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Red‐shifts and red herrings in geographical ecology

Red‐shifts and red herrings in geographical ecology Lennon, J. J. 2000. Red-shifts and red herrings in geographical ecology. – Ecography 23: 101– 113. I draw attention to the need for ecologists to take spatial structure into account more seriously in hypothesis testing. If spatial autocorrelation is ignored, as it usually is, then analyses of ecological patterns in terms of environmental factors can produce very misleading results. This is demonstrated using synthetic but realistic spatial patterns with known spatial properties which are subjected to classical correlation and multiple regression analyses. Correlation between an autocorrelated response variable and each of a set of explanatory variables is strongly biased in favour of those explanatory variables that are highly autocorrelated – the expected magnitude of the correlation coefficient increases with autocorrelation even if the spatial patterns are completely independent. Similarly, multiple regression analysis finds highly autocorrelated explanatory variables ‘‘significant’’ much more frequently than it should. The chances of mistakenly identifying a ‘‘significant’’ slope across an autocorrelated pattern is very high if classical regression is used. Consequently, under these circumstances strongly autocorrelated environmental factors reported in the literature as associated with ecological patterns may not actually be significant. It is likely that these factors wrongly described as important constitute a red-shifted subset of the set of potential explanations, and that more spatially discontinuous factors (those with bluer spectra) are actually relatively more important than their present status suggests. There is much that ecologists can do to improve on this situation. I discuss various approaches to the problem of spatial autocorrelation from the literature and present a randomisation test for the association of two spatial patterns which has advantages over currently available methods. J. J. Lennon, Centre for Biodi6ersity and Conser6ation, School of Biology, Uni6. of Leeds, Leeds, Yorkshire, U.K. LS2 9TJ (gen6jjl@gps.leeds.ac.uk). High-quality spatial data, often sampled across a spatially continuous matrix of quadrats, are increasingly available to geographical ecologists. Major new sources are improved automated data capture technology (e.g. satellite remote-sensing) and well-organised species surveys. While this is obviously to be welcomed, the uncritical application of simple statistical methods to these spatial data may in fact obscure more than it reveals. This is primarily a consequence of the presence of spatial autocorrelation in these geographical data. Spatial autocorrelation (Cliff and Ord 1973, Ripley 1981, Legendre 1993) is the correlation between pairs of points separated by a (spatial) distance. The usual case is for this correlation to be positive and to decrease with increasing distance between the points; the greater Accepted 15 June 1999 Copyright © ECOGRAPHY 2000 ISSN 0906-7590 Printed in Ireland – all rights reserved ECOGRAPHY 23:1 (2000) the distance between measurements, the weaker the dependency between them. Positive spatial autocorrelation is present, often strongly, in most spatial data in ecology. Although long known by statisticians as a source of problems for statistical inference, spatial autocorrelation has usually been mentioned, if at all, in passing by geographical ecologists: in general it has been ignored as a statistical inconvenience or simply not observed as a problem in the first place. Sometimes spatial autocorrelation is used as an inferential tool or is more of an object of study in itself (e.g. Sokal and Oden 1991, Koenig 1997). However, in general the impression given by many ecologists working with geographical data is effectively that of complacency, perhaps in the belief that simple, ularly vulnerable (although whether or not these are intrinsically smooth is an open question). Rainfall appears to be an intrinsically less autocorrelated factor, although this obviously depends on the quality of the data collection and processing steps. A comparison of published maps of any of these climatic factors with other common explanatory factors such as altitude or habitat coverage classifications immediately shows that the climatic factors are relatively smooth and hence more autocorrelated (although caution is needed since climatic maps are usually extensively interpolated). This means that when in the literature energetic climatic factors are reported as being more strongly associated with abundance or diversity than habitat type, altitude or rainfall, because of the discrimination against factors with bluer spectra this may not be the case. The only remedy for this uncertainty is re-analysis of affected published work, but this time taking spatial autocorrelation explicitly into account. It is unlikely that approaching the difficulties of spatial analysis with the kind of one-dimensional descriptions of spatial structure that seem to be the norm in ecology (k of the negative binomial, mean-variance ratios) will be entirely sufficient, although it is undoubtedly a start. There is the potential, at least, that using an inadequate description of spatial structure (in the belief that it is adequate) will lead to a similar trail of mistaken associations and conclusions as that produced by the application of classical correlation and regression to spatial problems. It may well be that the results from well-executed re-analyses will be broadly similar, but there is no way of telling until this has been done, and it is perhaps more likely that both spatially rougher or patchier environmental factors will become more important in our understanding of ecological spatial patterns and processes. be ignored as an inconvenience, it is likely that our understanding of inter-relationships between patterns of environmental variables and species spatial distributions, abundances and diversity gradients (to name but a few) will remain confused. Acknowledgements – I thank Eli Groner, Stephen Hartley and Bill Kunin for reading earlier drafts, and David Currie for his useful and challenging comments. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Ecography Wiley

