Skip to Main Content
U.S. Forest Service
Caring for the land and serving people

United States Department of Agriculture

Home > Search > Publication Information

  1. Share via EmailShare on FacebookShare on LinkedInShare on Twitter
    Dislike this pubLike this pub
    Author(s): Bernard R. Parresol
    Date: 2011
    Source: Natural Resource Modeling 24(1):61-101
    Publication Series: Scientific Journal (JRNL)
    Station: Southern Research Station
    PDF: Download Publication  (2.51 MB)


    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.

    Publication Notes

    • You may send email to to request a hard copy of this publication.
    • (Please specify exactly which publication you are requesting and your mailing address.)
    • We recommend that you also print this page and attach it to the printout of the article, to retain the full citation information.
    • This article was written and prepared by U.S. Government employees on official time, and is therefore in the public domain.


    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.


    Concentration, delta method, entropy, expected value, forest cover types, geometric distribution, physiographic provinces, simulated landscapes

    Related Search

    XML: View XML
Show More
Show Fewer
Jump to Top of Page