On Sampling Spatial Patterns by Distance Methods

Abstract

'Distance' or 'nearest neighbour' methods are often used as alternatives to counting plants within squares ('quadrat' methods) either to estimate the number of plants in a study region or to test the 'randomness' of their pattern.To be specific we will consider trees; Figure 1 illustrates a 10 metre square plot of pines (from Strand, 1972). The suggested procedures for density estirnation and for testing have been compared by Diggle (1975 1977), Diggle, Besag and Gleaves (1976), and Hines and Hines (1979). The method suggested by Hopkins (1954) invelves measuring the following squared distances: u from a random point to the nearest tree and v from a randomly chosen tree to its nearest neighbour. Edge effects should be made negligible by placillg the study region from which random points and plants are to be selected well within the region of interest. Hopkins' method has generally been preferred in comparison studies but is usually regarded as impracticable since, to find a random tree, all trees in the study regioIl should be counted and a randomly numbered tree chosen. Squared distances arise because the areas swept out in searches for the nearest trees are Fru and Frv, if the search is thought of in concentric circles about the chosen point or tree. The distribution tlleory assulnes that for a Poisson process the areas ru and xv will be independent. For this to hold it should be checked that the areas searched do not overlap, which constrains the number of samples that can be taken. We consider bounds on the sampling intensity and we introduce a semisystematic sampling scheme which allows a higher sampling intensity and permits Hopkins' method to be used without complete enumeration of the study region. A new test for 'randomness' related to Hopkins' test is introduced; a Monte Carlo study shows that this test and