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Josef Klusoň - One of the best experts on this subject based on the ideXlab platform.

Pierre Legendre - One of the best experts on this subject based on the ideXlab platform.

  • comparison of the mantel test and alternative approaches for detecting complex multivariate relationships in the spatial Analysis of genetic data
    Molecular Ecology Resources, 2010
    Co-Authors: Pierre Legendre, Mariejosee Fortin
    Abstract:

    : The Mantel test is widely used to test the linear or monotonic independence of the elements in two distance matrices. It is one of the few appropriate tests when the hypothesis under study can only be formulated in terms of distances; this is often the case with genetic data. In particular, the Mantel test has been widely used to test for spatial relationship between genetic data and spatial layout of the sampling locations. We describe the domain of application of the Mantel test and derived forms. Formula development demonstrates that the sum-of-squares (SS) partitioned in Mantel tests and regression on distance matrices differs from the SS partitioned in linear correlation, regression and Canonical Analysis. Numerical simulations show that in tests of significance of the relationship between simple variables and multivariate data tables, the power of linear correlation, regression and Canonical Analysis is far greater than that of the Mantel test and derived forms, meaning that the former methods are much more likely than the latter to detect a relationship when one is present in the data. Examples of difference in power are given for the detection of spatial gradients. Furthermore, the Mantel test does not correctly estimate the proportion of the original data variation explained by spatial structures. The Mantel test should not be used as a general method for the investigation of linear relationships or spatial structures in univariate or multivariate data. Its use should be restricted to tests of hypotheses that can only be formulated in terms of distances.

  • estimating and controlling for spatial structure in the study of ecological communities
    Global Ecology and Biogeography, 2010
    Co-Authors: Pedro R Peresneto, Pierre Legendre
    Abstract:

    Aim 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. Innovation 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. Main conclusions 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.

  • studying beta diversity ecological variation partitioning by multiple regression and Canonical Analysis
    Journal of Plant Ecology, 2008
    Co-Authors: Pierre Legendre
    Abstract:

    Aims Beta diversity is the variation in species composition among sites in a geographic region. Beta diversity is a key concept for understanding the functioning of ecosystems, for the conservation of biodiversity and for ecosystem management. The present report describes how to analyse beta diversity from community composition and associated environmental and spatial data tables. Methods Beta diversity can be studied by computing diversity indices for each site and testing hypotheses about the factors that may explain the variation among sites. Alternatively, one can carry out a direct Analysis of the community composition data table over the study sites, as a function of sets of environmental and spatial variables. These analyses are carried out by the statistical method of partitioning the variation of the diversity indices or the community composition data table with respect to environmental and spatial variables. Variation partitioning is briefly described herein. Important findings Variation partitioning is a method of choice for the interpretation of beta diversity using tables of environmental and spatial variables. Beta diversity is an interesting ‘currency’ for ecologists to compare either different sampling areas or different ecological communities cooccurring in an area. Partitioning must be based upon unbiased estimates of the variation of the community composition data table that is explained by the various tables of explanatory variables. The adjusted coefficient of determination provides such an unbiased estimate in both multiple regression and Canonical redundancy Analysis. After partitioning, one can test the significance of the fractions of interest and plot maps of the fitted values corresponding to these fractions.

  • variation partitioning of species data matrices estimation and comparison of fractions
    Ecology, 2006
    Co-Authors: Pedro R Peresneto, Stéphane Dray, Pierre Legendre, Daniel Borcard
    Abstract:

    Establishing relationships between species distributions and environmental characteristics is a major goal in the search for forces driving species distributions. Canonical ordinations such as redundancy Analysis and Canonical correspondence Analysis are invaluable tools for modeling communities through environmental predictors. They provide the means for conducting direct explanatory Analysis in which the association among species can be studied according to their common and unique relationships with the environmental variables and other sets of predictors of interest, such as spatial variables. Variation partitioning can then be used to test and determine the likelihood of these sets of predictors in explaining patterns in community structure. Although variation partitioning in Canonical Analysis is routinely used in ecological Analysis, no effort has been reported in the literature to consider appropriate estimators so that comparisons between fractions or, eventually, between different Canonical models are meaningful. In this paper, we show that variation partitioning as currently applied in Canonical Analysis is biased. We present appropriate unbiased estimators. In addition, we outline a statistical test to compare fractions in Canonical Analysis. The question addressed by the test is whether two fractions of variation are significantly different from each other. Such assessment provides an important step toward attaining an understanding of the factors patterning community structure. The test is shown to have correct Type I error rates and good power for both redundancy Analysis and Canonical correspondence Analysis.

