Spatial Dependence and Autocorrelation

Abstract

The detection, characterization, and significance testing of spatial pattern is the first step to understand spatial ecological data and the processes that generated them. Spatial dependence commonly occurs in ecological data and it is often argued that failure to account for spatial dependence can impact inferences in ecology and guidance for conservation. Here, we present the key concepts needed to understand why spatial dependence and related spatial autocorrelation occurs, estimate the degree of spatial dependence in data and potential spatial scale of the pattern, understand how the estimated spatial variance can be used to interpolate and simulate spatial patterns using kriging and related approaches, and identify the characteristic spatial scale(s) in the data using multiscale analysis. We illustrate these concepts with an example on Opuntia cactus and habitats in old fields. Our example shows how to estimate spatial dependence through the use of correlograms and semivariograms. It also shows how semivariogram modeling can be used for spatial interpolation via kriging and we contrast this to inverse distance weighting for interpolation. Finally, we show how multiscale analysis, such as wavelet analysis and Fourier transforms, can be implemented. We end by providing guidance on how ecologists can effectively diagnose spatial dependence in ecological data.