Less than eight (and a half) misconceptions of spatial analysis

Spatial analyses are indispensable analytical tools in biogeography and macroecology. In a recent Guest Editorial, Hawkins (Journal of Biogeography, 2012, 39, 1–9) raised several issues related to spatial analyses. While we concur with some points, we here clarify those confounding (1) spatial trends and spatial autocorrelation, and (2) spatial autocorrelation in the response variable and in the residuals. We argue that recognizing spatial autocorrelation in statistical modelling is not only a crucial step in model diagnostics, but that disregarding it is essentially wrong.

[1]  Noel A. C. Cressie,et al.  Statistics for Spatial Data: Cressie/Statistics , 1993 .

[2]  J. Kerr,et al.  Metabolic theory and diversity gradients: where do we go from here? , 2007, Ecology.

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

[4]  Boris Schröder,et al.  Decomposing environmental, spatial, and spatiotemporal components of species distributions , 2011 .

[5]  C. Dormann Response to Comment on “Methods to account for spatial autocorrelation in the analysis of species distributional data: a review” , 2009 .

[6]  Colin M Beale,et al.  Regression analysis of spatial data. , 2010, Ecology letters.

[7]  Marie-Josée Fortin,et al.  Spatial Autocorrelation in Ecological Studies: A Legacy of Solutions and Myths , 2009 .

[8]  A. Townsend Peterson,et al.  Novel methods improve prediction of species' distributions from occurrence data , 2006 .

[9]  C. Dormann Effects of incorporating spatial autocorrelation into the analysis of species distribution data , 2007 .

[10]  R. G. Davies,et al.  Methods to account for spatial autocorrelation in the analysis of species distributional data : a review , 2007 .

[11]  Peter Buhlmann,et al.  BOOSTING ALGORITHMS: REGULARIZATION, PREDICTION AND MODEL FITTING , 2007, 0804.2752.

[12]  Ingolf Kühn,et al.  A Wavelet-Based Extension of Generalized Linear Models to Remove the Effect of Spatial Autocorrelation: Wavelet-based Extension of Generalized Linear Models , 2010 .

[13]  Benjamin Gilbert,et al.  Variation partitioning in ecological communities: Do the numbers add up? , 2010 .

[14]  Ingolf Kühn,et al.  Incorporating spatial autocorrelation may invert observed patterns , 2006 .

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

[16]  Luc Anselin,et al.  Small Sample Properties of Tests for Spatial Dependence in Regression Models: Some Further Results , 1995 .

[17]  G. Carl,et al.  Analyzing spatial autocorrelation in species distributions using Gaussian and logit models , 2007 .

[18]  J. Diniz‐Filho,et al.  Spatial autocorrelation and red herrings in geographical ecology , 2003 .

[19]  Ingolf Kühn,et al.  Combining spatial and phylogenetic eigenvector filtering in trait analysis , 2009 .

[20]  Bradford A. Hawkins,et al.  Eight (and a half) deadly sins of spatial analysis , 2012 .

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

[22]  Ingolf Kühn,et al.  Relating geographical variation in pollination types to environmental and spatial factors using novel statistical methods. , 2006, The New phytologist.

[23]  Richard Field,et al.  Coefficient shifts in geographical ecology: an empirical evaluation of spatial and non-spatial regression , 2009 .

[24]  C. Ricotta,et al.  Accounting for uncertainty when mapping species distributions: The need for maps of ignorance , 2011 .

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

[26]  Carsten F. Dormann,et al.  A wavelet-based method to remove spatial autocorrelation in the analysis of species distributional data , 2008 .

[27]  Samuel M. Scheiner,et al.  Species richness, species-area curves and Simpson's paradox , 2000 .

[28]  W. Tobler A Computer Movie Simulating Urban Growth in the Detroit Region , 1970 .

[29]  P. Clifford,et al.  Modifying the t test for assessing the correlation between two spatial processes , 1993 .

[30]  Ingolf Kühn,et al.  Analyzing spatial ecological data using linear regression and wavelet analysis , 2008 .

[31]  José Alexandre Felizola Diniz-Filho,et al.  Modelling geographical patterns in species richness using eigenvector-based spatial filters , 2005 .

[32]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.