Evaluating Shrub‐Associated Spatial Patterns of Soil Properties in a Shrub‐Steppe Ecosystem Using Multiple‐Variable Geostatistics

Geostatistics are often calculated for a single variable at a time, even though many natural phenomena are functions of several variables. The objective of this work was to demonstrate a nonparametric approach for assessing the spatial characteristics of multiple‐variable phenomena. Specifically, we analyzed the spatial characteristics of resource islands in the soil under big sagebrush ( Artemisia tridentata Nutt.), a dominant shrub in the intermountain western USA. For our example, we defined resource islands as a function of six soil variables representing concentrations of soil resources, populations of microorganisms, and soil microbial physiological variables. By collectively evaluating the indicator transformations of these individual variables, we created a new data set, termed a multiple‐variable indicator transform or MVIT. Alternate MVITs were obtained by varying the selection criteria. Each MVIT was analyzed with variography to characterize spatial continuity, and with indicator kriging to predict the combined probability of their occurrence at unsampled locations in the landscape. Simple graphical analysis and variography demonstrated spatial dependence for all individual soil variables. Analysis also showed that ensembles of variables were not randomly distributed, but rather were correlated systematically within the landscape. Maps derived from ordinary kriging of MVITs suggested that the combined probabilities for encountering zones of above‐median resources were greatest near big sagebrush. As the selection criteria for defining a resource island became more stringent, the area of the resource island decreased. Cross‐variography revealed that big sagebrush was more positively correlated with MVIT resource islands than were grass species, the other major plant type.