SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION doi: /nature25783 Supplementary note 1 Description of root functional traits (1) Root diameter (D) measures the width of an individual root. Diameter plays the key role in root foraging strategies 106, and in demining the capacity of a plant to exploit a volume of soil 107. Larger diameter roots have a higher construction cost but benefit from longer average root lifespan 33,108 and greater transport efficiency of water and ions 19. Thin and soft first-order roots have the advantage of efficient soil exploration, but incur the tradeoff cost of sacrificing water conduction, tissue permanence, and the ability to penetrate the soil matrix 109,110. (2) Root tissue density (RTD; g cm -3 ) is calculated as the ratio of root dry mass (M; g) to its volume (V; cm 3 ) assuming that a root is a cylinder, and largely represents the fraction of vascular tissue in a single root segment. RTD is also often related to root growth rates, the physical defense capacity, and lifespan Species with a higher RTD are generally associated with a large proportion of sclerenchyma in root, which may grow slow in stressed environments 113. (3) Root length (L; mm) mainly regulates the absorbing surface area and the capacity to explore and exploit soil resources, thus plays an important role determining the competitive ability of plants 114,115. (4) Specific root length (SRL; cm g -1 ) measures root length (L; cm) production per unit dry mass (M; g), and that has long been used to indicate root length production efficiency 116 : SRL= L M = L V RTD = L ( π L 4 D2 ) RTD = 1 ( π 4 D2 ) RTD (1) 1

2 RESEARCH SUPPLEMENTARY INFORMATION Equation (1) shows that variation in SRL can be explained by two components: root diameter (D) and root tissue density (RTD) 112,117,118. SRL described root benefit in related to biomass investment 114, root proliferation 118,119, and environmental changes 117. (5) Root nitrogen (N) is an indicator of root metabolic activity, and is related to plant growth rate 120, root respiration 121 and root litter decomposition 122. (6) Root carbon (C) is associated with carbon investing strategy in building tissues and maintaining root function 108,112. (7) Root C:N ratio reflects the relative investment of C and N at the tissue level, and indicates the per biomass maintenance costs. It also correlates with the concentration of defense-related chemicals (e.g., lignin, tannin), and absorptive investments (such as proteins) 108,123. (8) Mycorrhizal colonization describes the percent of root length colonized by mycorrhizal fungal structures 124. It is closely related to the plant water and nutrient uptake 10, , as well as defense against pathogens

3 SUPPLEMENTARY INFORMATION RESEARCH Supplementary note 2 Root branching-order based approach For over half a century, the complex branching architecture of the plant fine root system has led to confusion in determining which roots to sample for measuring root traits 9,129. For convenience, most researchers have sampled fine roots according to an arbitrary diameter cutoff (e.g., 2 mm) for comparative root trait studies 11,12,130. In the past decade, this diameter cutoff approach has been gradually replaced by a branch order method, which recognizes the strong linkage between the position of an individual root on the branching fine-root system (or the branch order) and its morphology, anatomy, physiology (nutrient uptake rates and respiration rates) and lifespan 8,9,15,131. It has also been shown that the differences in root traits across species are greatest in first-order roots (the most distal and metabolically most active roots in a root system). Thus, choosing the lowest root orders is often the best method for comparative studies across species of vastly different root architecture and morphology 19,132,

4 RESEARCH SUPPLEMENTARY INFORMATION Supplementary note 3 Lack of pattern for root nitrogen content Consistent with studies base on the traditional definition of fine roots (<2 mm diameter), we found no relationship between root nitrogen vs. root diameter, SRL, or biome (Extend data Fig.1,3a). Nitrogen fixing taxa had slightly elevated root nitrogen 134,135 but there was no overall trend across functional groups (Extended Data Fig.3b). We infer that in contrast to the central role of nitrogen among leaf traits nitrogen plays a relatively minor role in the overall variation of root traits across plant species. References for Supplementary Information 106 Baylis, G. The magnolioid mycorrhiza and mycotrophy in root systems derived from it. (Academic Press, 1975). 107 Fitter, A. H. An architectural approach to the comparative ecology of plantroot systems. New Phytol. 106, (1987). 108 Eissenstat, D. & Yanai, R. The ecology of root lifespan. Adv. Ecol. Res. 27, 1-60 (1997). 109 Rieger, M. & Litvin, P. Root system hydraulic conductivity in species with contrasting root anatomy. J. Exp. Bot. 50, (1999). 110 Bengough, A. G., Croser, C. & Pritchard, J. A biophysical analysis of root growth under mechanical stress. Plant Soil 189, (1997). 111 Ryser, P. The importance of tissue density for growth and life span of leaves and roots: A comparison of five ecologically contrasting grasses. Funct. Ecol. 10, (1996). 112 Roumet, C., Urcelay, C. & Diaz, S. Suites of root traits differ between annual and perennial species growing in the field. New Phytol. 170, (2006). 113 Wahl, S. & Ryser, P. Root tissue structure is linked to ecological strategies of grasses. New Phytol. 148, (2000). Ryser, P. The mysterious root length. Plant Soil 2 4

