ALBERT

Description: We prove a spectral flow formula for one-parameter families of Hamiltonian systems under homoclinic boundary conditions, which relates the spectral flow to the relative Maslov index of a pair of curves of Lagrangians induced by the stable and unstable subspaces, respectively. Finally, we deduce sufficient conditions for bifurcation of homoclinic trajectories of one-parameter families of non-autonomous Hamiltonian vector fields.

Description: We consider the Schur–Horn problem for normal operators in von Neumann algebras, which is the problem of characterizing the possible diagonal values of a given normal operator based on its spectral data. For normal matrices, this problem is well known to be extremely difficult, and in fact, it remains open for matrices of size greater than $3$ . We show that the infinite-dimensional version of this problem is more tractable, and establish approximate solutions for normal operators in von Neumann factors of type I $_\infty$ , II, and III. A key result is an approximation theorem that can be seen as an approximate multivariate analogue of Kadison's Carpenter Theorem.

Description: We study the rate of convergence to zero of the tail entropy of $C^\infty$ maps. We give an upper bound of this rate in terms of the growth in $k$ of the derivative of order $k$ and give examples showing the optimality of the established rate of convergence. We also consider the case of multimodal maps of the interval. Finally, we prove that homoclinic tangencies give rise to $C^r$ $(r\geqslant 2)$ robustly non- $h$ -expansive dynamical systems.

Description: Let ${{\mathscr {C}}}^0_{{{\mathfrak {g}}}}$ be the category of finite-dimensional integrable modules over the quantum affine algebra $U_{q}'({{\mathfrak {g}}})$ and let $R^{A_\infty }{\mbox {-}\mathrm {gmod}}$ denote the category of finite-dimensional graded modules over the quiver Hecke algebra of type $A_{\infty }$ . In this paper, we investigate the relationship between the categories ${{\mathscr {C}}}^0_{A_{N-1}^{(1)}}$ and ${{\mathscr {C}}}^0_{A_{N-1}^{(2)}}$ by constructing the generalized quantum affine Schur–Weyl duality functors ${\mathcal {F}}^{(t)}$ from $R^{A_\infty }{\mbox {-}\mathrm {gmod}}$ to ${{\mathscr {C}}}^0_{A_{N-1}^{(t)}}\ (t=1,2)$ .

Description: We present new constructions of complex and $p$ -adic Darmon points on elliptic curves over base fields of arbitrary signature. We conjecture that these points are global and present numerical evidence to support our conjecture.

Description: We introduce a new framework for the analysis of the stability of solitons for the one-dimensional Gross–Pitaevskii equation. In particular, we establish the asymptotic stability of the black soliton with zero speed.

Description: Let $k$ and $n$ be positive even integers. For a cuspidal Hecke eigenform $h$ in the Kohnen plus space of weight $k-n/2+1/2$ for $\varGamma _0(4),$ let $I_n(h)$ be the Duke–Imamo $\bar {{\text {g}}}$ lu–Ikeda lift of $h$ in the space of cusp forms of weight $k$ for ${\rm Sp}_n({{\bf{Z}}}),$ and $f$ be the primitive form of weight $2k-n$ for ${\rm SL}_2({{\bf{Z}}})$ corresponding to $h$ under the Shimura correspondence. We then express the ratio $\displaystyle {\langle I_n(h), I_n(h) \rangle / \langle h, h \rangle }$ of the period of $I_n(h)$ to that of $h$ in terms of special values of certain $L$ -functions of $f$ . This proves the conjecture proposed by Ikeda concerning the period of the Duke–Imamo $\bar {{\text {g}}}$ lu–Ikeda lift.

Description: The Mediterranean region is a hot spot of climate change vulnerable to increased droughts and heat waves. Scaling carbon fluxes from leaf to landscape levels is particularly challenging under drought conditions. We aimed to improve the mechanistic understanding of the seasonal acclimation of photosynthesis and morphology in sunlit and shaded leaves of four Mediterranean trees ( Quercus ilex L., Pinus halepensis Mill., Arbutus unedo L. and Quercus pubescens Willd.) under natural conditions. V c,max and J max were not constant, and mesophyll conductance was not infinite, as assumed in most terrestrial biosphere models, but varied significantly between seasons, tree species and leaf position. Favourable conditions in winter led to photosynthetic recovery and growth in the evergreens. Under moderate drought, adjustments in the photo/biochemistry and stomatal/mesophyllic diffusion behaviour effectively protected the photosynthetic machineries. Severe drought, however, induced early leaf senescence mostly in A. unedo and Q. pubescens , and significantly increased leaf mass per area in Q. ilex and P. halepensis . Shaded leaves had lower photosynthetic potentials but cushioned negative effects during stress periods. Species-specificity, seasonal variations and leaf position are key factors to explain vegetation responses to abiotic stress and hold great potential to reduce uncertainties in terrestrial biosphere models especially under drought conditions.

Description: Plants experiencing drought stress are frequently more susceptible to pathogens, likely via alterations in physiology that create favorable conditions for pathogens. Common plant responses to drought include the production of reactive oxygen species (ROS) and the accumulation of free amino acids (AAs), particularly proline. These same phenomena also frequently occur during pathogenic attack. Therefore, drought-induced perturbations in AA and ROS metabolism could potentially contribute to the observed enhanced susceptibility. Furthermore, nitrogen (N) availability can influence AA accumulation and affect plant resistance, but its contributions to drought-induced susceptibility are largely unexplored. Here we show that drought induces accumulation of hydrogen peroxide (H 2 O 2 ) in Austrian pine ( Pinus nigra Arnold) shoots, but that shoot infection by the blight and canker pathogen Diplodia sapinea (Fr.) Fuckel leads to large reductions in H 2 O 2 levels in droughted plants. In in vitro assays, H 2 O 2 was toxic to D. sapinea , and the fungus responded to this oxidative stress by increasing catalase and peroxidase activities, resulting in substantial H 2 O 2 degradation. Proline increased in response to drought and infection when examined independently, but unlike all other AAs, proline further increased in infected shoots of droughted trees. In the same tissues, the proline precursor, glutamate, decreased significantly. Proline was found to protect D. sapinea from H 2 O 2 damage, while also serving as a preferred N source in vitro. Fertilization increased constitutive and drought-induced levels of some AAs, but did not affect plant resistance. A new model integrating interactions of proline and H 2 O 2 metabolism with drought and fungal infection of plants is proposed.

Description: Small differences in the sensitivity of stomatal conductance to light intensity on leaf surfaces may lead to large differences in total canopy transpiration ( E C ) with increasing canopy leaf area ( L ). Typically, the increase of L would more than compensate for the decrease of transpiration per unit of leaf area ( E L ), resulting in concurrent increase of E C . However, highly shade-intolerant species, such as Larix principis-rupprechtii Mayr., may be so sensitive to increased shading that such compensation is not complete. We hypothesized that in such a stand, windfall-induced spatial variation at a decameter scale would result in greatly reduced E L in patches of high L leading to lower E C than low competition patches of sparse canopy. We further hypothesized that quicker extraction of soil moisture in patches of lower competition will result in earlier onset of drought symptoms in these patches. Thus, patches of low L will transition from light to soil moisture as the factor dominating E L . This process should progressively homogenize E C in the stand even as the variation of soil moisture is increasing. We tested the hypotheses utilizing sap flux of nine trees, and associated environmental and stand variables. The results were consistent with only some of the expectations. Under non-limiting soil moisture, E L was very sensitive to the spatial variation of L , decreasing sharply with increasing L and associated decrease of mean light intensity on leaf surfaces. Thus, under the conditions of ample soil moisture maximum E C decreased with increasing patch-scale L . Annual E C and biomass production also decreased with L , albeit more weakly. Furthermore, variation of E C among patches decreased as average stand soil moisture declined between rain events. However, contrary to expectation, high L plots which transpired less showed a greater E L sensitivity to decreasing stand-scale soil moisture, suggesting a different mechanism than simple control by decreasing soil moisture. We offer potential explanations to the observed phenomenon. Our results demonstrate that spatial variation of L at decameter scale, even within relatively homogeneous, single-species, even-aged stands, can produce large variation of transpiration, soil moisture and biomass production and should be considered in 1-D soil–plant–atmosphere models.

Description: The main goal of this study was to develop a method for the extraction and indirect estimation of the quantity of calcium oxalate (CaOx) in the foliage of trees. Foliar tissue was collected from a single tree of each species (five conifers and five hardwoods) for comparison of extractions in different solvents using 10 replicates per species from the same pool of tissue. For each species, calcium (Ca) and oxalate were extracted sequentially in double deionized water and 2N acetic acid, and finally, five replicate samples were extracted in 5% (0.83N) perchloric acid (PCA) and the other five in 2N hydrochloric acid (HCl); three cycles of freezing and thawing were used for each solvent. Total ions were extracted by microwave digestion. Calcium was quantified with an inductively coupled plasma emission spectrophotometer method and oxalate was eluted and quantified using a high performance liquid chromatography method. This experiment was repeated again with two conifer and two hardwood species using four trees per species, and two analytical replicates for each tree. We report here that, regardless of age of individual trees within a species, time of collection or species type, the third extraction in PCA or HCl resulted in near equimolar quantities of Ca and oxalate ( r 2  ≥ 0.99). This method provides an easy estimate of the quantity of CaOx crystals using a small sample of foliar tissue. An additional benefit of PCA is that it precipitates the nucleic acids and proteins, allowing the quantification of several free/soluble metabolites such as amino acids, polyamines, organic acids and inorganic elements all from a single sample extract.

Description: The white-rot fungus Heterobasidion parviporum Niemelä & Korhonen establishes a necrotrophic interaction with Norway spruce ( Picea abies (L.) H.Karst.) causing root and butt rot and growth losses in living trees. The interaction occurs first with the bark and the outer sapwood, as the pathogen enters the tree via wounds or root-to-root contacts. Later, when the fungus reaches the heartwood, it spreads therein creating a decay column, and the interaction mainly occurs in the inner sapwood where the tree creates a reaction zone. While bark and outer sapwood interactions are well studied, little is known about the nature of the transcriptional responses leading to the creation of a reaction zone. In this study, we sampled bark and sapwood both proximal and distal to the reaction zone in artificially inoculated and naturally infected trees. We quantified gene expression levels of candidate genes in secondary metabolite, hormone biosynthesis and signalling pathways using quantitative polymerase chain reaction. An up-regulation of mainly the phenylpropanoid pathway and jasmonic acid biosynthesis was found at the inoculation site, when inoculations were compared with wounding. We found that transcriptional responses in inner sapwood were similar to those reported upon infection through the bark. Our data suggest that the defence mechanism is induced due to direct fungal contact irrespective of the tissue type. Understanding the nature of these interactions is important when considering tree breeding-based resistance strategies to reduce the spread of the pathogen between and within trees.

Description: Global warming and associated decreases in summer rainfall may threaten tree vitality and forest productivity in many regions of the temperate zone in the future. One option for forestry to reduce the risk of failure is to plant genotypes which combine high productivity with drought tolerance. Growth experiments with provenances from different climates indicate that drought exposure can trigger adaptive drought responses in temperate trees, but it is not well known whether and to what extent regional precipitation reduction can increase the drought resistance of a species. We conducted a common garden growth experiment with five European beech ( Fagus sylvatica L.) populations from a limited region with pronounced precipitation heterogeneity (816–544 mm year –1 ), where phylogenetically related provenances grew under small to large water deficits. We grew saplings of the five provenances at four soil moisture levels (dry to moist) and measured ~30 morphological (leaf and root properties, root : shoot ratio), physiological (leaf water status parameters, leaf conductance) and growth-related traits (above- and belowground productivity) with the aim to examine provenance differences in the drought response of morphological and physiological traits and to relate the responsiveness to precipitation at origin. Physiological traits were more strongly influenced by provenance (one-third of the studied traits), while structural traits were primarily affected by water availability in the experiment (two-thirds of the traits). The modulus of leaf tissue elasticity reached much higher values late in summer in plants from moist origins resulting in more rapid turgor loss and a higher risk of hydraulic failure upon drought. While experimental water shortage affected the majority of morphological and productivity-related traits in the five provenances, most parameters related to leaf water status were insensitive to water shortage. Thus, plant morphology, and root growth in particular, did respond to reduced water availability with higher phenotypic plasticity than did physiology. We conclude that beech provenances exposed to different precipitation regimes have developed some genotypic differences with respect to leaf water status regulation, but these adaptations are associated with only minor adaptation in plant morphology and they do not affect the growth rate of the saplings.

