Grégoire T Freschet
email: gregoire.freschet@sete.cnrs.fr

Catherine Roumet

Louise H Comas

Monique Weemstra

A Glyn Bengough

Boris Rewald

Richard D Bardgett

Gerlinde B De Deyn

PROF David Johnson

Jitka Klimešová

PROF Boris Rewald

Dr M Luke Mccormack

D R Ina

Christin Meier

Iván Dr

Prieto

Marcin Dr

Zadworny

PROF Arthur Gessler

Colleen M Dr

Iversen

D R Johannes

Peter Dr

Ryser

Oscar J Valverde-Barrantes

A Glyn Bengough

Martin Lukac

M Luke Mccormack

Ina C Meier

Loïc Pagès

Hendrik Poorter

Ivan Prieto

Nina Wurzburger

Marcin Zadworny

Agnieszka Bagniewska-Zadworna

Elison B Blancaflor

Ivano Brunner

Sarah E Hobbie

Colleen M Iversen

Liesje Mommer

Catherine Picon- Cochard

Johannes A Postma

Laura Rose

Peter Ryser

Michael Scherer-Lorenzen

Nadejda A Soudzilovskaia

Tao Sun

Alexandra Weigelt

Larry M York

Alexia Stokes

Jitka Klimesova

Iván Prieto

Catherine Picon-Cochard

Root traits as drivers of plant and ecosystem functioning: current understanding, pitfalls and future research needs

Keywords: below-ground ecology, ecosystem properties and processes, environmental gradients, plant functions, root traits, spatial and temporal scales, trait covariation, trait causal relationships

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I. Introduction

Plants are powerful ecosystem engineers. Extending both above-and below-ground, sometimes to a great height and depth, they shape the biosphere and its interactions with the uppermost lithosphere, the hydrosphere and the atmosphere (de Kroon & Visser, 2003;[START_REF] Schenk | Mapping the global distribution of deep roots in relation to climate and soil characteristics[END_REF]. Taken together, the effects of plants on the biosphere, atmosphere, and geosphere are key determinants of terrestrial ecosystem functioning. Below-ground, plant roots and their symbionts are central to the maintenance of multiple ecosystem functions [START_REF] Bardgett | Going underground: root traits as drivers of ecosystem processes[END_REF]Freschet & Roumet, 2017): roots play key roles in the transformation and circulation of elements and mineral/organic compounds across the spheres [START_REF] Prieto | Water release through plant roots: new insights into its consequences at the plant and ecosystem level[END_REF]Freschet et al., 2018b), and particularly in the formation, maintenance and stabilisation of soils [START_REF] Daynes | Development and stabilisation of soil structure via interactions between organic matter, arbuscular mycorrhizal fungi and plant roots[END_REF][START_REF] Dignac | Increasing soil C storage: mechanisms, effects of agricultural practices and proxies[END_REF]. Thus, an advanced mechanistic understanding of the effects of root systems on ecosystem functions has numerous potential applications, such as designing plant mixtures for nutrient retention in agrosystems, for stabilization of hillslopes, etc. [START_REF] Stokes | Desirable plant root traits for protecting natural and engineered slopes against landslides[END_REF][START_REF] Lavorel | A novel framework for linking functional diversity of plants with other trophic levels for the quantification of ecosystem services[END_REF][START_REF] Martin | Plant functional traits in agroecosystems: a blueprint for research[END_REF].

Root systems, among other plant parts, show a tremendous diversity of forms and properties [START_REF] Kutschera | Wurzelatlas mitteleuropäischer ackerunkräuter und kulturpflanzen[END_REF][START_REF] Robinson | Constraints on the form and function of root systems[END_REF][START_REF] Bodner | A statistical approach to root system classification[END_REF][START_REF] Iversen | A global Fine-Root Ecology Database to address belowground challenges in plant ecology[END_REF].

In recent decades, parallel developments in many areas of root research (e.g. morphology, physiology, architecture, biomechanics and anatomy, among others) have brought considerable advances in our understanding of the diversity in root traits and their

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This article is protected by copyright. All rights reserved contribution to plant and ecosystem functioning [START_REF] Freschet | A starting guide to root ecology: strengthening ecological concepts and standardizing root classification, sampling, processing and trait measurements[END_REF]. Such advances are key to strengthening the foundations of current dominating theoretical frameworks, often built on data from the same few easily-measurable traits [START_REF] Mcgill | Rebuilding community ecology from functional traits[END_REF][START_REF] Reich | The world-wide 'fast-slow' plant economics spectrum: a traits manifesto[END_REF]. For example, recent attempts to assemble a diverse set of trait data from a range of disciplines in root science permitted researchers to move from a single root economics spectrum [START_REF] Reich | The world-wide 'fast-slow' plant economics spectrum: a traits manifesto[END_REF][START_REF] Roumet | Root structure-function relationships in 74 species: evidence of a root economics spectrum related to carbon economy[END_REF] that only poorly explained root trait variation and its impact on plant performance [START_REF] Weemstra | Towards a multidimensional root trait framework: a tree root review[END_REF], towards a multidimensional 'root economics space' that further integrates aspects of symbiotic associations and is supported by traits closely related to functioning [START_REF] Bergmann | The fungal collaboration gradient dominates the root economics space in plants[END_REF]. However, despite major progress, numerous gaps remain in our understanding of trait-functioning relationships and we still lack a comprehensive overview of available knowledge that bridges research fields.

Here, sharing expertise from a range of fields in root research, we first synthesise recent advances in our understanding of demonstrated relationships between root traits and plant or ecosystem functioning (section-II, see Tables 1 &2 and Fig. 1 for an overview of this broad assessment). Additionally, two examples are more comprehensively assessed in order to illustrate the multiple direct and indirect roles of root traits as drivers of i) plant functioning, with an investigation of the relationships between root traits and plant nitrogen (N) uptake capacity, and ii) ecosystem functioning, by examining the linkages between root traits and soil reinforcement against shallow landslides (see Tables 3 &4 and Fig. 2 for an overview of these comprehensive assessments). Based on this two-step assessment, we critically evaluate the current strengths and gaps in our knowledge, and identify research challenges for the future. Specifically, we address three main research avenues that offer potential to improve our understanding of trait-function relationships. First, we consider the importance of using an informed selection of traits for exploring root trait-functioning relationships and discuss how sets of currently understudied traits may provide more insights than common, easy-tomeasure traits (section-III). We then discuss how our understanding of trait-trait relationships and hierarchies among traits can help us to advance our knowledge of the synergistic or antagonistic effects of different traits on plant and ecosystem functioning, and lead us one step further in linking genotypes to function (section-IV). Next, we address the opportunities and pitfalls when generalising trait-functioning patterns across plant species, growth forms, environmental contexts, and temporal and spatial scales (section-V). Our two examples of plant and ecosystem functioning are woven through the remainder of this paper to illustrate our purpose.

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II. An overview of trait-functioning relationships: rationale and limitations

To explore relationships between root traits and functions, we performed a broad, multidisciplinary assessment of empirical and demonstrated links between below-ground traits and plant and ecosystem functioning (Tables 1 &2). To do so, we first identified 15 key plant functions (Table 1) and nine ecosystem processes and properties (Table 2) based on their relevance to the functioning of natural and managed ecosystems. Drawing on literature in the fields of plant physiology, ecophysiology, ecology and soil science, we considered reviews and empirical studies where both root traits and functions were measured or conceptualised. We considered traits relevant for 16 research fields (as distinguished in [START_REF] Freschet | A starting guide to root ecology: strengthening ecological concepts and standardizing root classification, sampling, processing and trait measurements[END_REF]Fig. 1d), taking in aspects of root system architecture, physiology, morphology, anatomy, chemistry, biomechanics and biotic interactions. For each function we report: i) the root trait measured and its relationship to a function (positive or negative); ii) below-ground plant entities (e.g. root type, see [START_REF] Freschet | A starting guide to root ecology: strengthening ecological concepts and standardizing root classification, sampling, processing and trait measurements[END_REF] on which the trait would be most relevant to measure; and iii) contextual information explaining the rationale for and degree of confidence in the relationship (Tables 1 &2).

Trait selection was motivated by both the presence of a defined mechanistic relationship and empirical observations under controlled conditions or in situ. However, Tables 1 &2 are not consolidated accounts of demonstrated evidence. Most studies reported here cover only a handful of species; as such, they may rely on fortuitous relationships resulting from interactions among traits (as discussed in section-III) and on context-dependent observations that may not be widely generalizable across multiple species and biomes (see section-IV). In addition, we stress that Tables 1 &2 represent neither an exhaustive list of important traits nor all relevant references, but rather a broad overview of current knowledge where most relationships await confirmation. Highlighted key studies are provided to guide the audience to further reading.

Due to the limited, often contradictory state of current knowledge of root traitfunctioning relationships, we do not attempt to estimate the importance of the relationship but merely indicate current evidence for its existence (i.e. a single trait impacts a specific function). Our understanding of results from past studies is particularly limited by a range of methodological issues. This includes the absence of purposeful selection of complementary traits and root entities (see section-III), the lack of accounting for trait covariation and hierarchy (see section-IV), or the lack of knowledge on the influence of genetic diversity, environmental variation and scaling across temporal and spatial scales (see section-V).

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This article is protected by copyright. All rights reserved Despite these limitations, Tables 1 & 2 are useful because they provide an indication of the range of empirical and theoretical relationships between below-ground traits and plant and ecosystem functioning across research fields; link these relationships to selected references and standardized trait measurement protocols (as described in the handbook of root traits, see [START_REF] Freschet | A starting guide to root ecology: strengthening ecological concepts and standardizing root classification, sampling, processing and trait measurements[END_REF]; and highlight a number of rarely considered traits in order to connect different fields.

III. Trait selection

1. Measuring a complementary range of traits: are we focusing on the right ones?

Recent decades have seen the rise of approaches using a few easily measurable traits to capture plant and ecosystem functioning. Given the difficulties associated with specialized measurements of some key physiological, anatomical or chemical traits, most local-scale studies, which later feed global-scale analyses, make use of 'soft' traits (i.e. easily measurable traits, often vaguely related to a single or a number of functions) only, rather than a range of soft and 'hard' traits (i.e. those difficult to measure, but often more closely related to a precise function) selected on the basis of a comprehensive review of potentially relevant mechanisms or processes (but see for instance [START_REF] Maire | Trade-off between root nitrogen acquisition and shoot nitrogen utilization across 13 co-occurring pasture grass species[END_REF][START_REF] Belluau | Linking hard and soft traits: Physiology, morphology and anatomy interact to determine habitat affinities to soil water availability in herbaceous dicots[END_REF]Freschet et al., 2018a;[START_REF] Ros | What root traits determine grass resistance to phosphorus deficiency in production grassland?[END_REF]. For example, at the time of this survey, the FRED database (the most extensive fine-root trait database to date; [START_REF] Iversen | A global Fine-Root Ecology Database to address belowground challenges in plant ecology[END_REF] comprises a large number of observations for the five traits most easily measured (~5000 entries for root N concentration and classical morphological traits such as root diameter and specific root length, ~3200 for root tissue density), whereas only ~320 entries for indicators of root N uptake (e.g. net ion uptake rate, maximum net ion uptake rate) and ~220 observations for indicators of root exudation (e.g. acid phosphatase activity, carbon exudation rate). Here, we stress that if a trait is widely measured, it does not necessarily mean that it is of key functional importance.

During the construction of Tables 1 &2, many trait-functioning relationships appeared indirect, vaguely justified and/or poorly tested and led us to question the broad relevance of those traits most commonly measured for plant and ecosystem functioning. Moreover, Tables 1 &2 and Fig. 1 underscore that most ecosystem functions are likely influenced by a wider range of traits than typically assumed [START_REF] Mccormack | Building a better foundation: improving root-trait measurements to understand and model plant and ecosystem processes[END_REF][START_REF] Freschet | A starting guide to root ecology: strengthening ecological concepts and standardizing root classification, sampling, processing and trait measurements[END_REF]. In this respect, our review strengthens the idea that the search for simplified and generalizable patterns should not be at the expense of the mechanistic understanding of trait-functioning

Accepted Article

This article is protected by copyright. All rights reserved relationships [START_REF] Shipley | Reinforcing loose foundation stones in trait-based plant ecology[END_REF][START_REF] Belluau | Linking hard and soft traits: Physiology, morphology and anatomy interact to determine habitat affinities to soil water availability in herbaceous dicots[END_REF]. As such, we hope that Tables 1 & 2 will stimulate a debate on the merits of the classical notion that we must, by necessity, choose between studying few traits with a clear 'functional importance' or many easily measured traits [START_REF] Belluau | Linking hard and soft traits: Physiology, morphology and anatomy interact to determine habitat affinities to soil water availability in herbaceous dicots[END_REF]Freschet et al., 2018a).

