Likelihood-based surrogate dimension reduction

We consider the problem of surrogate sufficient dimension reduction, that is, estimating the central subspace of a regression model, when the covariates are contaminated by measurement error. When no measurement error is present, a likelihood-based dimension reduction method that relies on maximizing the likelihood of a Gaussian inverse regression model on the Grassmann manifold is well-known to have superior performance to traditional inverse moment methods. We propose two likelihood-based estimators for the central subspace in measurement error settings, which make different adjustments to the observed surrogates. Both estimators are computed based on maximizing objective functions on the Grassmann manifold and are shown to consistently recover the true central subspace. When the central subspace is assumed to depend on only a few covariates, we further propose to augment the likelihood function with a penalty term that induces sparsity on the Grassmann manifold to obtain sparse estimators. The resulting objective function has a closed-form Riemann gradient which facilitates efficient computation of the penalized estimator. We leverage the state-of-the-art trust region algorithm on the Grassmann manifold to compute the proposed estimators efficiently. Simulation studies and a data application demonstrate the proposed likelihood-based estimators perform better than inverse moment-based estimators in terms of both estimation and variable selection accuracy

Metacommunity ecology of Symbiodiniaceae hosted by the coral Galaxea fascicularis

Coral−algae symbiosis represents the trophic and structural basis of coral reef ecosystems. However, despite global threats to coral reefs and the dependence of coral health and stress resistance upon such mutualisms, little is known about the community ecology of endosymbiotic Symbiodiniaceae. Concepts and methods from metacommunity ecology may be used to help us understand the assembly and stability of symbiont communities and the mutualisms they comprise. In this study, we sampled colonies of the symbiont-generalist coral Galaxea fascicularis in southwestern Japan and assessed the effects of environmental and host factors on Symbiodinia ceae community composition, while simultaneously exploring residual correlations among symbiont types that may reflect non-random assembly processes such as species interactions. We metabarcoded the Symbiodiniaceae ribosomal internal transcribed spacer 2 (ITS2) region and characterized the endosymbiotic community using 2 different OTU identity cut-offs, and analyzed them with generalized dissimilarity modeling and joint species distribution modeling. We found that Symbiodiniaceae form discrete communities characterized by the dominance of ITS2 types C1, C21a, or D1, that are each associated with a different suite of co-occurring background types and tend to exclude each other in an endosymbiotic community. The communities showed modest responses to temperature, water depth, host genotype, polyp size, and bleaching status, and there was local sequence variation within the ITS2 types. After accounting for the effects of those variables, residual correlations remained in community composition, pointing to the possibility that Symbiodiniaceae community assembly in corals may be structured by interspecific competitive or facilitating interactions rather than only exogenous variables

Plant functional traits have globally consistent effects on competition.

Phenotypic traits and their associated trade-offs have been shown to have globally consistent effects on individual plant physiological functions, but how these effects scale up to influence competition, a key driver of community assembly in terrestrial vegetation, has remained unclear. Here we use growth data from more than 3 million trees in over 140,000 plots across the world to show how three key functional traits--wood density, specific leaf area and maximum height--consistently influence competitive interactions. Fast maximum growth of a species was correlated negatively with its wood density in all biomes, and positively with its specific leaf area in most biomes. Low wood density was also correlated with a low ability to tolerate competition and a low competitive effect on neighbours, while high specific leaf area was correlated with a low competitive effect. Thus, traits generate trade-offs between performance with competition versus performance without competition, a fundamental ingredient in the classical hypothesis that the coexistence of plant species is enabled via differentiation in their successional strategies. Competition within species was stronger than between species, but an increase in trait dissimilarity between species had little influence in weakening competition. No benefit of dissimilarity was detected for specific leaf area or wood density, and only a weak benefit for maximum height. Our trait-based approach to modelling competition makes generalization possible across the forest ecosystems of the world and their highly diverse species composition.We are especially grateful to the researchers whose long-term commitment to establish and maintain forest plots and their associated databases made this study possible, and to those who granted us data access: forest inventories and permanent plots of New Zealand, Spain (MAGRAMA), France, Switzerland, Sweden, US and Canada (for the provinces of Quebec provided by the Ministère des Ressources Naturelles du Québec, Ontario provided by OnTAP’s Growth and Yield Program of the Ontario Ministry of Natural Resources, Saskatchewan, Manitoba, New Brunswick, Newfoundland and Labrador), CTFS (BCI and LTER-Luquillo), Taiwan (Fushan), Cirad (Paracou with funding by CEBA, ANR-10-LABX-25-01), Cirad, MEFCP and ICRA (M’Baïki) and Japan. We thank MPI-BGC Jena, who host TRY, and the international funding networks supporting TRY (IGBP, DIVERSITAS, GLP, NERC, QUEST, FRB and GIS Climate). G.K. was supported by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Program (Demo-Traits project, no. 299340). The working group that initiated this synthesis was supported by Macquarie University and by Australian Research Council through a fellowship to M.W.This is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/nature1647