The effects of plants on the biosphere, atmosphere, and geosphere are key determinants of terrestrial ecosystem functioning. However, despite substantial progress made regarding plant belowground components, we are still only beginning to explore the complex relationships between root traits and functions. Drawing on literature in plant physiology, ecophysiology, ecology, agronomy and soil science, we review 24 aspects of plant and ecosystem functioning and their relationships with a number of traits of root systems, including aspects of architecture, physiology, morphology, anatomy, chemistry, biomechanics and biotic interactions. Based on this assessment, we critically evaluate the current strengths and gaps in our knowledge, and identify future research challenges in the field of root ecology. Most importantly, we found that below-ground traits with widest importance in plant and ecosystem Accepted Article This article is protected by copyright. All rights reserved functioning are not those most commonly measured. Also, the fair estimation of trait relative importance for functioning requires us to consider a more comprehensive range of functionally-relevant traits from a diverse range of species, across environments and over time series. We also advocate that establishing causal hierarchical links among root traits will provide a hypothesis-based framework to identify the most parsimonious sets of traits with strongest influence on the functions, and to link genotypes to plant and ecosystem functioning.

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Despite their difference in potential growth rate, the slow-growing Brachypodium pinnatum and the fast-growing Dactylis glomerata co-occur in many nutrient-poor calcareous grasslands. They are known to respond differently to increasing levels of N and P. An experiment was designed to measure which characteristics are affected by nutrient supply and contribute to the ecological performance of these species. Nutrient acquisition and root and shoot traits of these grasses were studied in a garden experiment with nine nutrient treatments in a factorial design of 3 N and 3 P levels each.D. glomerata was superior to B. pinnatum in nutrient acquisition and growth in all treatments. B. pinnatum was especially poor in P acquisition. Both species responded to increasing N supply and to a lesser extent to increasing P supply by decreasing their root length and increasing their leaf area per total plant weight. D. glomerata showed a higher plasticity. In most treatments, the root length ratio (RLR) and the leaf area ratio (LAR) were higher for D. glomerata. A factorization of these parameters into components expressing biomass allocation, form (root fineness or leaf thickness) and density (dry matter content) shows that the low density of the biomass ofD. glomerata was the main cause for the higher RLR and LAR. The biomass allocation to the roots showed a considerable plasticity but did not differ between the species. B. pinnatum had the highest leaf weight ratio. Root fineness was highly plastic in D. glomerata, the difference with B. pinnatum being mainly due to the thick roots of D. glomerata at high nutrient supply. The leaf area/leaf fresh weight ratio did not show any plasticity and was slightly higher for B. pinnatum.It is concluded, that the low density of the biomass of D. glomerata is the pivotal trait responsible for its faster growth at all nutrient levels. It enables simultaneously a good nutrient acquisition capacity by the roots as well as a superior carbon acquisition by the leaves. The high biomass density of B. pinnatum will then result in a lower nutrient requirement due to a slower turnover, which in the long term is advantageous under nutrient-poor conditions.

I.Introduction: continuing to face up to root ecology's challenges 975 II.Semantics: defining concepts for better understanding and communication 977III. Species-level vs ecosystem-level measurements 978

We noted that the tunneling-percolation framework is quite well understood at the extreme cases of percolationlike and hoppinglike behaviors but that the intermediate regime has not been previously discussed, in spite of its relevance to the intensively studied electrical properties of nanocomposites. Following that we study here the conductivity of dispersions of particle fillers inside an insulating matrix by taking into account explicitly the filler particle shapes and the interparticle electron-tunneling process. We show that the main features of the filler dependencies of the nanocomposite conductivity can be reproduced without introducing any a priori imposed cutoff in the interparticle conductances, as usually done in the percolationlike interpretation of these systems. Furthermore, we demonstrate that our numerical results are fully reproduced by the critical path method, which is generalized here in order to include the particle filler shapes. By exploiting this method, we provide simple analytical formulas for the composite conductivity valid for many regimes of interest. The validity of our formulation is assessed by reinterpreting existing experimental results on nanotube, nanofiber, nanosheet, and nanosphere composites and by extracting the characteristic tunneling decay length, which is found to be within the expected range of its values. These results are concluded then to be not only useful for the understanding of the intermediate regime but also for tailoring the electrical properties of nanocomposites.