into 50 size classes, based on total can change strongly when plants become reproductive, we plant dry mass. For each size bin we determined the median value included herbaceous plants only in the vegetative stage. Because of log-transformed leaf, stem, and root mass, and used these we were interested in the effect of size on biomass distribution, median mass values to calculate the slope (difference in biomass we included data from various harvests, if reported. For each of organ A/difference in biomass of organ B) over each adjacent genotype and species, we collected the mean values of leaf, stem, triplet using a central derivative kernel. That is, the slope over and root mass per harvest, where the number of plants harvested each three neighbouring classes was determined from the values generally was in the range of three to eight individuals. of the left and right class and this value was assigned to all three The data for field-grown plants comprised mainly shrubs and class members. The procedure was then reiterated shifting the trees, where individuals are more easily distinguishable than in triplet one bin to the right. This eventually leads to three slope herbaceous plants. This is important as we used individual plant estimates per class, which were averaged, plotted as a function of size as a relevant variable in the analysis. Data were included from total plant mass and smoothed by a Loess curve (Efron & Tibshi- large data compilations from the Western scientific literature rani, 1994). The median values and 95% confidence intervals (Cannell, 1982), the Eastern European literature (Usol’tsev, (CIs) of this Loess curve were derived after a bootstrapping proce- 2013) and Chinese papers and reports (Luo et al., 2014). These dure with 20 000 repetitions (Efron & Tibshirani, 1994). Apart literature compilations were supplemented with original data col- from increased flexibility, the advantage of this second approach lected for a range of species from C-accounting initiatives (Mon- is that the results are not constrained by the a priori choice of an tero et al., 2005; Kuyah et al., 2013; A. M. Jagodzinski et al., equation to fit the data. unpublished) and governmental reports, as well as primary litera- For the assessment of species-specific deviations from the over- ture on field-grown plants (e.g. Ovington & Olson, 1970). In all trends of biomass distribution with plant size, we again used cases where biomass data were provided per ground area rather the 50 size classes. All observations of LMF (or SMF or RMF) than per tree, we calculated values for the average tree, using the within a given size class were ranked and characterized by per- reported tree density. Following Niklas & Enquist (2002), we centiles. In this way, we corrected for the overall effect of size on ignored the reproductive biomass in these trees, which – if pre- mass fractions. The use of percentiles was inspired by the fact that sent – generally forms a relatively small fraction of total biomass LMF values were more variable for small than large plants. All (0.03–1.2%; Cannell, 1982). References for all publications from percentiles (indicated in this paper as pLMF, pSMF and pRMF) which data were taken are given in Supporting Information calculated for a given species across the 50 size bins were subse- Table S1. quently combined. For each species, the median percentile was The various assumptions related to data quality and represen- then calculated and the significance of deviations from the overall tativeness are discussed in Notes S1. Species names were checked median (50%) was tested using a t-test. with the Taxonomic Name Resolution Service (Boyle et al., All data were analysed using R software (R Core Team, 2014). 2013). In total, there are 11 217 records for 1207 species Phylogenetic analyses were conducted with package Diversitree reported in 1366 papers or scientific reports. A full list of refer- (FitzJohn, 2012) from the R software, using the phylogenetic tree ences is given in Table S1. The actual biomass data can be found published in Zanne et al. (2014). In the Diversitree package, only in Table S2. one value per species is used in the calculations, so we used the median response across all records for a given species for the anal- ysis, as specified earlier. For this analysis we only considered those Data analysis species for which at least four records were present in the Inspection of the allometric plots showed five out of the > 11 000 database. Because c. 20% of the species in our data set were not records to deviate strongly from the others. They were removed covered by the phylogenetic tree used, we also examined whether from the analysis. For the establishment of overall general trends there were systematic differences at the family level. For this anal- all other data were included, such that the trajectories of variables ysis, we only considered those families that were represented by with size combine intra- and interspecific variation. Allometric at least four species and at least four observations per species. Dif- relationships were first analysed with standard major axis (SMA) ferences between (groups of) species were tested statistically by lines fitted to log-transformed data, as predicted by MST to Welch’s t-test or ANOVA. explain the relationships. We subsequently fitted quadratic or cubic polynomials in stepwise Model 1 regression analysis and Results checked which model was best supported using the Bayesian information criterion and analysis of residuals. Two different Fixed or dynamic scaling exponents approaches were used for assessment of the changes in slope with plant size. First, we calculated the derivative of the fitted polyno- Our database contained > 11 000 records, including c. 3000 for mial equation. This is a somewhat rigid approach, always yielding herbaceous species and c. 8200 for woody species, and represent- a straight line in the case of a second-degree polynomial. We also ing c. 1200 species in total. More detail is given in Table S3. applied a procedure that allows more flexible relationships, first With plant dry mass varying from < 1 mg for 1-wk-old seedlings determining the slope over small intervals and subsequently (e.g. Erica cinerea) to over 14 000 kg in > 100-yr-old trees

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(Trilepsium madagascariensis), the database included plant size rather than discrete as predicted by MST2, and quantitatively, over > 10 orders of magnitude. Straight lines fitted to the log- in that the exponents differed numerically from the values pre- transformed leaf vs stem, leaf vs root and stem vs root biomass dicted by MST. While for young plants the scaling exponents data had r2 values up to 0.988 (Table 2a; for separate regressions involving leaf mass were close to 1.0, as shown by the 95% CI on herbaceous and woody species, see Table S4), although exami- in Fig. 1(d,e), for large plants the exponents declined to values nation of residuals (Fig. S1) showed clear patterns that reject the substantially below ¾. Stem vs root scaling did not comply with use of log-linear allometry to describe these data. Ignoring this the MST2 model either. Although we found values close to 1.0 problem, the value for the leaf vs stem scaling exponent was 0.74, for very small and large plants, plants of intermediate size had a very close to the ¾ predicted by MST, whereas both the leaf vs scaling exponent of up to 1.2 (Fig. 1f). Overall, there was only root (0.85) and stem vs root (1.15) scaling exponents were clearly a small interval of plant size during which quarter-power and significantly (P < 0.001) higher than those expected from the scaling or, for that matter, any single scaling coefficient was MST1 and MST2 models (post-transition point). Statistical anal- observed. ysis showed that a quadratic curve was more appropriate to fit the Thus, rather than a fixed allometry, we found small plants to data for leaf vs stem and leaf vs root scaling, whereas a cubic poly- show scaling coefficients of 1.0, whereas plants of intermediate nomial was more suitable for the stem vs root scaling. This was sizes show disproportionate increase in stem biomass distribu- confirmed by stepwise regression (P < 0.001 in all cases for the tion, and very large plants increase stem and root mass in equal additional terms), by evaluation of the Bayesian information cri- proportion. These changes were also clearly reflected in the clas- terion (Table 2b), and by inspection of the residuals (Fig. S1) mometric analysis. The overall trends in how biomass fractions even though the increase in r2 was small. These analyses clearly changed with size, shown as lines in Fig. 2, indicate that, up to rejected the MST1 and MST2 models, which assumed single 100 g total plant mass, the median RMF remained remarkably log-linear relationship with fixed exponents, in favour of leaf vs stable, with roots representing c. 30% of total plant mass, but stem, leaf vs root and stem vs root biomass allometries that shift that LMF declined from c. 0.50 to c. 0.30 over that range, while continuously and substantially with plant size (Fig. 1a–c). SMF increased from c. 0.20 to c. 0.40. Above a size of 100 g, We determined the actual values of scaling exponents and where almost all records in the data set pertain to woody plant how they changed with plant size in two ways: by calculating species, the changes in biomass distribution are yet more pro- the derivative of the fitted polynomials and by smoothing nounced: the RMF drops from c. 0.30 to c. 0.20, the average locally determined slopes. The two approaches yielded similar LMF decreases to 0.015 for very large trees, and SMF strongly conclusions: both leaf vs stem and leaf vs root scaling slopes increases up to c. 0.80. Above 1000 kg, stem and root mass frac- were significantly higher than ¾ for plants smaller than 10 and tions seem to stabilize. 1000 g, respectively, and both slopes were significantly lower than ¾ for trees exceeding 10 and 100 kg (Fig. 1d,e). We thus Differences in biomass distribution among lineages and found no indication of a constant scaling exponent across the functional groups size range considered. Our data contradicted the MST2 model both qualitatively, in that the shifting appeared continuous Subsequently, we tested the extent to which phylogeny affected these biomass distribution patterns, focusing on the deviation for each point from the main trends in median mass fractions as Table 2 Results of the fit for the allometric analysis measured by percentiles (pLMF, pSMF and pRMF). Species explained 55% and families 23% of the total variation in pLMF 2 (a) Regression ab95% CI for br across all observations. For pLMF, the full phylogenetic tree at LM vs SM 0.113 0.740 0.738–0.742 0.978 the species level is shown in Fig. S2, and a summary at the family LM vs RM 0.070 0.849 0.847–0.851 0.977 level is given in Fig. 3. There is a clear phylogenetic signal in the SM vs RM 0.058 1.147 1.145–1.149 0.988 gymnosperm families Pinaceae and, to a lesser extent, Cupres- saceae, which have a higher LMF than average for their size. Fur- 2 D (b) Regression ab1 b2 b3 r BIC ther detail is shown in Table 3, where the observed ranges in LM vs SM 0.213 0.795 0.0177 – 0.981 1360 pLMF, pSMF and pRMF are given for these families. Another LM vs RM 0.151 0.897 0.0184 – 0.979 891 clear contrast is that herbaceous graminoids (Cyperaceae and SM vs RM 0.126 1.144 0.0318 0.00606 0.989 799 Poaceae) show relatively high fractions of biomass in roots com- pared with other monocots and eudicotyledonous herbs of simi- (a) Standard major axis regression (SMA; model 2 regression) for the intercept (a) and slope (b) of the regression of leaf mass (LM) vs stem mass lar size. Several eudicot families with large numbers of species