  • Spatial modelling: a comprehensive framework for principal coordinate Analysis of neighbour matrices (PCNM)
    Ecological Modelling, 2006
    Co-Authors: Stéphane Dray, Pierre Legendre, Pedro R. Peres-neto
    Abstract:

    Spatial structures of ecological communities may originate either from the dependence of community structure on environmental variables or/and from community-based processes. In order to assess the importance of these two sources, spatial relationships must be explicitly introduced into statistical models. Recently, a new approach called principal coordinates of neighbour matrices (PCNM) has been proposed to create spatial predictors that can be easily incorporated into regression or Canonical Analysis models, providing a flexible tool especially when contrasted to the family of autoregressive models and trend surface Analysis, which are of common use in ecological and geographical Analysis. In this paper, we explore the theory of the PCNM approach and demonstrate how it is linked to spatial autocorrelation structure functions. The method basically consists of diagonalizing a spatial weighting matrix, then extracting the eigenvectors that maximize the Moran's index of autocorrelation. These eigenvectors can then be used directly as explanatory variables in regression or Canonical models. We propose improvements and extensions of the original method, and illustrate them with examples that will help ecologists choose the variant that will better suit their needs.

A Spanou - One of the best experts on this subject based on the ideXlab platform.

  • towards Canonical quantum gravity for g1 geometries in 2 1 dimensions with a λ term
    Classical and Quantum Gravity, 2008
    Co-Authors: T Christodoulakis, Evangelos Melas, G Doulis, Petros A Terzis, Thh Grammenos, G O Papadopoulos, A Spanou
    Abstract:

    The Canonical Analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper imposition of the quantum analogues of two linear (momentum) constraints reduces an initial collection of state vectors, consisting of all smooth functionals of the components (and/or their derivatives) of the spatial metric, to particular scalar smooth functionals. The demand that the midi-superspace metric (inferred from the kinetic part of the quadratic (Hamiltonian) constraint) must define on the space of these states an induced metric whose components are given in terms of the same states, which is made possible through an appropriate re-normalization assumption, severely reduces the possible state vectors to three unique (up to general coordinate transformations) smooth scalar functionals. The quantum analogue of the Hamiltonian constraint produces a Wheeler–DeWitt equation based on this reduced manifold of states, which is completely integrated.

  • towards Canonical quantum gravity for g1 geometries in 2 1 dimensions with a lambda term
    arXiv: General Relativity and Quantum Cosmology, 2008
    Co-Authors: T Christodoulakis, Evangelos Melas, G Doulis, Petros A Terzis, Thh Grammenos, G O Papadopoulos, A Spanou
    Abstract:

    The Canonical Analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper imposition of the quantum analogues of the two linear (momentum) constraints reduces an initial collection of state vectors, consisting of all smooth functionals of the components (and/or their derivatives) of the spatial metric, to particular scalar smooth functionals. The demand that the midi-superspace metric (inferred from the kinetic part of the quadratic (Hamiltonian) constraint) must define on the space of these states an induced metric whose components are given in terms of the same states, which is made possible through an appropriate re-normalization assumption, severely reduces the possible state vectors to three unique (up to general coordinate transformations) smooth scalar functionals. The quantum analogue of the Hamiltonian constraint produces a Wheeler-DeWitt equation based on this reduced manifold of states, which is completely integrated.

D. G. C. Mckeon - One of the best experts on this subject based on the ideXlab platform.

  • Canonical Analysis of a system with fermionic gauge symmetry
    Canadian Journal of Physics, 2013
    Co-Authors: D. G. C. Mckeon
    Abstract:

    A non-abelian gauge field with a topological action is coupled to a spin-3/2 Majorana spinor. The symmetries of this model are analyzed using the Dirac constraint formalism. These symmetries include a fermionic symmetry and the algebra of these symmetries closes; it is not the algebra of supergravity. The action is invariant without the need to introduce auxiliary fields.

