A Method for Mapping the Dense and Sparse Regions of a Forest Stand

SUMMARY A method is developed for defining and mapping the dense and sparse areas of a forest stand or any spatial point pattern where the coordinates of all the trees or point events are known. The method is then used on various sets of data, contour maps being produced by a computer package, SYMAP, showing the regions of high density of trees (dense areas, clumps), the regions of low density (sparse areas) and the intermediate regions. SUPPOSE the coordinates of all the members of a population consisting of points in the plane are known. The points may represent the positions of trees in a forest stand, the locations of towns in a county etc. Much work has been done on the analysis of spatial point patterns, see, for example, Bartlett (1975), Cox and Lewis (1976), Diggle et al. (1976), to name but a few. Often the analysis is designed to classify the spatial pattern as aggregated, random or regular; or designed to estimate the density of the point events; or to discover how the density varies over the plane. If we were dealing with two or more types within the pattern, one would probably be interested in the relationship between the types. These are just a few of the many problems in this field. Often the starting point for such analyses is to consider the special pattern referred to in spatial processes as the Poisson forest, where the points form a two-dimensional Poisson process. More tractable results are available for this model than for most others. We shall be concerned here with analysing spatial patterns by a new method which defines the dense and sparse regions within the pattern; using these definitions of denseness and sparseness a computer package is then used to draw a contour map of the so-defined regions. The most widely used method for producing density maps is that first discussed by Ashby and Pidgeon (1942) where the area to be mapped is divided into quadrats and then each quadrat is allocated a colour depending on the value of the density of point events within the quadrat. This and other methods for density mapping are discussed in Monkhouse and Wilkinson (1966), most methods requiring the choice of quadrat size and shape, while the following method to be discussed uses distance measurements, thus overcoming this problem. Intuitively, a particular small area within a spatial pattern is within a dense region if the local density there (i.e. the number of individuals per unit area for this small region) is some- what greater than the overall density. Similarly, in vague terms, a sparse area occurs in a region where the local density is somewhat less than the overall density. Obviously any definition of denseness and sparseness is somewhat arbitrary, but one definition is described below. In the sequel, the individuals in the population will be referred to as trees so as to distinguish the point events from points in the plane, and also as the methods considered are used on tree position data.