Scale detection in real and artificial landscapes using semivariance analysis

Semivariance analysis is potentially useful to landscape ecologists for detecting scales of variability in spatial data. We used semivariance analysis to compare spatial patterns of winter foraging by large ungulates with those of environmental variables that influence forage availability in northern Yellowstone National Park, Wyoming. In addition, we evaluated (1) the ability of semivariograms to detect known scales of variability in artificial maps with one or more distinct scales of pattern, and (2) the influence of the amount and spatial distribution of absent data on semivariogram results and interpretation. Semivariograms of environmental data sets (aspect, elevation, habitat type, and slope) for the entire northern Yellowstone landscape clearly identified the dominant scale of variability in each map layer, while semivariograms of ungulate foraging data from discontinuous study areas were difficult to interpret. Semivariograms of binary maps composed of a single scale of pattern showed clear interpretable results: the range accurately reflected the size of the blocks of which the maps were constructed. Semivariograms of multiple scale maps and hierarchical maps exhibited pronounced inflections which could be used to distinguish two or three distinct scales of pattern. To assess the sensitivity of semivariance analysis to absent data, often the product of cloud interference or incomplete data collection, we deliberately masked (deleted) portions of continuous northern Yellowstone map layers, using single scale artificial maps as masks. The sensitivity of semivariance analysis to random deletions from the data was related to both the size of the deleted blocks, and the total proportion of the original data set that was removed. Small blocks could be deleted in very high proportions without degrading the semivariogram results. When the size of deleted blocks was large relative to the size of the map, the corresponding variograms became sensitive to the total proportion of data removed: variograms were difficult or impossible to interpret when the proportion of data deleted was high. Despite success with artificial maps, standard semivariance analysis is unlikely to detect multiple scales of pattern in real ecological data. Semivariance analysis is recommended as an effective technique for quantifying some spatial characteristics of ecological data, and may provide insight into the scales of processes that structure landscapes.