Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions

We introduce an iterative method for computing the first eigenpair $(\lambda_{p},e_{p})$ for the $p$-Laplacian operator with homogeneous Dirichlet data as the limit of $(\mu_{q,}u_{q})$ as $q\rightarrow p^{-}$, where $u_{q}$ is the positive solution of the sublinear Lane-Emden equation $-\Delta_{p}u_{q}=\mu_{q}u_{q}^{q-1}$ with same boundary data. The method is shown to work for any smooth, bounded domain. Solutions to the Lane-Emden problem are obtained through inverse iteration of a super-solution which is derived from the solution to the torsional creep problem. Convergence of $u_{q}$ to $e_{p}$ is in the $C^{1}$-norm and the rate of convergence of $\mu_{q}$ to $\lambda_{p}$ is at least $O(p-q)$. Numerical evidence is presented.Comment: Section 5 was rewritten. Jed Brown was added as autho

Closing a gap in tropical forest biomass estimation : taking crown mass variation into account in pantropical allometries

Accurately monitoring tropical forest carbon stocks is a challenge that remains outstanding. Allometric models that consider tree diameter, height and wood density as predictors are currently used in most tropical forest carbon studies. In particular, a pantropical biomass model has been widely used for approximately a decade, and its most recent version will certainly constitute a reference model in the coming years. However, this reference model shows a systematic bias towards the largest trees. Because large trees are key drivers of forest carbon stocks and dynamics, understanding the origin and the consequences of this bias is of utmost concern. In this study, we compiled a unique tree mass data set of 673 trees destructively sampled in five tropical countries (101 trees > 100 cm in diameter) and an original data set of 130 forest plots (1 ha) from central Africa to quantify the prediction error of biomass allometric models at the individual and plot levels when explicitly taking crown mass variations into account or not doing so. We first showed that the proportion of crown to total tree aboveground biomass is highly variable among trees, ranging from 3 to 88 %. This proportion was constant on average for trees = 45 Mg. This increase coincided with a progressive deviation between the pantropical biomass model estimations and actual tree mass. Taking a crown mass proxy into account in a newly developed model consistently removed the bias observed for large trees (> 1 Mg) and reduced the range of plot- level error (in %) from [-23; 16] to [0; 10]. The disproportionally higher allocation of large trees to crown mass may thus explain the bias observed recently in the reference pantropical model. This bias leads to far- from- negligible, but often overlooked, systematic errors at the plot level and may be easily corrected by taking a crown mass proxy for the largest trees in a stand into account, thus suggesting that the accuracy of forest carbon estimates can be significantly improved at a minimal cost

Test of a theoretical equation of state for elemental solids and liquids

We propose a means for constructing highly accurate equations of state (EOS) for elemental solids and liquids essentially from first principles, based upon a particular decomposition of the underlying condensed matter Hamiltonian for the nuclei and electrons. We also point out that at low pressures the neglect of anharmonic and electron-phonon terms, both contained in this formalism, results in errors of less than 5% in the thermal parts of the thermodynamic functions. Then we explicitly display the forms of the remaining terms in the EOS, commenting on the use of experiment and electronic structure theory to evaluate them. We also construct an EOS for Aluminum and compare the resulting Hugoniot with data up to 5 Mbar, both to illustrate our method and to see whether the approximation of neglecting anharmonicity et al. remains viable to such high pressures. We find a level of agreement with experiment that is consistent with the low-pressure results.Comment: Minor revisions for consistency with published versio

SINE RNA Induces Severe Developmental Defects in Arabidopsis thaliana and Interacts with HYL1 (DRB1), a Key Member of the DCL1 Complex

The proper temporal and spatial expression of genes during plant development is governed, in part, by the regulatory activities of various types of small RNAs produced by the different RNAi pathways. Here we report that transgenic Arabidopsis plants constitutively expressing the rapeseed SB1 SINE retroposon exhibit developmental defects resembling those observed in some RNAi mutants. We show that SB1 RNA interacts with HYL1 (DRB1), a double-stranded RNA-binding protein (dsRBP) that associates with the Dicer homologue DCL1 to produce microRNAs. RNase V1 protection assays mapped the binding site of HYL1 to a SB1 region that mimics the hairpin structure of microRNA precursors. We also show that HYL1, upon binding to RNA substrates, induces conformational changes that force single-stranded RNA regions to adopt a structured helix-like conformation. Xenopus laevis ADAR1, but not Arabidopsis DRB4, binds SB1 RNA in the same region as HYL1, suggesting that SINE RNAs bind only a subset of dsRBPs. Consistently, DCL4-DRB4-dependent miRNA accumulation was unchanged in SB1 transgenic Arabidopsis, whereas DCL1-HYL1-dependent miRNA and DCL1-HYL1-DCL4-DRB4-dependent tasiRNA accumulation was decreased. We propose that SINE RNA can modulate the activity of the RNAi pathways in plants and possibly in other eukaryotes

