Book•
Numerical Ecology with R
07 Apr 2011-
TL;DR: This book is aimed at professional researchers, practitioners, graduate students and teachers in ecology, environmental science and engineering, and in related fields such as oceanography, molecular ecology, agriculture and soil science, who already have a background in general and multivariate statistics and wish to apply this knowledge to their data using the R language.
Abstract: Numerical Ecology with R provides a long-awaited bridge between a textbook in Numerical Ecology and the implementation of this discipline in the R language. After short theoretical overviews, the authors accompany the users through the exploration of the methods by means of applied and extensively commented examples. Users are invited to use this book as a teaching companion at the computer. The travel starts with exploratory approaches, proceeds with the construction of association matrices, then addresses three families of methods: clustering, unconstrained and canonical ordination, and spatial analysis. All the necessary data files, the scripts used in the chapters, as well as the extra R functions and packages written by the authors, can be downloaded from a web page accessible through the Springer web site(http://adn.biol.umontreal.ca/ numericalecology/numecolR/). This book is aimed at professional researchers, practitioners, graduate students and teachers in ecology, environmental science and engineering, and in related fields such as oceanography, molecular ecology, agriculture and soil science, who already have a background in general and multivariate statistics and wish to apply this knowledge to their data using the R language, as well as people willing to accompany their disciplinary learning with practical applications. People from other fields (e.g. geology, geography, paleoecology, phylogenetics, anthropology, the social and education sciences, etc.) may also benefit from the materials presented in this book. The three authors teach numerical ecology, both theoretical and practical, to a wide array of audiences, in regular courses in their Universities and in short courses given around the world. Daniel Borcard is lecturer of Biostatistics and Ecology and researcher in Numerical Ecology at Universite de Montreal, Quebec, Canada. Francois Gillet is professor of Community Ecology and Ecological Modelling at Universite de Franche-Comte, Besancon, France. Pierre Legendre is professor of Quantitative Biology and Ecology at Universite de Montreal, Fellow of the Royal Society of Canada, and ISI Highly Cited Researcher in Ecology/Environment.
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TL;DR: An analytical framework is developed for interrogation of subsurface microbial communities distributed across two geologically distinct formations of the unconfined aquifer underlying the Hanford Site in southeastern Washington State that quantitatively estimate influences of Drift, Selection and Dispersal.
Abstract: Spatial turnover in the composition of biological communities is governed by (ecological) Drift, Selection and Dispersal. Commonly applied statistical tools cannot quantitatively estimate these processes, nor identify abiotic features that impose these processes. For interrogation of subsurface microbial communities distributed across two geologically distinct formations of the unconfined aquifer underlying the Hanford Site in southeastern Washington State, we developed an analytical framework that advances ecological understanding in two primary ways. First, we quantitatively estimate influences of Drift, Selection and Dispersal. Second, ecological patterns are used to characterize measured and unmeasured abiotic variables that impose Selection or that result in low levels of Dispersal. We find that (i) Drift alone consistently governs ∼25% of spatial turnover in community composition; (ii) in deeper, finer-grained sediments, Selection is strong (governing ∼60% of turnover), being imposed by an unmeasured but spatially structured environmental variable; (iii) in shallower, coarser-grained sediments, Selection is weaker (governing ∼30% of turnover), being imposed by vertically and horizontally structured hydrological factors;(iv) low levels of Dispersal can govern nearly 30% of turnover and be caused primarily by spatial isolation resulting from limited exchange between finer and coarser-grain sediments; and (v) highly permeable sediments are associated with high levels of Dispersal that homogenize community composition and govern over 20% of turnover. We further show that our framework provides inferences that cannot be achieved using preexisting approaches, and suggest that their broad application will facilitate a unified understanding of microbial communities.
1,110 citations
Cites background from "Numerical Ecology with R"
...Spatial eigenvectors describe spatial relationships among communities across a range of spatial scales; the first eigenvector breaks sampling locations into broadly distributed clusters, and subsequent eigenvectors characterize spatial relationships at increasingly fine scales (Borcard and Legendre, 2002; Borcard et al., 2011; Heino et al., 2011)....
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...…among communities across a range of spatial scales; the first eigenvector breaks sampling locations into broadly distributed clusters, and subsequent eigenvectors characterize spatial relationships at increasingly fine scales (Borcard and Legendre, 2002; Borcard et al., 2011; Heino et al., 2011)....
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TL;DR: It is argued that all analyses in a study should take the spatial dependence in the data into account, unless it can be shown that there is no spatial autocorrelation in the allele frequency distribution that is under investigation, and it is urgent to develop additional statistical approaches that are based on a spatially explicit null model instead of the non‐spatial Island model.
Abstract: The genetic population structure of many species is characterised by a pattern of isolation by distance (IBD): due to limited dispersal, individuals that are geographically close tend to be genetically more similar than individuals that are far apart. Despite the ubiquity of IBD in nature, many commonly used statistical tests are based on a null model that is completely non-spatial, the Island model. Here, I argue that patterns of spatial autocorrelation deriving from IBD present a problem for such tests as it can severely bias their outcome. I use simulated data to illustrate this problem for two widely used types of tests: tests of hierarchical population structure and the detection of loci under selection. My results show that for both types of tests the presence of IBD can indeed lead to a large number of false positives. I therefore argue that all analyses in a study should take the spatial dependence in the data into account, unless it can be shown that there is no spatial autocorrelation in the allele frequency distribution that is under investigation. Thus, it is urgent to develop additional statistical approaches that are based on a spatially explicit null model instead of the non-spatial Island model.
