Spatial autocorrelation and red herrings in geographical ecology

Aim Spatial autocorrelation in ecological data can inflate Type I errors in statistical analyses. There has also been a recent claim that spatial autocorrelation generates 'red herrings', such that virtually all past analyses are flawed. We consider the origins of this phenomenon, the implications of spatial autocorrelation for macro-scale patterns of species diversity and set out a clarification of the statistical problems generated by its presence. Location To illustrate the issues involved, we analyse the species richness of the birds of western/central Europe, north Africa and the Middle East. Methods Spatial correlograms for richness and five environmental variables were generated using Moran's I coefficients. Multiple regression, using both ordinary least-squares (OLS) and generalized least squares (GLS) assuming a spatial structure in the residuals, were used to identify the strongest predictors of richness. Autocorrelation analyses of the residuals obtained after stepwise OLS regression were undertaken, and the ranks of variables in the full OLS and GLS models were compared. Results Bird richness is characterized by a quadratic north-south gradient. Spatial correlograms usually had positive autocorrelation up to c. 1600 km. Including the environmental variables successively in the OLS model reduced spatial autocorrelation in the residuals to non-detectable levels, indicating that the variables explained all spatial structure in the data. In principle, if residuals are not autocorrelated then OLS is a special case of GLS. However, our comparison between OLS and GLS models including all environmental variables revealed that GLS de-emphasized predictors with strong autocorrelation and long-distance clinal structures, giving more importance to variables acting at smaller geographical scales. Conclusion Although spatial autocorrelation should always be investigated, it does not necessarily generate bias. Rather, it can be a useful tool to investigate mechanisms operating on richness at different spatial scales. Claims that analyses that do not take into account spatial autocorrelation are flawed are without foundation.

[1]  L. M. Bini,et al.  The longitudinal distribution of copepods in Corumbá Reservoir, State of Goiás, Brazil , 2001, Hydrobiologia.

[2]  J. Kerr,et al.  The environmental basis of North American species richness patterns among Epicauta (Coleoptera: Meloidae) , 1999, Biodiversity & Conservation.

[3]  O. Vetaas.  The effect of canopy disturbance on species richness in a central Himalayan oak forest , 1997, Plant Ecology.

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

[5]  Jessica Gurevitch,et al.  Ecography 25: 601 -- 615, 2002 , 2022 .

[6]  José Alexandre Felizola Diniz-Filho,et al.  The mid-domain effect cannot explain the diversity gradient of Nearctic birds , 2002 .

[7]  J. Diniz‐Filho,et al.  Spatial Autocorrelation Analysis and the Identification of Operational Units for Conservation in Continuous Populations , 2002 .

[8]  K. Gaston,et al.  The University of Chicago Species Richness , Environmental Correlates , and Spatial Scale : A Test Using South African Birds , 2002 .

[9]  R. Whittaker,et al.  Species Diversity--Scale Matters , 2002, Science.

[10]  J. Diniz‐Filho,et al.  Null models and spatial patterns of species richness in South American birds of prey , 2002 .

[11]  Eric E. Porter,et al.  Area and the latitudinal diversity gradient for terrestrial birds , 2001 .

[12]  T. Boulinier,et al.  Ecological Biogeography of Southern Ocean Islands: The Importance of Considering Spatial Issues , 2001, The American Naturalist.

[13]  C. Rahbek,et al.  Geometric constraints explain much of the species richness pattern in African birds , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[14]  G. Graves,et al.  Multiscale assessment of patterns of avian species richness , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[15]  R. Whittaker,et al.  Scale and species richness: towards a general, hierarchical theory of species diversity , 2001 .

[16]  Noel A Cressie,et al.  Uncertainty and Spatial Linear Models for Ecological Data , 2001 .

[17]  David L. Fox,et al.  Ecological biogeography of North American mammals: species density and ecological structure in relation to environmental gradients , 2000 .

[18]  L. M. Bini,et al.  Local and Regional Species Richness Relationships in Viperid Snake Assemblages from South America: Unsaturated Patterns at Three Different Spatial Scales , 2000, Copeia.