Description: Many studies have demonstrated linkages between the occurrence of fog and ecophysiological functioning in cloud forests, but few have investigated hydraulic functioning as a determining factor that explains sharp changes in vegetation. The objective of this study was to compare the plant water status during cloud-immersed and non-immersed conditions and hydraulic vulnerability in branches and roots of species across a temperate, mountain fog ecotone. Because cloud forests are often dark, cool and very moist, we expected cloud forest species to have less drought-tolerant characteristics (i.e., lower P e and P 50 —the pressures required to induce a 12 and 50% loss in hydraulic conductivity, respectively) relative to non-cloud forest species in adjacent (lower elevation) forests. Additionally, due to the ability of cloud forest species to absorb cloud-fog water, we predicted greater improvements in hydraulic functioning during fog in cloud forest species relative to non-cloud forest species. Across the cloud forest ecotone, most species measured were very resistant to losses in conductivity with branch P 50 values from –4.5 to –6.0 MPa, hydraulic safety margins ( min – P 50 ) 〉1.5 MPa and low calculated hydraulic conductivity losses. Roots had greater vulnerabilities, with P 50 values ranging from –1.4 to –2.5 MPa, leading to greater predicted losses in conductivity (~20%). Calculated values suggested strong losses of midday leaf hydraulic conductance in three of the four species, supporting the hydraulic segmentation hypothesis. In both cloud forest and hardwood species, s were greater on foggy days than sunny days, demonstrating the importance of fog periods to plant water balance across fog regimes. Thus, frequent fog did not result in systemic changes in hydraulic functioning or vulnerability to embolism across our temperate cloud forest ecotone. Finally, roots functioned with lower hydraulic conductivity than branches, suggesting that they may serve as more sensitive indicators of hydraulic functioning in these mesic, foggy ecosystems.

Description: Climate warming is having an impact on distribution, acclimation and defence capability of plants. We compared the emission rate and composition of volatile organic compounds (VOCs) from silver birch ( Betula pendula (Roth)) provenances along a latitudinal gradient in a common garden experiment over the years 2012 and 2013. Micropropagated silver birch saplings from three provenances were acquired along a gradient of 7° latitude and planted at central (Joensuu 62°N) and northern (Kolari 67°N) sites. We collected VOCs emitted by shoots and assessed levels of herbivore damage of three genotypes of each provenance on three occasions at the central site and four occasions at the northern site. In 2012, trees of all provenances growing at the central site had higher total VOC emission rates than the same provenances growing at the northern site; in 2013 the reverse was true, thus indicating a variable effect of latitude. Trees of the southern provenance had lower VOC emission rates than trees of the central and northern provenances during both sampling years. However, northward or southward translocation itself had no significant effect on the total VOC emission rates, and no clear effect on insect herbivore damage. When VOC blend composition was studied, trees of all provenances usually emitted more green leaf volatiles at the northern site and more sesquiterpenes at the central site. The monoterpene composition of emissions from trees of the central provenance was distinct from that of the other provenances. In summary, provenance translocation did not have a clear effect in the short-term on VOC emissions and herbivory was not usually intense at the lower latitude. Our data did not support the hypothesis that trees growing at lower latitudes would experience more intense herbivory, and therefore allocate resources to chemical defence in the form of inducible VOC emissions.

Description: Virus-induced gene silencing (VIGS) has been shown to be an effective tool for investigating gene functions in herbaceous plant species, but has rarely been tested in trees. The establishment of a fast and reliable transformation system is especially important for woody plants, many of which are recalcitrant to transformation. In this study, we established a tobacco rattle virus (TRV)-based VIGS system for two Populus species, Populus euphratica and P.   x   canescens . Here, TRV constructs carrying a 266 bp or a 558 bp fragment of the phytoene desaturase (PDS) gene were Agrobacterium -infiltrated into leaves of the two poplar species. Agrobacterium -mediated delivery of the shorter insert, TRV2 -PePDS 266 , into the host poplars resulted in expected photobleaching in both tree species, but not the longer insert, PePDS 558 . The efficiency of VIGS was temperature-dependent, increasing by raising the temperature from 18 to 28 °C. The optimized TRV–VIGS system at 28 °C resulted in a high silencing frequency and efficiency up to 65–73 and 83–94%, respectively, in the two tested poplars. Moreover, syringe inoculation of Agrobacterium in 100 mM acetosyringone induced a more efficient silencing in the two poplar species, compared with other agroinfiltration methods, e.g., direct injection, misting and agrodrench. There were plant species-related differences in the response to VIGS because the photobleaching symptoms were more severe in P.   x   canescens than in P. euphratica. Furthermore, VIGS-treated P. euphratica exhibited a higher recovery rate (50%) after several weeks of the virus infection, compared with TRV-infected P.   x   canescens plants (20%). Expression stability of reference genes was screened to assess the relative abundance of PePDS mRNA in VIGS-treated P. euphratica and P.   x   canescens. PeACT7 was stably expressed in P. euphratica and UBQ-L was selected as the most suitable reference gene for P.   x   canescens using three different statistical approaches, geNorm, NormFinder and BestKeeper. Quantitative real-time PCR showed significant reductions in PDS transcripts (55–64%) in the photobleached leaves of both VIGS-treated poplar species. Our results demonstrate that the TRV-based VIGS provides a practical tool for gene functional analysis in Populus sp., especially in those poplar species which are otherwise recalcitrant to transformation.

Description: Latex, the cytoplasm of laticiferous cells localized in the inner bark of rubber trees ( Hevea brasiliensis Müll. Arg.), is collected by tapping the bark. Following tapping, latex flows out of the trunk and is regenerated, whereas in untapped trees, there is no natural exudation. It is still unknown whether the carbohydrates used for latex regeneration in tapped trees is coming from recent photosynthates or from stored carbohydrates, and in the former case, it is expected that latex carbon isotope composition of tapped trees will vary seasonally, whereas latex isotope composition of untapped trees will be more stable. Temporal variations of carbon isotope composition of trunk latex ( 13 C-L), leaf soluble compounds ( 13 C-S) and bulk leaf material ( 13 C-B) collected from tapped and untapped 20-year-old trees were compared. A marked difference in 13 C-L was observed between tapped and untapped trees whatever the season. Trunk latex from tapped trees was more depleted (1.6 on average) with more variable 13 C values than those of untapped trees. 13 C-L was higher and more stable across seasons than 13 C-S and 13 C-B, with a maximum seasonal difference of 0.7 for tapped trees and 0.3 for untapped trees. 13 C-B was lower in tapped than in untapped trees, increasing from August (middle of the rainy season) to April (end of the dry season). Differences in 13 C-L and 13 C-B between tapped and untapped trees indicated that tapping affects the metabolism of both laticiferous cells and leaves. The lack of correlation between 13 C-L and 13 C-S suggests that recent photosynthates are mixed in the large pool of stored carbohydrates that are involved in latex regeneration after tapping.

Description: Trees contain non-structural carbon (NSC), but it is unclear for how long these reserves are stored and to what degree they are used to support plant activity. We used radiocarbon ( 14 C) to show that the carbon (C) in stemwood NSC can achieve ages of several decades in California oaks. We separated NSC into two fractions: soluble (~50% sugars) and insoluble (mostly starch) NSC. Soluble NSC contained more C than insoluble NSC, but we found no consistent trend in the amount of either pool with depth in the stem. There was no systematic difference in C age between the two fractions, although ages increased with stem depth. The C in both NSC fractions was consistently younger than the structural C from which they were extracted. Together, these results indicate considerable inward mixing of NSC within the stem and rapid exchange between soluble and insoluble pools, compared with the timescale of inward mixing. We observed similar patterns in sympatric evergreen and deciduous oaks and the largest differences among tree stems with different growth rates. The 14 C signature of carbon dioxide (CO 2 ) emitted from tree stems was higher than expected from very recent photoassimilates, indicating that the mean age of C in respiration substrates included a contribution from C fixed years previously. A simple model that tracks NSC produced each year, followed by loss (through conversion to CO 2 ) in subsequent years, matches our observations of inward mixing of NSC in the stem and higher 14 C signature of stem CO 2 efflux. Together, these data support the idea of continuous accumulation of NSC in stemwood and that ‘vigor’ (growth rate) and leaf habit (deciduous vs evergreen) control NSC pool size and allocation.

Description: Gibberellins (GAs) are important regulators of plant shoot biomass growth, and GA 20-oxidase (GA20ox) is one of the major regulatory enzymes in the GA biosynthetic pathway. Previously, we showed that the expression levels of a putative GA20ox1 (i.e., PdGA20ox1 ) in stem tissue of 3-month-old seedlings of 12 families of Pinus densiflora were positively correlated with stem diameter growth across those same families growing in an even-aged 32-year-old pine forest (Park EJ, Lee WY, Kurepin LV, Zhang R, Janzen L, Pharis RP (2015) Plant hormone-assisted early family selection in Pinus densiflora via a retrospective approach. Tree Physiol 35:86–94). To further investigate the molecular function of this gene in the stem wood growth of forest trees, we produced transgenic poplar lines expressing PdGA20ox1 under the control of the 35S promoter (designated as 35S::PdGA20ox1). By age 3 months, most of the 35S::PdGA20ox1 poplar trees were showing an exceptional enhancement of stem wood growth, i.e., up to fourfold increases in stem dry weight, compared with the nontransformed control poplar plants. Significant increases in endogenous GA 1 , its immediate precursor (GA 20 ) and its catabolite (GA 8 ) in elongating internode tissue accompanied the increased stem growth in the transgenic lines. Additionally, the development of gelatinous fibers occurred in vertically grown stems of the 35S::PdGA20ox1 poplars. An analysis of the cell wall monosaccharide composition of the 35S::PdGA20ox1 poplars showed significant increases in xylose and glucose contents, indicating a qualitative increase in secondary wall depositions. Microarray analyses led us to find a total of 276 probe sets that were upregulated (using threefold as a threshold) in the stem tissues of 35S::PdGA20ox1 poplars relative to the controls. ‘Cell organization or biogenesis’- and ‘cell wall’-related genes were overrepresented, including many of genes that are involved in cell wall modification. Several transcriptional regulators, which positively regulate cell elongation through GA signaling, were also upregulated. In contrast, genes involved in defense signaling were appreciably downregulated in the 35S::PdGA20ox1 stem tissues, suggesting a growth versus defense trade-off. Taken together, our results suggest that PdGA20ox1 functions to promote stem growth and wood formation in poplar, probably by activating GA signaling while coincidentally depressing defense signaling.

Description: Bark beetles (Coleoptera: Curculionidae, Scolytinae) cause widespread tree mortality in coniferous forests worldwide. Constitutive and induced host defenses are important factors in an individual tree’s ability to survive an attack and in bottom-up regulation of bark beetle population dynamics, yet quantifying defense levels is often difficult. For example, in Pinus spp., resin flow is important for resistance to bark beetles but is extremely variable among individuals and within a season. While resin is produced and stored in resin ducts, the specific resin duct metrics that best correlate with resin flow remain unclear. The ability and timing of some pine species to produce induced resin is also not well understood. We investigated (i) the relationships between ponderosa pine ( Pinus ponderosa Lawson & C. Lawson) resin flow and axial resin duct characteristics, tree growth and physiological variables, and (ii) if mechanical wounding induces ponderosa pine resin flow and resin ducts in the absence of bark beetles. Resin flow increased later in the growing season under moderate water stress and was highest in faster growing trees. The best predictors of resin flow were nonstandardized measures of resin ducts, resin duct size and total resin duct area, both of which increased with tree growth. However, while faster growing trees tended to produce more resin, models of resin flow using only tree growth were not statistically significant. Further, the standardized measures of resin ducts, density and duct area relative to xylem area, decreased with tree growth rate, indicating that slower growing trees invested more in resin duct defenses per unit area of radial growth, despite a tendency to produce less resin overall. We also found that mechanical wounding induced ponderosa pine defenses, but this response was slow. Resin flow increased after 28 days, and resin duct production did not increase until the following year. These slow induced responses may allow unsuccessfully attacked or wounded trees to resist future bark beetle attacks. Forest management that encourages healthy, vigorously growing trees will also favor larger resin ducts, thereby conferring increased constitutive resistance to bark beetle attacks.

Description: Temperature responses and sensitivity of photosynthesis ( A n _ T ) and respiration for leaves at different ages are crucial to modeling ecosystem carbon (C) cycles and productivity of evergreen forests. Understanding the mechanisms and processes of temperature sensitivity may further shed lights on temperature acclimation of photosynthesis and respiration with leaf aging. The current study examined temperature responses of photosynthesis and respiration of young leaves (YLs) (fully expanded in current growth season) and old leaves (OLs) (fully expanded in last growth season) of Quercus aquifolioides Rehder and E.H. Wilson in an alpine oak forest, southwestern China. Temperature responses of dark respiration ( R dark ), net assimilation ( A n ), maximal velocity of carboxylation ( V cmax ) and maximum rate of electron transport ( J max ) were significantly different between the two leaf ages. Those differences implied different temperature response parameters should be used for leaves of different ages in modeling vegetation productivity and ecosystem C cycles in Q. aquifolioides forests and other evergreen forests. We found that RuBP carboxylation determined the downward shift of A n _ T in OLs, while RuBP regeneration and the balance between Rubisco carboxylation and RuBP regeneration made little contribution. Sensitivity of stomatal conductance to vapor pressure deficit changed in OLs and compensated part of the downward shift. We also found that OLs of Q. aquifolioides had lower A n due to lower stomatal conductance, higher stomatal conductance limitation and deactivation of the biochemical processes. In addition, the balance between R dark and A n changed between OLs and YLs, which was represented by a higher R dark / A n ratio for OLs.