532 citations
Cites background from "Numerical Ecology with R"
...Therefore, environmental data is almost invariably spatially autocorrelated (Legendre 1993; Borcard et al. 2011)....
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...There are many other ways in which the spatial dependency in the data can be incorporated into the statistical analysis and the statistical toolbox for such analyses is constantly expanding (Guillot et al. 2009; Borcard et al. 2011)....
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...However, such autocorrelation presents a problem for many statistical tests as the assumption of independence of the samples is violated (Borcard et al. 2011)....
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University of Lyon1, Institut de recherche pour le développement2, Institut Français3, University of Toronto4, Université de Montréal5, Université du Québec à Montréal6, Institut national de la recherche agronomique7, Norwegian School of Economics8, University of Alberta9, Norwegian Forest and Landscape Institute10, Imperial College London11, University of Oulu12
TL;DR: In this paper, the authors 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.
Abstract: 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.
511 citations
Cites methods from "Numerical Ecology with R"
...M6 variation partitioning Borcard et al. (1992), Borcard and Legendre (1994) yes ordination method...
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...M5 partial canonical ordination Borcard et al. (2004) yes ordination method...
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...Fully worked examples of several of the methods described in the following section are presented in Chapter 7 of Borcard et al. (2011)....
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TL;DR: This work identifies up to four life-history strategies that appear globally consistent across 143 species of reef corals: competitive, weedy, stress-tolerant and generalist taxa, which are primarily separated by colony morphology, growth rate and reproductive mode.
Abstract: Classifying the biological traits of organisms can test conceptual frameworks of life-history strategies and allow for predictions of how different species may respond to environmental disturbances. We apply a trait-based classification approach to a complex and threatened group of species, scleractinian corals. Using hierarchical clustering and random forests analyses, we identify up to four life-history strategies that appear globally consistent across 143 species of reef corals: competitive, weedy, stress-tolerant and generalist taxa, which are primarily separated by colony morphology, growth rate and reproductive mode. Documented shifts towards stress-tolerant, generalist and weedy species in coral reef communities are consistent with the expected responses of these life-history strategies. Our quantitative trait-based approach to classifying life-history strategies is objective, applicable to any taxa and a powerful tool that can be used to evaluate theories of community ecology and predict the impact of environmental and anthropogenic stressors on species assemblages.
502 citations
TL;DR: The resulting maps provide a new lens through which ecological systems can be understood; in the subsurface system investigated here they revealed that the influence of variable selection was associated with the rate at which redox conditions change with subsurfaced depth.
Abstract: Ecological community assembly is governed by a combination of (i) selection resulting from among-taxa differences in performance; (ii) dispersal resulting from organismal movement; and (iii) ecological drift resulting from stochastic changes in population sizes. The relative importance and nature of these processes can vary across environments. Selection can be homogeneous or variable, and while dispersal is a rate, we conceptualize extreme dispersal rates as two categories; dispersal limitation results from limited exchange of organisms among communities, and homogenizing dispersal results from high levels of organism exchange. To estimate the influence and spatial variation of each process we extend a recently developed statistical framework, use a simulation model to evaluate the accuracy of the extended framework, and use the framework to examine subsurface microbial communities over two geologic formations. For each subsurface community we estimate the degree to which it is influenced by homogeneous selection, variable selection, dispersal limitation, and homogenizing dispersal. Our analyses revealed that the relative influences of these ecological processes vary substantially across communities even within a geologic formation. We further identify environmental and spatial features associated with each ecological process, which allowed mapping of spatial variation in ecological-process-influences. The resulting maps provide a new lens through which ecological systems can be understood; in the subsurface system investigated here they revealed that the influence of variable selection was associated with the rate at which redox conditions change with subsurface depth.
474 citations
Cites methods from "Numerical Ecology with R"
...The spatial positions of sampled locations were used with Principal Coordinates of Neighbor Matrices’ (PCNM, now referred to as ‘Moran’s Eigenvector Maps’) to describe spatial eigenvectors (function ‘pcnm’ in R package ‘vegan’; Borcard and Legendre, 2002; Borcard et al., 2011)....
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...In variation partitioning, variation in community composition is explained using features deemed a priori to reflect spatial relationships or environmental differences among communities (e.g., Tuomisto et al., 2003; Cottenie, 2005; Legendre et al., 2009; Heino et al., 2011)....
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...Unexplained variation will, however, increase artificially if any of the following occur: (i) important environmental features have not been measured; (ii) spatial axes fail to capture idiosyncratic patterns in spatial isolation among communities; or (iii) community composition is non-linearly related to explanatory variables (see discussions in Laliberte et al., 2009; Legendre et al., 2009; Anderson et al., 2011)....
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...While it may appear that variation partitioning (Legendre and Legendre, 1998) was used here to estimate ecological-processinfluences, there are substantial differences between variation partitioning and our approach....
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