Beyond trait distances: Functional distinctiveness captures the outcome of plant competition

1. Functional trait distances between coexisting organisms reflect not only complementarity in the way they use resources, but also differences in their competitive abilities. Accordingly, absolute and relative trait distances have been widely used to capture the effects of niche dissimilarity and competitive hierarchies, respectively, on the performance of plants in competition. However, multiple dimensions of the plant phenotype are involved in these plant–plant interactions (PPI), challenging the use of relative trait distances to predict their outcomes. Furthermore, estimating the effects of competitive hierarchy on the performance of a group of coexisting plants remains particularly difficult since relative trait distances relate to the effects of a focal plant on another. 2. We argue that trait distinctiveness, an emerging facet of functional diversity that characterizes the eccentric position of a species (or genotype) in a phenotypic space, can reveal the unique role played by a given individual plant in a group of competing plants. We used the model crop species Oryza sativa spp. japonica to evaluate the ability of trait distances and trait distinctiveness to predict the outcome of intraspecific PPI on the performance of single genotype and genotype mixtures. We performed a screening experiment to characterize the phenotypic space of 49 rice genotypes based on 11 above-ground and root traits. We selected nine genotypes with contrasting positions in the phenotypic space and grew them in pots following a complete pairwise interaction design. 3. Relative distances and distinctiveness based on traits associated with light competition were by far the best predictors of the performance of single genotypes—taller genotypes that acquired resource faster being the best competitors—while absolute trait distances had no effect. These results indicate that competitive hierarchy for light dominates PPI in this experiment. Consistently, trait distinctiveness in plant height and age at flowering had the strongest, positive effects on mixture performance, confirming that functional distinctiveness captures the effects of trait hierarchies and asymmetric PPI at this scale. 4. Our findings shed new light on the role of trait diversity in regulating PPI and ecosystem processes and call for a greater consideration of functional distinctiveness in studies of coexistence mechanisms

Do native brown trout and non-native brook trout interact reproductively?

Reproductive interactions between native and non-native species of fish have received little attention compared to other types of interactions such as predation or competition for food and habitat. We studied the reproductive interactions between non-native brook trout (Salvelinus fontinalis) and native brown trout (Salmo trutta) in a Pyrenees Mountain stream (SW France). We found evidence of significant interspecific interactions owing to consistent spatial and temporal overlap in redd localizations and spawning periods. We observed mixed spawning groups composed of the two species, interspecific subordinate males, and presence of natural hybrids (tiger trout). These reproductive interactions could be detrimental to the reproduction success of both species. Our study shows that non-native species might have detrimental effects on native species via subtle hybridization behavior

Reconstructing the reproductive mode of an Ediacaran macro-organism.

Enigmatic macrofossils of late Ediacaran age (580-541 million years ago) provide the oldest known record of diverse complex organisms on Earth, lying between the microbially dominated ecosystems of the Proterozoic and the Cambrian emergence of the modern biosphere. Among the oldest and most enigmatic of these macrofossils are the Rangeomorpha, a group characterized by modular, self-similar branching and a sessile benthic habit. Localized occurrences of large in situ fossilized rangeomorph populations allow fundamental aspects of their biology to be resolved using spatial point process techniques. Here we use such techniques to identify recurrent clustering patterns in the rangeomorph Fractofusus, revealing a complex life history of multigenerational, stolon-like asexual reproduction, interspersed with dispersal by waterborne propagules. Ecologically, such a habit would have allowed both for the rapid colonization of a localized area and for transport to new, previously uncolonized areas. The capacity of Fractofusus to derive adult morphology by two distinct reproductive modes documents the sophistication of its underlying developmental biology.This work has been supported by the Natural Environment Research Council [grant numbers NE/I005927/1 to C.G.K., NE/J5000045/1 to J.J.M., NE/L011409/1 to A.G.L. and NE/G523539/1 to E.G.M.], and a Henslow Junior Research Fellowship from Cambridge Philosophical Society to A.G.L.This is the author accepted manuscript. The final version is available from NPG via http://dx.doi.org/10.1038/nature1464