5 SUPPLEMENTARY INFORMATION RESEARCH 114 Ryser, P. The mysterious root length. Plant Soil 286, 1-6 (2006). 115 Pregitzer, K. S., Kubiske, M. E., Yu, C. K. & Hendrick, R. L. Relationships among root branch order, carbon, and nitrogen in four temperate species. Oecologia 111, (1997). 116 Eissenstat, D. M. Costs and benefits of constructing roots of small diameter. J Plant Nutr. 15, (1992). 117 Ostonen, I. et al. Specific root length as an indicator of environmental change. Plant Biosyst. 141, (2007). 118 Eissenstat, D. M. On the relationship between specific root length and the rate of root proliferation - a field-study using citrus rootstocks. New Phytol. 118, (1991). 119 Hodge, A. The plastic plant: root responses to heterogeneous supplies of nutrients. New Phytol. 162, 9-24 (2004). 120 Comas, L. H. & Eissenstat, D. M. Linking fine root traits to maximum potential growth rate among 11 mature temperate tree species. Funct. Ecol. 18, (2004). 121 Burton, A., Pregitzer, K., Ruess, R., Hendrick, R. & Allen, M. Root respiration in North American forests: effects of nitrogen concentration and temperature across biomes. Oecologia 131, (2002). 122 Fan, P. & Guo, D. Slow decomposition of lower order roots: a key mechanism of root carbon and nutrient retention in the soil. Oecologia 163, (2010). 123 Yuan, Z. Y., Chen, H. Y. H. & Reich, P. B. Global-scale latitudinal patterns of plant fine-root nitrogen and phosphorus. Nat. Commun. 2, (2011). 124 Treseder, K. K. The extent of mycorrhizal colonization of roots and its influence on plant growth and phosphorus content. Plant Soil 371, 1-13 (2013). 125 Fitter, A. H. Costs and benefits of mycorrhizas - implications for functioning under natural conditions. Experientia 47, (1991). 5

6 RESEARCH SUPPLEMENTARY INFORMATION 126 Brundrett, M. C. Coevolution of roots and mycorrhizas of land plants. New Phytol. 154, (2002). 127 Read, D. J. & Perez-Moreno, J. Mycorrhizas and nutrient cycling in ecosystems - a journey towards relevance? New Phytol. 157, (2003). 128 Newsham, K. K., Fitter, A. H. & Watkinson, A. R. Multi-functionality and biodiversity in arbuscular mycorrhizas. Trends Ecol. Evol. 10, (1995). 129 Cannon, W. A. A tentative classification of root systems. Ecology 30, (1949). 130 Matamala, R., Gonzalez-Meler, M. A., Jastrow, J. D., Norby, R. J. & Schlesinger, W. H. Impacts of fine root turnover on forest NPP and soil C sequestration potential. Science 302, (2003). 131 Volder, A., Smart, D. R., Bloom, A. J. & Eissenstat, D. M. Rapid decline in nitrate uptake and respiration with age in fine lateral roots of grape: Implications for root efficiency and competitive effectiveness. New Phytol. 165, (2005). 132 Zadworny, M. et al. Patterns of structural and defense investments in fine roots of Scots pine (Pinus sylvestris L.) across a strong temperature and latitudinal gradient in Europe. Global Change Biol. 23, , (2016). 133 Comas, L. H. & Eissenstat, D. M. Patterns in root trait variation among 25 coexisting North American forest species. New Phytol. 182, (2009). 134 Craine, J. M. et al. Functional traits, productivity and effects on nitrogen cycling of 33 grassland species. Funct. Ecol. 16, (2002). 135 Tjoelker, M. G., Craine, J. M., Wedin, D., Reich, P. B. & Tilman, D. Linking leaf and root trait syndromes among 39 grassland and savannah species. New Phytol. 167, (2005). 6