Spatial nonstationarity and the scale of species–environment relationships in the Mojave Desert, California, USA

Species distribution models (SDM) have become a fertile area of research interest at the confluence of spatial ecology and GIScience and have been used to study a wide range of biogeographical phenomena, including invasive species, vector-borne diseases, and biological diversity. Scale is one of the most important considerations in any spatial analysis study because different spatial patterns emerge at different scales. An issue related to the ‘extent’ concept of scale that has more recently been recognized as important is spatial nonstationarity, which exists when processes or models of processes vary across space. This research examined the scale of species–environment relationships by a relatively new (in SDM) statistical method, geographically weighted regression (GWR). We tested four different types of species and 10 different types of environmental (climate and topography) variables in univariate GWR models to explore how stationarity and explanatory power varied with scale (as a function of GWR bandwidth size). The results suggest that the scale of species–environment relationships varies for both different types of species and different types of environmental variables. The two metrics used here – stationarity index and explained variance – did not show congruity in terms of a ‘characteristic scale.’ Species' relationships with climate and elevation variables became stationary at broader scales, and in some cases the models did not become stationary at the largest bandwidth tested. The complex topographic variables used here operate at finer scales and were often stationary across all scales or became stationary at small bandwidths. In addition to being instrumental for examining the effects of scale on spatial nonstationarity and a model's explanatory ability, GWR can also be used to explore potential geographical factors that result in nonstationarity.