(SM), LM vs root mass (RM), and SM vs RM, all based on log10-trans- also deviated significantly and consistently in biomass distribu- formed values. The 95% confidence interval for the slope and the r2 of the tion. The most notable ones are listed in Table 3 and include the equation are given. (b) Ordinary least square regression (OLS), with esti- Fagaceae, Proteaceae and Solanaceae. mates for the linear (b1), quadratic (b2) and cubic (b3) coefficients. a is the Although we found broad phylogenetic patterning at the clade value for the intercept, and D BIC shows the change in the value of the Bayesian information criterion as compared to a linear fit, for which the or family level, there was interesting variation below the family BIC was c. 5500 in all cases. The total number of observations was 11 217. level as well. For example, in the case of the gymnosperms, which were found to have a relatively high LMF (Fig. 4a), the

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1.4 (a) (d) 106 lin *** 5 10 qua *** 1.2 4 10 r 2 = 0.98 0.58 103 1.0 102 0.69 101 0.8 0

Leaf mass (g) 10 0.79 10–1 Slope leaf vs stem 10–2 0.6

10–3 0.90

0.4 –3 –2 –1 0 1 2 3 4 5 6 10 10 10 10 10 10 10 10 10 10 10–2 10–1 100 101 102 103 104 105 106 Stem mass (g) Total mass (g)

1.4 (b) (e) 106 lin *** 5 10 qua *** 1.2 104 r 2 = 0.98 0.68 103 1.0 102 0.79 101 0.8 0

Leaf mass (g) 10 0.90 Slope leaf vs root 10–1 10–2 0.6

10–3 1.01 0.4 10–3 10–2 10–1 100 101 102 103 104 105 106 10–2 10–1 100 101 102 103 104 105 106 Root mass (g) Total mass (g)

1.4 (c) (f) 6 10 lin *** 0.87 5 10 qua *** 1.2 cub *** 104 r 2 = 0.99 103 1.17 1.0 102 101 0.8 100 Stem mass (g)

1.14 Slope stem vs root 10–1

10–2 0.6

–3 10 0.79 0.4 10–3 10–2 10–1 100 101 102 103 104 105 106 10–2 10–1 100 101 102 103 104 105 106 Root mass (g) Total mass (g) Fig. 1 (a–c) The allometric relationship for (a) leaf vs stem mass; (b) leaf vs root mass; (c) stem vs root mass. Red and blue points represent data for woody (n = 8170) and herbaceous (n = 2960) species, respectively. The bold black lines show the overall fit of a quadratic (a, b) or cubic (c) regression. Numbers indicate the value for the slope of the line at the indicated white points. (d–f) The slope of the allometric relationship for (d) leaf vs stem mass; (e) leaf vs root mass; (f) stem vs root mass, all as a function of total plant dry mass. The bold lines indicate the Loess curve through the mean slope values, based on a bootstrap procedure with 20 000 repetitions. The shaded area indicates the 95% confidence interval of the slopes. The black dotted line indicates the value of (d, e) ¾ and (f) 1.0, as predicted by MST1 theory. lin, linear; qua, quadratic; cub, cubic.

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1.0 these lineages the higher pLMF of the evergreens corresponded (a) herb. to both a lower pSMF (P < 0.05) and a lower pRMF (P < 0.001) woody than deciduous species. The difference for the angiosperms was 0.8 r 2 = 0.78 found for both the tropical/subtropical species (P < 0.01) and for < ) the temperate/boreal trees (P 0.05). Inspection of the deviations –1 0.6 from the overall allometric plots among specific organs showed that differences among functional groups were attributable to 0.4 modulation of the leaf vs stem scaling and leaf vs root scaling, LMF (g g but that the stem vs root scaling showed very little group differen-

0.2 tiation (Fig. S3). A third contrast we investigated was between herbaceous C3 and C4 species. C4 species are thought to have a superior photo- 0.0 synthetic rate on average than C3 species, and, based on the (b) FEM framework, such a higher photosynthetic rate might be expected to drive preferential biomass distribution in the root 0.8 system. However, no difference was observed between C3 and C4 species in pLMF or pRMF within the monocotyledonous )

–1 0.6 clade (Fig. 4). For the eudicotyledonous clade, RMF was lower for the C4 species, but the number of C4 species in the analysis 0.4 (five) is still very low. Clade was an important factor in the con-

SMF (g g trast between annual and perennial herbs. Whereas no overall difference was found within the monocotyledonous clade (data 0.2 not shown), the eudicotyledonous annuals had higher invest- r 2 = 0.87 ment in leaves and stems as compared with perennial species of 0.0 the same size (Fig. 4). Further analysis by means of allometry (c) showed that, in contrast to the woody species, functional herba- r 2 = 0.21 ceous groups varied significantly in the stem vs root scaling 0.8 exponent (Fig. S3). )

–1 0.6 Discussion

2 0.4 The implication of high r in allometric relationships RMF (g g Our database covered > 10 orders of magnitude in plant size, 0.2 which is almost the full range of sizes of vascular plants in nature. Missing only is one additional order of magnitude for exception- ally large trees such as Sequoiadendron, which can reach 0.0 10–3 10–2 10–1 100 101 102 103 104 105 106 107 500 000 kg (Zinke & Stangenberger, 1994). All of the allometric 2 Total mass (g) relationships analysed showed very high r : whether we fitted lin- ear or more complicated curves to the log–log data, all r2 values Fig. 2 (a) Leaf mass fraction (LMF); (b) stem mass fraction (SMF) and (c) 2 root mass fraction (RMF), plotted as a function of total plant dry mass. Red exceeded 0.975. Given that ecological correlations often have r and blue points represent data for woody (n = 8170) and herbaceous values substantially lower than 0.50 (Møller & Jennions, 2002), (n = 2960) species, respectively. The bold line is a Loess curve fitted scaling theory has therefore been considered to provide a ‘general’ through the mean values of the 50 consecutive size classes that were biological law, which is quite an exceptional phenomenon in discerned (see the Materials and Methods section for an explanation). The 2 2 biology (Dhar & Giuliani, 2010). Further, the high r values of r indicates how much of the overall variation in the data is explained by – the Loess curve. log log fits also led to the inference that fixed exponent allomet- ric equations could explain biomass distribution to a large extent. For example, McCarthy et al. (2007) suggested that one could needle-leaved deciduous species (Larix, Metasequoia, and explain 97–99% of the variation in biomass distribution across Taxodium) had low values for pLMF relative to the needle-leaved the plant kingdom world-wide if one could accurately determine evergreen species (Fig. 4a; P < 0.01). These differences were mir- the allometric constant and scaling exponent of Eqn 1. However, rored in pSMF (P < 0.01), with far less divergence in pRMF. as emphasized in general by Nee et al. (2005) and exemplified in Contrasting biomass distribution patterns for deciduous vs ever- Notes S2 for the specific case of allometric relationships among green species are also present within the angiosperms: evergreens organs, the r2 value must be interpreted with care when the had higher pLMF than deciduous species among the woody underlying data span orders of magnitude. This is because r2 is species of the basal angiosperms and the eudicots (Fig. 4a). In mathematically determined to increase directly with the size

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Cupressaceae (15)

Cyperaceae (4**)Arecaceae (8)

Poaceae (83***)

eae (6***) Magnoliaceae (4) Pinaceae (58**) Lamiaceae (5) Oleac Proteaceae (12***) Solanaceae (8**) Rubiaceae (4) Melastomataceae (5) Apocynaceae (9) Boraginaceae (4)

Myrtaceae (31***) Asteraceae (29) Apiaceae (4)

Brassicaceae (6*) Amaranthaceae (9**) Fig. 3 Phylogenetic tree of the leaf mass e (6) Polygonaceae Dipterocarpacea (7) fraction (LMF) data at the family level. Data Fabaceae (70) are based on the deviations of the LMF of each record from the median trend line as Malvaceae (21**) Rosa ceae (16) shown in Fig. 2(a), and are given as Moraceae (8) percentiles which are subsequently averaged Anacardiaceae (4) Ca per species (see the Materials and Methods nnabaceae (4**) Urticaceae (6) section). Family names are colour-coded Aceraceae (6*) Rhamnaceae ( depending on the median LMF ranking Betulaceae (14) Fagaceae (25***) (pLMF) value considered over all species.

Legend Sapindaceae (4) Numbers behind the family name indicate pLMF < 35 Meliaceae (8) the number of species on which the data are 35−45 Rutaceae (7) based. Families where the pLMF averaged 45−55 4) 55−65 over species deviates significantly from the overall median are indicated: *, P < 0.05; **, > 65 Salicaceae (20**)

Euphorbiaceae (8) P < 0.01; ***, P < 0.001.

range over which the variables are considered, regardless of the The value of the scaling exponent strength of the proportionality of the variables or the precise shape of the relationship. Thus, r2 has very limited value for Ignoring at first the dynamic scaling relationships that were best inferring the structure of relationships across scales. Indeed, even supported by the data, and focusing on the log-linear allometric if the shoot and root system of plants were to show high variabil- relationships (Table 2), we found slopes to be very similar to ity in biomass distribution patterns, that is, if RMF values ranged those reported by Niklas (2004) for his data set with actual between 0.01 and 0.99 (and thus, shoot to root ratios were con- biomass observations. As our database contains 15-fold more data fined between 0.01 and 99), the r2 of the relationships between than considered by Niklas (2004), we conclude that the calcu- log-transformed shoot and root biomasses would still be c. 0.94 lated slopes are likely to be stable approximations for the log-lin- or higher (Notes S2). Hence, the fact that an allometric equation ear fits across all plants. As a result of our considerably higher ‘explains’ c. 97% of the variation in log-transformed shoot and degrees of freedom, however, we found much smaller CIs around root mass according to its r2 does not imply that the equation is the fitted coefficients. Consequently, none of the ¾ or 1.0 values highly informative, nor does it necessarily indicate a biological forecasted by the MST models for the scaling exponent were law that extends beyond the conclusion that plants or species with within the 95% CIs, although in the case of leaf vs stem scaling a larger root mass are highly likely to have larger shoot mass as the estimated slope was close to the predicted ¾. Thus, just as well. Moreover, it follows that, in comparing linear vs curved inclusion of ¾ in the 95% CI has previously been used to support allometric relationships, a high r2 for the linear relationship does the MST model, the much narrower CIs in our data set can be not necessarily imply that curvature is nonexistent or that it used to formally refute the model. More importantly, however, would add only marginal insight or predictive value. In short, the we found no indication that the scaling exponent was constant in r2 value of an allometric model spanning many orders of magni- any of the three relationships (Fig. 1; Table 2). We are the first – tude of size says little about the accuracy of the model’s assump- to our knowledge – to show this for an extended data set on plant tions, and it does not automatically support a constant scaling organ mass. However, dynamic exponents have also been exponent. As discussed later, the clasmometric approach is better observed in other fields of biology: Kolokotrones et al. (2010), suited for drawing inferences about the strength of relative pro- for example, found that for the relationship between metabolic portionality of organs, because it eliminates the dependence on rate and animal size the scaling exponent b decreased monotoni- absolute scale that leads to spurious inflation of r2 values in the cally with size, and changing exponents were also reported in the allometric approach. scaling of tree respiration with tree size (Cheng et al., 2010).

