Finding essential scales of spatial variation in ecological data: a multivariate approach.

The identification of spatial structures is a key step in understanding the ecological processes structuring the distribution of organisms. Spatial patterns in species distributions result from a combination of several processes occuring at different scales: identifying these scales is thus a crucial issue. Recent studies have proposed a new family of spatial predictors (PCNM: principal coordinates of neighbours matrices; MEMs: Moran's eigenvectors maps) that allow for modelling of spatial variation on different scales. To assess the multi-scale spatial patterns in multivariate data, these variables are often used as predictors in constrained ordination methods. However, the selection of the appropriate spatial predictors is still troublesome, and the identification of the main scales of spatial variation remains an open question. This paper presents a new statistical tool to tackle this issue: the multi-scale pattern analysis (MSPA). This ordination method uses MEMs to decompose ecological variability into several spatial scales and then summarizes this decomposition using graphical representations. A canonical form of MSPA can also be used to assess the spatial scales of the species-environment relationships. MSPA is compared to constrained ordination using simulated data, and illustrated using the famous oribatid mites dataset. The method is implemented in the free software R.

[1]  J. Osborne,et al.  Sample size and subject to item ratio in principal components analysis. , 2004 .

[2]  Calyampudi R. Rao.  The use and interpretation of principal component analysis in applied research , 1964 .

[3]  M. Fortin,et al.  Spatial pattern and ecological analysis , 1989, Vegetatio.

[4]  John Aitchison,et al.  The Statistical Analysis of Compositional Data , 1986 .

[5]  J. Wiens.  Spatial Scaling in Ecology , 1989 .

[6]  Pierre Legendre,et al.  All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices , 2002 .

[7]  P. Legendre,et al.  Partialling out the spatial component of ecological variation , 1992 .

[8]  D. Chessel,et al.  Biplot presentation of diet composition data : an alternative for fish stomach contents analysis , 2000 .

[9]  Maurice G. Kendall,et al.  The advanced theory of statistics , 1945 .

[10]  G. J. G. Upton,et al.  Spatial data Analysis by Example , 1985 .

[11]  Daniel A. Griffith,et al.  Semiparametric Filtering of Spatial Autocorrelation: The Eigenvector Approach , 2007 .

[12]  P. Legendre,et al.  Variation partitioning of species data matrices: estimation and comparison of fractions. , 2006, Ecology.

[13]  Stéphane Dray,et al.  The ade4 Package-II: Two-table and K-table Methods , 2007 .

[14]  A. M. Olson,et al.  Role of scale and environmental factors in regulation of community structure. , 1990, Trends in ecology & evolution.

[15]  Heng Tao Shen,et al.  Principal Component Analysis , 2009, Encyclopedia of Biometrics.

[16]  P. Legendre.  Spatial Autocorrelation: Trouble or New Paradigm? , 1993 .

[17]  Michael Tiefelsdorf,et al.  The Exact Distribution of Moran's I , 1995 .

[18]  Stéphane Dray,et al.  Spatial modelling: a comprehensive framework for principal coordinate analysis of neighbour matrices (PCNM) , 2006 .

[19]  C. Braak.  Canonical Correspondence Analysis: A New Eigenvector Technique for Multivariate Direct Gradient Analysis , 1986 .

[20]  Helene H. Wagner,et al.  DIRECT MULTI‐SCALE ORDINATION WITH CANONICAL CORRESPONDENCE ANALYSIS , 2004 .

[21]  Jason W. Osborne,et al.  Best practices in exploratory factor analysis: four recommendations for getting the most from your analysis. , 2005 .

[22]  A. Getis,et al.  Comparative Spatial Filtering in Regression Analysis , 2002 .

[23]  Hanna Tuomisto,et al.  DISSECTING THE SPATIAL STRUCTURE OF ECOLOGICAL DATA AT MULTIPLE SCALES , 2004 .

[24]  C. Sprenger,et al.  On Extreme Values of Moran's I and Geary's c , 2010 .

[25]  Jennifer L. Dungan,et al.  A balanced view of scale in spatial statistical analysis , 2002 .

[26]  Pedro R. Peres-Neto,et al.  A UNIFIED STRATEGY FOR ESTIMATING AND CONTROLLING SPATIAL, TEMPORAL AND PHYLOGENETIC AUTOCORRELATION IN ECOLOGICAL MODELS , 2006 .

[27]  Daniel A Griffith,et al.  Spatial modeling in ecology: the flexibility of eigenfunction spatial analyses. , 2006, Ecology.

[28]  Jean Thioulouse,et al.  The ade4 package - I : One-table methods , 2004 .

[29]  Daniel A. Griffith,et al.  SPATIAL AUTOCORRELATION and EIGENFUNCTIONS OF THE GEOGRAPHIC WEIGHTS MATRIX ACCOMPANYING GEO‐REFERENCED DATA , 1996 .

[30]  C.J.F. ter Braak,et al.  CANOCO - a FORTRAN program for canonical community ordination by [partial] [etrended] [canonical] correspondence analysis, principal components analysis and redundancy analysis (version 2.1) , 1988 .

[31]  Daniel A. Griffith,et al.  A linear regression solution to the spatial autocorrelation problem , 2000, J. Geogr. Syst..

[32]  P. Legendre,et al.  Multiscale spatial distribution of a littoral fish community in relation to environmental variables , 2005 .

[33]  Pierre Legendre,et al.  Environmental control and spatial structure in ecological communities: an example using oribatid mites (Acari, Oribatei) , 1994, Environmental and Ecological Statistics.

[34]  Marie-Josée Fortin,et al.  SPATIAL ANALYSIS OF LANDSCAPES: CONCEPTS AND STATISTICS , 2005 .