Red‐shifts and red herrings in geographical ecology

Ecography , Volume 23 (1) – Feb 1, 2000

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Publisher
Wiley
Copyright
Copyright © 2000 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0906-7590
eISSN
1600-0587
DOI
10.1111/j.1600-0587.2000.tb00265.x
Publisher site
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Abstract

Lennon, J. J. 2000. Red-shifts and red herrings in geographical ecology. – Ecography 23: 101– 113. I draw attention to the need for ecologists to take spatial structure into account more seriously in hypothesis testing. If spatial autocorrelation is ignored, as it usually is, then analyses of ecological patterns in terms of environmental factors can produce very misleading results. This is demonstrated using synthetic but realistic spatial patterns with known spatial properties which are subjected to classical correlation and multiple regression analyses. Correlation between an autocorrelated response variable and each of a set of explanatory variables is strongly biased in favour of those explanatory variables that are highly autocorrelated – the expected magnitude of the correlation coefficient increases with autocorrelation even if the spatial patterns are completely independent. Similarly, multiple regression analysis finds highly autocorrelated explanatory variables ‘‘significant’’ much more frequently than it should. The chances of mistakenly identifying a ‘‘significant’’ slope across an autocorrelated pattern is very high if classical regression is used. Consequently, under these circumstances strongly autocorrelated environmental factors reported in the literature as associated with ecological patterns may not actually be significant. It is likely that these factors wrongly described as important constitute a red-shifted subset of the set of potential explanations, and that more spatially discontinuous factors (those with bluer spectra) are actually relatively more important than their present status suggests. There is much that ecologists can do to improve on this situation. I discuss various approaches to the problem of spatial autocorrelation from the literature and present a randomisation test for the association of two spatial patterns which has advantages over currently available methods. J. J. Lennon, Centre for Biodi6ersity and Conser6ation, School of Biology, Uni6. of Leeds, Leeds, Yorkshire, U.K. LS2 9TJ (gen6jjl@gps.leeds.ac.uk). High-quality spatial data, often sampled across a spatially continuous matrix of quadrats, are increasingly available to geographical ecologists. Major new sources are improved automated data capture technology (e.g. satellite remote-sensing) and well-organised species surveys. While this is obviously to be welcomed, the uncritical application of simple statistical methods to these spatial data may in fact obscure more than it reveals. This is primarily a consequence of the presence of spatial autocorrelation in these geographical data. Spatial autocorrelation (Cliff and Ord 1973, Ripley 1981, Legendre 1993) is the correlation between pairs of points separated by a (spatial) distance. The usual case is for this correlation to be positive and to decrease with increasing distance between the points; the greater Accepted 15 June 1999 Copyright © ECOGRAPHY 2000 ISSN 0906-7590 Printed in Ireland – all rights reserved ECOGRAPHY 23:1 (2000) the distance between measurements, the weaker the dependency between them. Positive spatial autocorrelation is present, often strongly, in most spatial data in ecology. Although long known by statisticians as a source of problems for statistical inference, spatial autocorrelation has usually been mentioned, if at all, in passing by geographical ecologists: in general it has been ignored as a statistical inconvenience or simply not observed as a problem in the first place. Sometimes spatial autocorrelation is used as an inferential tool or is more of an object of study in itself (e.g. Sokal and Oden 1991, Koenig 1997). However, in general the impression given by many ecologists working with geographical data is effectively that of complacency, perhaps in the belief that simple, ularly vulnerable (although whether or not these are intrinsically smooth is an open question). Rainfall appears to be an intrinsically less autocorrelated factor, although this obviously depends on the quality of the data collection and processing steps. A comparison of published maps of any of these climatic factors with other common explanatory factors such as altitude or habitat coverage classifications immediately shows that the climatic factors are relatively smooth and hence more autocorrelated (although caution is needed since climatic maps are usually extensively interpolated). This means that when in the literature energetic climatic factors are reported as being more strongly associated with abundance or diversity than habitat type, altitude or rainfall, because of the discrimination against factors with bluer spectra this may not be the case. The only remedy for this uncertainty is re-analysis of affected published work, but this time taking spatial autocorrelation explicitly into account. It is unlikely that approaching the difficulties of spatial analysis with the kind of one-dimensional descriptions of spatial structure that seem to be the norm in ecology (k of the negative binomial, mean-variance ratios) will be entirely sufficient, although it is undoubtedly a start. There is the potential, at least, that using an inadequate description of spatial structure (in the belief that it is adequate) will lead to a similar trail of mistaken associations and conclusions as that produced by the application of classical correlation and regression to spatial problems. It may well be that the results from well-executed re-analyses will be broadly similar, but there is no way of telling until this has been done, and it is perhaps more likely that both spatially rougher or patchier environmental factors will become more important in our understanding of ecological spatial patterns and processes. be ignored as an inconvenience, it is likely that our understanding of inter-relationships between patterns of environmental variables and species spatial distributions, abundances and diversity gradients (to name but a few) will remain confused. Acknowledgements – I thank Eli Groner, Stephen Hartley and Bill Kunin for reading earlier drafts, and David Currie for his useful and challenging comments.

Journal

EcographyWiley

Published: Feb 1, 2000

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