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Table 3 The median percentile rank in leaf mass fraction (pLMF) per family 6012 170 140 9 70 20 100 5 40 60 averaged over all species measured for that family 90 (a) ≥ 4 observations per ≥ 1 observation per 70 + species species + 50 Median No. of Median No. of *** *** Family pLMF species P pLMF species P pLMF (%) 30 ns Cyperaceae 11 4 ** 31 11 * Oleaceae 16 6 *** 35 12 ns 10 Aceraceae 25 6 * 31 9 * Fagaceae 29 25 *** 40 49 ** 90 (b) Poaceae 34 83 *** 33 173 *** Salicaceae 37 20 ** 39 30 ** 70 Betulaceae 37 14 + 33 21 ** * Asteraceae 59 29 + 60 64 * 50 Pinaceae 59 58 ** 59 82 *** * ** * ns Malvaceae 66 21 58 32 ns pSMF (%) 30 *** Moraceae 68 8 + 62 11 ns Cupressaceae 68 15 * 61 20 + 10 Amaranthaceae 69 9 ** 68 13 ** Arecaceae 70 8 + 54 13 ns Myrtaceae 70 31 *** 56 64 ns 90 (c) Brassicaceae 72 6 * 77 8 ** Solanaceae 79 8 ** 81 9 *** 70 Cannabaceae 80 4 ** 72 7 * ns Proteaceae 81 12 *** 79 18 *** 50 ns ***

pRMF (%) ** pLMF values per species are considered over all size classes present in the 30 database. The analysis was carried out with emphasis either on the quality *** of the estimate per species (at least four independent records available per 10 species) or on the quantity of species (only one observation per species necessary for the species to be included). Data are most robust if they are consistent over the two approaches. P-values are given for the probability Mono. Mono. 3 4 Eudico. Eudico. that the averaged pLMF values deviate significantly from the median as Wo. Palm 3 4 He. C He. C He. C He. C derived by a t-test. Listed are only those families with a significant devia- Wo. Evg.Wo. Gymn. Dec.Wo. Gymn. Evg.Wo. Angio. Dec. Angio. tion in this respect. ns, nonsignificant (P > 0.10); +, 0.05 < P < 0.10; *, He. AnnualHe. Eudico. Perenn.Eudico. P < 0.05; **, P < 0.01; ***, P < 0.001). Fig. 4 Boxplots indicating the distribution of (a) leaf mass fraction (pLMF) rankings as well as (b) stem mass fraction (pSMF) and (c) root mass fraction (pRMF) rankings for various functional groups. Red and blue What is the overall pattern of how these scaling exponents boxes pertain to woody and herbaceous groups, respectively. The main change with size, and how could this pattern be explained from a box of the boxplots indicates the 25th and 75th percentiles, and the functional perspective? Our data set, like those of others (Enquist whiskers the 10th and 90th percentiles. The broken line shows the 50% value, which indicates no deviation from the mean trend. Woody palms & Niklas, 2002a; Niklas, 2004), represents a mixture of younger were not included in any other woody group. Numbers at the top of (a) and older plants. It therefore includes both comparisons across indicate the number of species on which each boxplot is based. Wo., ontogenetic stages for individuals of given species, and compar- woody; Evg., evergreen; Gymn., gymnosperms; Dec., deciduous; Angio., isons among species, thus representing evolutionary shifts in angiosperms; He., herbaceous; Mono, monocotyledons; Eudico., biomass distribution across species of different size. This does not Eudicotyledons; Perenn., perennial. Significance values based on t-tests for differences between adjacent groups are shown between the respective invalidate our data set as a test for MST, because the arguments boxes. (ns, nonsignificant; +, 0.05 < P < 0.10; *, P < 0.05; **, P < 0.01; ***, about size-related changes in organ structure and function used P < 0.001). by MST to predict invariance of scaling exponent b across species (i.e. in the evolutionary domain) would apply at least as well within species (i.e. within the ontogenetic domain) as across stems (Fig. 2). Most data for larger plants are from trees growing species. Thus, a fixed scaling exponent of ¾, as suggested by in plantations or natural forests. In the case of stands with equally MST1, would imply a completely fixed developmental pattern sized individuals, the amount of light, nutrients and water avail- throughout the vegetative stage. MST2 predicts a slightly differ- able to an individual are directly affected, and probably restricted, ent relationship in which scaling slopes are unity for young small by neighbours. Because these neighbouring trees limit horizontal plants but then quickly adjust to the values predicted by MST1 crown expansion, increasing leaf mass will generally manifest as at some transition point during development. Although plants increased leaf area per unit ground area (LAI). Because very little < 1 g indeed show relatively fixed scaling exponents close to 1.0, light remains to be intercepted when LAI exceeds a value of c.3– plants that achieve a size of 1–10 g begin to adjust their scaling 5 (Ellsworth & Reich, 1993; Anten et al., 1995), there will be lit- exponents gradually, with an increasing fraction of biomass in tle photosynthetic return on new leaf area investment, making

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more leaf area unprofitable for a given individual. Indeed, forests biomass distribution, but they do demonstrate that allometric in that growth phase often reach a plateau in leaf biomass or may scaling exponents are very likely to change with plant size as a even decline in leaf mass (Ryan et al., 1997; Fernandez-Martınez result of size-related changes in the return on investment in vari- et al., 2014). Although the response of an individual tree may be ous organs. Moreover, as these allometric trends were predicted different from that of a stand, the core assumption linking energy by developmental models, they apply equally well to comparisons capture to biomass in MST – namely, that plant growth is always in the ontogenetic and in the evolutionary domains. Together, proportional to the leaf mass present (Price et al., 2010) – is these models and our data strongly contradict the MST predic- clearly incorrect in closed canopies, where leaf biomass earns tions of constant scaling exponents, both empirically and theoret- diminishing returns. However, competition for light necessitates ically. We conclude that all results and economic principles are further investments in stem growth, most importantly in height consistent with scaling exponents that change dynamically with but also in diameter, for mechanical safety. Mechanical safety also plant size. necessitates additional root growth. Therefore, for competing trees whose lateral crown expansion is restricted by neighbours, Biomass distribution patterns as dependent on size we expect leaf biomass to saturate as the profitability of invest- ments in leaves declines, with investments gradually shifting to The virtue of the allometric analyses is that they determine rela- stems and roots, and more so to stems as a consequence of the tionships among traits, while implicitly accounting for size differ- direct benefit of height growth per se for light competition ences among plants. However, these analyses generally focus on (Dybzinski et al., 2011). These expectations were supported by the scaling exponent ‘b’ rather than the allometric constant ‘a’ our data set, for which we found a substantial decline in the (Glazier, 2010), and provide no insight into the specific values of leaf vs root and leaf vs stem scaling exponents with increasing biomass distribution variables (Poorter & Sack, 2012). Because plant size. the leaf vs stem and leaf vs root scaling exponents were < 1.0 over For trees over 10–100 kg, the strong prioritization of stem the full biomass range (Fig. 1d,e), it follows that larger plants will biomass distribution decreases somewhat, with stem vs root scal- have monotonic declines in LMF values, which was indeed the ing returning to unity again. At the same time, the relative change case (Fig. 2a). However, whereas organ size explained > 98% of in leaf biomass is at its lowest point, with scaling exponents the variation in the organ allometries, size only explained 78%, decreasing to as low as 0.66. An explanation for these changes 87% and 21% for LMF, SMF and RMF, respectively. The lower could involve the negative effect of height on water transport, r2 values in the clasmometric approach can be explained by the which can lead to a limitation of stomatal conductance and thus fact that the ‘autocorrelative’ effect of larger plants having larger photosynthetic rate and growth (Koch et al., 2004; Ryan et al., organs is removed in this type of calculation. Part of the remain- 2006; Steppe et al., 2011). These hydraulic factors, as well as ing variation is probably attributable to differences in environ- increased requirements for mechanical stability, may also favour mental conditions, which are difficult to quantify for this data greater biomass distribution to roots in tall trees (Nicoll & Ray, set, especially for availability of nutrients and water, or inherent 1996). Interestingly, a recent paper specifically modelled the variation within species. For the analysis of environmental effects architectural changes as well as the changes in hydraulics during the reader is referred to, for example, McCarthy & Enquist ontogeny and predicted the metabolic scaling exponent to (2007), Poorter et al. (2012) and Reich et al. (2014). decrease to 0.64 for large trees (Smith et al., 2014). Alternative The other part of the remaining variation will be attributable explanations that are inconsistent with quarter-power scaling to differences among species. In the following paragraphs, we dis- involve the influence of nutrient and/or water relations on cou- cuss the extent to which phylogeny and functional group explain pled carbon, nutrient, and water scaling (e.g. Reich et al., 2006; overall variation in biomass distribution patterns. As size had Savage et al., 2010). such a large influence on biomass distribution patterns (Fig. 2; We formalized our ideas of the role that increased biomass dis- Coleman et al., 1994), we analysed the deviation of each record tribution to stem biomass may play both in favouring light com- from the overall trends rather than considering the observed petition and in hindering water transport in a very simple biomass fractions per se. Focusing on pLMF as a measure of the mathematic model (Notes S3). Plants without constraints on deviations from the median, we found clear phylogenetic differ- and/or rewards for height growth show a constant, isometric ences (Figs 3, S2; Table 2), consistent with findings of previous biomass distribution throughout their life in this model. How- work, but importantly extending the range of variation and the ever, when the model is modified to reward height growth, types of comparisons. We discuss next the most interesting and biomass distribution shifts in favour of stems, with the stem vs clear contrasts, for woody and herbaceous species separately. root and leaf vs stem scaling exponents increasing and decreasing, respectively, as we observed in our data. A more sophisticated Interspecific variation in woody species model that applied a teleonomic approach to more detailed descriptions of canopy physiology and included mechanical safety One of the larger phylogenetic differences we found was that constraints (DESPOT; Buckley & Roberts, 2006b) gave similar woody gymnosperms invest relatively more in leaves and less in predictions, with leaf vs stem and leaf vs root scaling declining stems than woody angiosperms (Fig. 3; Table 3), in accordance during growth to 0.64 and 0.62, respectively. We do not suggest with conclusions of, for example, Korner€ (1994), McCarthy et al. that either of these models captures all subtleties of the biology of (2007) and Reich et al. (2014), which were based on much

