The Detection of Random Heterogeneity in Plant Populations

Summary Most tests oJ'spatial randomness distinguish between regular and aggregated departures jroms comiiplete spatial randomtiness. In this paper, a two-stage procedure Jor the detectioni of ranidomil heterogeneity is proposed, a preliminary test oj'randomnness is Jollowed, in appropriate cases, b) a heterogenieity test, thus effecting a four-way characterisation oJ'spatial point patterns as regular, ranidomsl-homiiogenous, ranidom-heterogeneous or aggregated. A useful starting point in the analysis of the spatial pattern presented by a particular plant population is to test the null hypothesis, JC0, that the individual plants, envisaged as point locations in the plane, are distributed completely at random or, more formally, that they constitute a partial realisation of a homogenous, two-dimensional, Poisson point process. Quadrat as discussed for example by Greig-Smith (1964) were originally Llsed in this context, but may be non-robust to changes in quadrat size (Holgate 1972) and a number of alternative tests have evolved, using plotless sampling techniques. Among such methods, the tests of Besag and Gleaves (1973) presuppose no knowledge of population density and aim to combine the intuitive appeal of Hopkins' (1954) test with the practicability of Holgate's (1965) ratio test. Let X represent the distance from a randomly selected point, P, to the nearest plant in the population, at Q say, and define QQT to be the line through Q, perpendicular to PQ. Now let Y be the distance from Q to the nearest plant in the population, excluding all plants which lie on the same side of QQT as does P. For a sample of m randomly selected points, and vectors of observations x and y, the T-square statistics may now be written as