Identifying the scale thresholds for field-data extrapolation via spatial analysis of landscape gradients

Despite recent advances in resolving the scale issue, it remains problematic that so many ecological field studies are still conducted only at small scales because of the constraints imposed by limited resources. To maximize the use of these data, it would be helpful if the researchers could provide guidelines for the appropriate range and scale for the extrapolation of the data and identify the new information that would be needed to extend the scope of their extrapolation. In this paper, we present a method that can be used to detect scale thresholds for the extrapolation of field data through spatial analyses of the physical landscape, using the Fushan Forest, Taiwan, as an example. First, the relationship between the vegetation and the physical landscape was inferred from sample-plot data; this information was in turn used to extrapolate the data over the whole forest area. We then compared the environmental variables in the sample plots versus those in the whole forest area via principal component analysis, landscape classification, and spatial autocorrelation analysis. Analyses of the entire Fushan Forest area showed that there are at least three major spatial scales at which physical gradients are expressed: elevation at the scale of the full forest extent (more than 3,000 m), topographic position at 550 m, and aspect at 250 m. Analyses of the sample plots showed that the plots captured only two of these gradients-topographic position and aspect, but not elevation. Therefore, information from the current field data can only be extrapolated to within 550 m from the sample plots; further information derived from cross-elevation samples is needed to extrapolate beyond that range.