New Phytologist (2015) Ó 2015 The Authors www.newphytologist.com New Phytologist Ó 2015 New Phytologist Trust New Phytologist Research 11 smaller data sets representing fewer lineages. Interestingly, the Interspecific variation in herbaceous species few deciduous gymnosperm species deviated markedly in biomass distribution pattern from the evergreen gymnosperms, indicated We found a large contrast in biomass distribution within the by their much lower pLMF and higher pSMF. A similar contrast herbaceous species between graminoids (Cyperaceae and in pLMF between deciduous and evergreen trees was also found Poaceae), which showed low pLMFs and high pRMFs, and in the woody angiosperms, for species characteristic of both trop- herbaceous eudicots, which showed the reverse. This difference ical/subtropical and temperate/boreal habitats, and in both small- has also been observed in experiments where graminoids and and large-sized individuals. Given that a much larger proportion herbaceous eudicots are grown under the same environmental of gymnosperm than angiosperm woody species are evergreen, it conditions, and it is consistent with observations that grasslands is likely that what was previously concluded to be a phylogenetic generally show very high RMF (Jackson et al., 1996; Poorter difference actually has a functional basis. et al., 2012). Because graminoids do not show secondary root Considered over all species for which data on larger trees growth, this may seem counterintuitive. Why do graminoids (> 100 kg) are present, the difference in actual LMF between the invest relatively strongly in root mass? One possible explanation two functional groups is more than two-fold, with mean ( SE) is that graminoids must develop more roots from the shoot base LMF being 0.018 ( 0.0005) for the deciduous species and to effectively explore the same root volume as eudicots. It has also 0.046 ( 0.0009) for the evergreens. This divergence in LMF been reported that roots of graminoids have lower protein con- could be explained mechanistically by assuming a yearly, fixed centrations and uptake rates of nitrogen per unit mass (Table 4). allocation of sugars to leaves equal for all tree species, in combi- Thus, the higher RMF might be a compensation for a lower nation with a much larger leaf turnover in the deciduous species, activity, although cause and effect could be reversed here as well. as a consequence of their two- to three-fold lower leaf lifespan. Other reasons are that graminoids may better survive grazing by An alternative and potentially complementary explanation is that quickly developing an extended well-anchored root system that plants regulate LMF directly on the basis of the proportion of resists the pulling forces of herbivores (Read & Stokes, 2006); leaf, stem and root required, with allocation of sugars simply that the storage of starch and nutrients in a larger pool of roots adjusted to that. The latter mechanism is consistent with pruning enables more retranslocation to new leaves after grazing or fire; or experiments with herbs, where LMF and RMF quickly recovered that grasses, by having less frequent associations with mycorrhizas to original values after half of the leaf or root mass was removed (Van der Heyden et al., 2015), invest more in roots themselves. (Brouwer, 1963; Poorter & Nagel, 2000). What could invoke A second contrast we analysed is between herbaceous C3 and such setpoints? An explanation at the system level would be based C4 species. Insofar as C4 species are thought to have higher pho- on the fact that forests in most regions of the world function with tosynthetic capacities than C3 species, high expectations are an LAI that differs little between deciduous and evergreen species placed on introducing this mechanism in C3 species with the aim (Iio et al., 2014). It is also known that, on average, the specific of boosting productivity (Von Caemmerer et al., 2012). How- leaf area (SLA; leaf area per unit leaf mass) of evergreen woody ever, given that plants with a superior photosynthetic rate and species is 2–3 times higher than that of deciduous species high sugar availability may readjust their biomass distribution (Poorter et al., 2009). Hence, all else being equal, the 2–3 times pattern by investing less in leaves and more in roots, the antici- – lower SLA in evergreens would have to be compensated by a 2 3 pated gains might partly disappear. In contrast, if C4 species time higher LMF to arrive at the more or less similar LAI. Our large database provides a basis for comparison of individ- ual plant groups in future studies, as it allows discoveries of dis- tinctive biomass distribution in given life forms and clades. As Table 4 Differences in root characteristics for herbaceous monocots and eudicots, as measured in the same experiment examples, we highlight findings for two groups of evergreen woody species. Our analysis showed that the arborescent palms Difference form a functional group with an especially distinct biomass distri- Variable Monocots Eudicots (%) P bution pattern (Fig. 4). Woody palms are among the dominant RMF 0.31 0.01 0.26 0.01 +20 * species in large part of the tropics (Ter Steege et al., 2013) and 1 (gROOT g PLANT) are particularly well adapted to survive hurricanes, and one might [Root organic N] 30 1.5 42 1.3 29 *** 1 therefore predict a particularly well-developed root system. How- (mg g ROOT) ** ever, the little information we were able to collect suggests instead Net NO3 uptake rate 2.4 0.3 3.9 0.4 40 1 1 that they have a high LMF, as do the other groups of evergreen (mmol g ROOT d ) Root respiration 54 2.6 64 3.9 16 * species. Another surprise was the consistently high pLMF and (nmol O g 1 s 1) low pRMF for Proteaceae, as these species generally come from 2 ROOT light-exposed, dry and nutrient-poor areas, where large RMFs This table shows a summary of the overall difference between 11 could be considered of survival value. It is possible that the herbaceous monocot and 13 herbaceous eudicot species. All species were ephemeral nature of their cluster roots (Lambers et al., grown in a growth chamber under conditions of unrestricted water and nutrient supply. More details can be found in Poorter et al. (1991). The dif- 2006), that is, fast fine-root turnover, lead to their low RMF ferences were tested at the species level with a Welch two-sample t-test. despite a potentially large fraction of photosynthates allocated to Data are mean values SE. Significance values: *, P < 0.05; **, P < 0.01; roots. ***, P < 0.001. RMF, root mass fraction.

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generally show reduced water loss compared with C3 species, they References could operate with a higher LMF and a lower RMF. However, Anten NPR, Schieving F, Medina E, Werger MJA, Schuffelen P. 1995. Optimal comparing the overall biomass distribution between C3 and C4 leaf area indices in C3 and C4 mono-and dicotyledonous species at low and herbs, we found evidence of neither scenario in the monocots, as high nitrogen availability. Physiologia Plantarum 95: 541–550. there was no overall difference between C and C species. There Bloom AJ, Chapin FS, Mooney HA. 1985. Resource limitation in plants – an 3 4 – is some indication for increased pLMF and decreased pRMF in economic analogy. Annual Review of Ecology and Systematics 16: 363 392. Boyle B, Hopkins N, Lu Z, Raygoza-Garay JA, Mozzherin D, Rees T, Matasci the eudicots, but note that the number of C4 species here is too N, Narro ML, Piel WH, McKay SJ. 2013. The taxonomic name resolution small for a firm conclusion. 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West GB, Brown JH, Enquist BJ. 1997. A general model for the origin of Table S2 Biomass data for leaves, stems and roots as well as – allometric scaling laws in biology. Science 276: 122 126. biomass distribution patterns and deviations from the overall Zanne AE, Tank DC, Cornwell WK, Eastman JM, Smith SA, FitzJohn RG, trends in biomass distribution as used in the current analyses McGlinn DJ, O’Meara BC, Moles AT, Reich PB et al. 2014. Three keys to the radiation of angiosperms into freezing environments. Nature 506:89–92. Zinke PJ, Stangenberger AG. 1994. Soil and nutrient element aspects of Table S3 Overview of the representation of various plant groups Sequoiadendron giganteum. In: Aune SP, ed. Symposium on giant sequoias: their in the database place in the ecosystem and society. Gen. Techn. Rep. PSW-GTR-151. Albany, CA, – USA: Pacific Southwest Research Station, Forest Service, USDA, 69 77. Table S4 Allometric scaling exponents as given for all records of all species, and for herbaceous and woody species separately Supporting Information Notes S1 Methodological assumptions. Additional supporting information may be found in the online version of this article. Notes S2 The inference value of r2 in plant allometric analyses. Fig. S1 Residuals of the allometric relationships after fitting an Notes S3 Explanation of a very simple model that shows SMA regression through log–log-transformed organ mass data. dynamic scaling exponents as a consequence of physiological or environmental constraints. Fig. S2 Phylogenetic tree of the Leaf Mass Fraction (LMF) data. Please note: Wiley Blackwell are not responsible for the content Fig. S3 Distribution of the deviations from the overall allometric or functionality of any supporting information supplied by the log–log curves for various functional groups. authors. Any queries (other than missing material) should be directed to the New Phytologist Central Office. Table S1 Literature references on which the database is built

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New Phytologist Supporting Information

Article title: How does biomass allocation change with size and differ among species? An analysis for 1200 plant species from five continents Authors: Hendrik Poorter, Andrzej M. Jagodzinski, Ricardo Ruiz-Peinado, Shem Kuyah, Yunjian Luo, Jacek Oleksyn, Vladimir A. Usoltsev, Thomas N. Buckley, Peter B. Reich, Lawren Sack Article acceptance date: 15 June 2015

The following Supporting Information is available for this article:

Fig. S1 Residuals of the allometric relationships after fitting a SMA regression through log-log transformed organ mass data.