Root N concentration, one of the most frequently measured root traits, provides a good illustration of the common discrepancy between the frequency of trait measurements and their functional importance. Clearly important for ecosystem N cycling, root N is often measured for its presumed role in determining the overall metabolic activity (Reich et al., 2008;[START_REF] Roumet | Root structure-function relationships in 74 species: evidence of a root economics spectrum related to carbon economy[END_REF] and, by extension, may be assumed to scale up proportionally with specific root uptake activities (e.g. [START_REF] Grassein | Studies of NH4 + and NO3uptake ability of subalpine plants and resource-use strategy identified by their functional traits[END_REF]. For example, above-ground we know that leaf N concentration is indeed strongly linked to leaf photosynthetic capacity, with more than 60% of leaf N contained in leaf photosynthetic compartments [START_REF] Evans | The allocation of protein nitrogen in the photosynthetic apparatus: costs, consequences, and control[END_REF]. However, although root N concentration is a good predictor of specific root respiration (Reich et al., 2008, 67 species, R 2 = 0.69; Roumet et al., 2016, 73 species, R 2 = 0.25) (Fig. 2), the multiple functional roles of root N (including nutrient uptake and assimilation, but also transport, defence compounds and stored N) imply that its use as an indicator of specific activities may remain highly speculative (Table 1, Fig. 2a). Specific root length (SRL) serves as another example of a very commonly measured but little understood 'soft' trait. It is typically interpreted as a large root surface (i.e. equivalent to specific root area) at a low cost of root construction, and is therefore assumed to mirror specific leaf area [START_REF] Reich | The world-wide 'fast-slow' plant economics spectrum: a traits manifesto[END_REF] and act as a gauge for soil resource uptake efficiency [START_REF] Ostonen | Specific root length as an indicator of environmental change[END_REF]. However, while this description is true, it is strongly reductive. First, it is not so much the surface of roots that would matter for below-ground resource uptake, but rather the volume of soil under influence by the root (e.g. the nitrate depletion zone around the root, or the frequency of root encounters during the flow of solutes in the soil), which depends more strongly on the length of roots deployed rather than its surface. Specific root length may thus be better referred to as a proxy for the volume of soil under influence by the root, and will most often be more closely related to soil resource uptake efficiency than specific root area. Second, it is rarely considered that cheaply constructed roots may have a much shorter lifespan [START_REF] Ryser | The importance of tissue density for growth and life span of leaves and roots: a comparison of five ecologically contrasting grasses[END_REF], and therefore, as a system, may have limited ability for long-term resource uptake, unless this trait is combined with a high root turnover rate. Third, SRL is a composite trait determined by the variation in root diameter and root tissue density (Fig. 2) and hence under control of complex internal plant construction trade-offs [START_REF] Kong | Leading dimensions in absorptive root trait variation across 96 subtropical forest species[END_REF][START_REF] Poorter | The limits to leaf and root plasticity: what is so special about specific root length?[END_REF]. Fourth, it remains poorly understood to what extent SRL

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This article is protected by copyright. All rights reserved trades-off with root mass fraction (Freschet et al., 2015a;Weemstra et al., 2020, Fig. 2) and mycorrhizal colonization [START_REF] Mccormack | Physical and functional constraints on viable belowground acquisition strategies[END_REF][START_REF] Bergmann | The fungal collaboration gradient dominates the root economics space in plants[END_REF], and acts in synergy with root hairs [START_REF] Forde | The nutritional control of root development[END_REF] and root branching density [START_REF] Eissenstat | Linking root traits to nutrient foraging in arbuscular mycorrhizal trees in a temperate forest[END_REF] to change the volume of soil explored or exploited by roots (sensu [START_REF] Lambers | Plant nutrient-acquisition strategies change with soil age[END_REF]Freschet & Roumet, 2017). A close inspection of these aspects is needed to resolve why SRL has been sometimes found to positively correlate with N uptake rates across species (Reich et al., 1998;[START_REF] Larson | Seedling root responses to soil moisture and the identification of a belowground trait spectrum across three growth forms[END_REF][START_REF] Grassein | Studies of NH4 + and NO3uptake ability of subalpine plants and resource-use strategy identified by their functional traits[END_REF]Hong et al., 2018, 30 species), but not in other cases [START_REF] Grassein | Relationships between functional traits and inorganic nitrogen acquisition among eight contrasting European grass species[END_REF][START_REF] Bowsher | Fine root tradeoffs between nitrogen concentration and xylem vessel traits preclude unified whole-plant resource strategies in Helianthus[END_REF][START_REF] Ravenek | Linking root traits and competitive success in grassland species[END_REF]Freschet et al., 2018a;Ma et al., 2018, 48 species).

Root N concentration and SRL are just two examples of traits where a more correct, mechanistic framing is key to truly understanding the link between traits and plant and ecosystem functioning. This issue may be inherent to below-ground plant ecology, where the relevance of many 'soft' traits was presumed based on the mechanistic understanding of their above-ground counterparts, but with little scrutiny of their actual functional significance below-ground. Ultimately, the identification of key traits for plant and ecosystem functioning needs to come from larger sets of measurements in future studies that include both 'soft' and 'hard' traits.

Estimating the relative importance of traits

Furthering our mechanistic knowledge of trait-functioning relationships requires not only the identification of traits that are relevant for a function (see Tables 1 &2), but also a consideration of the relative importance of these traits for the function. The relative importance of traits identified in Tables 1 & 2 is sometimes not known and often assumed, but rarely tested. To complicate the picture further, there is ample evidence from case studies that environmental conditions interact to shuffle the relative importance of traits for individual functions, possibly due to variations in costs and benefits of a given plant strategy. For example, the relative importance of a plant's ability to fix N2 in symbiosis with microbes strongly increases as soil N availability decreases, while in turn N2 fixation becomes increasingly constrained as soil P availability decreases (Batterman et al., 2013b). In a second example at the ecosystem level, efficient root hydraulic conductance can rapidly dry wet soil in climates with discontinuous rain events (e.g. [START_REF] Boldrin | Correlating hydrologic reinforcement of vegetated soil with plant traits during establishment of woody perennials[END_REF], and therefore help protect against shallow landslides. However, in climates with prolonged rainy seasons and

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This article is protected by copyright. All rights reserved with soils that are close to saturation for long periods of time, the efficiency of this trait is lost and the mechanical traits become more efficient at reinforcing soil [START_REF] Kim | Vegetation as a driver of temporal variations in slope stability: The impact of hydrological processes[END_REF]. Also, there can be distinct thresholds in the ability of traits to serve functions. For example, along a gradient of soil P availability, the dominant plant species strategy tend to shift from the reliance on thin roots at high P levels, towards increasing reliance on high root hair density and mycorrhizal symbiosis at low P levels, and eventually towards the use of highly specialized structures such as cluster roots on severely P-impoverished soils [START_REF] Lambers | Plant nutrient-acquisition strategies change with soil age[END_REF].

In summary, few studies to date have quantified comprehensive sets of relevant root traits across a range of species with contrasting ability to perform a function, or replicated such setups along environmental gradients (but see first attempts by [START_REF] Belluau | Linking hard and soft traits: Physiology, morphology and anatomy interact to determine habitat affinities to soil water availability in herbaceous dicots[END_REF]Freschet et al., 2018a;[START_REF] Ros | What root traits determine grass resistance to phosphorus deficiency in production grassland?[END_REF][START_REF] Henneron | Plant economic strategies of grassland species control soil carbon dynamics through rhizodeposition[END_REF]. Moreover, most studies do not measure the actual function of interest, but more easily measurable proxies for the function (e.g. 'long-term N accumulation in plants' rather than 'long-term uptake rate'; 'centrifuge model estimate' instead of 'in-situ measurement' of soil shear reinforcement; see Tables 3 &4). Although measuring the actual function often proves challenging, additional efforts may be needed to improve the relatedness of our proxies to the functions.

Considering multiple root types

To fully appreciate and understand the impact of root traits on plant or ecosystem functioning, consideration of what portion of the root system and root types are involved is needed (McCormack et al., 2015a;[START_REF] Klimešová | Belowground plant functional ecology: Towards an integrated perspective[END_REF]. Different parts of a root system may be important for distinct aspects of plant and soil functioning (Freschet & Roumet, 2017). For example, when studying the contribution of vegetation to soil reinforcement against shallow landslides, studying the entire root system is key to capturing the distribution of root diameters that cross the multiple potential shear (rupture) surfaces along a slope [START_REF] Stokes | Desirable plant root traits for protecting natural and engineered slopes against landslides[END_REF]. Thick structural roots act like soil nails, preventing soil collapse due to their mass, bending strength and stiffness. Thin and fine roots anchor plants to deeper soil layers (beneath the shear surface) and need to be strong when held under tension. Although several geotechnical models have considered the contribution of roots, irrespective of root types, to the reinforcement of potential shear planes that lie parallel to the soil surface (Table 4), these models generally overestimate slope stability, highlighting the need to better differentiate between the effects of distinct root types [START_REF] Schwarz | Quantifying lateral root reinforcement in steep slopes from a bundle of roots to tree stands[END_REF][START_REF] Mao | Three-dimensional modelling of slope stability in heterogeneous montane forest ecosystems[END_REF].

Accepted Article

This article is protected by copyright. All rights reserved With respect to N uptake by wheat (Triticum aestivum), average rates of uptake per unit length of root may be only a small proportion of predicted uptake rates [START_REF] Robinson | What limits nitrate uptake from soil? Plant[END_REF], probably due to a combination of physiological differences between individual roots and spatial clustering of root distribution. Using ion-selective microelectrode techniques, the most rapid N uptake was indeed found between 0 and 40 mm behind the root tip, decreasing between 40 and 60 mm [START_REF] Plassard | Local measurements of nitrate and potassium fluxes along roots of maritime pine. Effects of ectomycorrhizal symbiosis[END_REF][START_REF] Miller | Root nitrogen acquisition and assimilation[END_REF]. However, this longitudinal decrease may represent only a 2-to 3-fold difference in uptake rate, with transporter gene expression studies suggesting that mature parts of the root remain significant sites of uptake [START_REF] Miller | Root nitrogen acquisition and assimilation[END_REF][START_REF] Hawkins | Nitrogen uptake over entire root systems of tree seedlings[END_REF]. In maize (Zea mays), a nondestructive method was developed to fit small chambers around short root segments in hydroponics in order to measure starting and ending nitrate concentration to calculate net influx, which allowed simultaneous measurements of several root types and positions along the roots. By comparing 15-day and 20-day old plants, this study showed that maximum uptake rate may increase as the plant N demand increases, and that variation for this rate exists among lateral roots, basal roots, and shoot-borne roots [START_REF] York | Spatiotemporal variation of nitrate uptake kinetics within the maize (Zea mays L.) root system is associated with greater nitrate uptake and interactions with architectural phenes[END_REF]. Overall, despite growing knowledge on how root anatomy differs across root orders, much remains uncertain about how N uptake varies, and how this might differ among herbaceous and woody species (e.g. [START_REF] Hawkins | Nitrogen uptake over entire root systems of tree seedlings[END_REF] and across environments [START_REF] Gessler | Climate and forest management influence nitrogen balance of European beech forests: microbial N transformations and inorganic N net uptake capacity of mycorrhizal roots[END_REF].

These examples illustrate that much effort is required to further our knowledge of how various plant parts relate to specific functions. The spatial distribution of specific type of roots in the soil, and their ability to perform their function, is clearly dependent on the attributes of the rest of the root system. Focusing on trait-functioning relationships of a single root type may provide an incomplete picture of plant functioning and effects on ecosystem functions.

Towards widespread consideration of other types of traits

Our overview of root trait-functioning relationships (Tables 1 &2), and the visual illustration of their interconnections (Fig. 1), suggests that many understudied traits may be crucial for a range of plant functions and ecosystem properties and processes. Three categories of traits are frequently highlighted (Fig. 1d): those associated with mycorrhizal associations, belowground allocation and the spatial distribution of roots. More specifically, among other traits, mycorrhizal association type and colonization intensity, root length density and root mass fraction, root branching density, root hair length and density, vertical root distribution index

Accepted Article

This article is protected by copyright. All rights reserved and maximum rooting depth are particularly represented in our synthesis of trait-functioning relationships (Fig. 1a-c). Described below, these traits can impact plant and ecosystem functioning in several ways:

i) The reliance of plants on different 'types of mycorrhizal fungi' (e.g. [START_REF] Read | Mycorrhizas and nutrient cycling in ecosystemsa journey towards relevance?[END_REF][START_REF] Phillips | The mycorrhizal-associated nutrient economy: a new framework for predicting carbon-nutrient couplings in temperate forests[END_REF] and the 'intensity of root colonization' serve as excellent indicators of the degree to which a plant makes the trade-off between relying on its own functional capability or on symbioses with fungal partners [START_REF] Kong | Nonlinearity of root trait relationships and the root economics spectrum[END_REF][START_REF] Mccormack | Physical and functional constraints on viable belowground acquisition strategies[END_REF][START_REF] Bergmann | The fungal collaboration gradient dominates the root economics space in plants[END_REF]. Such critical determinants of plant resource acquisition and conservation strategies are also increasingly recognized as key drivers of a range of ecosystem properties and processes [START_REF] Soudzilovskaia | Global mycorrhizal plant distribution linked to terrestrial carbon stocks[END_REF].

ii) 'Root mass fraction' (or fine-root mass fraction, rhizome mass fraction, etc.) depicts the relative investment of biomass to specific belowground parts and therefore is a key trait in determining plant performance [START_REF] Wilson | A review of evidence on the control of shoot: root ratio, in relation to models[END_REF][START_REF] Poorter | Biomass allocation to leaves, stems and roots: meta-analyses of interspecific variation and environmental control[END_REF]. In association with SRL and total plant biomass, fine-root mass fraction determines total plant investment in fine-root length, which is a key determinant of the potential biophysical interactions between plants and the soil matrix.

iii) 'Root branching density' is increasingly recognized as a key determinant of root system architecture, with high branching density being typical of more clustered root systems favouring soil particle enmeshment and localised soil resource mining, and pre-emption against competitors [START_REF] Forde | The nutritional control of root development[END_REF][START_REF] Hodge | The plastic plant: root responses to heterogeneous supplies of nutrients[END_REF]. Low branching density, on the other hand, favours soil exploration [START_REF] Eissenstat | Linking root traits to nutrient foraging in arbuscular mycorrhizal trees in a temperate forest[END_REF] and may thus be most effective for the uptake of very mobile soil resources such as nitrate and water (e.g. [START_REF] Pedersen | Modelling diverse root density dynamics and deep nitrogen uptake-A simple approach[END_REF]. iv) Maintaining high 'root hair length and density' is a very efficient way for plants to maintain root contact with soil particles [START_REF] Carminati | Liquid bridges at the root-soil interface[END_REF], facilitate root anchorage and penetration into dense soils [START_REF] Haling | Root hairs improve root penetration, root-soil contact, and phosphorus acquisition in soils of different strength[END_REF][START_REF] Choi | Root hairs enhance Arabidopsis seedling survival upon soil disruption[END_REF], as well as reinforcing root interactions with the soil matrix (e.g. for resource uptake, exudation, connection to N2fixing symbionts, [START_REF] Holz | Root hairs increase rhizosphere extension and carbon input to soil[END_REF]. v) 'Vertical root distribution index' and 'maximum rooting depth' are additional descriptors of plant strategies to occupy soil volume and explore different horizons of soil [START_REF] Freschet | A starting guide to root ecology: strengthening ecological concepts and standardizing root classification, sampling, processing and trait measurements[END_REF]. The localization of roots in soil has straightforward implications for the interactions between plants and soil and the transfer of elements, impacting plant resource acquisition and the recycling or sequestration of organic compounds along the soil profile [START_REF] Jobbágy | The vertical distribution of soil organic carbon and its relation to climate and vegetation[END_REF][START_REF] Poirier | The root of the matter: Linking root traits and soil organic matter stabilization processes[END_REF][START_REF] Mackay | Conifers depend on established roots during drought: results from a coupled model of carbon allocation and hydraulics[END_REF].

