When are two landscape pattern indices significantly different?

Landscape pattern indices (LPI), which characterize various aspects of composition and configuration of categorical variables on a lattice (e.g., shape, clumping, proportion), have become increasingly popular for quantifying and characterizing various aspects of spatial patterns. Unlike in the case of spatial statistical models, when either the joint distribution of all values is characterized by a limited number of parameters, or the distribution is known for certain (usually random) cases, the distributions of LPI are not known. Therefore, comparisons of LPI or significance testing of differences among various landscapes and/or studies are uncertain. This paper scrutinizes six widely used LPI, which are computed based on categories mapped onto regular lattices. We designed a simulation using Gauss-Markov random fields to establish the empirical distributions of LPI as functions of landscape composition and configuration. We report the results for stationary binary landscapes. The confidence intervals for LPI are derived based on 1000 simulations of each given combination of parameters, and further details are evaluated for three illustrative cases. We report the distributions of the LPI along with their co-variation. Our results elucidate how proportion of cover classes and spatial autocorrelation simultaneously and significantly affect the outcome of LPI values. These results also highlight the importance and formal linkages between fully specified spatial stochastic models and spatial pattern analysis. We conclude that LPI must be compared with great care because of the drastic effects that both composition and configuration have on individual LPI values. We also stress the importance of knowing the expected range of variation about LPI values so that statistical comparisons and inferences can be made.