Red herrings remain in geographical ecology: a reply to Hawkins et al. (2007)

In a recent paper Hawkins et al. (2007) question whether the use of spatially explicit methods such as generalised least squares (GLS) is necessarily better than using simpler non-spatial methods such as ordinary least squares (OLS) for fitting linear models to spatial data. This is consistent with a wider review of the literature which found that 80% of ecological publications analysing spatial data ignore spatiallyexplicit modelling methods (Dormann 2007). Since the autocorrelations of the error term may be arbitrarily close to zero, it cannot be argued that OLS is always substantially worse than GLS, as OLS is the special case of GLS when the correlations are set to zero. However, this should never be used as an excuse to ignore GLS and instead to adopt OLS as the norm for spatial data: doing so may hinder sound inference in geographical ecology. It is the need to model correlation structures correctly that has motivated the substantial bodies of research in statistical methodologies summarised for spatially correlated data by Cressie (1993) and for temporally correlated data by Diggle et al. (1995) and Chatfield (2003). Ignoring spatial autocorrelation is to treat correlated observations as independent, and so is a form of pseudoreplication which has long been discredited in ecology (Hurlbert 1984). In this short response we make three main points: firstly, Hawkins et al. have misunderstood the ‘‘redshift’’ as described by Lennon (2000); secondly, the sub-sampling method they use to reach their conclusions is inappropriate; and thirdly, improved modelling of the covariance structure of the error term allows better statistical inference to be made from spatial datasets.