Canonical analysis, a generalization of multiple regression to multiple‐response variables, is widely used in ecology. Because these models often involve many parameters (one slope per response per ...predictor), they pose challenges to model interpretation. Among these challenges, we lack quantitative frameworks for estimating the overall importance of single predictors in multi‐response regression models.
Here we demonstrate that commonality analysis and hierarchical partitioning, widely used for both estimating predictor importance and improving the interpretation of single‐response regression models, are related and complementary frameworks that can be expanded for the analysis of multiple‐response models.
In this application, we (a) demonstrate the mathematical links between commonality analysis, variation and hierarchical partitioning; (b) generalize these frameworks to allow the analysis of any number of predictor variables or groups of predictor variables as in the case of variation partitioning; and (c) introduce and demonstrate the implementation of these generalized frameworks in the R package rdacca.hp.
摘要
典范分析(RDA、dbRDA和CCA)作为多元回归应用于多响应变量的拓展，广泛应用于生态学数据分析。但由于典范分析通常涉及很多参数(即每个响应变量与每个解释变量之间都有一个系数)，因此在模型解读方面面临很多困难。其中有个尚未解决的挑战是缺乏定量的框架来评估解释变量相对重要性。
本研究中，我们证明了广泛用于估计多元回归模型解释变量重要性和提高模型解读性的共性分析(commonality analysis)和层次分割(hierarchical partitioning)是相关且互补的框架。我们也把层次分割框架扩展用于多响应变量的典范分析模型。
这里我们 a)展示了共性分析、变差分解(variation partitioning)和层次分割之间的数学联系；b)开发了不限制解释变量(组)数的变差分解和层次分割的R包rdacca.hp；c)使用Doubs鱼类数据演示rdacca.hp的使用和结果的解读。
Beyond neutrality Clappe, Sylvie; Dray, Stéphane; Peres-Neto, Pedro R.
Ecology (Durham),
August 2018, Volume:
99, Issue:
8
Journal Article
Peer reviewed
The methods of direct gradient analysis and variation partitioning are the most widely used frameworks to evaluate the contributions of species sorting to metacommunity structure. In many cases, ...however, species are also driven by spatial processes that are independent of environmental heterogeneity (e.g., neutral dynamics). As such, spatial autocorrelation can occur independently in both species (due to limited dispersal) and the environmental data, leading to spurious correlations between species distributions and the spatialized (i.e., spatially autocorrelated) environment. In these cases, the method of variation partitioning may present high Type I error rates (i.e., reject the null hypothesis more often than the pre-established critical level) and inflated estimates regarding the environmental component that is used to estimate the importance of species sorting. In this paper, we (1) demonstrate that metacommunities driven by neutral dynamics (via limited dispersal) alone or in combination with species sorting leads to inflated estimates and Type I error rates when testing for the importance of species sorting; and (2) propose a general and flexible new variation partitioning procedure to adjust for spurious contributions due to spatial autocorrelation from the environmental fraction. We used simulated metacommunity data driven by pure neutral, pure species sorting, and mixed (i.e., neutral + species sorting dynamics) processes to evaluate the performances of our new methodological framework. We also demonstrate the utility of the proposed framework with an empirical plant dataset in which we show that half of the variation initially due to the environment by the standard variation partitioning framework was due to spurious correlations.
Variation partitioning based on canonical analysis is the most commonly used analysis to investigate community patterns according to environmental and spatial predictors. Ecologists use this method ...in order to understand the pure contribution of the environment independent of space, and vice versa, as well as to control for inflated type I error in assessing the environmental component under spatial autocorrelation. Our goal is to use numerical simulations to compare how different spatial predictors and model selection procedures perform in assessing the importance of the spatial component and in controlling for type I error while testing environmental predictors. We determine for the first time how the ability of commonly used (polynomial regressors) and novel methods based on eigenvector maps compare in the realm of spatial variation partitioning. We introduce a novel forward selection procedure to select spatial regressors for community analysis. Finally, we point out a number of issues that have not been previously considered about the joint explained variation between environment and space, which should be taken into account when reporting and testing the unique contributions of environment and space in patterning ecological communities. In tests of species-environment relationships, spatial autocorrelation is known to inflate the level of type I error and make the tests of significance invalid. First, one must determine if the spatial component is significant using all spatial predictors (Moran's eigenvector maps). If it is, consider a model selection for the set of spatial predictors (an individual-species forward selection procedure is to be preferred) and use the environmental and selected spatial predictors in a partial regression or partial canonical analysis scheme. This is an effective way of controlling for type I error in such tests. Polynomial regressors do not provide tests with a correct level of type I error.
