Accounting for Spatial Dependence in Ecological Data

Abstract

The presence of spatial dependence can impair the statistical inference and subsequent ecological interpretation of the pattern(s) observed. It is important to understand how statistical biases due to spatially structured data can affect a wide array of ecological questions ranging from species–environment relationships to predicting the spread of invasive species. Consequently, there is an increasing emphasis on formally accounting for spatial dependence in inferential problems in ecology and conservation. We provide an overview regarding several ways in which spatial dependence has been addressed in regression-like models of species–environment relationships. Regression models are frequently used in ecology and conservation to address a variety of problems, ranging from interpreting habitat suitability to forecasting the effects of climate change. We first describe the problem of spatial dependence on inferences in ecology and conservation. Then, we discuss how to diagnose problems of spatial dependence in regression models. Finally, we illustrate new advances to addressing these statistical problems using a variety of approaches aimed at accounting for spatial dependence in statistical analyses, including trend surface analysis, eigenvector mapping, autocovariate and autoregressive models, multilevel models, generalized least squares, and spatial mixed models. We apply these models to understanding relationships of species occurrence of the varied thrush (Ixoreus naevius) to elevational gradients in the western USA. This example illustrates that each of these approaches varies in its ability to account for spatial dependence, depending on the scale at which spatial dependence occurs. Overall, autoregressive and spatial mixed models have beneficial attributes regarding obtaining appropriate inferences in the presence of spatial dependence. We end by providing guidance on accounting for spatial dependence in regression models used in ecology and conservation.