Families of distributions for repeated samples of animal counts - rejoinder

The criterion of flexibility (Perry and Taylor, 1985, Journal of Animal Ecology 54, 931-953), that families of distributions with (n + 2) parameters should fit adequately to all n samples of animal counts over the full range of population densities usually encountered, was misinterpreted by Kemp (1987, Biometrics 43, 693-699). This criterion of goodness of fit is examined here for Perry and Taylor's Adès family, and one of Kemp's alternatives, a family of constrained negative binomial (c.n.b.) distributions, using extensive literature data. While the Adés fitted better than the c.n.b. in 15 of 22 sets, the evidence is not overwhelming because in 13 sets the difference was negligible or both families fitted adequately. However, of the remainder, the Adés fitted notably better to seven sets; these mainly comprised long-tailed distributions with large means, typical of pest species. Its use in practical applications with such data is discussed and the importance of its superior reliability stressed. Kemp's method of fitting is not recommended.