Accepted Article

This article is protected by copyright. All rights reserved While this set of traits merits further attention, the primary purpose of drawing up this subjective and non-exhaustive list is to emphasize that many dimensions of root effects on plant and ecosystem functioning require further consideration. Several 'hard' traits important for a range of functions (including some of the above-mentioned traits) present methodological challenges that limit their use (e.g. their study is labour-intensive, is not feasible in the field, requires complex equipment or implies known measurement inaccuracies). These challenges hinder conceptual formalization and testing of traitfunctioning relationships, particularly in connection to other traits. Some of these important, but particularly challenging traits include physiological traits such as i) root exudation rate, ii) root exudate composition, iii) root respiration, iv) root enzymatic activities, v) root nutrient absorption (and the synergistic role of mycorrhizal fungi) and vi) root nutrient resorption processes, which are important determinants of nutrient uptake and cycling, chemical and anatomical aspects of vii) root resistance to pathogens and viii) root resistance to mechanical stresses, and aspects of ix) root persistence and turnover in soils that further impact soil nutrient and ecosystem carbon cycling. While an exhaustive review of recent advances in the measurement of these 'hard' traits is beyond the scope of this synthesis, we emphasize that a range of studies are already bringing improvements that facilitate such challenging measurements (see for instance [START_REF] Phillips | New approach for capturing soluble root exudates in forest soils[END_REF]

IV. Trait-trait relationships

Considering trait inter-relations

The individual effects of root traits on plant and ecosystem functioning are not easy to single out [START_REF] Lavorel | Predicting changes in community composition and ecosystem functioning from plant traits: revisiting the Holy Grail[END_REF][START_REF] Lavorel | A novel framework for linking functional diversity of plants with other trophic levels for the quantification of ecosystem services[END_REF] (Fig. 1,2). The range of trade-offs and synergies typically observed among traits [START_REF] Poorter | Physiological mechanisms in plant growth models: do we need a supra-cellular systems biology approach?[END_REF][START_REF] Roumet | Root structure-function relationships in 74 species: evidence of a root economics spectrum related to carbon economy[END_REF][START_REF] Weemstra | Towards a multidimensional root trait framework: a tree root review[END_REF] suggests that plant internal (construction or evolutionary) constraints are likely to limit the number of possible adaptations of plants to environmental conditions.

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This article is protected by copyright. All rights reserved traits) or synergies (e.g. root bending resistance and root elastic modulus typically covary positively owing to the strong positive influence of lignin and cellulose concentrations on these two traits). The result of these constraints can be seen at both the intra-species and inter-species level. Therefore, a change in the expression of one trait may have several direct consequences for the expression of other traits. This network of inter-relations, as depicted in Fig. 2a and b by causal relationships and trait covariation connectors, is often very complex.

In addition, any trait that helps alleviate a limitation or adapt to a stress, changes the strength of the limitation/stress signal, which may reduce the need for other trait adjustments (Freschet et al., 2018a). As an example of this, Freschet et al. (2015a) showed that in a given environment most plant species tend to achieve similar levels of root length per mass of plant by developing either high SRL or high root mass fraction (depicted as causal links in Fig. 2a).

This observation holds across several levels of soil N availability (Freschet et al., 2015b). In this context, it appears reasonable to assume that under non-extreme resource limitation or stress conditions, different combinations of root trait values (e.g. high SRL and root hair length and density versus high root mass fraction and mycorrhizal colonization intensity) may result in a similar outcome with regard to plant function (e.g. N uptake capacity) [START_REF] Marks | Alternative designs and the evolution of functional diversity[END_REF][START_REF] Weemstra | The role of fine-root mass, specific root length and life span in tree performance: a whole-tree exploration[END_REF].

The variability of plant growth strategies also implies a range of interactions between root traits, with non-additive effects on plant and ecosystem functioning. For example, a species with a deep root system, high reliance on mycorrhiza and low litter decomposability may have a strong positive effect on soil organic carbon stock via deep soil carbon sequestration, whereas a similar species with shallow rooting may have only a marginal effect on soil carbon (e.g. [START_REF] Clemmensen | Roots and associated fungi drive longterm carbon sequestration in boreal forest[END_REF]. Similarly, although a deep rooting species may improve resistance to landslides and water uptake at depth, its effect will be noticeable only if a substantial amount of roots is found at depth (e.g. if it has a high index of vertical root distribution) [START_REF] Stokes | Desirable plant root traits for protecting natural and engineered slopes against landslides[END_REF].

Overall, it remains largely unknown whether syndromes of traits (i.e. consistent patterns of trait combinations; [START_REF] Bergmann | The fungal collaboration gradient dominates the root economics space in plants[END_REF] or syndromes of plastic trait adjustments (i.e. consistent patterns of plastic changes; Freschet et al., 2018) occur along well-characterized resource limitation, stress or disturbance gradients, or whether observed trends are mostly context-dependent (e.g. species-specific, community-specific). The identification of such syndromes may eventually help us summarize the covariation of trait values and their (antagonistic, additive, or synergistic) effects on plant and ecosystem function [START_REF] Lavorel | How fundamental plant functional trait relationships scale-up to trade-offs and synergies in ecosystem services[END_REF][START_REF] Herben | Effects of disturbance frequency and severity on plant traits: An assessment across a temperate flora[END_REF]. It would also help us discriminate between mechanistic

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This article is protected by copyright. All rights reserved and fortuitous trait-functioning relationships. Much remains to be done to evaluate the existence and consistency of such inter-relations. First, only a few causal relationships and indirect covariations (as depicted by black and orange connectors, respectively, in Fig. 2) between root traits have been identified (and even less so across traits from the entire plant).

Second, our knowledge is biased towards the aforementioned set of widely studied root traits (Fig. 2). Third, in complex natural environments, plants are subjected to many co-occurring environmental factors whose interaction is likely to drive trait expression in multiple directions simultaneously (e.g. [START_REF] Kumordzi | Geographic scale and disturbance influence intraspecific trait variability in leaves and roots of North American understorey plants[END_REF]Zhou et al., 2019). This may limit the value of our knowledge of syndromes of traits and plastic trait adjustments recorded across single environmental gradients. Indeed, these trait and environment integrations significantly influence function and fitness landscapes in multidimensional space [START_REF] York | Integration of root phenes for soil resource acquisition[END_REF], but more data are required to fully appreciate the complex relationships that are in place.

Accounting for causal relationships among traits

The functional or categorical grouping of individual root traits as illustrated by the horizontal dimension of Fig. 2 is useful to enhancing our understanding of plant and ecosystem function [START_REF] Mccormack | Building a better foundation: improving root-trait measurements to understand and model plant and ecosystem processes[END_REF]. At the same time, it is important to consider the causal relationships (or hierarchy) among traits, as represented by the vertical dimension of the same Figure (Fig. 2: vertical dimension, [START_REF] Rogers | Regulation of plant root system architecture: implications for crop advancement[END_REF]. Many traits, referred to as composite traits, can be broken down into component (i.e. underlying) traits. For example, SRL emerges from the interaction between root diameter and root tissue density, which are themselves influenced by root cortex thickness and stele diameter (Fig. 2a). Root tissue density is further determined by the cortex and stele anatomical and chemical traits [START_REF] Kong | Nonlinearity of root trait relationships and the root economics spectrum[END_REF]. Composite traits are particularly used because they are seen as concise indicators of plant functioning and often have the most direct influence (i.e. mechanistic link) on ecosystem functioning (see Fig. 2). The drawback is that composite traits are under the influence of several component traits that do not necessarily vary in synchrony (e.g. [START_REF] Poorter | The limits to leaf and root plasticity: what is so special about specific root length?[END_REF], and adjustments to even simple environmental gradients may therefore often be unpredictable. Specific root length is one key example of a trait that may be important for N uptake, but whose response to changes in N availability is highly variable (e.g. [START_REF] Poorter | The limits to leaf and root plasticity: what is so special about specific root length?[END_REF]Freschet et al., 2018a), owing to contrasting responses of its component traits to N availability.

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This article is protected by copyright. All rights reserved An understanding of causal links (or more generally, hierarchical organisation) between root traits is useful for the following three purposes. First, it provides a mechanistic basis (i.e. the hypothesis-based framework) to interpret the outcome of statistical model selection procedures (i.e. the set of variables retained in multivariate models linking traits to functions) or structural equation models. As such, an understanding of trait hierarchical organisation will hold the key to the identification of the most parsimonious sets of traits with strongest influence on the functions. As an example, for defining root N uptake capacity, root diameter is mostly important due to its effect on SRL and its covariation with cortex area fraction (Fig. 2). Second, knowledge of hierarchical relationships aids the identification of component traits whose influence spans several composite traits. With respect to plant N uptake capacity, cortex thickness is one such trait. It was shown to enhance the potential for roots to host mycorrhizal fungi, which is beneficial for root-fungi associations [START_REF] Kong | The nutrient absorption-transportation hypothesis: optimizing structural traits in absorptive roots[END_REF][START_REF] Kong | Nonlinearity of root trait relationships and the root economics spectrum[END_REF]. Cortex thickness also influences root diameter and root tissue density, which together determine SRL (Fig. 2). Therefore, despite being rarely measured, root cortex thickness underlies two of the most widely studied and measured morphological root traits and is of critical importance for the capacity to develop mycorrhizal symbiosis. Third, another key aspect of identifying component traits is the likelihood of being directly linked to plant genes. A better understanding of the component traits' genetics-and its regulation under given environmental conditions-will not only provide an evolutionary explanation of key (composite) traits and their selection, but may also foster breeding for root traits beneficial to a specific plant function. In this context, it would be useful to further differentiate between "genuine" composite traits, that are composed by traits with different (sets of) quantitativetrait loci (QTLs) responsible for each different component trait, from "integrated" composite traits where the underlying component traits are varying in a coordinated way as determined by pleiotropic, highly-linked QTLs or tight hormonal control-with nuances between those two extremes.

V. Generalizing across scales

Generalizing across species, plant growth forms and biomes

Our review of conceptual, experimental and observational studies of 24 aspects of plant and ecosystem functioning (Tables 1 &2), and two detailed examples (Fig. 2a,b; Tables 3 &4), emphasizes that the current knowledge of trait-functioning relationships relies on highly

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This article is protected by copyright. All rights reserved variable numbers of observations covering the range of traits and functions. The majority of these relationships are based on relatively few species from a narrow range of plant growth forms and most have not been replicated along environmental gradients or across contrasting climates and soil types. Some trait-functioning relationships have been established in the field, while others come from pot monoculture or common-garden experiments. In this context, generalising these relationships is hazardous. As discussed above, different sets of species or growth forms may display different syndromes of traits, which further vary along gradients, and may therefore display different trait-function relationships. With respect to direct measurements of soil reinforcement to protect against landslides, only two studies could be found that consider more than three species, and virtually all studies consider only one growth form in one location (Table 4). Regarding N uptake capacity, most studies target herbaceous species at the same growth stage and often grown in hydroponics or pot conditions (Table 3), which questions whether knowledge gained from these highly simplified systems can be generalized to natural systems.

Overall, large differences have been observed across contrasting environmental contexts, such as across biomes. With regard to plant N uptake, we know for example that the importance of N-fixation strongly decreases from early successional to late successional forests of the temperate biome, whereas its importance remains high along similar gradients in the tropics (Batterman et al., 2013a). Mycorrhizal effects on N uptake also vary strongly across biomes, with ectomycorrhizal fungi transferring less N to their hosts in biomes at higher latitudes than in tropical forests [START_REF] Mayor | Ectomycorrhizal impacts on plant nitrogen nutrition: emerging isotopic patterns, latitudinal variation and hidden mechanisms[END_REF]. Such examples illustrate that results gained in one system are unlikely to be directly generalizable to other systems.

Generally, further research bridging species from different plant growth forms and growing in contrasting environmental contexts is strongly needed to better inform our knowledge of trait-function relationships.

Meeting the challenge of up-scaling

Understanding the linkages between functional traits and plant and ecosystem functioning is often most critical at large spatial scales (e.g. entire agroecosystems or natural ecosystems, [START_REF] Suding | Scaling environmental change through the community-level: a trait-based response-and-effect framework for plants[END_REF][START_REF] Martin | Plant functional traits in agroecosystems: a blueprint for research[END_REF]. Several functional trait-based up-scaling approaches have been proposed to link plant traits to ecosystem functioning, including the community-weighted-mean trait approach [START_REF] Lavorel | Predicting changes in community composition and ecosystem functioning from plant traits: revisiting the Holy Grail[END_REF][START_REF] Violle | Let the concept of trait be functional![END_REF] and

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This article is protected by copyright. All rights reserved the pooled-species approach [START_REF] Klumpp | Using functional traits to predict grassland ecosystem change: a mathematical test of the response-and-effect trait approach[END_REF][START_REF] Prieto | Root functional parameters predict fine root decomposability at the community level[END_REF]. In the former, species are individually sampled (or non-destructively analysed), plant traits are measured at the level of individual species and a community trait value is calculated by weighting the trait values measured by the proportion that each species represents in the community (e.g., in terms of biomass or ground area cover). In the latter, pools of plants are sampled (or nondestructively analysed) over given ground area or soil volume and a community trait value is directly measured. In both instances, appropriate sampling resolution is key to capture a mix of plant organs representative of the community (see for example [START_REF] Ottaviani | The neglected belowground dimension of plant dominance[END_REF], as biotic and abiotic variations occur at multiple spatial scales, (e.g. changing spatial trophic networks, soil properties, [START_REF] Tscharntke | Landscape perspectives on agricultural intensification and biodiversityecosystem service management[END_REF].

