Derivation of two well-behaved theoretical contagion indices and their sampling properties and application for assessing forest landscape diversity

Abstract

Studies of spatial patterns of landscapes are useful to quantify human impact, predict wildlife effects, or describe variability of landscape features. A common approach to identify and quantify landscape structure is with a landscape scale model known as a contagion index. A contagion index quantifies two distinct components of landscape diversity: composition and configuration. Some landscape ecologists promote the use of relative contagion indices. It is demonstrated that relativized contagion indices are mathematically untenable. Two new theoretical contagion indices, r 1 and r 2 , are derived .using a mean value approach (Le., statistical expected value) instead of entropy. Behavior of r 1 and r 2 was investigated with simulated random, uniform, and aggregated landscapes. They are shown to be well-behaved and sensitive to composition and configuration. Distributional properties of f\ and r2 are derived. They are shown to be asymptotically unbiased, consistent, and asymptotically normally distributed. Variance formulas for r1 and r2 are developed using the delta method. The new index models are used to examine landscape diversity on three physiographic provinces in Alabama by analyzing the pattern and changes in forest cover types over the recent past. In comparing r1 and r2 , use of r1 in analysis of variance gave a more conservative test of contagion.

Citation

Parresol, Bernard R. 2011. Derivation of two well-behaved theoretical contagion indices and their sampling properties and application for assessing forest landscape diversity. Natural Resource Modeling 24(1):61-101.