Some problems in the analysis of spatial pattern

Measurement of spatial pattern is of interest in many fields of study including forestry, ecology, archaeology, geography, astronomy, etc. Some new methods for measuring various aspects of spatial patterns formed by point events in the plane, are proposed.Sampling a population in the plane is usually carried out using either quadrat counts or distance measurements. Only the latter are used in this Thesis, as the methods introduced are aimed at the plant biologist or forester studying patterns formed by trees in a forest stand, where distance sampling is the easiest.The first method introduced is a new conditioned distance ratio method for analysing spatial pattern, which attempts to place patterns on an envisaged regular/random/aggregation scale. Instead of using an index as with most previous methods, a histogram of certain distances is formed, and analysis is based on viewing and hypothesis testing of this histogram.Two new robust estimators of the density of a forest stand are described, which are unbiased for a wide range of spatial patterns. The first estimator has a coefficient which varies according to some quantitative feature of the spatial pattern. This is a new idea for obtaining robust estimators.What constitutes a clumped or sparse area within a spatial pattern is very subjective. A method for the defining and marking of such areas is described. A computer package is used for the actual drawing of the clumped and sparse areas.The final topic to be discussed is that of two species in the plane. The spectral theory of two-dimensional, bivariate point processes is given, and then used to study the relationship between two species cohabiting in the plane.All the methods described are used on data, some of which are simulated, the rest being the coordinates of real trees in a forest stand