Description: Plants allocate carbon (C) to sink tissues depending on phenological, physiological or environmental factors. We still have little knowledge on C partitioning into various cellular compounds and metabolic pathways at various ecophysiological stages. We used compound-specific stable isotope analysis to investigate C partitioning of freshly assimilated C into tree compartments (needles, branches and stem) as well as into needle water-soluble organic C (WSOC), non-hydrolysable structural organic C (stOC) and individual chemical compound classes (amino acids, hemicellulose sugars, fatty acids and alkanes) of Norway spruce ( Picea abies ) following in situ 13 C pulse labelling 15 days after bud break. The 13 C allocation within the above-ground tree biomass demonstrated needles as a major C sink, accounting for 86% of the freshly assimilated C 6 h after labelling. In needles, the highest allocation occurred not only into the WSOC pool (44.1% of recovered needle 13 C) but also into stOC (33.9%). Needle growth, however, also caused high 13 C allocation into pathways not involved in the formation of structural compounds: (i) pathways in secondary metabolism, (ii) C-1 metabolism and (iii) amino acid synthesis from photorespiration. These pathways could be identified by a high 13 C enrichment of their key amino acids. In addition, 13 C was strongly allocated into the n -alkyl lipid fraction (0.3% of recovered 13 C), whereby 13 C allocation into cellular and cuticular exceeded that of epicuticular fatty acids. 13 C allocation decreased along the lipid transformation and translocation pathways: the allocation was highest for precursor fatty acids, lower for elongated fatty acids and lowest for the decarbonylated n -alkanes. The combination of 13 C pulse labelling with compound-specific 13 C analysis of key metabolites enabled tracing relevant C allocation pathways under field conditions. Besides the primary metabolism synthesizing structural cell compounds, a complex network of pathways consumed the assimilated 13 C and kept most of the assimilated C in the growing needles.

Description: Non-structural carbohydrates (NSC) in plant tissue are frequently quantified to make inferences about plant responses to environmental conditions. Laboratories publishing estimates of NSC of woody plants use many different methods to evaluate NSC. We asked whether NSC estimates in the recent literature could be quantitatively compared among studies. We also asked whether any differences among laboratories were related to the extraction and quantification methods used to determine starch and sugar concentrations. These questions were addressed by sending sub-samples collected from five woody plant tissues, which varied in NSC content and chemical composition, to 29 laboratories. Each laboratory analyzed the samples with their laboratory-specific protocols, based on recent publications, to determine concentrations of soluble sugars, starch and their sum, total NSC. Laboratory estimates differed substantially for all samples. For example, estimates for Eucalyptus globulus leaves (EGL) varied from 23 to 116 (mean = 56) mg g –1 for soluble sugars, 6–533 (mean = 94) mg g –1 for starch and 53–649 (mean = 153) mg g –1 for total NSC. Mixed model analysis of variance showed that much of the variability among laboratories was unrelated to the categories we used for extraction and quantification methods (method category R 2 = 0.05–0.12 for soluble sugars, 0.10–0.33 for starch and 0.01–0.09 for total NSC). For EGL, the difference between the highest and lowest least squares means for categories in the mixed model analysis was 33 mg g –1 for total NSC, compared with the range of laboratory estimates of 596 mg g –1 . Laboratories were reasonably consistent in their ranks of estimates among tissues for starch ( r = 0.41–0.91), but less so for total NSC ( r = 0.45–0.84) and soluble sugars ( r = 0.11–0.83). Our results show that NSC estimates for woody plant tissues cannot be compared among laboratories. The relative changes in NSC between treatments measured within a laboratory may be comparable within and between laboratories, especially for starch. To obtain comparable NSC estimates, we suggest that users can either adopt the reference method given in this publication, or report estimates for a portion of samples using the reference method, and report estimates for a standard reference material. Researchers interested in NSC estimates should work to identify and adopt standard methods.

Description: We employed the warm temperate conifer Cunninghamia lanceolata (Lamb.) Hook. as a model of plantation forest species to investigate ecophysiological responses to root treatments (control (0%), and ~25, 50 or 75% of the initial root mass) under well-watered and water-limited conditions. Our results indicated that total root dry mass accumulation was negatively associated with the severity of root pruning, but there was evidence of multiple compensatory responses. The plants exhibited higher instantaneous and long-term (assessed by carbon isotope composition, 13 C) water-use efficiency in pruning treatments, especially under low water availability. Root pruning also increased the fine root/total root mass ratio, specific root length and fine root vitality in both water availability treatments. As a result of the compensatory responses, under well-watered conditions, height, stem dry mass accumulation, leaf/fine root biomass ratio (L/FR), transpiration rate, photosynthetic capacity and photosynthetic nitrogen-use efficiency ( E N ) were the highest under 25% pruning. Yet, all these traits except L/FR and foliage nitrogen content were severely reduced under 75% pruning. Drought negatively affected growth and leaf gas exchange rates, and there was a greater negative effect on growth, water potential, gas exchange and E N when 〉25% of total root biomass was removed. The stem/aboveground mass ratio was the highest under 25% pruning in both watering conditions. These results indicate that the responses to root severance are related to the excision intensity and soil moisture content. A moderate root pruning proved to be an effective means to improve stem dry mass accumulation.

Description: The timing of wood formation is crucial to determine how environmental factors affect tree growth. The long-lived bristlecone pine ( Pinus longaeva D. K. Bailey) is a foundation treeline species in the Great Basin of North America reaching stem ages of about 5000 years. We investigated stem cambial phenology and radial size variability to quantify the relative influence of environmental variables on bristlecone pine growth. Repeated cellular measurements and half-hourly dendrometer records were obtained during 2013 and 2014 for two high-elevation stands included in the Nevada Climate-ecohydrological Assessment Network. Daily time series of stem radial variations showed rehydration and expansion starting in late April–early May, prior to the onset of wood formation at breast height. Formation of new xylem started in June and lasted until mid-September. There were no differences in phenological timing between the two stands, or in the air and soil temperature thresholds for the onset of xylogenesis. A multiple logistic regression model highlighted a separate effect of air and soil temperature on xylogenesis, the relevance of which was modulated by the interaction with vapor pressure and soil water content. While air temperature plays a key role in cambial resumption after winter dormancy, soil thermal conditions coupled with snowpack dynamics also influence the onset of wood formation by regulating plant–soil water exchanges. Our results help build a physiological understanding of climate–growth relationships in P. longaeva , the importance of which for dendroclimatic reconstructions can hardly be overstated. In addition, environmental drivers of xylogenesis at the treeline ecotone, by controlling the growth of dominant species, ultimately determine ecosystem responses to climatic change.

Description: Seasonal analyses of cambial cell production and day-by-day stem radial increment can help to elucidate how climate modulates wood formation in conifers. Intra-annual dynamics of wood formation were determined with microcores and dendrometers and related to climatic signals in Norway spruce ( Picea abies (L.) Karst.). The seasonal dynamics of these processes were observed at two sites of different altitude, Savignano (650 m a.s.l.) and Lavazè (1800 m a.s.l.) in the Italian Alps. Seasonal dynamics of cambial activity were found to be site specific, indicating that the phenology of cambial cell production is highly variable and plastic with altitude. There was a site-specific trend in the number of cells in the wall thickening phase, with the maximum cell production in early July (DOY 186) at Savignano and in mid-July (DOY 200) at Lavazè. The formation of mature cells showed similar trends at the two sites, although different numbers of cells and timing of cell differentiation were visible in the model shapes; at the end of ring formation in 2010, the number of cells was four times higher at Savignano (106.5 cells) than at Lavazè (26.5 cells). At low altitudes, microcores and dendrometers described the radial growth patterns comparably, though the dendrometer function underlined the higher upper asymptote of maximum growth in comparison with the cell production function. In contrast, at high altitude, these functions exhibited different trends. The best model was obtained by fitting functions of the Gompertz model to the experimental data. By combining radial growth and cambial activity indices we defined a model system able to synchronize these processes. Processes of adaptation of the pattern of xylogenesis occurred, enabling P. abies to occupy sites with contrasting climatic conditions. The use of daily climatic variables in combination with plant functional traits obtained by sensors and/or destructive sampling could provide a suitable tool to better investigate the effect of disturbances on response strategies in trees and, consequently, contribute to improving our prediction of tree growth and species resilience based on climate scenarios.

Description: In deciduous trees growing in temperate forests, bud break and growth in spring must rely on intrinsic carbon (C) reserves. Yet it is unclear whether growth and C storage occur simultaneously, and whether starch C in branches is sufficient for refoliation. To test in situ the relationships between growth, phenology and C utilization, we monitored stem growth, leaf phenology and stem and branch nonstructural carbohydrate (NSC) dynamics in three deciduous species: Carpinus betulus L., Fagus sylvatica L. and Quercus petraea (Matt.) Liebl. To quantify the role of NSC in C investment into growth, a C balance approach was applied. Across the three species, 〉95% of branchlet starch was consumed during bud break, confirming the importance of C reserves for refoliation in spring. The C balance calculation showed that 90% of the C investment in foliage (7.0–10.5 kg tree –1 and 5–17 times the C needed for annual stem growth) was explained by simultaneous branchlet starch degradation. Carbon reserves were recovered sooner than expected, after leaf expansion, in parallel with stem growth. Carpinus had earlier leaf phenology (by ~25 days) but delayed cambial growth (by ~15 days) than Fagus and Quercus , the result of a competitive strategy to flush early, while having lower NSC levels.

Description: Fungal infections result in decreases in photosynthesis, induction of stress and signaling volatile emissions and reductions in constitutive volatile emissions, but the way different physiological processes scale with the severity of infection is poorly known. We studied the effects of infection by the obligate biotrophic fungal pathogen Melampsora larici-populina Kleb., the causal agent of poplar leaf rust disease, on photosynthetic characteristics, and constitutive isoprene and induced volatile emissions in leaves of Populus balsamifera var. suaveolens (Fisch.) Loudon. exhibiting different degrees of damage. The degree of fungal damage, quantified by the total area of chlorotic and necrotic leaf areas, varied between 0 (noninfected control) and ~60%. The rates of all physiological processes scaled quantitatively with the degree of visual damage, but the scaling with damage severity was weaker for photosynthetic characteristics than for constitutive and induced volatile release. Over the whole range of damage severity, the net assimilation rate per area ( A A ) decreased 1.5-fold, dry mass per unit area 2.4-fold and constitutive isoprene emissions 5-fold, while stomatal conductance increased 1.9-fold and dark respiration rate 1.6-fold. The emissions of key stress and signaling volatiles (methanol, green leaf volatiles, monoterpenes, sesquiterpenes and methyl salicylate) were in most cases nondetectable in noninfested leaves, and increased strongly with increasing the spread of infection. The moderate reduction in A A resulted from the loss of photosynthetically active biomass, but the reduction in constitutive isoprene emissions and the increase in induced volatile emissions primarily reflected changes in the activities of corresponding biochemical pathways. Although all physiological alterations in fungal-infected leaves occurred in a stress severity-dependent manner, modifications in primary and secondary metabolic pathways scaled differently due to contrasting operational mechanisms.

Description: Current knowledge of the genetic mechanisms underlying the inheritance of photosynthetic activity in forest trees is generally limited, yet it is essential both for various practical forestry purposes and for better understanding of broader evolutionary mechanisms. In this study, we investigated genetic variation underlying selected chlorophyll a fluorescence (ChlF) parameters in structured populations of Scots pine ( Pinus sylvestris L.) grown on two sites under non-stress conditions. These parameters were derived from the OJIP part of the ChlF kinetics curve and characterize individual parts of primary photosynthetic processes associated, for example, with the exciton trapping by light-harvesting antennae, energy utilization in photosystem II (PSII) reaction centers (RCs) and its transfer further down the photosynthetic electron-transport chain. An additive relationship matrix was estimated based on pedigree reconstruction, utilizing a set of highly polymorphic single sequence repeat markers. Variance decomposition was conducted using the animal genetic evaluation mixed-linear model. The majority of ChlF parameters in the analyzed pine populations showed significant additive genetic variation. Statistically significant heritability estimates were obtained for most ChlF indices, with the exception of DI 0 /RC, D0 and P0 ( F v / F m ) parameters. Estimated heritabilities varied around the value of 0.15 with the maximal value of 0.23 in the ET 0 /RC parameter, which indicates electron-transport flux from Q A to Q B per PSII RC. No significant correlation was found between these indices and selected growth traits. Moreover, no genotype  x  environment interaction (G  x  E) was detected, i.e., no differences in genotypes’ performance between sites. The absence of significant G  x  E in our study is interesting, given the relatively low heritability found for the majority of parameters analyzed. Therefore, we infer that polygenic variability of these indices is selectively neutral.

