Application of the$\mathop m\limits^* - m$ method to the analysis of spatial patterns by changing the quadrat sizemethod to the analysis of spatial patterns by changing the quadrat size

Summary

A method for the analysis of spatial pattern using quadrats of different sizes is developed on the basis of the relationship of mean crowding ($\mathop m\limits^*$) to mean density (m). The$\mathop m\limits^*$-on-m regression obtained by successive changes in quadrat size in a single population (unit-size relation) shows a characteristic pattern according to the type of distribution. By aid of the ρ-index proposed here, we can distinguish the random, aggregated and uniform distributions of the basic components (individual or group of individuals). The ρ serves as an index of spatial correlation between neighbouring quadrats, and it also provides information on the approximate area occupied by clump (colony), distribution pattern of individuals within clumps, and possibly the distribution pattern of clumps themselves.

Even in a specified type of distribution, the unit-size$\mathop m\limits^* - m$ relation is not necessarily identical with the$\mathop m\limits^* - m$ relation for a series of populations at a particular quadrat size (series relation). The changes in the series$\mathop m\limits^* - m$ relationship with successive changes of quadrat sizes are also considered for some basic patterns of distributions. The combined use of the unit-size and the series$\mathop m\limits^* - m$ relations for a set of populations of the species under study may provide a satisfactory picture of the spatial pattern characteristic of the species.

Application of the method is illustrated by using distribution data of several species of animals and plants. The advantage of the present method over other methods are discussed, and the formulae for determining the optimum quadrat unit in sampling surveys are given.