Whether in the community-weighted-mean trait approach or pooled-species trait approach, effects on ecosystem functioning are typically assumed to be proportional to abundance (which can be expressed per unit root biomass, length or surface) to determine the functioning of the whole system [START_REF] Grime | Benefits of plant diversity to ecosystems: immediate, filter and founder effects[END_REF][START_REF] Garnier | Plant functional markers capture ecosystem properties during secondary succession[END_REF]. However, there are multiple reasons why such an approach can only capture parts of the plant community and ecosystem functioning. Depending on the system: (i) diversity effects, including competition, complementarity and facilitation, can add to the effect of species taken individually (e.g. [START_REF] Hodge | Plant nitrogen capture from organic matter as affected by spatial dispersion, interspecific competition and mycorrhizal colonization[END_REF][START_REF] Santonja | Plant litter diversity increases microbial abundance, fungal diversity, and carbon and nitrogen cycling in a Mediterranean shrubland[END_REF]Mahaut et al., 2019); (ii) some subordinate species can produce disproportionate effects on ecosystem functioning [START_REF] Mariotte | Do subordinate species punch above their weight? Evidence from aboveand below-ground[END_REF]; (iii) interactions across multiple trophic levels can drive plant community and ecosystem function [START_REF] Lavorel | A novel framework for linking functional diversity of plants with other trophic levels for the quantification of ecosystem services[END_REF]; (iv) the relative importance of traits shifts depending on the environmental context (e.g. [START_REF] Lambers | Plant nutrient-acquisition strategies change with soil age[END_REF]; (v) small to large scale heterogeneity in ecosystem composition and function can maintain substantial levels of ecosystem function across all scales [START_REF] Tscharntke | Landscape perspectives on agricultural intensification and biodiversityecosystem service management[END_REF]; and (vi) feedbacks between biotic and abiotic components, critical for ecosystem functioning and stability [START_REF] Veldhuis | Ecological autocatalysis: a central principle in ecosystem organization?[END_REF], are not apparent by considering the biotic components alone. For these reasons, scaling up from species traits or pooled-species traits to ecosystem-level functioning must be done with caution, and especially so in natural and semi-natural systems where biotic and abiotic interactions are even more complex than in low-diversity agricultural fields.

Nonetheless, the endeavour of up-scaling from traits to community and ecosystem yields multiple benefits. Most importantly, it provides a mechanistic framework (using or generating causal hypotheses for observed relationships) to test the contributions of traits (from species or pooled-species) to community and ecosystem functioning [START_REF] Lavorel | How fundamental plant functional trait relationships scale-up to trade-offs and synergies in ecosystem services[END_REF]. Up-scaling also has the potential to fill in the gap between the small-scale

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This article is protected by copyright. All rights reserved mechanistic understanding of reduced systems and large-scale integrative, but mostly descriptive assessments. In that respect, the community-weighted-mean trait and pooledspecies trait approaches represent complementary approaches to tackle the problem at different levels of reductionism. Both approaches have advantages and drawbacks. Clearly, the pooled-species approach is far less time consuming when studying roots and limits the biases associated with estimations of root abundance [START_REF] Ottaviani | The neglected belowground dimension of plant dominance[END_REF] and root species identification. As such, this approach would generally help integrating aspects of both spatial and temporal variation in community traitecosystem functioning relationships (as discussed below), especially in ecosystems with large numbers of dominant and subordinate species.

However, with respect to ecological modelling, since plant community composition varies across geographical location and time, such measurements of community traits are unlikely to be reused to predict ecosystem functioning from the crossing of community traits with species composition databases; as such, species-level traits might be preferred. So far, few studies have tested to what extent the knowledge gained on the linkages between single species or pooled-species functional traits and plant and ecosystem functioning can be used to infer such relationships in complex ecosystems [START_REF] Garnier | Plant functional markers capture ecosystem properties during secondary succession[END_REF][START_REF] Vile | Ecosystem productivity can be predicted from potential relative growth rate and species abundance[END_REF][START_REF] Hales | Modelling biome-scale root reinforcement and slope stability[END_REF][START_REF] Long | Relationships between plant traits, soil properties and carbon fluxes differ between monocultures and mixed communities in temperate grassland[END_REF]. Taking the example of root trait effects on plant N uptake, empirical studies most often measure the physiological ability of distinct species to take up N under controlled conditions (hydroponics or pot experiments, e.g. [START_REF] Maire | Trade-off between root nitrogen acquisition and shoot nitrogen utilization across 13 co-occurring pasture grass species[END_REF][START_REF] Grassein | Relationships between functional traits and inorganic nitrogen acquisition among eight contrasting European grass species[END_REF], or quantify community-wide N uptake based on the budgeting approach (e.g. [START_REF] Finzi | Increases in nitrogen uptake rather than nitrogen-use efficiency support higher rates of temperate forest productivity under elevated CO2[END_REF], 15 N labelling [START_REF] Hong | Which root traits determine nitrogen uptake by alpine plant species on the Tibetan Plateau?[END_REF] or even molecular approaches quantifying gene expression (e.g. [START_REF] Kraiser | A holistic view of nitrogen acquisition in plants[END_REF]. However, between these two extremes, few studies have attempted to explicitly relate ecosystem-scale measurements to individual species trait values (but see [START_REF] Gessler | Field and laboratory experiments on net uptake of nitrate and ammonium by the roots of spruce (Picea abies) and beech (Fagus sylvatica) trees[END_REF][START_REF] Craine | Functional traits, productivity and effects on nitrogen cycling of 33 grassland species[END_REF][START_REF] Soussana | A trade-off between nitrogen uptake and use increases responsiveness to elevated CO2 in infrequently cut mixed C3 grasses[END_REF][START_REF] Soussana | Gemini: A grassland model simulating the role of plant traits for community dynamics and ecosystem functioning. Parameterization and evaluation[END_REF] for attempts with planted grass and tree species).

Interestingly, the reverse approach of down-scaling has sometimes been used successfully, starting from the observation of major differences in functioning between systems, and tracking back the causes to individual root traits. As an example, ectomycorrhizal versus arbuscular mycorrhizal dominated forests give rise to differences in coupled carbon-nitrogen cycling (see [START_REF] Phillips | The mycorrhizal-associated nutrient economy: a new framework for predicting carbon-nutrient couplings in temperate forests[END_REF][START_REF] Wurzburger | Experimental evidence that mycorrhizal nitrogen strategies affect soil carbon[END_REF]Zhu et al., 2018). Nonetheless, a species-level approach of root trait-soil function relationships would be useful to further identify the set of mechanistic linkages involved [START_REF] Wurzburger | From mycorrhizal fungal traits to ecosystem propertiesand back again[END_REF].

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This article is protected by copyright. All rights reserved Another major challenge of up-scaling lies in the adequate characterization of plant community or ecosystem functioning at large scales. For example, soil reinforcement by roots at small scales (e.g. soil cores) is often used to predict resistance to landslides at the hillslopescale, using geotechnical slope-scale models (e.g. [START_REF] Genet | The influence of plant diversity on slope stability in moist evergreen deciduous forest[END_REF], but validation of models in the field is usually limited. Although it is possible to perform controlled, slope-scale experimental tests (e.g. [START_REF] Schwarz | Quantifying lateral root reinforcement in steep slopes from a bundle of roots to tree stands[END_REF], and to physically model scaled-slopes in the laboratory (that reproduce the stress-distribution obtained in large-scale slopes, [START_REF] Sonnenberg | Centrifuge modelling of soil slopes reinforced with vegetation[END_REF][START_REF] Liang | Scaling of the reinforcement of soil slopes by living plants in a geotechnical centrifuge[END_REF], the logistical problems involved render these tests extremely complex to carry out. Nonetheless, whilst these field and laboratory experiments are useful for testing realistic slopes to ultimate-failure, not all important processes or failure mechanisms that operate in the field may be captured. For that reason, future studies need to take particular care to consider the best possible proxies for up-scaling and understanding ecosystem functioning.

Another way to consider scaling belowground trait data within an ecosystem or globally is to improve the representation of root form and function in terrestrial biosphere models [START_REF] Warren | Root structural and functional dynamics in terrestrial biosphere models--evaluation and recommendations[END_REF]. Simulation modelling translates mechanistic understanding to mathematical relations that can be explored in silico [START_REF] Marshall-Colon | Crops in silico: generating virtual crops using an integrative and multi-scale modeling platform[END_REF]. Such models range from the simulation of explicit three-dimensional root architecture and surrounding soil matrix [START_REF] Dunbabin | Modelling root-soil interactions using three-dimensional models of root growth, architecture and function[END_REF], to more simple models scaling up trait measurements to the whole plant [START_REF] Weemstra | The role of fine-root mass, specific root length and life span in tree performance: a whole-tree exploration[END_REF], agricultural systems [START_REF] Rosenzweig | The agricultural model intercomparison and improvement project (AgMIP): protocols and pilot studies[END_REF] or the globe [START_REF] Warren | Root structural and functional dynamics in terrestrial biosphere models--evaluation and recommendations[END_REF]. In recent years, several syntheses have called for an appropriate conceptualization of roots and their role in ecosystem functioning in terrestrial biosphere models [START_REF] Smithwick | Improving the representation of roots in terrestrial models[END_REF][START_REF] Iversen | The unseen iceberg: Plant roots in arctic tundra[END_REF]McCormack et al., 2015b). This approach, sometimes referred to as 'model-experiment' integration (or Mod-Ex) combines current empirical understanding with model conceptualization, parameterization, and validation in an iterative process to improve model representation of the natural world.

While much work remains to be done, empirical input into the ways in which models aggregate or generalize across root functional types or plant species, and the way in which models implicitly or explicitly represent root function, can have large impacts on our understanding of ecosystem processes (Zhu et al., 2016;[START_REF] Mccormack | Building a better foundation: improving root-trait measurements to understand and model plant and ecosystem processes[END_REF]. In the context of crop breeding, for example, many combinations of root traits can be considered in various environments with regard to their effect on a particular function. These combinations can be validated across a restrained set of real-cases, and being used for prioritizing future research directions, similar to the use of digital prototyping in manufacturing [START_REF] York | Functional phenomics: an emerging field integrating high-throughput phenotyping, physiology, and bioinformatics[END_REF]. In

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This article is protected by copyright. All rights reserved global biosphere and climate studies, simulation models can also aid the prioritization of research through sensitivity analyses, for example by identifying key traits whose variation have large consequences for the function of interest (McCormack et al., 2015b). But, most importantly, when tested against empirical data, the results of simulations can discriminate between diverse theoretical models, or reveal (structural or context-dependent) gaps in our mechanistic representation of trait-functioning relationships [START_REF] Song | Significant inconsistency of vegetation carbon density in CMIP5 Earth System Models against observational data[END_REF].

Considering spatial and temporal variation

A range of methodologies have been developed above-ground, such as eddy covariance towers or remote sensing, that provide large amounts of data on certain plant traits and ecosystem functions at an ecosystem scale and across space and time. However, such approaches have low resolution regarding aspects of spatial variability in functioning and are unlikely to extend to belowground traits. Generally, there is growing evidence of strong small-scale variability in root traits [START_REF] Defrenne | Intraspecific fine-root trait-environment relationships across interior douglas-fir forests of western Canada[END_REF][START_REF] Kumordzi | Geographic scale and disturbance influence intraspecific trait variability in leaves and roots of North American understorey plants[END_REF] that may lead to substantial small-scale variability in functioning. Given the overarching importance of soil properties and biotic (e.g. plant-plant; plant-microbes) interactions, and their typically high heterogeneity at small spatial scales [START_REF] Jackson | Geostatistical patterns of soil heterogeneity around individual perennial plants[END_REF][START_REF] Ettema | Spatial soil ecology[END_REF], root trait-function relationships might differ strongly over short distances (e.g. centimetres or metres). To date, it remains unclear how the spatial assemblage of species and root traits at small scales might relate to the effects estimated by species averages. Spatially aggregated data may contain little information on the range of trait values occurring within the plant community, the relative abundance of each value, or the existence of several groups of contrasting trait values (e.g. bimodal distributions of trait values), which hampers our ability to understand their consequences for the functioning of ecosystems (e.g., [START_REF] Valencia | Functional diversity enhances the resistance of ecosystem multifunctionality to aridity in Mediterranean drylands[END_REF][START_REF] Violle | Functional rarity: the ecology of outliers[END_REF].

Likewise, soil properties vary with depth (especially when contrasting soil horizons occur) and characterizing the relative importance of roots and root traits at different depths is therefore necessary to accurately link them to plant and soil functioning [START_REF] Germon | Unexpected phenology and lifespan of shallow and deep fine roots of walnut trees grown in a silvoarable Mediterranean agroforestry system[END_REF][START_REF] Fort | Root traits are related to plant water-use among rangeland Mediterranean species[END_REF]Chitra-Tarak et al., 2019). For example, the capacity for N acquisition generally decreases with soil depth due to a decline in the availability of soil N [START_REF] Wiesler | Root growth and nitrate utilization of maize cultivars under field conditions[END_REF][START_REF] Tückmantel | Root exudation patterns in a beech forest: Dependence on soil depth, root morphology, and environment[END_REF]. These patterns can differ across soil types and plant species: in alpine grasslands on Cambisol, the uptake of N was found to decline sharply from

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This article is protected by copyright. All rights reserved 67% in the top 5 cm of soil to 33% in the 5-15 cm layer below [START_REF] Schleuss | Nitrogen uptake in an alpine Kobresia pasture on the Tibetan Plateau: localization by 15N labeling and implications for a vulnerable ecosystem[END_REF], whereas it was only 44% in the top 30 cm, 32% at 30-60 cm and 24% in the 60-120 cm layer for maize in an agricultural field on Luvisol [START_REF] Wiesler | Root growth and nitrate utilization of maize cultivars under field conditions[END_REF]. Additionally, changes in trait values typically occur across contrasting soil horizons [START_REF] Mccormack | Building a better foundation: improving root-trait measurements to understand and model plant and ecosystem processes[END_REF][START_REF] Trocha | The interactive impact of root branch order and soil genetic horizon on root respiration and nitrogen concentration[END_REF], including, for example, the typical patterns of declining root density [START_REF] Jackson | A global analysis of root distributions for terrestrial biomes[END_REF] and physiological activity [START_REF] Göransson | The vertical distribution of N and K uptake in relation to root distribution and root uptake capacity in mature Quercus robur, Fagus sylvatica and Picea abies stands[END_REF][START_REF] Tückmantel | Root exudation patterns in a beech forest: Dependence on soil depth, root morphology, and environment[END_REF] with depth. As a consequence, most ecologists assume that (physiological, morphological, etc.) trait measurements made on roots from the topsoil are likely to adequately estimate plant N uptake capacity when N resource is concentrated in the topsoil.