Description: The ethylene response factor (ERF) family is one of the largest plant-specific transcription factor families, playing an important role in plant development and response to stresses. The ERF76 gene is a member of the poplar ERF transcription factor gene family. First, we validated that the ERF76 gene expressed in leaf and root tissues is responsive to salinity stress. We then successfully cloned the ERF76 cDNA fragment containing an open reading frame from di-haploid Populus simonii   x   Populus nigra and proved that ERF76 protein is targeted to the nucleus. Finally, we transferred the gene into the same poplar clone by the Agrobacterium -mediated leaf disc method. Using both RNA-Seq and reverse transcription-quantitative polymerase chain reaction, we validated that expression level of ERF76 is significantly higher in transgenic plants than that in the nontransgenic control. Using RNA-Seq data, we have identified 375 genes that are differentially expressed between the transgenic plants and the control under salt treatment. Among the differentially expressed genes, 16 are transcription factor genes and 45 are stress-related genes, both of which are upregulated significantly in transgenic plants, compared with the control. Under salt stress, the transgenic plants showed significant increases in plant height, root length, fresh weight, and abscisic acid (ABA) and gibberellin (GA) concentration compared with the control, suggesting that overexpression of ERF76 in transgenic poplar upregulated the expression of stress-related genes and increased the ability of ABA and GA biosynthesis, which resulted in stronger tolerance to salt stress.

Description: Summer droughts are likely to increase in frequency and intensity across Europe, yet long-lived trees may have a limited ability to tolerate drought. It is therefore critical that we improve our understanding of phenotypic plasticity to drought in natural populations for ecologically and economically important trees such as Populus nigra L. A common garden experiment was conducted using ~500 wild P. nigra trees, collected from 11 river populations across Europe. Phenotypic variation was found across the collection, with southern genotypes from Spain and France characterized by small leaves and limited biomass production. To examine the relationship between phenotypic variation and drought tolerance, six genotypes with contrasting leaf morphologies were subjected to a water deficit experiment. ‘North eastern’ genotypes were collected at wet sites and responded to water deficit with reduced biomass growth, slow stomatal closure and reduced water use efficiency (WUE) assessed by 13 C. In contrast, ‘southern’ genotypes originating from arid sites showed rapid stomatal closure, improved WUE and limited leaf loss. Transcriptome analyses of a genotype from Spain (Sp2, originating from an arid site) and another from northern Italy (Ita, originating from a wet site) revealed dramatic differences in gene expression response to water deficit. Transcripts controlling leaf development and stomatal patterning, including SPCH , ANT , ER , AS1 , AS2 , PHB , CLV1 , ERL1–3 and TMM , were down-regulated in Ita but not in Sp2 in response to drought.

Description: Isoprene is the most abundant type of nonmethane, biogenic volatile organic compound in the atmosphere, and it is produced mainly by terrestrial plants. The tropical tree species Ficus septica Burm. F. (Rosales: Moraceae) has been shown to cease isoprene emissions when exposed to temperatures of 12 °C or lower and to re-induce isoprene synthesis upon subsequent exposure to temperatures of 30 °C or higher for 24 h. To elucidate the regulation of genes underlying the disabling and then induction of isoprene emission during acclimatization to ambient temperature, we conducted gene expression analyses of F. septica plants under changing temperature using quantitative real-time polymerase chain reaction and western blotting. Transcription levels were analyzed for 17 genes that are involved in metabolic pathways potentially associated with isoprene biosynthesis, including isoprene synthase ( ispS ). The protein levels of ispS were also measured. Changes in transcription and protein levels of the ispS gene, but not in the other assessed genes, showed identical temporal patterns to isoprene emission capacity under the changing temperature regime. The ispS protein levels strongly and positively correlated with isoprene emission capacity ( R 2  = 0.92). These results suggest that transcriptional regulation of ispS gave rise to the temporal variation in isoprene emission capacity in response to changing temperature.

Description: Clonal integration between ramets can be an ecological advantage of clonal plant species in environments where resources are patchily distributed. We investigated physiological integration among Populus balsamifera L. ramets under drought stress in order to demonstrate water sharing between connected ramets. Pairs of connected ramets were grown in separate pots in the greenhouse where half of ramets had the parental root connection severed and half were left intact. Drought stress was applied to one ramet, and growth, specific leaf area (SLA), net photosynthesis, stomatal conductance, leaf water potential and carbon isotopic composition ( 13 C) were measured after an 8-week growing period. Droughted ramets connected to watered ramets were able to maintain high gas exchange activity and water potential, similar to watered ramets. Leaf water potential and SLA results showed that the root connection was more beneficial for proximal compared with distal ramets. The parental root connection also allowed droughted ramets to discriminate more against 13 C compared with severed ramets. In conclusion, this study shows compelling evidence of physiological integration of connected P. balsamifera ramets through water sharing.

Description: A formula for the norm of a bilinear Schur multiplier acting from the Cartesian product $\mathcal S^2\times \mathcal S^2$ of two copies of the Hilbert–Schmidt classes into the trace class $\mathcal S^1$ is established in terms of linear Schur multipliers acting on the space $\mathcal S^\infty $ of all compact operators. Using this formula, we resolve Peller's problem on Koplienko–Neidhardt trace formulae. Namely, we prove that there exist a twice continuously differentiable function $f$ with a bounded second derivative, a self-adjoint (unbounded) operator $A$ and a self-adjoint operator $B\in \mathcal S^2$ such that \[ f(A+B)-f(A)-\left.\frac{d}{dt}(f(A+tB))\right\vert_{t=0}\notin \mathcal S^1. \]

Description: Let $\mu $ be a probability measure on $ \mathbb R^n$ with a bounded density $f$ . We prove that the marginals of $f$ on most subspaces are well-bounded. For product measures, studied recently by Rudelson and Vershynin, our results show there is a trade-off between the strength of such bounds and the probability with which they hold. Our proof rests on new affinely invariant extremal inequalities for certain averages of $f$ on the Grassmannian and affine Grassmannian. These are motivated by Lutwak's dual affine quermassintegrals for convex sets. We show that key invariance properties of the latter, due to Grinberg, extend to families of functions. The inequalities we obtain can be viewed as functional analogues of results due to Busemann–Straus, Grinberg and Schneider. As an application, we show that without any additional assumptions on $\mu $ , any marginal $\pi _E(\mu )$ , or a small perturbation thereof, satisfies a nearly optimal small-ball probability.

Description: Let $\pi :X\to \mathbb {P}^1_{\mathbb {Q}}$ be a non-singular conic bundle over $\mathbb {Q}$ having $n$ non-split fibres and denote by $N(\pi ,B)$ the cardinality of the fibres of Weil height at most $B$ that possess a rational point. Serre showed in 1990 that a direct application of the large sieve yields \[ N(\pi,B)\ll B^2(\log B)^{-n/2} \] and raised the problem of proving that this is the true order of magnitude of $N(\pi ,B)$ under the necessary assumption that there exists at least one smooth fibre with a rational point. We solve this problem for all non-singular conic bundles of rank at most 3. Our method comprises the use of Hooley neutralisers, estimating divisor sums over values of binary forms, and an application of the Rosser–Iwaniec sieve.

Description: We associate a dimer algebra $A$ to a Postnikov diagram $D$ (in a disc) corresponding to a cluster of minors in the cluster structure of the Grassmannian ${\rm Gr}(k,n)$ . We show that $A$ is isomorphic to the endomorphism algebra of a corresponding Cohen–Macaulay module $T$ over the algebra $B$ used to categorify the cluster structure of ${\rm Gr}(k,n)$ by Jensen–King–Su. It follows that $B$ can be realised as the boundary algebra of $A$ , that is, the subalgebra $eAe$ for an idempotent $e$ corresponding to the boundary of the disc. The construction and proof uses an interpretation of the diagram $D$ , with its associated plabic graph and dual quiver (with faces), as a dimer model with boundary. We also discuss the general surface case, in particular computing boundary algebras associated to the annulus.

Description: We describe a ring whose category of Cohen–Macaulay modules provides an additive categorification of the cluster algebra structure on the homogeneous coordinate ring of the Grassmannian of $k$ -planes in $n$ -space. More precisely, there is a cluster character defined on the category which maps the rigid indecomposable objects to the cluster variables and the maximal rigid objects to clusters. This is proved by showing that the quotient of this category by a single projective–injective object is Geiss–Leclerc–Schröer's category Sub $Q_k$ , which categorifies the coordinate ring of the big cell in this Grassmannian.

Description: We develop a way of seeing a complete orientable hyperbolic 4-manifold $ {\mathcal {M}}$ as an orbifold cover of a Coxeter polytope $ {\mathcal {P}} \subset \mathbb {H}^4$ that has a facet colouring. We also develop a way of finding a totally geodesic sub-manifold $ {\mathcal {N}}$ in $ {\mathcal {M}}$ , and describing the result of mutations along $ {\mathcal {N}}$ . As an application of our method, we construct an example of a complete orientable hyperbolic 4-manifold $ {\mathcal {X}}$ with a single non-toric cusp and a complete orientable hyperbolic 4-manifold ${\mathcal {Y}}$ with a single toric cusp. Both $ {\mathcal {X}}$ and $ {\mathcal {Y}}$ have twice the minimal volume among all complete orientable hyperbolic 4-manifolds.

Description: The covariogram $g_{K}$ of a convex body $K$ in $ \mathbb {R}^n$ is the function that associates to each $x\in \mathbb {R}^n$ the volume of the intersection of $K$ with $K+x$ . Determining $K$ from the knowledge of $g_K$ is known as the Covariogram Problem. It is equivalent to determining the characteristic function $1_K$ of $K$ from the modulus of its Fourier transform $\widehat {{1_K}}$ in $ \mathbb {R}^n$ , a particular instance of the Phase Retrieval Problem. We connect the Covariogram Problem to two aspects of the Fourier transform $\widehat {{1_K}}$ seen as a function in $\mathbb {C}^n$ . The first connection is with the problem of determining $K$ from the knowledge of the zero set of $\widehat {{1_K}}$ in $\mathbb {C}^n$ . To attack this problem T. Kobayashi studied the asymptotic behavior at infinity of this zero set. We obtain this asymptotic behavior assuming less regularity on $K$ and we use this result as an essential ingredient for proving that when $K$ is sufficiently smooth and in any dimension $n$ , $K$ is determined by $g_K$ in the class of sufficiently smooth bodies. The second connection is with the irreducibility of the entire function $\widehat {{1_K}}$ . This connection also shows a link between the Covariogram Problem and the Pompeiu Problem in integral geometry.

Description: Let $\varphi :X\to S$ be a morphism between smooth complex analytic spaces and let $f=0$ define a free divisor on $S$ . We prove that if the deformation space $T^1_{X/S}$ of $\varphi $ is a Cohen–Macaulay $\mathcal {O}_X$ -module of codimension 2, and all of the logarithmic vector fields for $f=0$ lift via $\varphi $ , then $f\circ \varphi =0$ defines a free divisor on $X$ ; this is generalized in several directions. Among applications we recover a result of Mond–van Straten, generalize a construction of Buchweitz–Conca, and show that a map $\varphi :\mathbb {C}^{n+1}\to \mathbb {C}^n$ with critical set of codimension 2 has a $T^1_{X/S}$ with the desired properties. Finally, if $X$ is a representation of a reductive complex algebraic group $G$ and $\varphi $ is the algebraic quotient $X\to S=X\!{/\!/} G$ with $X\!{/\!/} G$ smooth, then we describe sufficient conditions for $T^1_{X/S}$ to be Cohen–Macaulay of codimension 2. In one such case, a free divisor on $\mathbb {C}^{n+1}$ lifts under the operation of ‘castling’ to a free divisor on $\mathbb {C}^{n(n+1)}$ , partially generalizing work of Granger–Mond–Schulze on linear free divisors. We give several other examples of such representations.

Description: Let $M^n$ be a compact manifold of dimension $n$ with free $T^k$ -action. We consider collapsings of $M$ on $N=M/T^k$ such that the sectional curvature and diameter of $M$ satisfy $|K(M)|\leq a$ and $ {\rm diam}(M) 〈 d$ , and give examples of collapsings for all $k$ such that the first non-zero eigenvalue of Laplacian acting on 1-forms and 2-forms of $M$ are bounded above by $c(M)\cdot \hbox {inj}(M)^{2k}$ . Moreover, we prove that the first non-zero eigenvalue of Laplacian acting on 1-forms of all principal $T^k$ -bundle $M$ over $N$ is bounded below by $c(n,a,d,N)\cdot {\rm Vol}(M)^2$ and $c\cdot \hbox {inj}(M)^{2k}$ when $M$ collapses on $N$ .

Description: We give explicit atomic bases of arbitrary coefficient-free cluster algebras of types A and à . This entails showing that the minimal elements of the positive semiring of these cluster algebras form a linear basis over the integers for the cluster algebra.

Description: We prove that strongly F -regular and F -pure singularities satisfy Bertini-type theorems (including in the context of pairs) by building upon a framework of Cumino, Greco and Manaresi (compare with the work of Jouanolou and Spreafico). We also prove that F -injective singularities fail to satisfy even the most basic Bertini-type results.

