Date of Award
Doctor of Philosophy
The boundary definition problem involves the selection of appropriate criteria and methods for portraying boundaries of geographical distributions. Although this is a very important consideration in many academic fields, particularly geography, biology and sociology, apparently very little attention has been devoted to it in the literature. Boundaries are, as a rule, rather carelessly and subjectively drawn.;Various approaches to bounding discrete point distributions are explored in this thesis. These approaches fall into two categories based on the amount of information available about the distribution. In some caes, only locations are known and a boundary must be defined based soley on the geometric relationships of the locations in Cartesian space. In other instances, varying degrees of environmental information is available, which may be considered during the boundary definition process.;In reality, very few boundaries are known with any degree of precision. In fact, the argument is advanced that most boundaries are actually an abstraction and that no such line actually exists. In order to assess the relative promise of various approaches to boundary definition, several distributions with defined boundaries were produced in a computer simulation process. The ability of various methods to draw boundaries to approximate these defined boundaries is evaluated. In addition, the ability of various methods of boundary definition to reproduce a section of the range limits of a tree species is evaluated.;Methods evaluated are the convex hull, the spanning circle, the bounding isoline, the modified convex hull, probability surface mapping, density contouring and discriminant analysis. Additional methods are discussed in principle but are not further evaluated.;Two methods are found to produce very accurate boundaries over a wide range of applications. The modified convex hull is recommended to bound distributions where little or no information is available about conditions which are conducive to the existence of the phenomena in question. In cases where significant environmental data is available, highly reliable boundaries may be produced by discriminant analysis.
Averack, Richard, "The Boundary Definition Problem: Statistical And Geometric Approaches" (1983). Digitized Theses. 1225.