However, there are many reasons why such an approximation may be inadequate. First, strong competition for N in the topsoil might make root investment in deeper horizons more profitable, as sometimes observed in biodiversity studies (e.g. [START_REF] Mueller | Root depth distribution and the diversity-productivity relationship in a long-term grassland experiment[END_REF], resulting in more evenly distributed resource uptake across the soil profile. Second, soil N availability interacts with other soil resources, particularly water. Seasonal fluctuations of soil water availability across the soil profile following, for example, changes in water table level and precipitation patterns may reverse the N availability gradient along the profile [START_REF] Prieto | Water release through plant roots: new insights into its consequences at the plant and ecosystem level[END_REF]. As such, a good characterization of spatial variations in soil properties (vertically, but also sometimes horizontally; [START_REF] Březina | Nutrient patches are transient and unpredictable in an unproductive mountain grassland[END_REF], integrated over long periods of time, might be needed to guide a sound root sampling design (and the measure of e.g., physiological and morphological traits) from the range of soil layers that matter for N uptake. Also, architectural traits or traits representing (vertical and horizontal) root distribution may be important predictors of the match between root presence and N availability [START_REF] Freschet | A starting guide to root ecology: strengthening ecological concepts and standardizing root classification, sampling, processing and trait measurements[END_REF].

There is also growing evidence that, in parallel to seasonal changes in environmental conditions, such as soil resource availability [START_REF] Chitra-Tarak | The roots of the drought: Hydrology and water uptake strategies mediate forest-wide demographic response to precipitation[END_REF][START_REF] Březina | Nutrient patches are transient and unpredictable in an unproductive mountain grassland[END_REF] or soil organism community composition and activity [START_REF] Bardgett | A temporal approach to linking aboveground and belowground ecology[END_REF], root trait values vary temporally at both the species and community levels (e.g. [START_REF] Picon-Cochard | Effect of species, root branching order and season on the root traits of 13 perennial grass species[END_REF][START_REF] Zadworny | Seasonal variation in chemistry, but not morphology, in roots of Quercus robur growing in different soil types[END_REF]. For example, seasonal changes in carbohydrate concentration of below-ground organs affects plant resprouting ability during some parts of the growing season in temperate regions, a feature often used to improve the efficiency of mechanical control of weeds [START_REF] Sosnová | To resprout or not to resprout? Modeling population dynamics of a root-sprouting monocarpic plant under various disturbance regimes[END_REF]. Many root traits are also dependent on the stage of root system development (e.g. architectural traits such as root branching density, coarse to fine root ratio; [START_REF] Freschet | A starting guide to root ecology: strengthening ecological concepts and standardizing root classification, sampling, processing and trait measurements[END_REF] and root age (e.g. [START_REF] Volder | Rapid decline in nitrate uptake and respiration with age in fine lateral roots of grape: implications for root efficiency and competitive effectiveness[END_REF]. Within a single root axis of maize, for example, tensile strength can vary by about 1.5 orders of magnitude, being greatest in the older root tissue far from the root apex [START_REF] Loades | Effect of root age on the biomechanics of seminal and nodal roots of barley (Hordeum vulgare L.) in contrasting soil environments[END_REF]. This phenomenon is

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This article is protected by copyright. All rights reserved particularly true for woody species, whose architecture and size can change dramatically during their life, with many consequences for trait values and their impact on ecosystem functioning. The importance of ontogenetic stage however also applies to herbaceous species (both annual and perennial) even after reaching maturity, for example due to changes in resource accumulation in roots or rhizomes. Additionally, root phenology differs strongly among species [START_REF] Mccormack | Variability in root production, phenology, and turnover rate among 12 temperate tree species[END_REF], growth forms (Blume-Werry et al., 2016) and biomes (Abramoff & Finzi, 2014). In extreme cases, some species may display no or few absorptive roots at specific times of the year, with periodic flushes of new relatively shortlived fine roots at times of resource availability, as seen in arid climate [START_REF] Liu | Life span and structure of ephemeral root modules of different functional groups from a desert system[END_REF]. In cold climate with short growing season, however, species with long-lived overwintering root systems may be more successful than species with fall-senescing root systems that are produced for each growing season anew [START_REF] Courchesne | Regional distribution patterns of wetland monocots with different root turnover strategies are associated with local variation in soil temperature[END_REF]. Similarly, long-lived roots and rhizomes may contribute better to soil reinforcement against landslides than ephemeral roots by providing a more consistent contribution to improve soil strength.

A better understanding of root phenology is therefore key to the meaningful measurement of root trait values (in relation to the focal function) and our understanding of temporal variation in root trait effects on plant and ecosystem functioning. The timing of root sampling must be carefully considered, so as to match the period when the focal function is most relevant. For example, in ecosystems defined by high seasonality, measuring root traits at the peak of plant productivity (sometimes halfway between the seasonal increase and reduction in growth activities) may be a reasonable benchmark for approximating the relationship between root traits and plant nutrient uptake capacity. However, the timing of nutrient uptake is rarely examined (but see [START_REF] Trinder | A new hammer to crack an old nut: interspecific competitive resource capture by plants is regulated by nutrient supply, not climate[END_REF][START_REF] Jesch | Below-ground resource partitioning alone cannot explain the biodiversity-ecosystem function relationship: A field test using multiple tracers[END_REF][START_REF] Dovrat | Symbiotic dinitrogen fixation is seasonal and strongly regulated in water-limited environments[END_REF] and may not be directly proportional to plant growth rate. Further, some studies suggest that N can be taken up as soon as it is available [START_REF] Jackson | Roots, nitrogen transformations, and ecosystem services[END_REF], suggesting that a good match between plant uptake capacity and the temporality of N fluxes is of critical importance for N uptake (e.g. [START_REF] Edwards | Nitrogen uptake by Carex aquatilis during the winterspring transition in a low Arctic wet meadow[END_REF]. Regarding the capacity of plants to provide resistance against landslides, it would be best to measure root traits at the time of the year when landslides are most frequent, e.g., when soil is saturated, during the rainy season (in tropical systems) or during snow melt [START_REF] Stokes | Desirable plant root traits for protecting natural and engineered slopes against landslides[END_REF], or to differentiate between relationships measured at different times of the year.

Another consideration relates to the temporal variation in species composition within ecosystems, for example during succession or in response to changes in land use. Plant effects on ecosystem functioning can last for long periods after changes in plant community

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This article is protected by copyright. All rights reserved composition have occurred [START_REF] Fraterrigo | Effects of past land use on spatial heterogeneity of soil nutrients in southern Appalachian forests[END_REF] and mismatches between traits and function are therefore likely to be observed in rapidly changing ecosystems [START_REF] Foster | The importance of land-use legacies to ecology and conservation[END_REF]. In the same way, plant species, and their root systems, that established first at a location may not only influence the rooting patterns of other species, but also disproportionately drive the observed relationships between traits and functioning [START_REF] Delory | When history matters: The overlooked role of priority effects in grassland overyielding[END_REF].

In summary, knowledge of spatial and temporal variation in root traits and their effects, over different spatial and temporal scales, is especially needed to allow more informed recommendation on the location and timing of measurements. Hierarchical spatial sampling and sequential sampling would provide invaluable information on the spatial and temporal fluctuation of root traits and their impact on ecosystem functioning.

Of intra-versus interspecific variation and the use of databases

Ecologists have identified and measured phenotypic traits in a wide variety of species, either under laboratory conditions or in the field. Various attempts have been made to include these data into comprehensive/inclusive databases considering plant traits per se [START_REF] Kleyer | The LEDA Traitbase: a database of life-history traits of the Northwest European flora[END_REF][START_REF] Iversen | A global Fine-Root Ecology Database to address belowground challenges in plant ecology[END_REF][START_REF] Kattge | TRY plant trait databaseenhanced coverage and open access[END_REF] as well as the plant symbiotic relationships with mycorrhizal fungi [START_REF] Soudzilovskaia | FungalRoot: global online database of plant mycorrhizal associations[END_REF] and with N-fixing bacteria [START_REF] Tedersoo | Global database of plants with root-symbiotic nitrogen fixation: NodDB[END_REF]. Although below-ground traits are still strongly underrepresented in global compilations, especially regarding organs other than fine roots [START_REF] Klimešová | Belowground plant functional ecology: Towards an integrated perspective[END_REF], such databases represent a large amount of trait data that can be related to vegetation composition [START_REF] Bruelheide | sPlot -A new tool for global vegetation analyses[END_REF] and climate and soil maps. Consequently, relationships between root traits and ecosystem functioning can now be addressed at global scales (e.g. [START_REF] See | Global patterns in fine root decomposition: climate, chemistry, mycorrhizal association and woodiness[END_REF].

However, in global analyses, one trait value per species is generally considered and averaged over all available data, under the assumption that the average will be a good reflection of the 'inherent' trait for a given species. This generalisation is made even though trait expression is adjusted to the specific environmental condition that plants experience [START_REF] Valladares | Quantitative estimation of phenotypic plasticity: bridging the gap between the evolutionary concept and its ecological applications[END_REF]. Root trait values can strongly differ between plants grown in laboratory versus field experiments [START_REF] Poorter | Pampered inside, pestered outside? Differences and similarities between plants growing in controlled conditions and in the field[END_REF], for instance as a consequence of different environmental conditions [START_REF] Li | Diverse belowground resource strategies underlie plant species coexistence and spatial distribution in three grasslands along a precipitation gradient[END_REF][START_REF] Kumordzi | Geographic scale and disturbance influence intraspecific trait variability in leaves and roots of North American understorey plants[END_REF], along gradients of plant diversity or density with different types of plant-plant interactions [START_REF] Salahuddin | Root order-based traits of Manchurian walnut & larch and their plasticity under interspecific competition[END_REF], or with changing interactions between trophic levels [START_REF] Huber | A belowground herbivore shapes root defensive chemistry in natural plant populations[END_REF]. [START_REF] Ostonen | Specific root length as an indicator of environmental change[END_REF]

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This article is protected by copyright. All rights reserved showed for example that intraspecific variation of SRL can be as high as 10-fold across a large environmental gradient. Not accounting for such differences between sites may be one of the key reasons for low predictability of trait-functioning relationships in functional ecology [START_REF] Shipley | Reinforcing loose foundation stones in trait-based plant ecology[END_REF].

Due to the potential for large differences between traits and their level of intraspecific variability, getting a clearer view on which traits are most variable or invariant would be critical for data reuse in syntheses of trait-functioning relationships [START_REF] Funk | Revisiting the Holy Grail: using plant functional traits to understand ecological processes[END_REF][START_REF] Mccormack | Building a better foundation: improving root-trait measurements to understand and model plant and ecosystem processes[END_REF]. For above-ground traits, intraspecific variation has only recently begun to be properly addressed across large numbers of species (e.g. [START_REF] Siefert | A global meta-analysis of the relative extent of intraspecific trait variation in plant communities[END_REF]. For root traits, it may be some time before we have a good insight into the contribution of genetic and environmental factors to trait variation [START_REF] Klimešová | Is the scaling relationship between carbohydrate storage and leaf biomass in meadow plants affected by the disturbance regime?[END_REF]. The complexity of the issue is increased further when one considers the importance of genotype-genotype interactions of plants and root-microbial symbionts, which can also have substantial effects on trait expression and key functions [START_REF] Johnson | The importance of individuals: intraspecific diversity of mycorrhizal plants and fungi in ecosystems[END_REF]. Overall, while the characterisation of trait intraspecific variability is critical, it must be stressed that a good characterisation of phenotypic traits also depends on a good characterisation of environmental conditions experienced by plants. This is especially true below-ground where the small-scale heterogeneity of soils limits the value of large-scale databases (Freschet et al., 2017).

VI. Conclusion and perspectives

Our overview of root trait-functioning relationships has raised seven main insights: 1) Below-ground traits with the widest importance in plant and ecosystem functioning are not necessarily those that are the most commonly measured. Meanwhile, the relevance of commonly measured (soft) traits to plant and ecosystem functioning is often indirect and insubstantial, or requiring further testing.

2) Assessing the relative importance of traits for functioning requires quantifying a comprehensive range of functionally relevant traits (on different root entities), including hard traits, from a diverse range of species, as well as replication across environmental gradients or contrasting environmental contexts.

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This article is protected by copyright. All rights reserved 3) Establishing causal links between root traits provides a mechanistic basis (i.e. the hypothesis-based framework) to interpret the outcome of statistical model selection procedure (i.e. the set of variables retained in multivariate models linking traits to functions) or structural equation models. As such, it holds the key to identifying the most parsimonious sets of traits with strongest influence on the functions. 4) Accounting for causal relationships among traits is key to identifying the component traits that link most strongly with a limited set of genes on the one hand, and plant or ecosystem functioning on the other, and therefore to inform us of potential linkages between genotypes and functioning. 5) Investigating syndromes of traits and syndromes of trait plastic adjustments will help us identify the linkages between 'soft' and 'hard' traits, in order to demonstrate when and to what extent 'soft' traits can confidently be used as proxies for 'hard' traits. 6) Our ability to scale-up from root, to plant, to species, to community and ecosystem functioning requires more critical investigation and comprehensive experimental/empirical tests, and, in some cases, the incorporation of spatio-temporal variation as well as belowground process conceptualization and testing within the framework of terrestrial biosphere models. 7) Accounting for (the often large) intra-specific variation in trait-functioning relationships in global models requires databases with well contextualized data (e.g. locally measured soil parameters).

Another major contribution of this synthesis lies in the broad overview of root trait-function relationships gathered within Tables 1 &2. These Tables give an overview of both the range of effects that root traits can have on ecosystem functioning and the range of traits potentially required to adequately capture the effects of roots on most plant functions and ecosystem properties and processes. They provide key references on multiple topics, which should benefit to all who want to broaden their view of root ecology. These Tables further highlight several functionally important, but rarely considered traits from various research fields.

Overall, this synthesis represents a close companion to the recent description of standardized measurement protocols for a substantial set of root traits [START_REF] Freschet | A starting guide to root ecology: strengthening ecological concepts and standardizing root classification, sampling, processing and trait measurements[END_REF].