Description: This is the second of a pair of papers on the Delta-group structure on the braid and mapping class groups of a surface. We obtain a description of the homotopy groups of these Delta-groups and generalize to an arbitrary surface the Berrick–Cohen–Wong–Wu exact sequence relating the Brunnian braid groups of the 2-sphere to its homotopy groups. We prove a similar result for Brunnian mapping class groups.

Description: We construct a geometric realization of the Khovanov–Lauda–Rouquier algebra R associated with a symmetric Borcherds–Cartan matrix A = ( a ij ) i , j I via quiver varieties. As an application, if a ii != 0 for any i I , we prove that there exists a one-to-one correspondence between Kashiwara's lower global basis (or Lusztig's canonical basis) of U A – (g) (respectively, V A ( )) and the set of isomorphism classes of indecomposable projective graded modules over R (respectively, R ).

Description: The purpose of this paper is to study the nature of quasi-invariant measures for finitely generated non-discrete subgroups of Diff ( S 1 ). For this, we apply ideas involving the closure of these groups to find out that the regularity of the measure depends on a ‘measurable version’ of well-known problems concerning stable self-intersection of Cantor sets. As applications, we prove that every d -quasiconformal probability measure for a non-solvable and non-discrete group must be absolutely continuous. Concerning singular quasi-invariant measures, it is also proved that their associated Hausdorff measures must either be zero or of infinite mass, a result contrasting with the case of dynamically defined Cantor sets and also applicable to the examples of singular stationary measures constructed by Kaimanovich and Le Prince. As a further application of our methods, a theorem of rigidity for measurable conjugations between groups as above is obtained.

Description: We study the space of period polynomials associated with modular forms of integral weight for finite-index subgroups of the modular group. For the modular group, this space is endowed with a pairing, corresponding to the Petersson inner product on modular forms via a formula of Haberland, and with an action of Hecke operators, defined algebraically by Zagier. We generalize Haberland's formula to (not necessarily cuspidal) modular forms for finite-index subgroups, and we show that it conceals two stronger formulas. We extend the action of Hecke operators to period polynomials of modular forms, we show that the pairing on period polynomials appearing in Haberland's formula is nondegenerate, and we determine the adjoints of Hecke operators with respect to it. We give a few applications for 1 ( N ): an extension of the Eichler–Shimura isomorphism to the entire space of modular forms; the determination of the relations satisfied by the even and odd parts of period polynomials associated with cusp forms, which are independent of the period relations; and an explicit formula for Fourier coefficients of Hecke eigenforms in terms of their period polynomials, generalizing the Coefficient theorem of Manin.

Description: We develop theorems which produce a multitude of hyperbolic triples for the finite classical groups. We apply these theorems to prove that every quasisimple group except Alt (5) and SL 2 (5) is a Beauville group. In particular, we settle a conjecture of Bauer, Catanese and Grunewald which asserts that all non-abelian finite quasisimple groups except for the alternating group Alt (5) are Beauville groups.

Description: Let U R d be open and convex. We prove that every (not necessarily Lipschitz or strongly) convex function f : U -〉 R can be approximated by real analytic convex functions, uniformly on all of U . We also show that C 0 -fine approximation of convex functions by smooth (or real analytic) convex functions on R d is possible in general if and only if d = 1. Nevertheless, for d ≥ 2, we give a characterization of the class of convex functions on R d which can be approximated by real analytic (or just smoother) convex functions in the C 0 -fine topology. It turns out that the possibility of performing this kind of approximation is not determined by the degree of local convexity or smoothness of the given function, but by its global geometrical behaviour. We also show that every C 1 convex and proper function on U can be approximated by C convex functions in the C 1 -fine topology, and we provide some applications of these results, concerning prescription of (sub-)differential boundary data to convex real analytic functions, and smooth surgery of convex bodies.

Description: Wood biophysical properties and the dynamics of water storage discharge and refilling were studied in the trunk of canopy tree species with diverse life history and functional traits in subtropical forests of northeast Argentina. Multiple techniques assessing capacitance and storage capacity were used simultaneously to improve our understanding of the functional significance of internal water sources in trunks of large trees. Sapwood capacitances of 10 tree species were characterized using pressure–volume relationships of sapwood samples obtained from the trunk. Frequency domain reflectometry was used to continuously monitor the volumetric water content in the main stems. Simultaneous sap flow measurements on branches and at the base of the tree trunk, as well as diurnal variations in trunk contraction and expansion, were used as additional measures of stem water storage use and refilling dynamics. All evidence indicates that tree trunk internal water storage contributes from 6 to 28% of the daily water budget of large trees depending on the species. The contribution of stored water in stems of trees to total daily transpiration was greater for deciduous species, which exhibited higher capacitance and lower sapwood density. A linear relationship across species was observed between wood density and growth rates with the higher wood density species (mostly evergreen) associated with lower growth rates and the lower wood density species (mostly deciduous) associated with higher growth rates. The large sapwood capacitance in deciduous species may help to avoid catastrophic embolism in xylem conduits. This may be a low-cost adaptation to avoid water deficits during peak water use at midday and under temporary drought periods and will contribute to higher growth rates in deciduous tree species compared with evergreen ones. Large capacitance appears to have a central role in the rapid growth patterns of deciduous species facilitating rapid canopy access as these species are less shade tolerant than evergreen species.

Description: Nuclear magnetic resonance (NMR) and NMR imaging (magnetic resonance imaging) offer the possibility to quantitatively and non-invasively measure the presence and movement of water. Unfortunately, traditional NMR hardware is expensive, poorly suited for plants, and because of its bulk and complexity, not suitable for use in the field. But does it need to be? We here explore how novel, small-scale portable NMR devices can be used as a flow sensor to directly measure xylem sap flow in a poplar tree ( Populus nigra L.), or in a dendrometer-like fashion to measure dynamic changes in the absolute water content of fruit or stems. For the latter purpose we monitored the diurnal pattern of growth, expansion and shrinkage in a model fruit (bean pod, Phaseolus vulgaris L.) and in the stem of an oak tree ( Quercus robur L.). We compared changes in absolute stem water content, as measured by the NMR sensor, against stem diameter variations as measured by a set of conventional point dendrometers, to test how well the sensitivities of the two methods compare and to investigate how well diurnal changes in trunk absolute water content correlate with the concomitant diurnal variations in stem diameter. Our results confirm the existence of a strong correlation between the two parameters, but also suggest that dynamic changes in oak stem water content could be larger than is apparent on the basis of the stem diameter variation alone.

Description: While natural spatial temperature gradients between measurement needles have been thoroughly investigated for continuous heat-based sap flow methods, little attention has been given to how natural changes in stem temperature impact heat pulse-based methods through temporal rather than spatial effects. By modelling the theoretical equation for both an ideal instantaneous pulse and a step pulse and applying a finite element model which included actual needle dimensions and wound effects, the influence of a varying stem temperature on heat pulse-based methods was investigated. It was shown that the heat ratio (HR) method was influenced, while for the compensation heat pulse and T max methods changes in stem temperatures of up to 0.002 °C s –1 did not lead to significantly different results. For the HR method, rising stem temperatures during measurements led to lower heat pulse velocity values, while decreasing stem temperatures led to both higher and lower heat pulse velocities, and to imaginary results for high flows. These errors of up to 40% can easily be prevented by including a temperature correction in the data analysis procedure, calculating the slope of the natural temperature change based on the measured temperatures before application of the heat pulse. Results of a greenhouse and outdoor experiment on Pinus pinea L. show the influence of this correction on low and average sap flux densities.

Description: The control of plant transpiration by stomata under water stress and recovery conditions is of paramount importance for plant performance and survival. Although both chemical and hydraulic signals emitted within a plant are considered to play a major role in controlling stomatal dynamics, they have rarely been assessed together. The aims of this study were to evaluate (i) the dynamics of chemical and hydraulic signals at leaf, stem and root level, and (ii) their effect on the regulation of stomatal conductance ( g s ) during water stress and recovery. Measurements of g s , water potential, abscisic acid (ABA) content and loss of hydraulic functioning at leaf, stem and root level were conducted during a water stress and recovery period imposed on 1-year-old olive plants ( Olea europaea L.). Results showed a strong hydraulic segmentation in olive plants, with higher hydraulic functioning losses in roots and leaves than in stems. The dynamics of hydraulic conductance of roots and leaves observed as water stress developed could explain both a protection of the hydraulic functionality of larger organs of the plant (i.e., branches, etc.) and a role in the down-regulation of g s . On the other hand, ABA also increased, showing a similar pattern to g s dynamics, and thus its effect on g s in response to water stress cannot be ruled out. However, neither hydraulic nor non-hydraulic factors were able to explain the delay in the full recovery of g s after soil water availability was restored.

Description: For isohydric trees mid-day water uptake is stable and depends on soil water status, reflected in pre-dawn leaf water potential ( pd ) and mid-day stem water potential ( md ), tree hydraulic conductance and a more-or-less constant leaf water potential ( l ) for much of the day, maintained by the stomata. Stabilization of l can be represented by a linear relationship between canopy resistance ( R c ) and vapor pressure deficit ( D ), and the slope ( B D ) is proportional to the steady-state water uptake. By analyzing sap flow (SF), meteorological and md measurements during a series of wetting and drying ( D / W ) cycles in a nectarine orchard, we found that for the range of md relevant for irrigated orchards the slope of the relationship of R c to D , B D is a linear function of md . R c was simulated using the above relationships, and its changes in the morning and evening were simulated using a rectangular hyperbolic relationship between leaf conductance and photosynthetic irradiance, fitted to leaf-level measurements. The latter was integrated with one-leaf, two-leaf and integrative radiation models, and the latter gave the best results. Simulated R c was used in the Penman–Monteith equation to simulate tree transpiration, which was validated by comparing with SF from a separate data set. The model gave accurate estimates of diurnal and daily total tree transpiration for the range of md s used in regular and deficit irrigation. Diurnal changes in tree water content were determined from the difference between simulated transpiration and measured SF . Changes in water content caused a time lag of 90–105 min between transpiration and SF for md between –0.8 and –1.55 MPa, and water depletion reached 3 l h –1 before noon. Estimated mean diurnal changes in water content were 5.5 l day –1  tree –1 at md of –0.9 MPa and increased to 12.5 l day –1  tree –1 at –1.45 MPa, equivalent to 6.5 and 16.5% of daily tree water use, respectively. Sixteen percent of the dynamic water volume was in the leaves. Inversion of the model shows that md can be predicted from D and R c , which may have some importance for irrigation management to maintain target values of md . That relationship will be explored in future research.

Description: Let $G$ be a compact connected Lie group, or more generally a path connected topological group of the homotopy type of a finite CW-complex, and let $X$ be a rational nilpotent $G$ -space. In this paper, we analyze the homotopy type of the homotopy fixed point set $X^{hG}$ , and the natural injection $k\colon X^G\hookrightarrow X^{hG}$ . We show that if $X$ is elliptic, that is, it has finite-dimensional rational homotopy and cohomology, then each path component of $X^{hG}$ is also elliptic. We also give an explicit algebraic model of the inclusion $k$ based on which we can prove, for instance, that for $G$ a torus, $\pi _* (k)$ is injective in rational homotopy but, often, far from being a rational homotopy equivalence.

Description: We employ the ergodic-theoretic machinery of scenery flows to address classical geometric measure-theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its set-theoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-similarity. These are sharp general formulations of phenomena that had been earlier found to hold in a number of special cases.

Description: A notion of tangential thickness of a manifold is introduced. An extensive calculation within the class of lens and fake lens spaces leads to a classification of such manifolds with thickness 1, 3 or 2 $k$ , for $k\geq 1$ . On the other hand, calculations of tangential thickness in terms of the dimension of the manifold and the rank of the fundamental group show very interesting and quite surprising correlations between these invariants.

Description: Extending a classical result of Widom from 1969, polynomials with small supremum norms are constructed for a large family of compact sets $\Gamma$ : their norm is at most a constant times the theoretical lower limit ${{\rm cap}}(\Gamma )^n$ , where ${{\rm cap}}(\Gamma )$ denotes logarithmic capacity. The construction is based on a discretization of the equilibrium measure, and the polynomials have the additional property that outside the given set $\Gamma$ they increase as fast as possible, namely as ${{\rm cap}}(\Gamma )^n\exp (ng_{ \overline {{{}C}}\setminus \Gamma }(z))$ , with the Green's function with pole at infinity in the exponent. This latter fact allows us to use these polynomials as building blocks in constructing Dirac delta-type polynomials around corners: if a compact set $K$ has a corner at some point $z_0$ , then Dirac delta-type polynomials (fast decreasing polynomials) peaking at $z_0$ are polynomials $P_n(z)$ with $P_n(z_0)=1$ that decrease as $|P_n(z)|\prec \exp (-n^ \beta |z-z_0|^ \gamma )$ on the set $K$ as $z$ moves away from $z_0$ . The possible $(\beta , \gamma )$ pairs are completely described in turn of the angle $\alpha \pi$ at $z_0$ ( $\beta \lt 1$ and $\gamma \ge \beta /(2- \alpha )$ or $\beta =1$ and $\gamma 〉 \beta /(2- \alpha )$ ). As application of these fast decreasing polynomials sharp Nikolskii- and Markov-type inequalities are proved for Jordan domains with corners. The paper uses distortion properties of conformal maps, potential theoretic techniques as well as the theory of weighted logarithmic potentials.