Fig. S2 Phylogenetic tree of the Leaf Mass Fraction (LMF) data.

Fig. S3 Distribution of the deviations from the overall allometric log-log curves for various functional groups.

 Note S1 Methodological assumptions

Note S2 Inference value of r2 in plant allometric analyses

Note S3 Explanation of a very simple model that shows dynamic scaling exponents as a consequence of physiological or environmental constraints.

Table S1 Literature references on which the database is built.

Table S2 Biomass data for leaves, stems and roots as well as biomass distribution patterns

(LMF, SMF and RMF) and deviations from the overall trends in biomass distribution (pLMF, pSMF and pRMF) as used fr the current analyses.

Table S3 Overview of the representation of various plant groups in the database.

Table S4 Allometric scaling exponents as given for all records of all species, and for herbaceous and woody species separately.

Fig. S1 Residuals after fitting a SMA regression through log-log transformed organ mass data. For clarity, the residuals are binned for the 50 size classes, and the median residuals for each size class are connected with a red line.

Poorter et al., Suppl. Fig. 1

1.5 a

1.0

0.5

0.0

-0.5

residual log(Leaf Mass) -1.0

-1.5 10-4 10-3 10-2 10-1 100 101 102 103 104 105 106 107 Stem Mass (g)

1.5 b

1.0

0.5

0.0

-0.5

residual log(Leaf Mass) -1.0

-1.5 10-3 10-2 10-1 100 101 102 103 104 105 106 107 Root Mass (g)

1.5 c

1.0

0.5

0.0

-0.5

residual log(Stem Mass) -1.0

-1.5 10-3 10-2 10-1 100 101 102 103 104 105 106 107 Root Mass (g)

Fig. S2 Phylogenetic tree of the Leaf Mass Fraction (LMF) data. Data are based on the deviations of the LMF of each record from the median trend line (pLMF) as shown in Fig. 2a, expressed as percentiles and calculated per size class (see Methods). Note that a pLMF of 50 indicates that the species does not deviate from the median trend. The total number of species included is 482. The species colour indicates the average pLMF for that species, for explanation of the colour code see the legend of the figure. > 65 55 −65 45 −55 35 −45 pLMF <35 Legend

Calamagrostis canadensis (10)

Corynephorus canescens (9) canescens Corynephorus

Anthoxanthum odoratum (7) odoratum Anthoxanthum Deschampsia cespitosa (23) cespitosa Deschampsia

Schizachyrium scoparium (11) Alopecurus geniculatus (4)

Phalaris arundinacea (12) arundinacea Phalaris

Arrhenatherum elatius (4) elatius Arrhenatherum Koeleria macrantha (5) macrantha Koeleria Heteropogon contortus (5) Phragmites australis (4)

Hemarthria altissima (4) Phleum pratense (40) Pennisetum clandestinum (4) Sorghum halepense (5) (9) cristatus Cynosurus

Agrostis gigantea (4)

Andropogon gerardii (7) (44) glomerata Dactylis

Lolium multiflorum (5) multiflorum Lolium

Aegilops speltoides (6) speltoides Aegilops Triticum monococcum (6) monococcum Triticum

Holcus lanatus (35) lanatus Holcus Triticum aestivum (67) aestivum Triticum

Molinia caerulea (6) (50) perenne Lolium

Panicum coloratum (10) (4) geniculata Aegilops

Panicum miliaceum (7) (5) barbata Avena

Triticum turgidum (6) turgidum Triticum Sorghum bicolor (8) Poa pratensis (46) (26) ovina Festuca

Aegilops neglecta (4) neglecta Aegilops

Danthonia decumbens (9) Panicum virgatum (6) Poa costiniana (4) (7) triuncialis Aegilops Lolium rigidum (6) rigidum Lolium

Panicum capillare (20) Briza media (15)

Oryza sativa (26) (4) rubra Festuca

Urochloa brizantha (6) (4) sativa Avena

Bouteloua curtipendula (9) (4) trachycaulus Elymus

Poa annua (17) (6) canadensis Elymus Aegilops tauschii (9) tauschii Aegilops

Poa trivialis (9) (4) phoenicoides Brachypodium

Liriodendron tulipifera (16) (14) jubatum Hordeum

Hordeum secalinum (4) secalinum Hordeum Bromus hordeaceus (20) hordeaceus Bromus

Zea mays (36) (28) repens Elymus Hordeum vulgare (28) vulgare Hordeum

Hordeum murinum (10) murinum Hordeum

Cenchrus ciliaris (7) (5) cereale Secale

Bouteloua gracilis (8) (22) pinnatum Brachypodium

Brachypodium distachyon (4) distachyon Brachypodium Buxus sempervirens (4) Spartina anglica (4) Setaria viridis (5) (9) madritensis Bromus

Liquidambar formosana (11)Manglietia fordiana (5)

Liquidambar styraciflua (9) Sassafras tzumu (5) Bromus tectorum (7) tectorum Bromus

Ranunculus repens (4) (4) ramosus Bromus Grevillea robusta (5) (33) inermis Bromus

Clematis vitalba (9) (10) erectus Bromus

TerminaliaOenotheraEpilobium ivorensis biennis ciliatum (10) (31) (4)

Sonneratia caseolaris (4) (4) bigelowii Carex

Lythrum salicaria (10) (21) humilis Chamaerops Washingtonia robusta (21) robusta Washingtonia

Arthrostemma ciliatum (4) (19) guineensis Elaeis

Carex diandra (15) diandra Carex

Bellucia pentamera (6) Vitis vinifera (5) (25) crinita Carex

Juncus effusus (6) effusus Juncus

Syzygium samarangenseSonneratia (5) alba (6) (6) nigra Carex

Mauritiella aculeata (18) aculeata Mauritiella

Cocos nucifera (8) nucifera Cocos Miconia calvescens (4) (16) flexuosa Mauritia Melaleuca viridiflora (4) Backhousia myrtifolia (4)

Clidemia hirta (4)

Corymbia tessellaris (4) (22) calamus Acorus

Iris versicolor (4) versicolor Iris

Juniperus communis (10) communis Juniperus

Eucalyptus marginata (4) (8) thurifera Juniperus

CorymbiaAgonis citriodora flexuosa (8) (4) (4) australis Agathis

Illicium henryi (5) henryi Illicium

Eucalyptus cloeziana (6) (5) procera Juniperus Cupressus funebris (29) funebris Cupressus

Eucalyptus pauciflora (7) (8) orientalis Platycladus Eucalyptus delegatensis (4) (11) obtusa Chamaecyparis

Metasequoia glyptostroboides (12) glyptostroboides Metasequoia

EucalyptusEucalyptus microtheca sieberi (12) (7) (27) hodginsii Fokienia

Thuja occidentalis (14) occidentalis Thuja Taxodium distichum (22) distichum Taxodium Cryptomeria japonica (71) japonica Cryptomeria

Eucalyptus crebra (4) (12) cryptomerioides Taiwania EucalyptusEucalyptusEucalyptus camaldulensis platyphylla urophylla (43) (4) (5) (375) lanceolata Cunninghamia Eucalyptus tereticornis (5)

EucalyptusEucalyptus globulus grandis (17) (40)

Erysimum cheiranthoides (20)

Pinus elliottii (10) elliottii Pinus Arabidopsis thaliana (6) (11) palustris Pinus

Carica papaya (4) (33) radiata Pinus Pinus ponderosa (16) ponderosa Pinus

Pinus taeda (86) taeda Pinus Pinus tabuliformis (236) tabuliformis Pinus

Pinus contorta (23) contorta Pinus Cakile maritima (7) (49) yunnanensis Pinus

CochlospermumRaphanusBrassica vitifolium sativus napus (4)(11) (19)

Gonystylus bancanusSinapis alba (4) (6)

Pinus thunbergii (20) thunbergii Pinus

Pinus kesiya (4) kesiya Pinus Pinus taiwanensis (9) taiwanensis Pinus

Pinus densiflora (28) densiflora Pinus HopeaHopea wightiana helferi (4) (4) (1010) sylvestris Pinus

ShoreaHopea singkawang odorata (4) (5)

Pinus mugo (12) mugo Pinus Pinus resinosa (11) resinosa Pinus

TheobromaFirmiana cacaosimplex (10) (4) (149) massoniana Pinus

Brachychiton populneus (4)

Pinus nigra (33) nigra Pinus

Ochroma pyramidaleTilia cordata (5) (7) (5) roxburghii Pinus

Pinus halepensis (28) halepensis Pinus

Ceiba pentandra (5) (32) pinea Pinus

Gossypium hirsutum (18) (38) pinaster Pinus

GossypiumHibiscus barbadense asper (6) (4) (24) canariensis Pinus Pinus brutia (14) brutia Pinus

Abutilon theophrasti (25) (28) banksiana Pinus Dacryodes excelsa (5) (15) strobus Pinus

Mangifera indica (6) (50) koraiensis Pinus Pinus sibirica (18) sibirica Pinus

PistaciaRhus lentiscus typhina (13) (5) (6) crassifolia Picea

Pistacia terebinthus (9) (8) koraiensis Picea

Acer platanoides (7) (45) obovata Picea

Acer pensylvanicum (6) (9) asperata Picea

Acer saccharinum (5) (428) abies Picea Picea mariana (25) mariana Picea

Acer pseudoplatanusAcer rubrum (32) (7) (8) rubens Picea

Picea purpurea (4) purpurea Picea

Acer saccharum (26) (13) schrenkiana Picea

Diploglottis Blighiadiphyllostegia sapida (6)(5) (5) engelmannii Picea

Swietenia macrophylla (10) (45) glauca Picea

Khaya senegalensis (5) (18) sitchensis Picea Larix kaempferi (53) kaempferi Larix

CedrelaToona odorata ciliata (12) (4) (16) sibirica Larix Larix laricina (18) laricina Larix