  • peculiarities of the Canonical Analysis of the two dimensional first order einstein hilbert action in terms of the metric tensor or the metric density
    Modern Physics Letters A, 2005
    Co-Authors: N. Kiriushcheva, S. V. Kuzmin, D. G. C. Mckeon
    Abstract:

    The peculiarities of doing a Canonical Analysis of the first-order formulation of the Einstein–Hilbert action in terms of either the metric tensor gαβ or the metric density along with the affine connection are discussed. It is shown that the difference between using gαβ as opposed to hαβ appears only in two spacetime dimensions. Despite there being a different number of constraints in these two approaches, both formulations result in there being a local Poisson brackets algebra of constraints with field independent structure constants, closed off-shell generators of gauge transformations and off-shell invariance of the action. The formulation in terms of the metric tensor is analyzed in detail and compared with earlier results obtained using the metric density. The gauge transformations, obtained from the full set of first-class constraints, are different from a diffeomorphism transformation in both cases.

  • peculiarities of the Canonical Analysis of the first order form of the einstein hilbert action in two dimensions in terms of the metric tensor or the metric density
    arXiv: High Energy Physics - Theory, 2005
    Co-Authors: N. Kiriushcheva, S. V. Kuzmin, D. G. C. Mckeon
    Abstract:

    The peculiarities of doing a Canonical Analysis of the first order formulation of the Einstein-Hilbert action in terms of either the metric tensor $g^{\alpha \beta}$ or the metric density $h^{\alpha \beta}= \sqrt{-g}g^{\alpha \beta}$ along with the affine connection are discussed. It is shown that the difference between using $g^{\alpha \beta}$ as opposed to $h^{\alpha \beta}$ appears only in two spacetime dimensions. Despite there being a different number of constraints in these two approaches, both formulations result in there being a local Poisson brackets algebra of constraints with field independent structure constants, closed off shell generators of gauge transformations and off shell invariance of the action. The formulation in terms of the metric tensor is analyzed in detail and compared with earlier results obtained using the metric density. The gauge transformations, obtained from the full set of first class constraints, are different from a diffeomorphism transformation in both cases.

T Christodoulakis - One of the best experts on this subject based on the ideXlab platform.

  • towards Canonical quantum gravity for g1 geometries in 2 1 dimensions with a λ term
    Classical and Quantum Gravity, 2008
    Co-Authors: T Christodoulakis, Evangelos Melas, G Doulis, Petros A Terzis, Thh Grammenos, G O Papadopoulos, A Spanou
    Abstract:

    The Canonical Analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper imposition of the quantum analogues of two linear (momentum) constraints reduces an initial collection of state vectors, consisting of all smooth functionals of the components (and/or their derivatives) of the spatial metric, to particular scalar smooth functionals. The demand that the midi-superspace metric (inferred from the kinetic part of the quadratic (Hamiltonian) constraint) must define on the space of these states an induced metric whose components are given in terms of the same states, which is made possible through an appropriate re-normalization assumption, severely reduces the possible state vectors to three unique (up to general coordinate transformations) smooth scalar functionals. The quantum analogue of the Hamiltonian constraint produces a Wheeler–DeWitt equation based on this reduced manifold of states, which is completely integrated.

  • towards Canonical quantum gravity for g1 geometries in 2 1 dimensions with a lambda term
    arXiv: General Relativity and Quantum Cosmology, 2008
    Co-Authors: T Christodoulakis, Evangelos Melas, G Doulis, Petros A Terzis, Thh Grammenos, G O Papadopoulos, A Spanou
    Abstract:

    The Canonical Analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper imposition of the quantum analogues of the two linear (momentum) constraints reduces an initial collection of state vectors, consisting of all smooth functionals of the components (and/or their derivatives) of the spatial metric, to particular scalar smooth functionals. The demand that the midi-superspace metric (inferred from the kinetic part of the quadratic (Hamiltonian) constraint) must define on the space of these states an induced metric whose components are given in terms of the same states, which is made possible through an appropriate re-normalization assumption, severely reduces the possible state vectors to three unique (up to general coordinate transformations) smooth scalar functionals. The quantum analogue of the Hamiltonian constraint produces a Wheeler-DeWitt equation based on this reduced manifold of states, which is completely integrated.