Spatial Autocorrelation in Ecological Studies: A Legacy of Solutions and Myths

Article excerpt

A major aim of including the spatial component in ecological studies is to characterize the nature and intensity of spatial relationships between organisms and their environment. The growing awareness by ecologists of the importance of including spatial structure in ecological studies (for hypothesis development, experimental design, statistical analyses, and spatial modeling) is beneficial because it promotes more effective research. Unfortunately, as more researchers perform spatial analysis, some misconceptions about the virtues of spatial statistics have been carried through the process and years. Some of these statistical concepts and challenges were already presented by Cliff and Ord in 1969. Here, we classify the most common misconceptions about spatial autocorrelation into three categories of challenges: (1) those that have no solutions, (2) those where solutions exist but are not well known, and (3) those where solutions have been proposed but are incorrect. We conclude in stressing where new research is needed to address these challenges.

Introduction

A central goal in ecology since Watts's crucial article (1947) is to understand the relation between observed pattern (e.g., in the form of spatial structure) and the processes that both generate it and arise from it. However, the consensus is that we cannot safely deduce process from pattern, in part because different processes can give rise to indistinguishable spatial signatures (Fortin and Dale 2005). Nevertheless, knowledge of the characteristics of spatial structure is almost always the first step to understanding ecological complexity. Hence, the current norm for ecological studies is to acknowledge the importance of spatial aspects of the systems under study (Levin 1992; Legendre 1993; Dungan et al. 2002; Fortin and Dale 2005; Wagner and Fortin 2005), and to include them as much as possible in a study's design (Legendre et al. 2002), analysis (Legendre et al. 2004), or modeling (Keitt et al. 2002; Lichstein et al. 2002; Griffith and Peres-Neto 2006; Dormann et al. 2007).

One outcome of this practice is that ecologists now are so used to performing spatial analyses that they may forget that this was not always the case. Spatial "awareness" was evident in studies of ecological processes and their resulting pattern (Watts 1947), but quantification of pattern using spatial statistics came later, using spatial methods developed in other fields such as human geography, in which the seminal work of Cliff and Ord (1969, 1973, 1981) was most influential. This influence has worked its way from Cliff and Ord's original article (1969) through a variety of channels, such as Sokal and Oden (1978a, b), Cormack and Ord (1979), and Legendre and Fortin (1989), into the general ecological literature.

Today, the concepts originally introduced or explained by Cliff and Ord (1969) may seem more important than their technical contributions, although those did lead to further developments. Of the range of topics discussed by Cliff and Ord (1969), many of the original challenges still remain, whereas many of the technical concerns have become less relevant; for example, concerns about normality and limiting distributions are now superceded by reliance on randomization techniques.

The key message to ecologists stemming from Cliff and Ord's (1969) article, and their subsequent books (1973, 1981), is that the presence of spatial autocorrelation can have large impacts on statistical inference, impacts that cannot be ignored. Cliff and Ord (1969) also stress the importance of estimating spatial autocorrelation using weighting methods, and using neighbors beyond the first order: these are now common practice (Fortin and Dale 2005). This was not the case in the 1960s, motivating Cliff and Ord (1969) to address some of the characteristics they perceived as weaknesses in the approaches of Geary (1954) or Moran (1950).

As for the critical statistical issues related to the evaluation and implications of spatial autocorrelation, we suggest that there remain three types of challenges: (1) those that have no solutions, (2) those where solutions exist but are not well known, and (3) those where "solutions" have been proposed but are incorrect. …