## LSU Historical Dissertations and Theses

1998

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

Quang Van Cao

#### Abstract

Studies of spatial patterns of landscapes are useful to quantify human impact, predict wildlife effects, or describe various landscape features. A robust landscape index should quantify two distinct components of landscape diversity: composition and configuration. One category of landscape index is the contagion index. A generalized measure of contagion is defined as a function of concentration. From this definition two contagion indices, $\Gamma\sb1$ (a new index) and $\Gamma\sb2$ (an entropy formulation), are derived from expected values of geometric random variables. A widely used relative contagion index, $RC\sb2,$ is shown to be a scaled version of $\Gamma\sb2.$. Distributional properties of $\\Gamma\sb1,\ \\Gamma\sb2,$ and $\\Gamma\sb{2({\rm scaled})}$ (i.e., $R\ C\sb2)$ are derived. They are shown to be asymptotically unbiased, consistent, and asymptotically normally distributed. Variance formulas for $\\Gamma\sb1,\ \\Gamma\sb2,$ and $\\Gamma\sb{2\rm(scaled)}$ are derived using the delta method A Monte Carlo study using subseries analysis and replicate histograms, for variance and distribution assessment, was done as a validity check. Behavior of $\Gamma\sb1,\ \Gamma\sb2,$ and $RC\sb2$ were investigated with simulated random, uniform, and aggregated landscapes. Both $\Gamma\sb1$ and $\Gamma\sb2$ provide acceptable measures of contagion. The index $RC\sb2$ is shown to be an index of evenness, and not of contagion. It is demonstrated that relativized contagion indices are mathematically untenable. As an application, the pattern and changes in forest cover types over the last two decades were analyzed on three landscape level physiographic provinces of the state of Alabama: (i) The Great Appalachian Valley Province, (ii) The Blue Ridge-Talladega Mountain Province, and (iii) The Piedmont Province. The USDA Forest Service conducts periodic surveys of forest resources nationwide from plots distributed on a 3-mile by 3-mile (4.8-km by 4.8-km) grid randomly established within each county. Using forest inventory and analysis survey data on forest cover types, stratified by physiographic province, the $\\Gamma\sb1$ and $\\Gamma\sb2$ contagion values and their variances were calculated for each province for the survey years 1972, 1982, and 1990. One-way analysis of variance was used for hypothesis testing of contagion values across time and between provinces. Contagion values were very similar indicating similar processes operating across the physiographic provinces over the last two decades. In comparing $\\Gamma\sb1$ and $\\Gamma\sb2,$ use of $\\Gamma\sb1$ in analysis of variance gave a more conservative test of contagion.

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