Spatial Autocorrelation: Trouble or New Paradigm?

TLDR

Autocorrelation is a common statistical property of ecological variables that manifests as patches and gradients, and it challenges standard statistical tests because it violates the assumption of independence. The paper aims to describe and measure autocorrelation in ecological variables, emphasize mapping techniques, and present methods for incorporating spatial structure into ecological models. The authors describe mapping techniques for measuring autocorrelation, discuss proper statistical testing in its presence, propose two modeling approaches—polynomial coordinates and geographic distance matrices—and provide a table of available spatial analysis software. The two approaches are compared in the concluding section.

Abstract

Autocorrelation is a very general statistical property of ecological variables observed across geographic space; it most common forms are patches and gradients. Spatial autocorrelation, which comes either from the physical forcing of environmental variables or from community processes, presents a problem for statistical testing because autocorrelated data violate the assumption of independence of most standard statistical procedures. The paper discusses first how autocorrelation in ecological variables can be described and measured, with emphasis on mapping techniques. Then, proper statistical testing in the presence of autocorrelation is briefly discussed. Finally, ways are presented of explicitly introducing spatial structures into ecological models. Two approaches are proposed; in the raw—data approach, the spatial structure takes the form of a polynomial of the x and y geographic coordinates of the sampling stations; in the matrix approach, the spatial structure is introduced in the form of a geographic distance matrix among locations. These two approaches are compared in the concluding section. A table provides a list of computer programs available for spatial analysis.