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This article is protected by copyright. All rights reserved These two syntheses elucidate connections between the multiple and at times secluded fields of root ecological research and, as such, are meant to inspire novel multidisciplinary approaches. They should encourage researchers more familiar with above-ground aspects of plant ecology to integrate below-ground concepts into their vision of trait-functioning relationships. While we purposely limited our review to below-ground aspects only, we cannot stress enough that these relationships should be considered for entire plants, whenever possible, since plant impacts on (plant and ecosystem) functioning often rely on the integration of both above-and below-ground traits.

Finally, this synthesis brings a range of arguments that call for the design of more comprehensive studies. Studies tackling some, if not all of the above recommendations can be designed that limit the fortuitous, indirect and context-dependent nature of gathered results (as opposed to studies measuring few traits on few species in one single context). We believe that such a set of recommendations will be instrumental in moving towards an integrated, mechanistic knowledge of trait-functioning relationships and open the way to safe applications for ecosystem and agroecosystem management. Achieving a more mechanistic understanding of multivariate trait-functioning relationships will further help us strengthen (or reconsider) the foundations of current dominating theoretical frameworks, often built on data from few soft traits.

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Supporting Information

Additional Supporting Information may be found online in the Supporting Information tab for this article: Notes S1. Full list of references for papers cited in Tables 1,2, 3 & 4.

Tables Table 1. Broad, multidisciplinary assessment of theoretical and demonstrated links between below-ground traits and 15 aspects of plant functioning.

PLANT FUNCTIONS CC Belowground traits Entity of interest References (examples of) Rationale

Soil space occupancy (from explorative to exploitative strategies) This function includes both exploration and exploitation strategies (whose traits generally trade-off).

Maximum rooting depth* (explorative)

Whole root system Thorup-Kristensen, 2001;Maeght et al., 2013;Fan et al., 2017 Reflects the potential range of soil layers colonized by roots.

Lateral rooting extent* (explorative)

Whole root system Schenk & Jackson, 2002a Reflects the potential area of ground colonized by roots.

Horizontal* and vertical root distribution index* (explorative)

Whole root system, fine-roots Gale & Gringal, 1987;[START_REF] Jackson | A global analysis of root distributions for terrestrial biomes[END_REF] A homogeneous distribution below the soil surface and across depths is typical of an explorative rather than an exploitative strategy.

Root length density* (exploitative)

Whole root system, fine-roots Eissenstat, 1992;Robinson et al., 1994;Reich et al., 1998;[START_REF] Ravenek | Linking root traits and competitive success in grassland species[END_REF] Increases the spatial coverage of a given soil volume.

Root mass fraction* (exploitative)

Whole root system, fine-roots [START_REF] Poorter | Biomass allocation to leaves, stems and roots: meta-analyses of interspecific variation and environmental control[END_REF]Freschet et al., 2015 Increases the proportional investment of plants towards the root system or specific parts of the root system.

Specific root length* (explorative or exploitative)

Whole root system, fine-roots Bauhus & Messier, 1999;[START_REF] Ostonen | Specific root length as an indicator of environmental change[END_REF] Increases the length of root exploring or exploiting the soil per unit root mass invested.

Root branching density* (exploitative)

Whole root system, absorptive roots Wiersum, 1958;Fitter & Stickland 1991;Larigauderie & Richards, 1994;[START_REF] Eissenstat | Linking root traits to nutrient foraging in arbuscular mycorrhizal trees in a temperate forest[END_REF]Zhao et al., 2018 ;Lynch et al., 2019 Typically increases with soil resource patchiness as very thin roots tend to proliferate (strong increase in root branching density) in nutrient-rich hotspots. While higher branching density increases local soil exploitation, lower branching might enable larger soil volume exploration.

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Root elongation rate* (explorative or exploitative)

First-order roots [START_REF] Forde | The nutritional control of root development[END_REF]Rewald & Leuschner, 2009;[START_REF] Eissenstat | Linking root traits to nutrient foraging in arbuscular mycorrhizal trees in a temperate forest[END_REF] On pioneer roots, measures the capacity of root systems to send roots to depth (explorative). On absorptive roots, characterizes the capacity of root systems to respond to fluctuating resource availability (exploitative).

Time of root growth initiation* First-order roots Langlois et al., 1983;Eissenstat & Caldwell, 1988 Measures the capacity of root systems to pre-occupy soil patches before competitors.

Root branching angle* (explorative)

Highest order roots Trachsel et al., 2013;[START_REF] York | Integration of root phenes for soil resource acquisition[END_REF]Miguel et al., 2015 Larger (i.e. steeper) The longer lateral spread by clonal growth organ (stolon, rhizome) the farther away (from older roots) new roots must be established.

Plant N acquisition

See traits associated to "Soil space occupancy" (+)

Whole root system, absorptive roots [START_REF] Maire | Trade-off between root nitrogen acquisition and shoot nitrogen utilization across 13 co-occurring pasture grass species[END_REF]Simon et al., 2017;Freschet et al., 2018 Most "Soil space occupancy" traits can be important for this function as they determine the temporal and spatial localisation of roots in soil and the efficiency of soil exploration and exploitation.

Net N uptake rate* (+) Whole root system, absorptive roots Garnier, 1991;Poorter et al., 1991;Garnier et al., 1998 When measured on short time periods (from hours to days), this measure primarily represents plant N uptake. Over longer periods (days to months) this measure also takes into account N loss due to leaching, herbivory and senescence.

Michaelis-Menten constant (Km)* (+)

Whole root system, absorptive roots Robinson et al., 1994;Miller et al., 2007;[START_REF] Grassein | Relationships between functional traits and inorganic nitrogen acquisition among eight contrasting European grass species[END_REF] The Km is a measure of the affinity of a transport system for its substrate; the lower the Km the faster nutrients can be taken up at low availability.

Ability to fix N* (+) Nodules Sprent, 2009;Afkhami et al., 2018;[START_REF] Tedersoo | Global database of plants with root-symbiotic nitrogen fixation: NodDB[END_REF] Provides N to the plant from atmospheric source N2 via microbial root symbionts.

Nitrogen fixation rate* (+) Nodules Carlsson & Huss-Danell, 2003;Batterman et al., 2013a;Yelenik et al., 2013;Ament et al., 2018 Increases the rate of atmospheric N acquisition.

Mycorrhizal association type* Absorptive roots [START_REF] Read | Mycorrhizas and nutrient cycling in ecosystemsa journey towards relevance?[END_REF]Read et al., 2004;Lambers et al., 2009;[START_REF] Phillips | The mycorrhizal-associated nutrient economy: a new framework for predicting carbon-nutrient couplings in temperate forests[END_REF]Liese et al., 2018;Pellitier & Zak, 2018 Different mycorrhizal types have different enzymatic capacities and ability to explore soil volumes and thereby different abilities to take up N. Also, AM, ECM, and ERM fungi represent a gradient from limited saprotrophic capabilities and greater reliance on inorganic N as primary N source to the ability to produce extracellular enzymes and greater use of increasingly complex organic N forms.

Root hair length* and density* (+)

Absorptive roots Robinson & Rorison, 1987;Freschet et al., 2018 Root hairs increase the absorptive surface area of non-woody roots, which is important for N uptake as well as uptake of other nutrients.

Ratio of absorptive to transport roots* (+/-) Fine-roots Schneider et al., 2017;[START_REF] Trocha | The interactive impact of root branch order and soil genetic horizon on root respiration and nitrogen concentration[END_REF] Increases N uptake rate. However, root cortical senescence can also increase N reallocation from senescing tissue and reduce root respiration and root N requirements.

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Mycorrhizal colonization intensity* (+)

Absorptive roots Miller et al., 1995;[START_REF] Hodge | Plant nitrogen capture from organic matter as affected by spatial dispersion, interspecific competition and mycorrhizal colonization[END_REF]Treseder, 2013 Mycorrhizal fungi are physiologically and morphologically welladapted to acquire N from soil. The colonization intensity provides a first approximation of the association between the plant and mycorrhizal partner. However, it should be noted that there is still significant variation in the potential benefit provided by the fungi based on the fungi identity, the total hyphal production and the local environmental context.

Root cortical aerenchyma (+/-) Absorptive roots Postma & Lynch, 2011;Schneider et al., 2017 Decreases radial N transport but increases nutrient uptake efficiency by decreasing metabolic costs.

Maximum net uptake capacity (Imax)* (+)

Absorptive roots Robinson et al., 1994;Garnier et al., 1998;[START_REF] Grassein | Studies of NH4 + and NO3uptake ability of subalpine plants and resource-use strategy identified by their functional traits[END_REF] Imax represents a potential rate at non-limiting substrate availability that might, however, not be fully expressed under in situ conditions.

Mycorrhizal hyphal length (+) Absorptive roots Miller et al., 1995;Chen et al., 2016;[START_REF] Mccormack | Physical and functional constraints on viable belowground acquisition strategies[END_REF] The hyphal length associated with a colonized root provides a closer approximation of both the potential benefit and cost of the mycorrhizal symbiosis than colonization intensity alone.

Specific root respiration* (+) Absorptive roots Poorter et al., 1991;Reich et al., 1998;Rewald et al., 2016 Root respiration is related simultaneously to maintenance, growth and nutrient uptake of roots and is therefore inconsistently linked to nutrient uptake. It also varies with N form.

Root N concentration (+) Absorptive roots Loqué & von Wirén, 2004;[START_REF] Grassein | Relationships between functional traits and inorganic nitrogen acquisition among eight contrasting European grass species[END_REF][START_REF] Grassein | Studies of NH4 + and NO3uptake ability of subalpine plants and resource-use strategy identified by their functional traits[END_REF] Root nitrogen is involved in all metabolic processes related to N uptake but is also stored in roots and included in root defence compounds and is therefore inconsistently linked to nutrient uptake.

Plant P acquisition

See traits associated to "Soil space occupancy" (+)

Whole root system, absorptive roots Lynch et al., 2011;Laliberté et al., 2015;[START_REF] Ros | What root traits determine grass resistance to phosphorus deficiency in production grassland?[END_REF] Most "Soil space occupancy" traits can be important for this function.

Net P uptake rate* (+) Whole root system, absorptive roots Itoh, 1987;Föhse et al., 1988 When measured on short time periods (from hours to days), this measure primarily represents plant P uptake. Over longer periods (days to months) this measure also takes into account P loss due to leaching, herbivory and senescence.

Mycorrhizal association type* Absorptive roots Read, 1991;[START_REF] Read | Mycorrhizas and nutrient cycling in ecosystemsa journey towards relevance?[END_REF]Philipps et al., 2013;Lambers et al., 2009 Distinct mycorrhizal types have differing capacity to extract P from soils. AM fungi have greater influence on plant P acquisition (representing up to 90% of plant P uptake) than ECM fungi (up to 70%). AM fungal extramatrical mycelia express specific transporters to take up Pi from the periarbuscular space (i.e., they bypass roots). ECM and ERM fungi can access organic forms of P that are not available to AM fungi.

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This article is protected by copyright. All rights reserved Lambers et al., 2012;Ryan et al., 2014;Zhang et al., 2016 Excretion of acidifying/chelating compounds (e.g., citric acid, malic acid) enhances the solubility of inorganic P, although evidence exists mostly for Proteaceae and crops.

Mycorrhizal hyphal length (+) Absorptive roots Miller et al., 1995;Laliberté et al., 2015;Chen et al., 2016;[START_REF] Mccormack | Physical and functional constraints on viable belowground acquisition strategies[END_REF] The amount of hyphal length associated with a colonized root provides a closer approximation of both the potential benefit and cost of the mycorrhizal symbiosis than colonization intensity alone.

Michaelis-Menten constant (Km)* (+)

Whole root system, absorptive roots Itoh, 1987;Lambers et al., 2006 The Km is a measure of the affinity of a transport system for its substrate; the lower the Km the faster nutrients can be taken up at low availability. However, the diffusion of inorganic phosphate in soil is the key limiting factor for P uptake so that kinetic parameters of the P-uptake system may have only small effects on the overall uptake capacity of plants.

Plant water acquisition

See traits associated to "Soil space occupancy" (+)

Whole root system, absorptive roots [START_REF] Fort | Root traits are related to plant water-use among rangeland Mediterranean species[END_REF]Chitra-Tarak et al., 2019 Most "Soil space occupancy" traits can be important for this function, especially in soils with heterogeneous water distribution.

Root hair length* and density* (+)

Absorptive roots Segal et al., 2008;[START_REF] Carminati | Liquid bridges at the root-soil interface[END_REF] Improve the contact of roots with water films of soil particles.

Cortical thickness* (-) Absorptive roots

Huang & Eissenstat, 2000;Comas et al., 2012 Thinner cortex resulting in less impedance to water movement towards the stele.

Fraction of passage cells in exodermis* (+)

Absorptive roots Enstone & Peterson, 1992;Peterson & Enstone, 1996;Huang et al., 1995;Peterson & Waite, 1996 Higher density of passage cells enhances water movement towards the stele.

Mycorrhizal colonization intensity* (+)

Absorptive roots Augé et al., 2001;Querejeta et al., 2003;Querejeta et al., 2012;[START_REF] Prieto | Root functional parameters predict fine root decomposability at the community level[END_REF] Allows water transfer to the plant and improves root contact with the soil.

Hydraulic conductance* (+) Whole root system, fine-roots Muhsin & Zwiazek, 2002;Eldhuset et al., 2013;Zadworny et al., 2018 Increases the potential flow of water from the roots to upper parts of the plant.

Vulnerability to embolism (-)

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This article is protected by copyright. All rights reserved CC: colour code, in dark blue: trait of prime importance for performing the plant function in at least some environmental conditions; medium blue: trait of secondary importance in at least some environmental conditions; light blue: trait of potential but unknown importance due to missing or low experimental evidence. * refers to traits whose measurement protocols are described in [START_REF] Freschet | A starting guide to root ecology: strengthening ecological concepts and standardizing root classification, sampling, processing and trait measurements[END_REF]. (+) versus (-) refers to the positive or negative effect of one trait on the function, respectively. (explorative) versus (exploitative) refers to traits that increase the overall volume of soil explored or improve the exploitation of a more limited volume of soil, respectively. 'Entity of interest' refers to a range of plant belowground parts as described in [START_REF] Freschet | A starting guide to root ecology: strengthening ecological concepts and standardizing root classification, sampling, processing and trait measurements[END_REF]. The full list of references is available as Supplementary Notes S1.