Cedrela fissilis (4) (56) decidua Larix

Ailanthus altissima (4) (30) menziesii Pseudotsuga

Citrus reticulata (8) (101) gmelinii Larix

Citrus aurantium (9) (11) veitchii Abies

Citrus sinensis (4) (51) alba Abies

Flindersia brayleyana (13) Abies sibirica (24) sibirica Abies

Larrea tridentata (12) (10) fraseri Abies

Euonymus europaeus (5) (6) fabri Abies Gymnosporia senegalensis (4) (5) canadensis Tsuga

Ceratopetalum apetalum (4)

Callicoma(7) serratifoliasylvestris (4)Elaeocarpus Tsuga heterophylla (5)

Elaeocarpus reticulatus (4) reticulatus Elaeocarpus Prunella vulgaris (21)

Bruguiera sexangula (4) sexangula Bruguiera Mentha aquatica (4)

Rhizophora mangle (17) mangle Rhizophora Origanum vulgare (7)

Hypericum perforatum (7) perforatum Hypericum Tectona grandis (14)

Garcinia mangostana (5) mangostana Garcinia Scrophularia nodosa (8)

Populus euphratica (9) euphratica Populus Verbascum thapsus (4)

Populus deltoides (20) deltoides Populus Tabebuia rosea (5)

Populus trichocarpa (5) trichocarpa Populus Markhamia lutea (7)

Populus balsamifera (4) balsamifera Populus Avicennia germinans (10)

Populus tremula (48) tremula Populus Avicennia marina (5)

Populus nigra (6) nigra Populus Plantago euryphylla (4)

Populus tremuloides (90) tremuloides Populus Plantago major (71)

Populus alba (5) alba Populus Plantago lanceolata (41)

Salix eriocephala (4) eriocephala Salix Ligustrum vulgare (5)

Salix sericea (4) sericea Salix Fraxinus angustifolia (15)

Salix caprea (8) caprea Salix Fraxinus excelsior (7)

Salix cinerea (6) cinerea Salix Phillyrea latifolia (8)

Hevea brasiliensis (11) brasiliensis Hevea Phillyrea angustifolia (5)

Manihot esculenta (6) esculenta Manihot Olea europaea (29)

Vernicia fordii (4) fordii Vernicia Solanum dulcamara (18)

Jatropha curcas (5) curcas Jatropha Solanum tuberosum (4)

Croton urucurana (4) urucurana Croton Solanum lycopersicum (65)

Triadica sebifera (6) sebifera Triadica Physalis peruviana (29)

Cucumis sativus (13) sativus Cucumis Capsicum annuum (9)

Nothofagus cunninghamii (8) cunninghamii Nothofagus Datura stramonium (14)

Nothofagus antarctica (4) antarctica Nothofagus Atropa belladonna (6)

Fagus sylvatica (178) sylvatica Fagus Nicotiana tabacum (24)

Fagus crenata (17) crenata Fagus Convolvulus arvensis (6)

Castanea sativa (12) sativa Castanea Gardenia jasminoides (5)

Castanopsis fissa (8) fissa Castanopsis Genipa americana (5)

Castanopsis cuspidata (4) cuspidata Castanopsis Coffea arabica (4)

Quercus ilex (53) ilex Quercus Palicourea crocea (7)

Quercus coccifera (9) coccifera Quercus Asclepias incarnata (8)

Quercus acutissima (4) acutissima Quercus Nerium oleander (19)

Quercus variabilis (11) variabilis Quercus Plumeria rubra (4)

Quercus suber (53) suber Quercus Dyera costulata (4)

Quercus velutina (8) velutina Quercus Cordia borinquensis (4)

Quercus rubra (34) rubra Quercus Cordia sinensis (5)

Quercus petraea (18) petraea Quercus Cordia alliodora (7)

Quercus faginea (16) faginea Quercus Echium plantagineum (4)

Quercus robur (226) robur Quercus Xanthium strumarium (7)

Quercus mongolica (19) mongolica Quercus Helianthus annuus (23)

Quercus lusitanica (5) lusitanica Quercus Galinsoga parviflora (8)

Quercus aliena (7) aliena Quercus Eupatorium japonicum (4)

Quercus pyrenaica (20) pyrenaica Quercus Eupatorium cannabinum (4)

Quercus canariensis (18) canariensis Quercus Chromolaena odorata (4)

Quercus macrocarpa (4) macrocarpa Quercus Eutrochium maculatum (14)

Quercus alba (4) alba Quercus Ageratina adenophora (8)

Casuarina equisetifolia (11) equisetifolia Casuarina Bidens frondosa (6)

Alnus rubra (14) rubra Alnus Achillea millefolium (20)

Alnus incana (8) incana Alnus Achillea ptarmica (12)

Alnus cremastogyne (16) cremastogyne Alnus Leucanthemum vulgare (30)

Alnus glutinosa (81) glutinosa Alnus Artemisia annua (4)

Corylus avellana (30) avellana Corylus Solidago canadensis (5)

Ostrya virginiana (4) virginiana Ostrya Rudbeckia hirta (4)

Carpinus betulus (35) betulus Carpinus Bellis perennis (4)

Betula alleghaniensis (11) alleghaniensis Betula Scorzoneroides autumnalis (23)

Betula lenta (7) lenta Betula Taraxacum officinale (23)

Betula papyrifera (48) papyrifera Betula Lactuca sativa (9)

Betula nana (4) nana Betula Hieracium scabrum (6)

Betula populifolia (11) populifolia Betula Centaurea maculosa (5)

Betula pubescens (29) pubescens Betula Cirsium vulgare (5)

Betula pendula (216) pendula Betula Cirsium arvense (5)

Betula platyphylla (7) platyphylla Betula Cichorium intybus (21)

Rhamnus alaternus (11) alaternus Rhamnus Lobelia cardinalis (6)

Rhamnus cathartica (5) cathartica Rhamnus Pimpinella saxifraga (9)

Ceanothus tomentosus (6) tomentosus Ceanothus Daucus carota (4)

Urtica dioica (34) dioica Urtica Anthriscus sylvestris (7)

Cecropia obtusifolia (7) obtusifolia Cecropia Oenanthe aquatica (4)

Ulmus americana (5) americana Ulmus Pittosporum undulatum (7)

Cannabis sativa (4) sativa Cannabis Hedera helix (11)

Celtis australis (4) australis Celtis Succisa pratensis (10)

Trema micrantha (5) micrantha Trema Lonicera implexa (4)

Milicia excelsa (7) excelsa Milicia Viburnum lantana (12)

Morus alba (8) alba Morus Viburnum opulus (12)

Broussonetia papyrifera (4) papyrifera Broussonetia Sambucus nigra (15)

Brosimum rubescens (20) rubescens Brosimum Ilex aquifolium (10)

Ficus insipida (8) insipida Ficus Gaultheria shallon (5)

Ficus carica (4) carica Ficus Rhododendron tomentosum (4)

Ficus benjamina (4) benjamina Ficus Arbutus unedo (8)

Ficus retusa (4) retusa Ficus Cariniana micrantha (6)

Geum rivale (4) rivale Geum Cariniana legalis (4)

Geum urbanum (23) urbanum Geum Manilkara bidentata (4)

Rubus ulmifolius (5) ulmifolius Rubus Schima superba (10)

Rosa canina (7) canina Rosa Lysimachia vulgaris (7)

Potentilla reptans (4) reptans Potentilla Ardisia crenata (5)

Potentilla neumanniana (4) neumanniana Potentilla Impatiens parviflora (31)

Prunus laurocerasus (5) laurocerasus Prunus Cornus sanguinea (17)

Prunus serotina (37) serotina Prunus Chenopodium album (14)

Prunus padus (22) padus Prunus Beta vulgaris (14) Poorter etal.

Prunus persica (8) persica Prunus Alternanthera philoxeroides (11) Suppl. Fig.2

Prunus spinosa (4) spinosa Prunus Amaranthus hypochondriacus (12)

Sorbus aucuparia (21) aucuparia Sorbus Amaranthus cruentus (16)

Crataegus monogyna (13) monogyna Crataegus Amaranthus retroflexus (14)

Cercis siliquastrum (4) siliquastrum Cercis Amaranthus blitum (8)

Ceratonia siliqua (19) siliqua Ceratonia Amaranthus tricolor (36)

Colophospermum mopane (4) mopane Colophospermum Silene vulgaris (27)

Brachystegia spiciformis (4) spiciformis Brachystegia Silene uniflora (4)

Schotia brachypetala (4) brachypetala Schotia Silene dioica (18)

Caesalpinia eriostachys (4) eriostachys Caesalpinia Rumex acetosa (23)

Senna obtusifolia (11) obtusifolia Senna Rumex thyrsiflorus (4)

Gleditsia triacanthos (20) triacanthos Gleditsia Rumex obtusifolius (8)

Peltophorum africanum (4) africanum Peltophorum Rumex crispus (7)

Parkinsonia aculeata (12) aculeata Parkinsonia Trifolium repens (34)

Prosopis glandulosa (32) glandulosa Prosopis Trifolium subterraneum (5)

Anadenanthera colubrina (4) colubrina Anadenanthera Medicago sativa (9)

Leucaena leucocephala (16) leucocephala Leucaena Pisum sativum (9)

Mimosa tenuiflora (6) tenuiflora Mimosa Vicia faba (5)

Acacia nilotica (6) nilotica Acacia Vicia cracca (5)

Acacia tortilis (7) tortilis Acacia Cicer arietinum (6)

Piptadenia stipulacea (4) stipulacea Piptadenia Lotus corniculatus (5)

Acacia saligna (18) saligna Acacia Robinia pseudoacacia (17)

Cedrelinga cateniformis (6) cateniformis Cedrelinga Sesbania herbacea (4)

Acacia dealbata (6) dealbata Acacia Glycine max (28)

Acacia mearnsii (16) mearnsii Acacia Phaseolus lunatus (6)

Acacia melanoxylon (15) melanoxylon Acacia Phaseolus vulgaris (29)

Acacia tetragonophylla (8) tetragonophylla Acacia Amburana cearensis (10)

Acacia aulacocarpa (4) aulacocarpa Acacia Spartium junceum (6) Acacia aneura (7) aneura Acacia Dalbergia miscolobium (4) Arachis hypogaea (6)

Fig. S3 Distribution of the deviations from the overall allometric log-log curves for various functional groups for (a) Leaf mass vs. stem mass scaling (b) Leaf mass vs. Root mass scaling and (c) Stem mass vs. Root mass scaling. The overall allometric curves were first determined by a Loess fit, and for all observations the deviations from the fitted line were calculated and averaged over species. Species averages were then used to determine boxplots of the distribution of values per species. The boxplot indicates the 10th, 25th, 50th, 75th and 90th percentile. Wo.: woody; He.: herbaceous; Evg.: evergreen; Dec.: deciduous; Perenn.: perennial; Gymn.: gymnosperms; Angio.: angiosperms; Mono: monocotyledons; Eudico.: Eudicotyledons. Significance values indicate t-tests for significant deviation from 0, which indicates no deviation from the overall allometric curve. +, 0.05 < P < 0.10; *, P < 0.05; **, P < 0.01; ***, P < 0.001).

