The Effect of Quadrat Size on the Estimation of the Parameters of Neyman's and Thomas's Distributions

Of the various theoretical contagious distributions which have been applied to plant and insect populations, two especially have found favour with plant ecologists. These are the Neyman type A series and the Thomas series. Evans (1953), using data from several sources, tested the goodness of fit of three contagious series (Neyman's type A, the negative binomial and the Polya-Aeppli) to numerous observed frequency distributions of plants and insects. He found that of these three series the Neyman's type A generally gave the best fit to plant populations. He did not try fitting Thomas's series. Very often both Neyman's type A and Thomas's series give good fits to observational results. Each has two adjustable parameters and in both series, one parameter is supposed to denote the density of the clusters in which the individual plants occur; while the other gives the mean number of plants per cluster. However, the parameters for the two series, which are presumed to give estimates of two biologically significant figures, differ widely. Both the series are based on the same two assumptions: firstly that plants occur in randomly distributed clusters, and secondly that the number of individuals (seedlings or vegetative shoots) per cluster is also random; in Neyman's type A series the number of individuals per cluster is a Poisson variate; in Thomas's series it is a Poisson variate plus one. The two series are, therefore, not very different. Neyman's series (Neyman, 1939). was developed to account for the contagious distributions found among insect larvae. At the time quadrat counts were made the larvae had not travelled far from the randomly distributed egg-masses from which they had hatched and the clusters were necessarily of limited size; their radii could not exceed the distance a larva could have travelled in its lifetime.