[19]  Jeremy J. D. Greenwood,et al.  Bird diversity and environmental gradients in Britain: a test of the species–energy hypothesis , 2000 .

[20]  Fox,et al.  Testing for local species saturation with nonindependent regional species pools , 2000 .

[21]  Jack J. Lennon,et al.  Red-shifts and red herrings in geographical ecology , 2000 .

[22]  R. Freckleton,et al.  The Ecological Detective: Confronting Models with Data , 1999 .

[23]  A. Ruggiero.  Spatial patterns in the diversity of mammal species: A test of the geographic area hypothesis in South America , 1999 .

[24]  Koenig,et al.  Spatial autocorrelation of ecological phenomena. , 1999, Trends in ecology & evolution.

[25]  R. Whittaker,et al.  Climate and woody plant diversity in southern Africa : relationships at species, genus and family levels , 1998 .

[26]  W. Koenig,et al.  Testing for spatial autocorrelation in ecological studies , 1998 .

[27]  W. Koenig,et al.  Spatial Autocorrelation in California Land Birds , 1998 .

[28]  Jean-Pierre Rossi,et al.  Relating species density to environmental variables in presence of spatial autocorrelation: a study case on soil nematodes distribution , 1998 .

[29]  Eileen M. O'Brien.  Water‐energy dynamics, climate, and prediction of woody plant species richness: an interim general model , 1998 .

[30]  J. Kerr,et al.  Lepidopteran richness patterns in North America , 1998 .

[31]  R. Hilborn,et al.  The Ecological Detective: Confronting Models with Data , 1997 .

[32]  R. Tateishi,et al.  Mapping evapotranspiration and water balance for global land surfaces , 1996 .

[33]  Chung-Hyun Ahn,et al.  Development of Global 30-minute grid Potential Evapotranspiration Data Set , 1994 .

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

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

[36]  Eileen M. O'Brien.  Climatic Gradients in Woody Plant Species Richness: Towards an Explanation Based on an Analysis of Southern Africa's Woody Flora , 1993 .

[37]  S. Levin.  The problem of pattern and scale in ecology , 1992 .

[38]  Pierre Legendre,et al.  Study of spatial components of forest cover using partial Mantel tests and path analysis , 1992 .

[39]  D. Currie.  Energy and Large-Scale Patterns of Animal- and Plant-Species Richness , 1991, The American Naturalist.

[40]  F. Vuilleumier.  Handbook of the Birds of Europe, the Middle East and North Africa. The Birds of the Western Palearctic. Volume V: Tyrant Flycatchers to Thrushes , 1990 .

[41]  D Hémon,et al.  Assessing the significance of the correlation between two spatial processes. , 1989, Biometrics.

[42]  Pierre Legendre,et al.  Aquatic heterotrophic bacteria: Modeling in the presence of spatial autocorrelation , 1988 .

[43]  S. Cramp.  Tyrant flycatchers to thrushes , 1988 .

[44]  David J. Currie,et al.  Large-scale biogeographical patterns of species richness of trees , 1987, Nature.

[45]  D. Griffith.  Spatial Autocorrelation: A Primer , 1987 .

[46]  J. Turner,et al.  Does Solar Energy Control Organic Diversity? Butterflies, Moths and the British Climate , 1987 .

[47]  S. Hurlbert.  Pseudoreplication and the Design of Ecological Field Experiments , 1984 .

[48]  E. Mayr.  Handbook of the Birds of Europe, the Middle East and North Africa: The Birds of the Western Palearctic. Volume 1: Ostrich to Ducks. Stanley Cramp , 1978 .

[49]  R. Sokal,et al.  Spatial autocorrelation in biology: 1. Methodology , 1978 .

[50]  Robert R. Sokal,et al.  Spatial autocorrelation in biology: 2. Some biological implications and four applications of evolutionary and ecological interest , 1978 .

[51]  H. Southern,et al.  Handbook of the Birds of Europe, the Middle East and North Africa; the Birds of the Western Palearctic , 1978 .

[52]  A. V. Humboldt.  Ansichten der Natur, mit wissenschaftlichen Erläuterungen , 1849 .