Poorter et al. Suppl. Fig. 3

0.8 a 0.6 *** ** 0.4 *** 0.2 *** *** *** 0.0

deviation -0.2 +

Leaf vs. Stem ** -0.4

-0.6 0.8 b 0.6 *** *** 0.4 *** *** 0.2 *** *** 0.0 * + deviation -0.2 *** Leaf vs. Root -0.4

-0.6 0.8 c 0.6

0.4 * 0.2

0.0 + -0.2 *** deviation ** **

Stem vs. Root -0.4 + -0.6 . . n. o m Gymn. . Angi Mono. Mono. . 3 4 Eudico. Eudico. l Eudico Wo. Palm 3 4 a He. C He. C He. C He. C Wo. Evg Wo. Dec. Wo.Gy Evg Wo. Dec. Angio. He. AnnuHe. Perenn. Eudico.

Note S1. Methodological assumptions

There were four important assumptions in our methodology, shared with previous studies. First, we assumed that differences among studies in how the whole plant was separated into leaf, stem and root would have only a small effect on the patterns analysed. Not all investigators followed exactly the same protocol, and not all described their specific protocol. Ideally, organs would be consistently defined by function; for example, leaf lamina, as the organ most active in photosynthesis, would ideally be consistently separated from petioles and, in grasses, from leaf sheaths, which mainly function to position the leaf blades in a favourable location and for water and sugar transport (Pérez-Harguindeguy et al., 2013 and references therein). However, in a number of reports petioles and/or leaf bases were included in the leaf fraction. We made a correction only in the case of palm trees, where leaves can be up to 8 meters long with petioles as thick as small branches of dicotyledonous trees (Corley & Tinker, 2003). In those cases we subtracted petiole and rachis from total leaf mass, using supplementary data of other publications as necessary. We also presumed that differences among studies in the separation of stems and roots would not have a strong effect on the analyses. Our second assumption was that root mass was accurately measured. The extraction of roots from solid substrates can be challenging (Mokany et al., 2006). On the one hand, root mass can be overestimated if roots are not cleaned well enough of adhering soil particles; on the other hand, root mass is underestimated if not all roots are recovered. Based on sophisticated methods where the root diameter of various roots were taken into account, the fraction of unrecovered root mass or volume for a Pinus root system was estimated to be 17% in young plants but only 4% in older ones (Danjon et al., 2013; Chmura et al., 2013). The effect of such error would be relatively modest, though for large field-grown trees no estimates are available. Third, we assumed that total plant biomass is a far more important driver for biomass distribution than the age or – for trees – the ontogenetic stage of a plant. Some studies focused on size-related changes within species, while others, especially in zoology, have focused on differences across species when measured at the adult reproductive stage. In plants, modular and indeterminate growth generates far more variability in size at any ontogenetic stage than in animals, and size imposes a variety of functional constraints. It is also a strong determinant in competition. We therefore decided to include both younger and older plants, as long as they matched the criteria given in Material and Methods. Ontogeny will be an important factor, especially when flowering occurs in monocarpic species. We therefore excluded all herbs as well as monocarpic woody species in the generative phase. Consequently, the overall database has both ontogenetic and interspecific components, and total plant size is considered to be the main driver.

Our fourth assumption was that the plants for each size class in the dataset constitute a representative subsample with respect to growth conditions, functional group, and phylogeny. That is, for all sizes of plants there are individuals grown at various environmental conditions (high/low temperature, nutrients, densities, etc.). Larger trees were only grown and harvested in the field, so we also assume that the mix of conditions for small trees (partly experimental, partly field) was not very different from those of larger trees (partly plantations, partly natural). Thus, we supposed environmental effects to be randomly and equally distributed over the full range of data, adding noise to the data set, but without driving any substantial systematic deviations.

References

- Chmura DJ, Guzicka M, Rozkowski R, Chałupka W. 2013. Variation in aboveground and belowground biomass in progeny of selected stands of Pinus sylvestris. Scandinavian Journal of Forest Research 28: 724-734. - Corley RHV, Tinker PB. 2003. The Oil Palm. Oxford, UK: Blackwell Science.

- Danjon F, Caplan JS, Fortin M, Meredieu C. 2013. Descendant root volume varies as a function of root type: estimation of root biomass lost during uprooting in Pinus pinaster. Frontiers in Plant Science 4: 402. - Mokany K, Raison RJ, Prokushkin AS. 2006. Critical analysis of root:shoot ratios in terrestrial biomes. Global Change Biology 12: 84-96. - Pérez-Harguindeguy N, Díaz S, Garnier E, Lavorel S, Poorter H, Jaureguiberry P, Bret- Harte MS, Cornwell WK, Craine JM,Gurvich DE et al. 2013. New handbook for standardised measurement of plant functional traits worldwide. Australian Journal of Botany 61: 167-234.

Note S2. Inference value of r2 in plant allometric analyses

Sensitivity analysis of the effect of a predefined range in Root Mass Fraction (RMF: fraction of Total Plant Mass (TM) invested in roots) on the explained variance (r2) of the relationship between log(root mass) and log(shoot mass). The predefined ranges were chosen to be narrow from a biological perspective (0.4 < RMF < 0.6), realistic (0.07 < RMF < 0.70; as observed for the current data set based on the 0.5th and 99.5th percentile), very wide (0.01 < RMF < 0.99) and improbably wide (0.001 < RMF < 0.999). Each correlation was based on 20,000 random drawings as explained below. Overall variation in simulated plant mass was either 10 orders of magnitude, or 1 order of magnitude.

r2 1010-fold 10-fold Range in RMF range in TM range in TM 0.40 – 0.60 0.999 0.886 0.07 – 0.70 0.982 0.170 0.01 – 0.99 0.941 0.011 0.001 – 0.999 0.932 0.020

Simulations To evaluate the meaning to be attached to the actual value of r2 in allometric relationships, we simulated a population of plants with substantial variation in biomass, drawing randomly from a uniform distribution of log-transformed total plant mass, for a range that comprised 10 orders of magnitude in biomass. This is more or less similar to the current dataset. For each of these plants, root mass was then calculated, after simulating a Root Mass Fraction by randomly drawing from a uniform distribution with values ranging from – in the first scenario - 0.40 to 0.60. Shoot mass was then simply the difference between the mass of the total plant and the roots. We drew samples for 20,000 simulated plants in total, and subsequently calculated the r2 of the allometric relationship between the log-transformed shoot and root mass for all 20,000 observations. The analysis was then repeated with three other scenarios with increasingly wider intervals for the RMF.

The compiled data showed very tight relationships between organs (r2 ≥0.932; see table above), and between each organ and total plant biomass (r2 ≥0.992). We analysed how such high r2 values for the relationships between the biomass of two organs should be interpreted, and whether it permits the inference of a fixed scaling exponent, in principle. We simulated cases with various ranges in RMF. In the case of relatively narrow variation in RMF (0.40-0.60), we found that the allometric relationship yielded an r2 higher than 0.99. However, when allowing

RMF to vary randomly across the range actually observed in our compiled dataset (99% of the cases were in the 0.07-0.70 range), the r2 still exceeded 0.98. Only in simulations when the range in allocation became much larger than normally observed (0.01 – 0.99 or wider) was the r2 <0.95. Indeed, even if the shoot and root system of plants showed highly variable proportionality, that is when RMF ranged between 0.01 and 0.99 (and thus, shoot:root ratios were confined between 0.01 and 99), the correlation between log-transformed shoot and root biomass was still around 0.94 or higher. The high r2s were predominantly due to the large range of biomass considered; the r2 dropped dramatically with increasing range of RMF when the same allometric relationship is considered over one rather than ten orders of magnitude in plant size (Table above). Hence, the fact that an allometric equation “explains” ~97% of the variation in shoot and root mass according to its r2, does not allow the inference of the central tendency of biomass allocation. Direct examination of the allometries, and potential shifts in the allometries are necessary to establish the central trend, and whether it is fixed or dynamic.