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This article is protected by copyright. All rights reserved et al., 2004;Reich et al., 2008;[START_REF] Bardgett | Going underground: root traits as drivers of ecosystem processes[END_REF] The contribution of root respiration represents on average 40-50% of the total soil CO2 efflux but varies strongly among species.

Mycorrhizal colonization intensity*

Absorptive roots Rillig et al., 2001;Gleixner et al., 2002;Kögel-Knabner, 2002;Allen et al., 2003;Langley & Hungate, 2003;Fernandez et al., 2016;[START_REF] Poirier | The root of the matter: Linking root traits and soil organic matter stabilization processes[END_REF] Mycorrhizal fungi synthesize hydrophobic and recalcitrant compounds, such as chitin and melanin, respectively, which are discussed to be less biodegradable and to accumulate in soils (at least in ecosystems experiencing cold climates).

Root lifespan* and turnover* Whole root system, fine-roots Jackson et al., 1997;Fan & Guo, 2010;McCormack et al., 2015;Klimešová et al., 2018 Root lifespan regulates the quantity and quality of root-derived organic matter transferred into the soil organic matter pool. Fineroots and low-order roots, which have a short lifespan and turnover rapidly, represent a substantial input of C into the soil.

Root litter mass loss rate* Whole root system, fine-roots Silver & Miya, 2001;Zhang & Wang, 2015;[START_REF] See | Global patterns in fine root decomposition: climate, chemistry, mycorrhizal association and woodiness[END_REF] Determines the rate at which C from litters is released into the atmosphere or enters the soil in the form of particulate organic matter or dissolved organic matter.

Root exudation rate* Fine-roots Tisdall & Oades, 1982;Kuzyakov, 2010;Phillips et al., 2011;Keiluweit et al., 2015;[START_REF] Tückmantel | Root exudation patterns in a beech forest: Dependence on soil depth, root morphology, and environment[END_REF][START_REF] Henneron | Plant economic strategies of grassland species control soil carbon dynamics through rhizodeposition[END_REF] Enhanced root exudation increases the microbial activity and accelerates the breakdown of soil organic matter in the rhizosphere (priming effect). Meanwhile root exudates can act as binding agents to stabilize soil aggregates and thus enhance the stabilization of occluded soil organic matter.

Root hair length and density* First-order roots Gould et al., 2016;[START_REF] Poirier | The root of the matter: Linking root traits and soil organic matter stabilization processes[END_REF] Root hairs can physically attach soil particles and contribute to the formation of stable soil aggregates enriched in C.

Mycorrhizal hyphal length

Absorptive roots Miller & Jastrow, 1990;Degens, 1997;Wilson et al., 2009;Wu et al., 2014 Increased hyphal length leads to greater enmeshment of soil particles and increases soil aggregate stability and soil organic C stabilisation.

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Ability to fix N* Nodules Cole et al., 1995;Binkley, 2005;Kaye et al., 2000;Fornara & Tilman, 2008;De Deyn et al., 2011 The biological fixation of N2 by N2-fixing root symbiotic bacteria generally increases the plant belowground and aboveground primary productivity. The presence of N2-fixing species also tends to increase soil organic C accumulation.

Root branching density* Absorptive roots [START_REF] Poirier | The root of the matter: Linking root traits and soil organic matter stabilization processes[END_REF] A high branching density contributes to stabilizing soil aggregates through enmeshment of soil particles and higher production of exudates by root tips.

See traits associated to "Hydraulic redistribution" (+) Domec et al., 2010 Affects topsoil organic matter and litter decomposition.

Ecosystem N cycling This process includes N inputs, losses, retention and transformation. Its complexity may not be meaningfully simplified into that accelerate versus decelerate the element cycling.

See traits associated to "Soil space occupancy"

Whole root system, absorptive roots Fornara et al., 2011;Abalos et al., 2014;De Vries et al., 2016 Most "Soil space occupancy" traits can be important for this process. The density and distribution of roots determines the location of root exudates, litter inputs and nutrient uptake.

See traits associated to "Plant N acquisition"

Whole root system, absorptive roots van der Krift & Berendse, 2001;Scherer-Lorenzen et al., 2003;Personeni & Loiseau, 2005;Batterman et al., 2013b;Leroux et al., 2013;Moreau et al., 2019 Most traits associated to "Plant N acquisition" can be important for this process. The capacity of plants to acquire N from soil, and compete with microorganisms, across a range of locations in the soil influences N cycling.

Root lifespan* and turnover* Whole root system, fine-roots Jackson et al., 1997;Fan & Guo, 2010;McCormack et al., 2015 Influences the input of litter (and N-containing compounds) into the soil.

Root litter nutrient release rate*

Whole root system, fine-roots Parton et al., 2007 Determines the rate at which N is transferred from litter to soil.

Root N concentration* Whole root system, absorptive roots et al., 2006;Parton et al., 2007;Legay et al., 2014;Cantarel et al., 2015;Thion et al., 2016 Root N is positively related to litter N release rate (lower N immobilization rate), N mineralisation and nitrification (e.g. archaeal ammonia oxidisers are more abundant in the rhizosphere of high N roots than low N roots).

Hobbie

Mycorrhizal association type* Absorptive roots [START_REF] Phillips | The mycorrhizal-associated nutrient economy: a new framework for predicting carbon-nutrient couplings in temperate forests[END_REF]Lin et al., 2017;[START_REF] Wurzburger | Experimental evidence that mycorrhizal nitrogen strategies affect soil carbon[END_REF]Zhu et al., 2018 Ecosystems dominated by AM, ERM and ECM plants are characterized by different C and mineral nutrient cycles due to the different enzymatic capacities of the symbionts. AM, ECM, and ERM fungi represent a gradient from limited saprotrophic capabilities and greater reliance on inorganic N as primary N source to the ability to produce extracellular enzymes and greater use of increasingly complex organic N forms.

Root exudation rate* Fine-roots Phillips et al., 2011;[START_REF] Tückmantel | Root exudation patterns in a beech forest: Dependence on soil depth, root morphology, and environment[END_REF]Moreau et al., 2019 Enhanced root exudation increases soil microbial activity and accelerates the breakdown of (fast-cycling) organic N forms in the rhizosphere. Roots can exude/secrete nitrification and denitrification inhibitors.

Ecosystem P cycling

See traits associated to "Plant P acquisition"

Whole root system, absorptive roots [START_REF] Lambers | Plant nutrient-acquisition strategies change with soil age[END_REF][START_REF] Ros | What root traits determine grass resistance to phosphorus deficiency in production grassland?[END_REF] Most traits associated to "Plant P acquisition", including traits associated to "Soil space occupancy", can be important for this process. The capacity of plants to acquire P from soil, with or without mycorrhizal symbiosis, across a range of locations in the soil influences P cycling.

Root lifespan* and turnover* Whole root system, fine-roots Jackson et al., 1997;Fan & Guo, 2010;McCormack et al., 2015 Influences the input of litter (and P-containing compounds) into the soil. The ease of trait measurement is approximated by colour ranging from blue ('hard' traits) to green ('soft' traits). * 'Enzymes' refers to the range of enzymes related to N uptake, assimilation and transport in roots. Imax stands for 'root maximum net ion uptake rate' and Km for 'root Michaelis-Menten constant'.

  for soluble root exudates;[START_REF] Lak | Specific root respiration of three plant species as influenced by storage time and conditions[END_REF], for specific root respiration;[START_REF] Griffiths | A multiple ion-uptake phenotyping platform reveals shared mechanisms that affect nutrient uptake by maize roots[END_REF], for multiple ion-uptake phenotyping;Arnaud et al., 2019, for in-situ root imaging)

Figure 2

 2 Figure 2 provides a range of examples where causal relationships between traits during tissue construction leads to trade-offs (e.g. mycorrhizal colonization intensity typically covaries negatively with SRL owing to the opposite effects of root cortex area fraction on the two

  Zhou M, Wang J, Bai W, Zhang Y, & Zhang W. 2019. The response of root traits to precipitation change of herbaceous species in temperate steppes. Functional Ecology 33: 2030-2041. Zhu K, McCormack ML, Lankau RA, Egan JF, Wurzburger N. 2018. Association of ectomycorrhizal trees with high carbon-to-nitrogen ratio soils across temperate forests is driven by smaller nitrogen not larger carbon stocks. Journal of Ecology 106: 524-535. Zhu Q, Iversen CM, Riley WJ, Slette IJ, Vander Stel HM. 2016. Root traits explain observed tundra vegetation nitrogen uptake patterns: Implications for trait-based land models. Journal of Geophysical Research -Biogeosciences 121: 3101-3112.

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure 2. Direct, indirect and hierarchical relationships between the (non-exhaustive) range of root traits that have been linked to (a) long-and short-term N uptake and (b) soil reinforcement against shallow landslides. Black arrows represent causal relationships. + andrepresent the direction of the relationship. Trait position along the vertical axis depicts trait hierarchical relationships, with lower levels representing 'composite' traits and upper levels representing 'underlying' traits (see main text). Major trait covariations are also shown with orange dotted arrows. The ease of trait measurement is approximated by colour ranging from

  root branching angles promote exploration of deep soil and increase soil volume explored in conditions of competition with neighbouring plants.

	Persistence of connection	Rhizomes, stolons,	Jónsdóttir & Watson,	Longer lifespan of rhizomes and shoot bearing roots enables
	between ramets* (explorative)	shoot-bearing roots	1997; Weiser et al., 2016;	sharing of resources among ramets in a clone over longer period
			Klimešová et al., 2018	and larger area and enables also longer on-spot occupancy.
				Longer persistence of connections is also generally related to
				longer root lifespan.
	Lateral spread* (explorative) Rhizomes, stolons,	Weiser & Smyčka, 2015;
		shoot-bearing roots	Klimešová et al., 2018

  Whole root systemSchenk & Jackson, 2002a Reflects the potential area of ground colonized by roots.

	Plant regeneration
	Bud bank size* (+)	Whole root system,	Klimešová & Klimeš, 2007;	Belowground bud bank allows plant regeneration after
		rhizomes	Ott et al., 2019	aboveground disturbance
	Depth of buds in bud bank (+) Whole root system,	Lubbe & Henry, 2019; Ott	Deeper buds are more resistant to disturbance like fire or
		rhizomes	et al., 2019	ploughing. On the other hand, deeper buds require more
				resource storage and time to produce new aboveground shoots.
	See traits associated to "Plant	Tubers, rhizomes,	de Moraes et al., 2016	Most "Plant storage" traits can be important for this function.
	storage" (+)	tap roots, corms,		Storage organs support regrowth of new aboveground parts.
		bulbs
	Ability to produce adventitious	Whole root system Klimešová et al., 2017a	Adaptation of plants to soil disturbance (numerous perennial
	shoots on roots (+)			weeds of arable land possess ability to resprout from roots). Some
				species may produce adventitious shoots spontaneously, some
				only in response to disturbance.
	Plant lateral spread and belowground dispersal
	Ability to produce rhizomes (+) Rhizomes	Groff & Kaplan, 1988	Rhizomes (belowground stems with adventitious roots) allow the
				colonization of new ground while relying to some extent on
				resources from well-established ramets.
	Lateral spread* (explorative) Rhizomes, stolons, Whole root system,	Weiser & Smyčka, 2015; Qian et al., 2017	The longer lateral spread by clonal growth organ (stolon, rhizome) Plant regeneration capacity provides plants with the ability to
		shoot-bearing roots tubers, rhizomes,	Klimešová et al., 2018	the farther away (from older roots) new roots must be survive intense drought periods despite the loss of aboveground
		tap roots, corms,		established. biomass.
	Ability to produce adventitious	Whole root system, bulbs	Groff & Kaplan, 1988	Facilitates establishment of new rooted areas along belowground
	roots (+) See traits associated to "Plant	rhizomes Tubers, rhizomes,		(rhizomes) or aboveground (stolons, decumbent shoots) stems
	storage" (+)	tap roots, corms,		and splitting a clone to physically independent parts.
	Lateral rooting extent*	bulbs
	(explorative)
	Ability to produce adventitious	Shoot-bearing roots Groff & Kaplan, 1988;	Common among species of dry and disturbed areas to extend
	shoots on roots (+)		Klimešová et al., 2017a	plant spread and to overcome bud bank limitation.
	See traits associated to "Plant	Tubers, rhizomes,	de Moraes et al., 2016;	Most "Plant storage" traits can be important for this function as
	storage" (+)	tap roots, corms,	Klimešová et al., 2017b	they often serve both functions.
		bulbs
	See traits associated to "Root	Root and rhizome	Klimešová et al., 2012	Facilitates movement of roots and rhizomes into new areas.
	penetration force in soil" (+)	apices
	Persistence of connection	Rhizomes, shoot	Jónsdóttir & Watson,	Longer lifespan of rhizomes and shoot bearing roots enables
	between ramets* (+)	bearing roots	1997	sharing of resources among ramets in a clone over a longer period
				and larger area and enables longer on-spot occupancy.
	Initiation and establishment of mycorrhizal symbioses		This function refers to mycorrhizal fungi as well as pathogenic
				hyphae.
	Root cortex thickness* (+)	Absorptive roots	Brundrett, 2002; Comas	Larger parenchyma cortex enhances associations with
			et al., 2012; Zadworny et	mycorrhizal colonization by providing larger space for
			al., 2016; Kong et al.,	mycorrhizal fungal hyphae and arbuscules.
			2017
	See traits associated to "Plant P	Absorptive roots	Oldroyd, 2013; Raven et	Most "Plant P acquisition" traits can be important for this
	acquisition" (-)		al., 2018	function. Plants with higher P acquisition capacities and
				therefore higher P status are less likely to establish symbioses.
	Root cortex area fraction* (+) Absorptive roots	Comas et al., 2012;	A large cortex area fraction theoretically implies a higher
			Burton et al., 2013; Gu et	possibility for connection to symbionts by providing larger space
			al., 2014; Valverde-	for mycorrhizal fungal hyphae and arbuscules.
			Barrantes et al., 2016

de

Moraes et al., 2016

Most "Plant storage" traits can be important for this function.

Storage organs support regrowth of new aboveground parts.

Table 2 .

 2 Broad, multidisciplinary assessment of theoretical and demonstrated links between below-ground traits and nine aspects of ecosystem functioning.

