Empirical patterns of the effects of changing scale on landscape metrics

While ecologists are well aware that spatial heterogeneity is scale-dependent, a general understanding of scaling relationships of spatial pattern is still lacking. One way to improve this understanding is to systematically examine how pattern indices change with scale in real landscapes of different kinds. This study, therefore, was designed to investigate how a suite of commonly used landscape metrics respond to changing grain size, extent, and the direction of analysis (or sampling) using several different landscapes in North America. Our results showed that the responses of the 19 landscape metrics fell into three general categories: Type I metrics showed predictable responses with changing scale, and their scaling relations could be represented by simple scaling equations (linear, power-law, or logarithmic functions); Type II metrics exhibited staircase-like responses that were less predictable; and Type III metrics behaved erratically in response to changing scale, suggesting no consistent scaling relations. In general, the effect of changing grain size was more predictable than that of changing extent. Type I metrics represent those landscape features that can be readily and accurately extrapolated or interpolated across spatial scales, whereas Type II and III metrics represent those that require more explicit consideration of idiosyncratic details for successful scaling. To adequately quantify spatial heterogeneity, the metric-scalograms (the response curves of metrics to changing scale), instead of single-scale measures, seem necessary.