Evaluating empirical scaling relations of pattern metrics with simulated landscapes


  • Weijun Shen,

  • G. Darrel Jenerette,

  • Jianguo Wu,

  • Robert H. Gardner

W. Shen, Landscape Ecology and Modelling Lab. (LEML), School of Life Sciences, Arizona State Univ., Tempe, AZ 85287, USA and South China Inst. of Botany, Chinese Acad. of Sciences, Guangzhou 510650, China. – G. D. Jenerette and J. Wu(jingle.wu@asu.edu), Landscape Ecology and Modelling Lab. (LEML), School of Life Sciences, Arizona State Univ., P. O. Box 874501, Tempe, AZ 85287-4501, USA. – R. H. Gardner, Appalachian Lab., Center for Environmental Science, Univ.of Maryland, Frostburg, MD 21532, USA.


Landscape patterns demonstrate scale-dependent properties that have been parsimoniously described by empirical scaling functions. These functions, derived from multiple-scale analysis of real landscapes, are evaluated here for their generality and robustness via a series of simulated landscapes with known landscape patterns. A factorial design was used to generate these landscapes, varying the number of classes, class abundance distribution, and patch dispersion. The results confirm that the three types of scaling relations were both general and robust. Type I metrics were predictable with simple scaling functions (e.g. power laws or linear functions); Type II metrics showed stair-case like response patterns and were essentially not predictable; Type III metrics exhibited erratic response patterns that were unpredictable in most cases. However, significant differences were found between real and simulated landscapes when landscape extent was increased. Systematic changes in grain size show that the predictability of scaling relations increases with the number of classes, the evenness of class abundance distribution, and the aggregation of patch dispersion. However, random patch dispersion seemed to enhance the predictability of scaling relations when changing spatial extent.