	ECOSYSTEM PROCESSES AND PROPERTIES
	CC Belowground traits	Entity of interest	References (examples of) Rationale
	Ecosystem C cycling			This process includes C inputs, losses, retention and
				transformation. Its complexity may not be meaningfully
				simplified into traits that accelerate versus decelerate the
				element cycling.
	See traits associated to "Soil	Whole root system,	Jastrow et al., 1998;	Most "Soil space occupancy" traits can be important for this
	space occupancy"	absorptive roots,	Jobbagy & Jackson, 2000;	process because they determine the location (i.e. biotic and
		rhizomes	Rasse et al., 2005; De	abiotic conditions) of root effects on soil, influences the amount
			Deyn et al., 2008; Wang	of contact surface between roots and soil (e.g. physical
			et al., 2010; Clemmensen	enmeshment of soil aggregates), influences the amount of root-
			et al., 2013; Pérès et al.,	derived C inputs to soil (e.g. litter, exudates), soil moisture and
			2013; Cornelissen et al.,	nutrient availability.
			2014; Liao et al., 2014;
			Gould et al., 2016; Poirier
			et al., 2018
	Mycorrhizal association type* Absorptive roots	Langley et al., 2006;	Ecosystems dominated by arbuscular mycorrhizal, ericoid
			Phillips et al., 2013;	mycorrhizal and ectomycorrhizal fungi plants are characterized
			Averill et al., 2014;	by different carbon and mineral nutrient cycles due to the
			Soudzilovskaia et al.,	different enzymatic capacities of the symbionts. Ecosystems
			2015, 2019	dominated by plants in symbiosis with ectomycorrhizal fungi
				store 70% more C in soils than ecosystems dominated by
				arbuscular mycorrhizal-associated plants.
	Specific root respiration*	Absorptive roots	Bond-Lamberty

Janeček &[START_REF] Sosnová | To resprout or not to resprout? Modeling population dynamics of a root-sprouting monocarpic plant under various disturbance regimes[END_REF] Martínez-Vilalta et al., 2016 Storage in specialized organs represents the largest part of C storage and, in contrast to storage in other types of roots, represents an active storage strategy rather than passive accumulation due to limitation of growth (e.g. by nutrients, cold).

Trees (3) Boreal forest, temperate forest

Acknowledgements

This work was supported by the New Phytologist Trust via financial support to the 25th New Phytologist Workshop "Root traits as predictors of plant and soil functions: Aggregating current knowledge to build better foundations for root ecological science", held in January 2019 in Montpellier, France. We also acknowledge support from Camille Noûs and the Cogitamus Laboratory. J.K. was supported by the Grant agency of the Czech Republic (19-13103S). M.Z. was supported by the Institute of Dendrology, Polish Academy of Sciences. C.M.I was supported by the Biological and Environmental Research program in the United States Department of Energy's Office of Science.

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This article is protected by copyright. All rights reserved Reich PB, Tjoelker MG, Pregitzer KS, Wright IJ, Oleksyn J, Machado J-L. 2008. Scaling of respiration to nitrogen in leaves, stems and roots of higher land plants. Ecology Letters 11: 793-801. Reich PB, Tjoelker MG, Walters MB, Vanderklein DW, Buschena C. 1998. Close association of RGR, leaf and root morphology, seed mass and shade tolerance in

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Author contributions

GTF initiated and coordinated the writing of the manuscript. GTF, CR, MW and AS organized the Workshop and chaired the sessions, with help from LHC. GTF, CR, LHC, MW, GB, BR, RDB, GBD, DJ, JK, ML, MLM, ICM, LP, HP, IP, NW, MZ and AS participated in the Workshop. GTF, CR, AS, MW, GB, LHC, BR, HP, JK, IP, NW, CMI and LY drafted some parts of the manuscript and all authors, including AB-Z, EBB, IB, AG, SEH, LM, CP-C, JAP, LR, PR, MS-L, NAS, TS, OJV and AW, contributed to the writing of the manuscript.

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This article is protected by copyright. All rights reserved Xylem lumen area (+)

Whole root system, fine-roots [START_REF] Violle | Let the concept of trait be functional![END_REF]Valenzuela-Estrada et al., 2008;Long et al., 2013;[START_REF] Kong | Leading dimensions in absorptive root trait variation across 96 subtropical forest species[END_REF] Greater conduit lumen area may exhibit enhanced hydraulic conductance.

Aquaporin expression (+) Absorptive roots Johnson et al., 2014 Facilitates radial, symplastic conductance of water.

Lignin concentration* (-) Absorptive roots Ranathunge et al., 2003Ranathunge et al., , 2004;;Naseer et al., 2012 Lignins may act as apoplastic barriers limiting radial water transport across roots.

Root penetration of soil

Root growth pressure (+) First-order roots Dexter, 1987;Clark & Barraclough, 1999 Root growth pressure is essential to root penetration, although there is limited evidence of its variation as a trait.

Mean root diameter* (+) First-order roots Materechera et al., 1992 Thicker roots are generally better at penetrating hard soils to greater depth.

Number of main root axes (+) Whole root system Jakobson & Dexter, 1987;Landl et al., 2017 In structured soils containing many cracks and biopores, plants with many main axes may penetrate more effectively.

Root buckling resistance (+) First-order roots Clark et al., 2008;Burr-Hersey et al., 2017 Species and genotypes differ substantially in their ability to penetrate hard soils without buckling or altering their growth trajectory.

Root cap friction coefficient (-) First-order roots Bengough & McKenzie, 1997;Iijima et al., 2003 Sloughing of root border cells and root exudate production decreases the mechanical resistance to root growth and aids root penetration.

Plant nutrient and C conservation

Lifespan* (+) Whole root system, rhizomes McCormack et al., 2012;[START_REF] Liu | Life span and structure of ephemeral root modules of different functional groups from a desert system[END_REF][START_REF] Klimešová | Belowground plant functional ecology: Towards an integrated perspective[END_REF] Decreases losses associated to root turnover.

Root resorption efficiency and proficiency (+)

Whole root system, absorptive roots

Gordon [START_REF] Jobbágy | The vertical distribution of soil organic carbon and its relation to climate and vegetation[END_REF]Freschet et al., 2010 Decreases losses associated to root senescence.

Specific respiration rate* (-) Whole root system Walk et al., 2006;Rewald et al., 2014Rewald et al., , 2016 Respiration is a major driver of C loss.

Ratio of absorptive to transport roots* (-) Fine-roots Lynch, 2019;Schneider et al., 2017 Root cortical senescence reduces metabolic maintenance costs.

See traits associated to "Plant protection against pathogens and herbivory" (+)

Whole root system Kaplan et al., 2008;Moore & Johnson, 2017 Traits providing "Plant protection against pathogens and herbivory" are important for this function.

Root tissue density* (+) Whole root system [START_REF] Ryser | The importance of tissue density for growth and life span of leaves and roots: a comparison of five ecologically contrasting grasses[END_REF][START_REF] Liu | Life span and structure of ephemeral root modules of different functional groups from a desert system[END_REF]Bumb et al., 2018;Lynch, 2019 Increases root lifespan, plant mechanical resistance and decreases plant palatability. Evidence gathered aboveground for leaf tissue density (e.g. leaf dry matter content) theoretically applies belowground. However, reduced tissue density due to aerenchyma formation, increase in cortical cell sizes or decrease in cortical cell numbers may also reduce metabolic costs.

Plant storage

Ability to produce storage structures (+)

Tubers, rhizomes, tap roots, corms, bulbs [START_REF] Klimešová | Belowground plant functional ecology: Towards an integrated perspective[END_REF]Pausas et al., 2018 Substantially improves the overall capacity of plants to store C and nutrients.

Total belowground carbohydrate storage* (+)

Tubers, rhizomes, tap roots, corms, bulbs

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This article is protected by copyright. All rights reserved [START_REF] Ryser | The importance of tissue density for growth and life span of leaves and roots: a comparison of five ecologically contrasting grasses[END_REF]Bezemer et al., 2004;Kaplan et al., 2008;Rasmann et al., 2009;Moore & Johnson, 2018 Decreases plant palatability.

Mycorrhizal colonization intensity* (+)

Absorptive roots Newsham et al., 1995;Jung et al., 2012;Babikova et al., 2014 Provides protection against some herbivores and pathogens.

Fraction of passage cells in exodermis* (-)

Absorptive roots Kamula et al., 1994 Exodermal passage cells provide the major penetration sites for the colonization of pathogenic fungi.

See traits associated to "Plant resistance to uprooting" (+)

Whole root system Ennos, 2000;Burylo et al., 2009 Prevents uprooting during grazing by aboveground herbivores and total root system disruption during grazing by belowground herbivores.

Root lignin concentration* (+) Whole root system, absorptive roots

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Root branching density* (+) Whole root system Dupuy et al., 2005a;Devkota et al., 2006;Burylo et al., 2009 The tensile force required to uproot whole plants is positively related to the root branching density and number of root tips per unit volume of soil. & Mattheck, 1996 Increases resistance to failure due to root bending during lateral sway.

Presence of sinker roots along lateral roots (+)

Lateral roots Danjon et al., 2005 Sinker roots capture a mass of soil and so increase the weight of the root-soil plate. During lateral sway, a heavier root-soil plate will improve resistance to overturning.

Presence of a taproot (+) Taproot Ennos, 1993;Fourcaud et al., 2008;Burylo et al., 2010;Yang et al., 2017 If shallow lateral roots are growing horizontally from the taproot, then the taproot constitutes the main root element that contributes to anchorage rigidity. Longer taproots anchor the plant better in soil.

Plant tolerance to waterlogging

Presence of aerenchyma tissue (+)

Absorptive roots, adventitious roots, rhizomes Kohl et al., 1996;Colmer, 2003;Colmer & Voesenek, 2009;Abiko et al., 2012;Sauter, 2013 Improves root tissue oxygenation by conducting air along the roots (and rhizomes).

Presence of pneumatophores (+)

Pneumatophores Purnobasuki & Suzuki, 2005;Zhang et al., 2015;da Ponte et al., 2019 Pneumatophores (i.e. aerial roots) are morpho-anatomical adaptations of roots with negative geotropism that emerge above the water surface to take up oxygen.

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Root tissue porosity (+) Whole root system Gibberd et al., 2001;Purnobasuki & Suzuki, 2004;Ding et al., 2017;Striker & Colmer, 2017 Enhances the internal movements of gases and increases root oxygenation in anaerobic soils.

Tolerance to high ethanol concentration (+)

Whole root system Jackson et al., 1982;Boamfa et al., 2005;Maricle et al., 2014 Ethanol toxicity is a prime cause of the injury and death of flooded plants.

Fine root regrowth rate (+) Whole root system Vidoz et al., 2010;Luo et al., 2011;Sauter 2013;Dawood et al., 2014 Adventitious roots functionally replace primary root systems that may deteriorate during flooding due to oxygen deficiency. Due to differences in rates of chemical exudation, hyphal production, and exploration distances among species of mycorrhizal fungi, species identity is likely to be an important determinant for faster or slower weathering rates.

Root secondary growth (+) Whole root system Misra et al., 1986;Richter & Markewitz, 1995 The radial force widening a crack is the product of the radial pressure and the contact area of root surface in the crack.

Hydraulic redistribution

Diverse root growth angles* (+)

Whole root system Hultine et al., 2003a;Hultine et al., 2003bScholz et al., 2008;Siqueira et al., 2008 Extensive distribution of roots in higher and lower soil horizons allows connection between wet and drier soil layers.

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Maximum rooting depth* (+) Whole root system Burgess et al., 1998;Burgess, 2000;Scholz et al., 2008;Maeght et al., 2013 Presence of roots at depth allows access to wetter soil layers in soils experiencing drying of the upper horizons, which is critical for hydraulic lift.

See traits associated to "Plant resistance and survival to drought" (+)

Whole root system, absorptive roots Domec et al., 2004;McElrone et al., 2007;Warren et al., 2008;Grigg et al., 2010;Prieto et al., 2012a ;Prieto et al., 2014 Most traits favouring "Plant resistance to drought", including traits favouring "Plant water acquisition", will contribute to maintaining a functional root system during periods of soil drying and therefore allow hydraulic redistribution.

See traits associated to "Plant water acquisition" (+)

Whole root system, absorptive roots Egerton-Warburton et al., 2008;Prieto et al., 2012b Root and mycorrhizal traits favouring "plant water acquisition" increase water flow through the root system.

Vertical root mass distribution index* (+)

Whole root system Schenk & Jackson, 2002a, 2002b High proportion of roots in deeper soil horizons may reinforce hydraulic lift.

Root turnover* (+) Absorptive roots Espeleta et al., 2004 Determines the presence of active roots in soil layers that absorb and redistribute water.

See traits associated to "Plant lateral spread and belowground dispersal" (+)

Whole root system Jónsdóttir & Watson, 1997;Stuefer, 1998 Redistribution of water can occur in the horizontal plane via plant clonal connectors.

Ecosystem evapotranspiration

See traits associated to "Plant water acquisition" (+)

Whole root system, absorptive roots Nepstad et al., 1994;Augé et al., 2008;Fort et al., 2017 Most traits associated to "Plant water acquisition" facilitate the transfer of water from the soil to the plant and favour evapotranspiration.

See traits associated to "Hydraulic redistribution" (+)

Domec et al., 2010

Facilitates the transfer of water from deep soils to shallower soil horizons.

Soil inter-particle cohesion

This property relates to soil surficial erosion.

See traits associated to "Soil space occupancy" (+) CC: colour code, in dark blue: trait of prime importance for performing the ecosystem process or property in at least some environmental conditions; medium blue: trait of secondary importance in at least some environmental conditions; light blue: trait of potential but unknown importance due to missing or low experimental evidence. * refers to traits whose measurement protocols are described in [START_REF] Freschet | A starting guide to root ecology: strengthening ecological concepts and standardizing root classification, sampling, processing and trait measurements[END_REF]. (+) versus (-) refers to the positive or negative effect of one trait on the function, respectively. 'Entity of interest' refers to a range of plant belowground parts as described in [START_REF] Freschet | A starting guide to root ecology: strengthening ecological concepts and standardizing root classification, sampling, processing and trait measurements[END_REF]. The full list of references is available as Supplementary Notes S1.

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