Description: We consider for every $n\in \mathbb {N}$ an algebra $\mathcal {A}_{n}$ of germs at $0\in \mathbb {R}^{n}$ of continuous real-valued functions, such that we can associate to every germ $f\in \mathcal {A}_{n}$ a (divergent) series $\mathcal {T}(f)$ with non-negative real exponents, which can be thought of as an asymptotic expansion of $f$ . We require that the $\mathbb {R}$ -algebra homomorphism $f\mapsto \mathcal {T}(f)$ be injective (quasianalyticity property). In this setting, we prove analogue results to Denef and van den Dries’ quantifier elimination theorem and Hironaka's rectilinearization theorem for subanalytic sets.

Description: Suppose that $F(x)\in \mathbb {Z}[\![x]\!]$ is a Mahler function and that $1/b$ is in the radius of convergence of $F(x)$ for an integer $b\geq 2$ . In this paper, we consider the approximation of $F(1/b)$ by algebraic numbers. In particular, we prove that $F(1/b)$ cannot be a Liouville number. If, in addition, $F(x)$ is regular, we show that $F(1/b)$ is either rational or transcendental, and in the latter case that $F(1/b)$ is an $S$ -number or a $T$ -number in Mahler's classification of real numbers.

Description: We develop techniques for computing zeta functions associated with nilpotent groups, not necessarily associative algebras, and modules, as well as Igusa-type zeta functions. At the heart of our method lies an explicit convex-geometric formula for a class of $p$ -adic integrals under non-degeneracy conditions with respect to associated Newton polytopes. Our techniques prove to be especially useful for the computation of topological zeta functions associated with algebras, resulting in the first systematic investigation of their properties.

Description: We give a bordism-theoretic characterization of those closed almost contact $(2q{+ }1)$ -manifolds (with $q\geq 2$ ) that admit a Stein fillable contact structure. Our method is to apply Eliashberg's $h$ -principle for Stein manifolds in the setting of Kreck's modified surgery. As an application, we show that any simply connected almost contact 7-manifold with torsion-free second homotopy group is Stein fillable. We also discuss the Stein fillability of exotic spheres and examine subcritical Stein fillability.

Description: Casson-type invariants emerging from Donaldson theory over certain negative-definite four-manifolds were recently suggested by Teleman. These are defined by an algebraic count of points in a zero-dimensional moduli space of flat instantons. Motivated by the cobordism programme of proving Witten's conjecture, we use a moduli space of ${\rm PU}(2)$ Seiberg–Witten monopoles to exhibit an oriented one-dimensional cobordism of the instanton moduli space to the empty space. The Casson-type invariant must therefore vanish.

Description: The dynamical and stationary behaviors of a fourth-order equation in the unit ball with clamped boundary conditions and a singular reaction term are investigated. The equation arises in the modeling of microelectromechanical systems and includes a positive voltage parameter $\lambda$ . It is shown that there is a threshold value $\lambda _* 〉 0$ of the voltage parameter such that no radially symmetric stationary solution exists for $\lambda 〉 \lambda _* $ , while at least two such solutions exist for $\lambda \in (0,\lambda _* )$ . Local and global well-posedness results are obtained for the corresponding hyperbolic and parabolic evolution problems as well as the occurrence of finite time singularities when $\lambda 〉 \lambda _* $ .

Description: Assuming the generalized Riemann hypothesis, we prove a quantitative estimate for the number of simple zeros on the critical line for $L$ -functions attached to classical holomorphic newforms.

Description: In this paper, we consider a $\mathbb {Q}$ -Fano $3$ -fold weighted complete intersection of codimension $2$ in the $85$ families listed in Iano-Fletcher's list and determine which cycle is a maximal center or not. For each maximal center, we construct either a birational involution which untwists the maximal singularity or a Sarkisov link centered at the cycle to another explicitly described Mori fiber space. As a consequence, nineteen families are proved to be birationally rigid and the remaining $66$ families are proved to be birationally non-rigid.

Description: Suppose that a sequence of numbers $x_n$ (a ‘signal’) is transmitted through a noisy channel. The receiver observes a noisy version of the signal with additive random fluctuations, $x_n + \xi _n$ , where $\xi _n$ is a sequence of independent standard Gaussian random variables. Suppose further that the signal is known to come from some fixed space ${\mathscr {X}}$ of possible signals. Is it possible to fully recover the transmitted signal from its noisy version? Is it possible to at least detect that a non-zero signal was transmitted? In this paper, we consider the case in which signals are infinite sequences and the recovery or detection are required to hold with probability 1. We provide conditions on the space ${\mathscr {X}}$ for checking whether detection or recovery are possible. We also analyze in detail several examples including spaces of Fourier transforms of measures, spaces with fixed amplitudes and the space of almost periodic functions. Many of our examples exhibit critical phenomena, in which a sharp transition is made from a regime in which recovery is possible to a regime in which even detection is impossible.

Description: In this paper, we study the semi-stable subcategories of the category of representations of a Euclidean quiver, and the possible intersections of these subcategories. Contrary to the Dynkin case, we find out that the intersection of semi-stable subcategories may not be semi-stable. However, only a finite number of exceptions occur, and we give a description of these subcategories. Moreover, one can attach a simplicial fan in $\mathbb {Q}^n$ to any acyclic quiver $Q$ , and this simplicial fan allows one to completely determine the canonical presentation of any element in $\mathbb {Z}^n$ . This fan has a nice description in the Dynkin and Euclidean cases: it is described using an arrangement of convex codimension-1 subsets of $\mathbb {Q}^n$ , each such subset being indexed by a real Schur root or a set of quasi-simple objects. This fan also characterizes when two different stability conditions give rise to the same semi-stable subcategory.

Description: The $j$ -multiplicity plays an important role in the intersection theory of Stückrad–Vogel cycles, while recent developments confirm the connections between the $\epsilon$ -multiplicity and equisingularity theory. In this paper, we establish, under some constraints, a relationship between the $j$ -multiplicity of an ideal and the degree of its fiber cone. As a consequence, we are able to compute the $j$ -multiplicity of all the ideals defining rational normal scrolls. By using the standard monomial theory, we can also compute the $j$ - and $\epsilon$ -multiplicity of ideals defining determinantal varieties: The found quantities are integrals which, quite surprisingly, are central in random matrix theory.

Description: Drought-related tree die-off episodes have been observed in all vegetated continents. Despite much research effort, however, the multiple interactions between carbon starvation, hydraulic failure and biotic agents in driving tree mortality under field conditions are still not well understood. We analysed the seasonal variability of non-structural carbohydrates (NSCs) in four organs (leaves, branches, trunk and roots), the vulnerability to embolism in roots and branches, native embolism (percentage loss of hydraulic conductivity (PLC)) in branches and the presence of root rot pathogens in defoliated and non-defoliated individuals in a declining Scots pine ( Pinus sylvestris L.) population in the NE Iberian Peninsula in 2012, which included a particularly dry and warm summer. No differences were observed between defoliated and non-defoliated pines in hydraulic parameters, except for a higher vulnerability to embolism at pressures below –2 MPa in roots of defoliated pines. No differences were found between defoliation classes in branch PLC. Total NSC (TNSC, soluble sugars plus starch) values decreased during drought, particularly in leaves. Defoliation reduced TNSC levels across tree organs, especially just before (June) and during (August) drought. Root rot infection by the fungal pathogen Onnia P. Karst spp. was detected but it did not appear to be associated to tree defoliation. However, Onnia infection was associated with reduced leaf-specific hydraulic conductivity and sapwood depth, and thus contributed to hydraulic impairment, especially in defoliated pines. Infection was also associated with virtually depleted root starch reserves during and after drought in defoliated pines. Moreover, defoliated and infected trees tended to show lower basal area increment. Overall, our results show the intertwined nature of physiological mechanisms leading to drought-induced mortality and the inherent difficulty of isolating their contribution under field conditions.

Description: Non-structural carbohydrates (NSCs) are critical to maintain plant metabolism under stressful environmental conditions, but we do not fully understand how NSC allocation and utilization from storage varies with stress. While it has become established that storage allocation is unlikely to be a mere overflow process, very little empirical evidence has been produced to support this view, at least not for trees. Here we present the results of an intensively monitored experimental manipulation of whole-tree carbon (C) balance (young Picea abies (L.) H Karst.) using reduced atmospheric [CO 2 ] and drought to reduce C sources. We measured specific C storage pools (glucose, fructose, sucrose, starch) over 21 weeks and converted concentration measurement into fluxes into and out of the storage pool. Continuous labeling ( 13 C) allowed us to track C allocation to biomass and non-structural C pools. Net C fluxes into the storage pool occurred mainly when the C balance was positive. Storage pools increased during periods of positive C gain and were reduced under negative C gain. 13 C data showed that C was allocated to storage pools independent of the net flux and even under severe C limitation. Allocation to below-ground tissues was strongest in control trees followed by trees experiencing drought followed by those grown under low [CO 2 ]. Our data suggest that NSC storage has, under the conditions of our experimental manipulation (e.g., strong progressive drought, no above-ground growth), a high allocation priority and cannot be considered an overflow process. While these results also suggest active storage allocation, definitive proof of active plant control of storage in woody plants requires studies involving molecular tools.

Description: This study quantified the effect of soil warming on sap flow density ( Q s ) of Pinus cembra L. at the treeline in the Central Tyrolean Alps. To enhance soil temperature we installed a transparent roof construction above the forest floor around six trees. Six other trees served as controls in the absence of any manipulation. Roofing enhanced growing season mean soil temperature by 1.6, 1.3 and 1.0 °C at 5, 10 and 20 cm soil depth, respectively, while soil water availability was not affected. Sap flow density (using Granier-type thermal dissipation probes) and environmental parameters were monitored throughout three growing seasons. During the first year of treatment, no warming effect was detected on Q s . However, soil warming caused Q s to increase significantly by 11 and 19% above levels in control trees during the second and third year, respectively. This effect appeared to result from warming-induced root production, a reduction in viscosity and perhaps an increase also in root hydraulic conductivity. Hardly affected were leaf-level net CO 2 uptake rate and conductance for water vapour, so that water-use efficiency stayed unchanged as confirmed by needle 13 C analysis. We conclude that tree water loss will increase with soil warming, which may alter the water balance within the treeline ecotone of the Central Austrian Alps in a future warming environment.

Description: Process-based models that link seasonally varying environmental signals to morphological features within tree rings are essential tools to predict tree growth response and commercially important wood quality traits under future climate scenarios. This study evaluated model portrayal of radial growth and wood anatomy observations within a mature maritime pine ( Pinus pinaster (L.) Aït.) stand exposed to seasonal droughts. Intra-annual variations in tracheid anatomy and wood density were identified through image analysis and X-ray densitometry on stem cores covering the growth period 1999–2010. A cambial growth model was integrated with modelled plant water status and sugar availability from the soil–plant–atmosphere transfer model MuSICA to generate estimates of cell number, cell volume, cell mass and wood density on a weekly time step. The model successfully predicted inter-annual variations in cell number, ring width and maximum wood density. The model was also able to predict the occurrence of special anatomical features such as intra-annual density fluctuations (IADFs) in growth rings. Since cell wall thickness remained surprisingly constant within and between growth rings, variations in wood density were primarily the result of variations in lumen diameter, both in the model and anatomical data. In the model, changes in plant water status were identified as the main driver of the IADFs through a direct effect on cell volume. The anatomy data also revealed that a trade-off existed between hydraulic safety and hydraulic efficiency. Although a simplified description of cambial physiology is presented, this integrated modelling approach shows potential value for identifying universal patterns of tree-ring growth and anatomical features over a broad climatic gradient.

Description: Selecting plantation species to balance water use and production requires accurate models for predicting how species will tolerate and respond to environmental conditions. Although interspecific variation in water use occurs, species-specific parameters are rarely incorporated into physiologically based models because often the appropriate species parameters are lacking. To determine the physiological control over water use in Eucalyptus , five stands of Eucalyptus species growing in a common garden were measured for sap flux rates and their stomatal response to vapour pressure deficit ( D ) was assessed. Maximal canopy conductance and whole-canopy stomatal sensitivity to D and reduced water availability were lower in species originating from more arid climates of origin than those from humid climates. Species from humid climates showed a larger decline in maximal sap flux density ( J Smax ) with reduced water availability, and a lower D at which stomatal closure occurred than species from more arid climates, implying larger sensitivity to water availability and D in these species. We observed significant ( P  〈 0.05) correlations of species climate of origin with mean vessel diameter ( R 2  = 0.90), stomatal sensitivity to D ( R 2  = 0.83) and the size of the decline in J Smax to restricted water availability ( R 2  = 0.94). Thus aridity of climate of origin appears to have a selective role in constraining water-use response among the five Eucalyptus plantation species. These relationships emphasize that within this congeneric group of species, climate aridity constrains water use. These relationships have implications for species choices for tree plantation success against drought-induced losses and the ability to manage Eucalyptus plantations against projected changes in water availability and evaporation in the future.

