FOREST VEGETATION AND SITE RELATIONS: THEORY, METHODS, AND APPLICATION TO THE FORESTS OF MONTANA (SYSTEMS, FUZZY SETS, TOPOLOGY)

This study establishes a theoretical model of vegetation ecology through dynamic systems theory. The model treats vegetation composition and the physical environment as abstract dynamic systems coupled by the physiological requirements of the component species and the modification of environment by vegetation. The properties of the abstract systems are explored and compared to current ecological theories of vegetation.; I then develop three methods of vegetation analysis based on the theoretical model. The three methods of analysis employ primarily fuzzy set theory and point set topology. All three methods are concerned with determining the mapping from vegetation space to environment space, as outlined in the theoretical model.; The first method, ecological topology or clique analysis, defines a maximum similitude subrelation on vegetation samples, and determines the maximum range of environmental variables within sets of similar plots.; The second method, fuzzy set ordination, provides a theoretical basis for interpretation of ordinations in fuzzy set theory. The algorithms of fuzzy set ordination are defined and demonstrated on a sample data set, and applied to a real data set in a sequence of examples.; The third method is chi-square analysis of similar pairs. In a manner analogous to chi-square analysis of genotype frequencies, pairs of similar plots are analyzed to determine which environmental factors, if any, are shared by similar plots more often than would be expected.; The three methods are applied to a large set of forest vegetation samples from the state of Montana to determine the effects of elevation, aspects, soil parent material, soil texture, and geographic distribution on vegetation composition. The strongest effect is due to geographic distribution, as related primarily to climate. The next strongest effect appears to be due to topography, and is largely related to elevation, rather than aspect. Finally, soil parent material exhibits a dichotomy of effects. Igneous parent materials exert influence primarily through effects on nutrient availability and sedimentary parent materials exert influence primarily through effects on soil moisture availability. As measured in this study, soil texure has no effect on vegetation composition.