Red-shifts and red herrings in geographical ecology

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 o f environmental factors can produce very misleading results. This is demons trated using synthetic but realistic spatial patterns with known spatial pr operties which are subjected to classical correlation and multiple regressi on analyses. Correlation between an autocorrelated response variable and ea ch of a set of explanatory variables is strongly biased in favour of those explanatory variables that are highly autocorrelated - the expected magnitu de of the correlation coefficient increases with autocorrelation even if th e spatial patterns are completely independent. Similarly, multiple regressi on 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 cla ssical regression is used. Consequently, under these circumstances strongly autocorrelated environmental factors reported in the literature as associa ted 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 discon tinuous factors (those with bluer spectra) are actually relatively more imp ortant than their present status suggests. There is much that ecologists ca n do to improve on this situation. I discuss various approaches to the prob lem of spatial autocorrelation from the literature and present a randomisat ion test for the association of two spatial patterns which has advantages o ver currently available methods.