Description: Mixtures can be more productive than monocultures and may therefore use more water, which may make them more susceptible to droughts. The species interactions that influence growth, transpiration and water-use efficiency (WUE, tree growth per unit transpiration) within a given mixture vary with intra- and inter-annual climatic variability, stand density and tree size, but these effects remain poorly quantified. These relationships were examined in mixtures and monocultures of Eucalyptus globulus Labill. and Acacia mearnsii de Wildeman. Growth and transpiration were measured between ages 14 and 15 years. All E. globulus trees in mixture that were growing faster than similar sized trees in monocultures had higher WUE, while trees with similar growth rates had similar WUE. By the age of 14 years A. mearnsii trees were beginning to senesce and there were no longer any relationships between tree size and growth or WUE. The relationship between transpiration and tree size did not differ between treatments for either species, so stand-level increases in transpiration simply reflected the larger mean tree size in mixtures. Increasing neighbourhood basal area increased the complementarity effect on E. globulus growth and transpiration. The complementarity effect also varied throughout the year, but this was not related to the climatic seasonality. This study shows that stand-level responses can be the net effect of a much wider range of individual tree-level responses, but at both levels, if growth has not increased for a given species, it appears unlikely that there will be differences in transpiration or WUE for that species. Growth data may provide a useful initial indication of whether mixtures have higher transpiration or WUE, and which species and tree sizes contribute to this effect.

Description: Tree growth is frequently linked to weather conditions prior to the growing season but our understanding of these lagged climate signatures is still poorly developed. We investigated the influence of masting behaviour on the relationship between growth and climate in European Beech ( Fagus sylvatica L.) using a rare long-term dataset of seed production and a new regional tree ring chronology. Fagus sylvatica is a masting species with synchronous variations in seed production which are strongly linked to the temperature in the previous two summers. We noted that the weather conditions associated with years of heavy seed production (mast years) were the same as commonly reported correlations between growth and climate for this species. We tested the hypothesis that a trade-off between growth and reproduction in mast years could be responsible for the observed lagged correlations between growth and previous summers' temperatures. We developed statistical models of growth based on monthly climate variables, and show that summer drought (negative correlation), temperature of the previous summer (negative) and temperature of the summer 2 years previous (positive) are significant predictors of growth. Replacing previous summers' temperature in the model with annual seed production resulted in a model with the same predictive power, explaining the same variance in growth. Masting is a common behaviour in many tree species and these findings therefore have important implications for the interpretation of general climate–growth relationships. Lagged correlations can be the result of processes occurring in the year of growth (that are determined by conditions in previous years), obviating or reducing the need for ‘carry-over’ processes such as carbohydrate depletion to be invoked to explain this climate signature in tree rings. Masting occurs in many tree species and these findings therefore have important implications for the interpretation of general climate–growth relationships.

Description: The physiological response of plants growing in their natural habitat is strongly determined by seasonal variations in environmental conditions and the interaction of abiotic and biotic stresses. Here, leaf water and nutrient contents, changes in cellular redox state and endogenous levels of stress-related phytohormones (abscisic acid (ABA), salicylic acid and jasmonates) were examined during the rainy and dry season in Vellozia gigantea , an endemic species growing at high elevations in the rupestrian fields of the Espinhaço Range in Brazil. Enhanced stomatal closure and increased ABA levels during the dry season were associated with an efficient control of leaf water content. Moreover, reductions in 12- oxo -phytodienoic acid (OPDA) levels during the dry season were observed, while levels of other jasmonates, such as jasmonic acid and jasmonoyl-isoleucine, were not affected. Changes in ABA and OPDA levels correlated with endogenous concentrations of iron and silicon, hydrogen peroxide, and vitamin E, thus indicating complex interactions between water and nutrient contents, changes in cellular redox state and endogenous hormone concentrations. Results also suggested crosstalk between activation of mechanisms for drought stress tolerance (as mediated by ABA) and biotic stress resistance (mediated by jasmonates), in which vitamin E levels may serve as a control point. It is concluded that, aside from a tight ABA-associated regulation of stomatal closure during the dry season, crosstalk between activation of abiotic and biotic defences, and nutrient accumulation in leaves may be important modulators of plant stress responses in plants growing in their natural habitat.

Description: The presence of the American root-rot disease fungus Heterobasidion irregulare Garbel. & Otrosina was detected in Italian coastal pine forests ( Pinus pinea L.) in addition to the common native species Heterobasidion annosum (Fries) Brefeld. High levels of tropospheric ozone (O 3 ) as an atmospheric pollutant are usually experienced in Mediterranean pine forests. To explore the effect of interaction between the two Heterobasidion species and ozone pollution on P. pinea , an open-top chamber (OTC) experiment was carried out. Five-year-old P. pinea seedlings were inoculated with the fungal species considered ( H. irregulare , H. annosum and mock-inoculation as control), and then exposed in charcoal-filtered open-top chambers (CF-OTC) and non-filtered ozone-enriched chambers (NF+) from July to the first week of August 2010 at the experimental facilities of Curno (North Italy). Fungal inoculation effects in an ozone-enriched environment were assessed as: (i) the length of the inoculation lesion; (ii) chlorophyll a fluorescence (ChlF) responses; and (iii) analysis of resin terpenes. Results showed no differences on lesion length between fungal and ozone treatments, whereas the short-term effects of the two stress factors on ChlF indicate an increased photosynthetic efficiency, thus suggesting the triggering of compensation/repair processes. The total amount of resin terpenes is enhanced by fungal infection of both species, but depressed by ozone to the levels observed in mock-inoculated plants. Variations in terpene profiles were also induced by stem base inoculations and ozone treatment. Ozone might negatively affect terpene defences making plants more susceptible to pathogens and insects.

Description: Let $\pi : X \to Y$ be a morphism of projective varieties and suppose that $\alpha $ is a pseudo-effective numerical cycle class satisfying $\pi _{*}\alpha =0$ . A conjecture of Debarre, Jiang, and Voisin predicts that $\alpha $ is a limit of classes of effective cycles contracted by $\pi $ . We establish new cases of the conjecture for higher codimension cycles. In particular, we prove a strong version when $X$ is a fourfold and $\pi $ has relative dimension 1.

Description: Let $R$ be a group of prime order $r$ that acts on the $r'$ -group $G$ , let $RG$ be the semidirect product of $G$ with $R$ , let ${\mathbb {F}}$ be a field and $V$ be a faithful completely reducible $\mathbb {F}[{RG}]$ -module. Trivially, $C_{G}({R})$ acts on $C_{V}({R})$ . Let $K$ be the kernel of this action. What can be said about $K$ ? This question is considered when $G$ is soluble. It turns out that $K$ is subnormal in $G$ or $r$ is a Fermat or half-Fermat prime. In the latter cases, the subnormal closure of $K$ in $G$ is described. Several applications to the theory of automorphisms of soluble groups are given.

Description: The mono-epi (ME) exact structure on the morphisms of an exact category $(\mathcal {A}; \mathcal {E})$ is introduced and used to prove ideal versions of Salce's Lemma, Christensen's (Ghost) Lemma, and Wakamatsu's Lemma for an exact category. Salce's Lemma establishes a bijective correspondence $\mathcal {I} \mapsto \mathcal {I}^{\perp }$ between the class of special precovering ideals of $(\mathcal {A}; \mathcal {E})$ and that of its special preenveloping ideals. ME-extensions of morphisms are used to define an extension $\mathcal {I} \diamond \mathcal {J}$ of ideals. Christensen's Lemma asserts that the class of special precovering (respectively, special preenveloping) ideals is closed under products and extensions and that the bijective correspondence of Salce's Lemma satisfies $(\mathcal {I} \mathcal {J})^{\perp } = \mathcal {J}^{\perp } \diamond \mathcal {I}^{\perp }$ and $(\mathcal {I} \diamond \mathcal {J})^{\perp } = \mathcal {J}^{\perp } \mathcal {I}^{\perp }.$ Wakamatsu's Lemma asserts that if a covering ideal $\mathcal {I}$ is closed under ME-extensions, then it is a special precovering ideal. As an application, it is proved that if $G$ is a finite group and $\Phi $ is the ideal of phantom morphisms in the category $k[G]$ - $\rm Mod,$ then $\Phi ^{n-1}$ is the object ideal generated by projective modules, where $n$ is the nilpotency index of the Jacobson radical $J.$ If $R$ is a semiprimary ring, with $J^n =0,$ then $\Phi ^n$ is generated by projective modules. For a right coherent ring $R$ over which every cotorsion left $R$ -module has a coresolution of length $n$ by pure injective modules, $\Phi ^{n+1}$ is generated by flat modules.

Description: We complete the equisingular deformation classification of irreducible singular plane sextic curves. As a by-product, we also compute the fundamental groups of the complement of all but a few maximizing sextics.

Description: Let $P_{n}(x)= \sum _{i=0}^n \xi _i x^i$ be a Kac random polynomial where the coefficients $\xi _i$ are i.i.d. copies of a given random variable $\xi $ . Our main result is an optimal quantitative bound concerning real roots repulsion. This leads to an optimal bound on the probability that there is a real double root. As an application, we consider the problem of estimating the number of real roots of $P_n$ , which has a long history and in particular was the main subject of a celebrated series of papers by Littlewood and Offord from the 1940s. We show, for a large and natural family of atom variables $\xi $ , that the expected number of real roots of $P_n(x)$ is exactly $({2}/{\pi }) \log n +C +o(1)$ , where $C$ is an absolute constant depending on the atom variable $\xi $ . Prior to this paper, such a result was known only for the case when $\xi $ is Gaussian.

Description: The goal of this article was to study the Iwasawa theory of an abelian variety $A$ that has complex multiplication by a complex multiplication (CM) field $F$ that contains the reflex field of $A$ , which has supersingular reduction at every prime above $p$ . To do so, we make use of the signed Coleman maps constructed in our companion article [Kâzım Büyükboduk and Antonio Lei, ‘Integral Iwasawa theory of motives for non-ordinary primes’, 2014, in preparation, draft available upon request] to introduce signed Selmer groups as well as a signed $p$ -adic $L$ -function via a reciprocity conjecture that we formulate for the (conjectural) Rubin–Stark elements (which is a natural extension of the reciprocity conjecture for elliptic units). We then prove a signed main conjecture relating these two objects. To achieve this, we develop along the way a theory of Coleman-adapted rank- $g$ Euler–Kolyvagin systems to be applied with Rubin–Stark elements and deduce the main conjecture for the maximal $\mathbb {Z}_p$ -power extension of $F$ for the primes failing the ordinary hypothesis of Katz.

Description: We introduce a notion of rough paths on embedded submanifolds and demonstrate that this class of rough paths is natural. On the way, we develop a notion of rough integration and an efficient and intrinsic theory of rough differential equations (RDEs) on manifolds. The theory of RDEs is then used to construct parallel translation along manifold-valued rough paths. Finally, this framework is used to show that there is a one-to-one correspondence between rough paths on a $d$ -dimensional manifold and rough paths on $d$ -dimensional Euclidean space. This last result is a rough path analogue of Cartan's development map and its stochastic version which was developed by Eells and Elworthy and Malliavin.

Description: We show that several important normal subgroups $\Gamma $ of the mapping class group of a surface satisfy the following property: any free, ergodic, probability measure-preserving action $\Gamma \curvearrowright X$ is stably $OE$ -superrigid. These include the central quotients of most surface braid groups and most Torelli groups and Johnson kernels. In addition, we show that all these groups satisfy the measure equivalence rigidity and we describe all their lattice-embeddings. Using these results in combination with previous results from Chifan–Ioana–Kida [‘ $W^*$ -superrigidity for arbitrary actions of central quotients of braid groups’, Math. Ann. 361 (2015) 925–959], we deduce that any free, ergodic, probability measure-preserving action of almost any surface braid group is stably $W^*$ -superrigid, that is, it can be completely reconstructed from its von Neumann algebra.

Description: Motivated by recent work in the mathematics and engineering literature, we study integrability and non-tangential regularity on the two-torus for rational functions that are holomorphic on the bidisk. One way to study such rational functions is to fix the denominator and look at the ideal of polynomials in the numerator such that the rational function is square integrable. A concrete list of generators is given for this ideal as well as a precise count of the dimension of the subspace of numerators with a specified bound on bidegree. The dimension count is accomplished by constructing a natural pair of commuting contractions on a finite-dimensional Hilbert space and studying their joint generalized eigenspaces. Non-tangential regularity of rational functions on the polydisk is also studied. One result states that rational inner functions on the polydisk have non-tangential limits at every point of the $n$ -torus. An algebraic characterization of higher non-tangential regularity is given. We also make some connections with the earlier material and prove that rational functions on the bidisk which are square integrable on the two-torus are non-tangentially bounded at every point. Several examples are provided.

