Statistical tests of the broken-stick model of species-abundance relations

Abstract

The broken-stick model of MacArthur has been generally accepted as providing a good description of species-abundance relations for certain animal communities, such as birds and fishes. Most of the conclusions about the validity of the model, however, appear to have been reached either through visual comparison of observed and predicted abundance plots or through indirect results, such as the relation between diversity and number of species. As a basis for a more quantitative and direct test of the model, a sample of 130 breeding-bird censuses was selected from Audubon Field Notes . The theoretical and observed distributions of δ s (the difference between the two largest relative abundances) were compared; the agreement was considered to be marginally satisfactory. One possible source of bias in the test is that the argument of the broken-stick distribution is a continuous variable, while the observations are reported as discrete variables. An integer-variable analog of the broken-stick model was devised and the theoretical and observed distributions of N s (the largest absolute abundance) were compared. In this case the agreement was definitely unsatisfactory. The observed values of N s were generally larger than the theoretical median values, and almost one-half of them fell in the fourth quartile of the theoretical distribution.