We investigate the electronic properties of ultrathin hexagonal boron nitride (h-BN) crystalline layers with different conducting materials (graphite, graphene, and gold) on either side of the ...barrier layer. The tunnel current depends exponentially on the number of h-BN atomic layers, down to a monolayer thickness. Conductive atomic force microscopy scans across h-BN terraces of different thickness reveal a high level of uniformity in the tunnel current. Our results demonstrate that atomically thin h-BN acts as a defect-free dielectric with a high breakdown field. It offers great potential for applications in tunnel devices and in field-effect transistors with a high carrier density in the conducting channel.
There are few phenomena in condensed matter physics that are defined only by the fundamental constants and do not depend on material parameters. Examples are the resistivity quantum, h/e2 (h is ...Planck's constant and e the electron charge), that appears in a variety of transport experiments and the magnetic flux quantum, h/e, playing an important role in the physics of superconductivity. By and large, sophisticated facilities and special measurement conditions are required to observe any of these phenomena. We show that the opacity of suspended graphene is defined solely by the fine structure constant, a = e2/hc feminine 1/137 (where c is the speed of light), the parameter that describes coupling between light and relativistic electrons and that is traditionally associated with quantum electrodynamics rather than materials science. Despite being only one atom thick, graphene is found to absorb a significant (pa = 2.3%) fraction of incident white light, a consequence of graphene's unique electronic structure.
An obstacle to the use of graphene as an alternative to silicon electronics has been the absence of an energy gap between its conduction and valence bands, which makes it difficult to achieve low ...power dissipation in the OFF state. We report a bipolar field-effect transistor that exploits the low density of states in graphene and its one-atomic-layer thickness. Our prototype devices are graphene heterostructures with atomically thin boron nitride or molybdenum disulfide acting as a vertical transport barrier. They exhibit room-temperature switching ratios of ≈50 and ≈10,000, respectively. Such devices have potential for high-frequency operation and large-scale integration.
Species spatial distributions are the result of population demography, behavioral traits, and species interactions in spatially heterogeneous environmental conditions. Hence the composition of ...species assemblages is an integrative response variable, and its variability can be explained by the complex interplay among several structuring factors. The thorough analysis of spatial variation in species assemblages may help infer processes shaping ecological communities. We suggest that ecological studies would benefit from the combined use of the classical statistical models of community composition data, such as constrained or unconstrained multivariate analyses of site-by-species abundance tables, with rapidly emerging and diversifying methods of spatial pattern analysis. Doing so allows one to deal with spatially explicit ecological models of beta diversity in a biogeographic context through the multiscale analysis of spatial patterns in original species data tables, including spatial characterization of fitted or residual variation from environmental models. We summarize here the recent progress for specifying spatial features through spatial weighting matrices and spatial eigenfunctions in order to define spatially constrained or scale-explicit multivariate analyses. Through a worked example on tropical tree communities, we also show the potential of the overall approach to identify significant residual spatial patterns that could arise from the omission of important unmeasured explanatory variables or processes.
Species distributional or trait data based on range map (extent-of-occurrence) or atlas survey data often display spatial autocorrelation, i.e. locations close to each other exhibit more similar ...values than those further apart. If this pattern remains present in the residuals of a statistical model based on such data, one of the key assumptions of standard statistical analyses, that residuals are independent and identically distributed (i.i.d), is violated. The violation of the assumption of i.i.d. residuals may bias parameter estimates and can increase type I error rates (falsely rejecting the null hypothesis of no effect). While this is increasingly recognised by researchers analysing species distribution data, there is, to our knowledge, no comprehensive overview of the many available spatial statistical methods to take spatial autocorrelation into account in tests of statistical significance. Here, we describe six different statistical approaches to infer correlates of species' distributions, for both presence/absence (binary response) and species abundance data (poisson or normally distributed response), while accounting for spatial autocorrelation in model residuals: autocovariate regression; spatial eigenvector mapping; generalised least squares; (conditional and simultaneous) autoregressive models and generalised estimating equations. A comprehensive comparison of the relative merits of these methods is beyond the scope of this paper. To demonstrate each method's implementation, however, we undertook preliminary tests based on simulated data. These preliminary tests verified that most of the spatial modeling techniques we examined showed good type I error control and precise parameter estimates, at least when confronted with simplistic simulated data containing spatial autocorrelation in the errors. However, we found that for presence/absence data the results and conclusions were very variable between the different methods. This is likely due to the low information content of binary maps. Also, in contrast with previous studies, we found that autocovariate methods consistently underestimated the effects of environmental controls of species distributions. Given their widespread use, in particular for the modelling of species presence/absence data (e.g. climate envelope models), we argue that this warrants further study and caution in their use. To aid other ecologists in making use of the methods described, code to implement them in freely available software is provided in an electronic appendix.
PDF