Note S3. Accounting for changes in the economics of C allocation during growth

The central features of the economics of plant carbon allocation are that the effect of C investment in any pool on growth must be saturating – i.e., growth rate G approaches a finite limit as C in any pool approaches infinity – and that the effects of each C investment on growth rate are not independent: if investment is high in one pool, this increases the return on investment in other pools due to their mutual influence on photosynthesis. Perhaps the simplest implementation of these features is

 cs  cr  cl  G        kc ss   kc rr   kc ll 

Apart from the saturation constants kj, the carbon pools are indistinguishable in this model. When carbon allocation is optimised in this model (by modulating allocation over time, during growth, so that the marginal products for each pool remain equal: G/cs = G/cr = G/ci), allocation is isometric:

2 1 1.8 L vs S 0.9 LMF L vs R 0.8 SMF 1.6 S vs R RMF 1.4 0.7 exponents 1.2 0.6

fractions 0.5

1

scaling 0.4 0.8

0.6 mass 0.3 0.4 0.2 0.2 0.1 allometric 0 0 1 10 100 1000 10000 1 10 100 1000 10000 total biomass (arbitrary units) total biomass (arbitrary units)

(The lines for LMF and RMF have been shifted up by 0.01 and down by 0.01, respectively, to make them visible.) To capture what happens during height growth, we must incorporate the effect of height, which influences the economics of allocation to stems, roots and leaves differently. Suppose that height growth brings diminishing returns because its benefits for light capture are counteracted by its negative impact on water transport. This can be expressed qualitatively by multiplying G by a hyperbolic function of height analogous to the terms for the carbon pools:

 cs  cr  cl  h  G         kc ss   kc rr   kc ll   kh h  where h is height. Height also depends on stem carbon. Supposing that height is proportional to the 2/3 power of stem diameter as specified by buckling theory, and that stem carbon is 1/(1+1/(2/3)) 2/5 •/(α+1) proportional to the product of height and diameter, it follows that h  cs =cs = cs = β cs where β = α/(α+1) and α = 2/3 and β = 2/5 nominally. Then

h c   s  kh   kc h hs and  c  1  c  c  G   s  r  l         kckc hsss   kc rr   kc ll 

This model predicts increasing scaling exponents for stem relative to roots, decreasing exponents for leaf relative to stem, increasing SMF and decreasing RMF and SMF -- as observed:

2 1 1.8 L vs S 0.9 LMF L vs R 0.8 SMF 1.6 S vs R RMF 1.4 0.7 exponents 1.2 0.6

fractions 0.5

1

scaling 0.4 0.8

0.6 mass 0.3 0.4 0.2 0.2 0.1 allometric 0 0 1 10 100 1000 10000 1 10 100 1000 10000 total biomass (arbitrary units) total biomass (arbitrary units)

Interpretation We do not suggest that this model should be directly interpreted as a mechanistic model for predicting changes in allometry during plant growth and neither should be the exact values of scaling exponents or mass fractions. For one, it omits many important features that may influence the economics of carbon allocation, such as the mechanical demands for below- ground anchorage, the effect of leaf investment on hydraulic conductance, the respiratory and hydraulic costs of height growth, the loss of leaf and fine root investments to senescence and the conversion of sapwood to heartwood, and the return of nutrients to the soil from leaf litter

during growth. To incorporate all of these features requires a radically more detailed and mechanistically explicit model, and it is unlikely that any such model will apply generally enough across types of plants and environments to permit general theories of allometric scaling to be deduced. Instead, the analysis above shows that when MST's fundamental assumption about plant carbon economics – namely, that growth is directly proportional to leaf biomass – is minimally elaborated to include qualitative features of the economics of stem and root carbon investment, it quickly emerges that allometric scaling constants should vary continuously and in complex fashion during plant growth.

Simulation methods

We simulated the growth model described above using ks = kr = kl = 1 with initial biomass pool sizes equal to 1/6 so that the total initial biomass was 0.5. For simulations including the saturating positive effect of height, we set kh = 1. In each time step, the marginal product for each biomass pool was computed numerically using a small biomass increment (10-5), and the biomass pool with the greatest marginal product was incremented by the biomass available for allocation, which was computed as the product of G and an arbitrary timestep of 0.3. This ensured that the marginal products remained approximately equal across biomass pools during the simulated growth period.

Table S1. Literature references on which the database is built.

Herbaceous species:

A-E Alameda et al. (2012) Soil Till. Res. 120: 121-129; Ali (2000) Plant Sci. 152: 173-179; Ali et al. (2013) J. Plant Growth Regul. 32: 604-614; Almeida et al. (1999) Plant Soil 210: 159-166; Ambrose & Sciuchetti (1962) J. Pharm. Sci. 51: 934-938; Andrews et al. (1992) Ann. Bot. 70: 271-276; Anten et al. (2003) Ecology 84: 2905-2918; Balachandran et al. (1997) Plant Physiol. 114: 475-481; Bar & Pressman (1996) J. Am. Soc. Hortic. Sci. 121: 649-655; Barker et al. (1996) New Phytol. 133: 637-642; Barnes et al. (1993) Crop Sci. 33: 1041-1046; Barrett & Gifford (1995) J. Biogeogr. 22: 331-339; Bar-Tal et al. (1995) Sci. Hortic. 63: 195-208; Baruch et al. (2000) Int. J. Plant Sci. 161: 107-118; Benner & Bazzaz (1988) J. Ecol. 76: 19-40; Bennett & Runeckles (1977) Crop Sci. 17: 443-445; Boot & Den Dubbelden (1990) Oecologia 85: 115-121; Bourdot et al. (1984) New Phytol. 97: 653-663; Brown et al. (1995) J. Am. Soc. Hortic. Sci. 120: 808-813; Brummett & Sciuchetti (1960) J. Pharm. Sci. 49: 274–277; Bullock (1984) Oecologia 63: 426-428; Bunce (1990) Ann. Bot. 65: 637-642; Carmi et al. (1983) Photosynthetica 17: 240- 245; Carter et al. (1997) New Phytol. 136: 245-253; Causin & Wulff (2003) Can. J. Bot. 81: 152- 163; Chabot (1978) New Phytol. 80: 87-98; Chapin et al. (1989) Oecologia 79: 96-105; Clevering (1997) Wetlands Ecol. Manage. 5: 275-287; Clough et al. (1979a) Oecologia 38: 13- 21; Clough et al. (1979b) Plant Physiol. 64: 25-30; Coleman & Bazzaz (1992) Ecology 73: 1244- 1259; Corre (1983b) Acta Bot. Neerl. 32: 185-202; Cowan & Reekie (2008) Plant Biol. 10: 202- 210; Cramer et al. (1995) J. Exp. Bot. 46: 1569-1577; Cris & Stout (1929) Agric. Exp. Stat. MSC, No 6.; Cunniff et al. (2008) Glob. Change Biol. 14: 576-586; Cure et al. (1987) Bot. Gaz. 148: 67-72; Dai et al. (1992) Crop Sci. 32: 1269-1274; Dale (1964) Ann. Bot. 28: 127-135; De Groot et al. (2001) Plant Cell Environ. 24: 1309-1317; De Pinheiro & Marcelis (2000) Ann. Bot. 86: 1073-1080; Debez et al. (2004,2006) Plant Soil 262: 179-189; Env. Exp. Bot. 57: 285-295; Delgado et al. (1993) J. Exp. Bot. 44: 1-7; DeLucia et al. (1985) Photosynth. Res. 7: 175-184; Den Dubbelden & Oosterbeek (1995) Funct. Ecol. 9: 628-634; Den Hertog et al. (1993) Vegetatio 104/105: 369-387; Den Hertog et al. (1996) Physiol. Plant. 98: 77-88; Detling et al. (1979) Oecologia 41: 127-134; Dias-Filho (2002) Pesq. agropec. Bras. 37: 439-447; Dippery et al. (1995) Oecologia 101: 13-20; Donnelly et al. (2001) New Phytol. 149: 265-271; Dueck et al. (1999) AB-DLO report 207, WUR; Dunn et al. (1987) J. Exp. Bot. 38: 433-441; Elemans (2004) Acta Oecol. 26: 197-202; Eng et al. (1985) J. Hortic. Sci. 60: 389-395; Evans & Hughes (1961) New Phytol. 60: 150-180; Evans & Poorter (2001) Plant Cell Environ. 24: 755-767; Eze et al. (1973) Ann. Bot. 37: 315-329;

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Table S3 Overview of the representation of various plant groups in the database. Data are provided for the total number of observations for herbaceous and woody species, the % of the total observations related to each phylogenetic class, the % of all observations of a phylogenetic class that were made in the field (rather than in a growth chamber, a glasshouse, an Open Top Chamber or in an experimental field), and the total number of species represented by the observations in a phylogenetic class.

Functional # of Phylogenetic % of total % of the # of # of species Type observations class observations observations per in the made in the phylogenetic database field class Herbaceous 2954 Monocots 12.2 0 192

Eudicots 14.2 0 210

Woody 8178 Gymnosperms 33.4 80 108 Basal 0.8 54 23 Angiosperms Monocots 1.2 55 14

Eudicots 37.7 35 643

Intermediate 69 Eudicots 0.6 1 15

Table S4 Allometric scaling exponents as given for all records of all species, and for herbaceous and woody species separately. (a) Standard Major Axis regression (SMA; model 2 regression) for the intercept (α) and slope (β) of the regression of leaf mass (LM) vs. root mass (RM), stem mass (SM) vs. root mass, and leaf mass vs. stem mass, all based on log10-transformed values. The 95% confidence interval for the slope, as well as the r2 of the equation are given. (b) Ordinary least square regression (OLS), tested for linear and quadratic relationships. a is the value for the intercept, b1, b2 and b3 are the values for the linear, the quadratic and the cubic component, respectively. The degrees of freedom was >3000 for herbaceous species and >8,200 for woody species.

(A) Regression α β 95% CI for β r2 Species All LM vs. SM 0.113 0.740 0.738 - 0.742 0.978 LM vs. RM 0.070 0.849 0.847 - 0.851 0.977 SM vs. RM -0.058 1.147 1.145 - 1.149 0.988 Herbaceous LM vs. SM 0.239 0.864 0.855 - 0.872 0.928 LM vs. RM 0.192 0.985 0.972 - 0.991 0.931 SM vs. RM -0.054 1.140 1.128 - 1.153 0.904 Woody LM vs. SM 0.127 0.728 0.725 - 0.730 0.971 LM vs. RM 0.077 0.834 0.831 - 0.837 0.970 SM vs. RM -0.069 1.146 1.143 - 1.149 0.987

(B) Regression a b b b r2 Species 1 2 3 All LM vs. SM 0.213 0.795 -0.0177 - 0.981 LM vs. RM 0.151 0.897 -0.0184 - 0.979 SM vs. RM -0.126 1.144 0.0318 -0.00606 0.989 Herbaceous LM vs. SM 0.216 0.819 -0.0082 0.926 LM vs. RM 0.173 0.918 -0.0219 0.931 SM vs. RM -0.102 1.081 - 0.901 Woody LM vs. SM 0.225 0.790 -0.0221 0.00094 0.977 LM vs. RM 0.110 0.897 -0.00356 0.975 SM vs. RM -0.147 1.138 0.0408 -0.00748 0.990