Description: We propose a construction of a tensor exact category $\mathcal {F}_X^m$ of Artin–Tate motivic sheaves with finite coefficients $\mathbb {Z}/m$ over an algebraic variety $X$ (over a field $K$ of characteristic prime to $m$ ) in terms of étale sheaves of $\mathbb {Z}/m$ -modules over $X$ . Among the objects of $\mathcal {F}_X^m$ , in addition to the Tate motives $\mathbb {Z}/m(j)$ , there are the cohomological relative motives with compact support $\mathcal {M}_{cc}^m(Y/X)$ of varieties $Y$ quasi-finite over $X$ . Exact functors of inverse image with respect to morphisms of algebraic varieties and direct image with compact supports with respect to quasi-finite morphisms of varieties $Y\longrightarrow X$ act on the exact categories $\mathcal {F}_X^m$ . Assuming the existence of triangulated categories of motivic sheaves $\mathcal {D}\mathcal {M}(X,\mathbb {Z}/m)$ over algebraic varieties $X$ over $K$ and a weak version of the ‘six operations’ in these categories, we identify $\mathcal {F}_X^m$ with the exact subcategory in $\mathcal {D}\mathcal {M}(X,\mathbb {Z}/m)$ consisting of all the iterated extensions of the Tate twists $\mathcal {M}_{cc}^m(Y/X)(j)$ of the motives $\mathcal {M}_{cc}^m(Y/X)$ . An isomorphism of the $\mathbb {Z}/m$ -modules ${\rm Ext}$ between the Tate motives $\mathbb {Z}/m(j)$ in the exact category $\mathcal {F}_X^m$ with the motivic cohomology modules predicted by the Beilinson–Lichtenbaum étale descent conjecture (recently proved by Voevodsky, Rost et al. ) holds for smooth varieties $X$ over $K$ if and only if the similar isomorphism holds for Artin–Tate motives over fields containing $K$ . When $K$ contains a primitive $m$ -root of unity, the latter condition is equivalent to a certain Koszulity hypothesis, as shown in our previous paper [Positselski, ‘Mixed Artin–Tate motives with finite coefficients’, Mosc. Math. J. 11 (2011) 317–402].

Description: We present new algorithms for computing zeta functions of algebraic varieties over finite fields. In particular, let $X$ be an arithmetic scheme (scheme of finite type over $\textbf {Z}$ ), and for a prime $p$ let $\zeta _{X_p}(s)$ be the local factor of its zeta function. We present an algorithm that computes $\zeta _{X_p}(s)$ for a single prime $p$ in time $p^{1/2+o(1)}$ , and another algorithm that computes $\zeta _{X_p}(s)$ for all primes $p 〈 N$ in time $N \log ^{3+o(1)} N$ . These generalise previous results of the author from hyperelliptic curves to completely arbitrary varieties.

Description: Initial growth of germinated seeds is an important life history stage, critical for establishment and succession in forests. Important questions remain regarding the differences among species in early growth potential arising from shade tolerance. In addition, the role of leaf habit in shaping relationships underlying shade tolerance-related differences in seedling growth remains unresolved. In this study we examined variation in morphological and physiological traits among seedlings of 10 forest tree species of the European temperate zone varying in shade tolerance and leaf habit (broadleaved winter-deciduous species vs needle-leaved conifers) during a 10-week period. Seeds were germinated and grown in a controlled environment simulating an intermediate forest understory light environment to resolve species differences in initial growth and biomass allocation. In the high-resource experimental conditions during the study, seedlings increased biomass allocation to roots at the cost of leaf biomass independent of shade tolerance and leaf habit. Strong correlations between relative growth rate (RGR), net assimilation rate (NAR), leaf area ratio (LAR), specific leaf area (SLA) and leaf mass fraction (LMF) indicate that physiology and biomass allocation were equally important determinants of RGR as plant structure and leaf morphology among these species. Our findings highlight the importance of seed mass- and seed size-related root morphology (specific root length—SRL) for shade tolerance during early ontogeny. Leaf and plant morphology (SLA, LAR) were more successful in explaining variation among species due to leaf habit than shade tolerance. In both broadleaves and conifers, shade-tolerant species had lower SRL and greater allocation of biomass to stems (stem mass fraction). Light-seeded shade-intolerant species with greater SRL had greater RGR in both leaf habit groups. However, the greatest plant mass was accumulated in the group of heavy-seeded shade-tolerant broadleaves. The results of our study suggest that the combinations of plant attributes enhancing growth under high light vary with shade tolerance, but differ between leaf habit groups.

Description: Rhizospheric nitric oxide (NO) and carbon dioxide (CO 2 ) are signalling compounds known to affect physiological processes in plants. Their joint influence on tree nitrogen (N) nutrition, however, is still unknown. Therefore, this study investigated, for the first time, the combined effect of rhizospheric NO and CO 2 levels on N uptake and N pools in European beech ( Fagus sylvatica L.) seedlings depending on N availability. For this purpose, roots of seedlings were exposed to one of the nine combinations (i.e., low, ambient, high NO plus CO 2 concentration) at either low or high N availability. Our results indicate a significant effect of rhizospheric NO and/or CO 2 concentration on organic and inorganic N uptake. However, this effect depends strongly on NO and CO 2 concentration, N availability and N source. Similarly, allocation of N to different N pools in the fine roots of beech seedlings also shifted with varying rhizospheric gas concentrations and N availability.

Description: Respiration from vegetation is a substantial part of the global carbon cycle and the responses of plant respiration to daily and seasonal fluctuations in temperature and light must be incorporated in models of terrestrial respiration to accurately predict these CO 2 fluxes. We investigated how leaf respiration ( R ) responded to changes in leaf temperature ( T leaf ) and irradiance in field-grown saplings of an evergreen tree ( Eucalyptus pauciflora Sieb. ex Spreng). Seasonal shifts in the thermal sensitivity of leaf R in the dark ( R dark ) and in the light ( R light ) were assessed by allowing T leaf to vary over the day in field-grown leaves over a year. The Q 10 of R (i.e., the relative increase in R for a 10 °C increase in T leaf ) was similar for R light and R dark and had a value of ~2.5; there was little seasonal change in the Q 10 of either R light or R dark , indicating that we may be able to use similar functions to model short-term temperature responses of R in the dark and in the light. Overall, rates of R light were lower than those of R dark , and the ratio of R light / R dark tended to increase with rising T leaf , such that light suppression of R was reduced at high T leaf values, in contrast to earlier work with this species. Our results suggest we cannot assume that R light / R dark decreases with increasing T leaf on daily timescales, and highlights the need for a better mechanistic understanding of what regulates light suppression of R in leaves.

Description: Climate-related variations in functional traits of boreal tree species can result both from physiological acclimation and genetic adaptation of local populations to their biophysical environment. To improve our understanding and prediction of the physiological and growth responses of populations to climate change, we studied the role of climate of seed origin in determining variations in functional traits and its implications for tree improvement programs for a commonly reforested boreal conifer, white spruce ( Picea glauca (Moench) Voss). We evaluated growth, root-to-shoot ratio (R/S), specific leaf area (SLA), needle nitrogen ( N mass ), total non-structural carbohydrates (NSC) and photosynthetic traits of 3-year-old seedlings in a greenhouse experiment using seed from six seed orchards (SO) representing the different regions where white spruce is reforested in Québec. Height and total dry mass (TDM) were positively correlated with photosynthetic capacity ( A max ), stomatal conductance ( g s ) and mesophyll conductance ( g m ). Total dry mass, but not height growth, was strongly correlated with latitude of seed origin (SO) and associated climate variables. A max , g s , g m and more marginally, photosynthetic nitrogen-use efficiency (PNUE) were positively associated with the mean July temperature of the SO, while water use efficiency (WUE) was negatively associated. Maximum rates of carboxylation ( V cmax ), maximum rates of electron transport ( J max ), SLA, N mass , NSC and R/S showed no pattern. Our results did not demonstrate a higher A max for northern seed orchards, although this has been previously hypothesized as an adaptation mechanism for maintaining carbon uptake in northern regions . We suggest that g s , g m , WUE and PNUE are the functional traits most associated with fine-scale geographic clines and with the degree of local adaptation of white spruce populations to their biophysical environments. These geographic patterns may reflect in situ adaptive genetic differences in photosynthetic efficiency along the cline.

Description: We evaluated the long-term (1995–2008) trends in foliar and sapwood metabolism, soil solution chemistry and tree mortality rates in response to chronic nitrogen (N) additions to pine and hardwood stands at the Harvard Forest Long Term Ecological Research (LTER) site. Common stress-related metabolites like polyamines (PAs), free amino acids (AAs) and inorganic elements were analyzed for control, low N (LN, 50 kg NH 4 NO 3  ha –1  year –1 ) and high N (HN, 150 kg NH 4 NO 3  ha –1  year –1 ) treatments. In the pine stands, partitioning of excess N into foliar PAs and AAs increased with both N treatments until 2002. By 2005, several of these effects on N metabolites disappeared for HN, and by 2008 they were mostly observed for LN plot. A significant decline in foliar Ca and P was observed mostly with HN for a few years until 2005. However, sapwood data actually showed an increase in Ca, Mg and Mn and no change in PAs in the HN plot for 2008, while AAs data revealed trends that were generally similar to foliage for 2008. Concomitant with these changes, mortality data revealed a large number of dead trees in HN pine plots by 2002; the mortality rate started to decline by 2005. Oak trees in the hardwood plot did not exhibit any major changes in PAs, AAs, nutrients and mortality rate with LN treatment, indicating that oak trees were able to tolerate the yearly doses of 50 kg NH 4 NO 3 ha –1  year –1 . However, HN trees suffered from physiological and nutritional stress along with increased mortality in 2008. In this case also, foliar data were supported by the sapwood data. Overall, both low and high N applications resulted in greater physiological stress to the pine trees than the oaks. In general, the time course of changes in metabolic data are in agreement with the published reports on changes in soil chemistry and microbial community structure, rates of soil carbon sequestration and production of woody biomass for this chronic N study. This correspondence of selected metabolites with other measures of forest functions suggests that the metabolite analyses are useful for long-term monitoring of the health of forest trees.

Description: To buffer against the high spatial and temporal heterogeneity of the riparian habitat, riparian tree species, such as black poplar ( Populus nigra L.), may display a high level of genetic variation and phenotypic plasticity for functional traits. Using a multisite common garden experiment, we estimated the relative contribution of genetic and environmental effects on the phenotypic variation expressed for individual leaf area, leaf shape, leaf structure and leaf carbon isotope discrimination ( 13 C) in natural populations of black poplar. Twenty-four to 62 genotypes were sampled in nine metapopulations covering a latitudinal range from 48°N to 42°N in France and in Italy and grown in two common gardens at Orléans (ORL) and at Savigliano (SAV). In the two common gardens, substantial genetic variation was expressed for leaf traits within all metapopulations, but its expression was modulated by the environment, as attested by the genotype x environment ( G x E ) interaction variance being comparable to or even greater than genetic effects. For LA, G x E interactions were explained by both changes in genotype ranking between common gardens and increased variation in SAV, while these interactions were mainly attributed to changes in genotype ranking for 13 C. The nine P. nigra metapopulations were highly differentiated for LA, as attested by the high coefficient of genetic differentiation ( Q ST = 0.50 at ORL and 0.51 at SAV), and the pattern of metapopulation differentiation was highly conserved between the two common gardens. In contrast, they were moderately differentiated for 13 C ( Q ST = 0.24 at ORL and 0.25 at SAV) and the metapopulation clustering changed significantly between common gardens. Our results evidenced that the nine P. nigra metapopulations present substantial genetic variation and phenotypic plasticity for leaf traits, which both represent potentially significant determinants of populations' capacities to respond, on a short-term basis and over generations, to environmental variations.

Description: Conifers have incurred high mortality during recent global-change-type drought(s) in the western USA. Mechanisms of drought-related tree mortality need to be resolved to support predictions of the impacts of future increases in aridity on vegetation. Hydraulic failure, carbon starvation and lethal biotic agents are three potentially interrelated mechanisms of tree mortality during drought. Our study compared a suite of measurements related to these mechanisms between 49 mature piñon pine ( Pinus edulis Engelm.) trees that survived severe drought in 2002 (live trees) and 49 trees that died during the drought (dead trees) over three sites in Arizona and New Mexico. Results were consistent over all sites indicating common mortality mechanisms over a wide region rather than site-specific mechanisms. We found evidence for an interactive role of hydraulic failure, carbon starvation and biotic agents in tree death. For the decade prior to the mortality event, dead trees had twofold greater sapwood cavitation based on frequency of aspirated tracheid pits observed with scanning electron microscopy (SEM), smaller inter-tracheid pit diameter measured by SEM, greater diffusional constraints to photosynthesis based on higher wood 13 C, smaller xylem resin ducts, lower radial growth and more bark beetle (Coleoptera: Curculionidae) attacks than live trees. Results suggest that sapwood cavitation, low carbon assimilation and low resin defense predispose piñon pine trees to bark beetle attacks and mortality during severe drought. Our novel approach is an important step forward to yield new insights into how trees die via retrospective analysis.