Ades: New Ecological Families of Species-Specific Frequency Distributions that Describe Repeated Spatial Samples with an Intrinsic Power-Law Variance-Mean Property

Abstract

SUMMARY (1) The Ades are families of new three-parameter distributions (named after J. M. Ades) with two parameters (r and r) common to all distributions within a family, and one (;,) unique to each. When fitted to sets of data, the total number of parameters is only two more than the number of sets. (2) Families of Ades distributions performed as well as, or better than, negative binomials when fitted to seven classical species' data sets comprising seventy-three histograms (samples) with 9345 sample units (counts) containing 89 516 individual insects, with means ranging from 0.09 to 216 and corresponding variances from 0.15 to 193 058. (3) The form of the frequency distributions ranged from low-density, highlyasymmetrical, with a very high proportion of zeros ('Poisson type') to high-density, either long-tailed or almost symmetrical ('lognormal type'), corresponding well to those encountered in the literature. (4) Frequency distributions within an Ades family conformed accurately to the variance-mean power-law relationship. (5) Where two species' regressions intersect, the two species' frequency distributions may be quite different for the same variance and mean. (6) Fitted values of the negative binomial k differed widely between samples within each data set and varied with density according to functional forms predicted previously.