On the Relative Abundance of Bird Species.

One approach to the study of the structure of animal communities for which there is a considerable amount of raw data is the comparison of abundances of the species of a group of organisms in a given locality. The basic information is a list of species found and the abundance of each. This can best be plotted by ranking the species from commonest to rarest along the abscissa and plotting their abundances along the ordinate. For convenience, the abscissa is graduated logarithmically. Earlier investigations,' discussed elsewhere,2 fit known statistical curves of uncertain biological meaning to the data. A more fruitful approach seems to be to predict curves on the basis of simple biological hypotheses and to compare these with the data. Three such hypotheses will be discussed here. First, however, the evidence cited by Lack,3 combined with the observation that censuses yield similar results when taken in the same habitat either at the same time in different places or in the same place in different years, indicates, for birds at least, that the observed populations are not under the control of very local or rapid temporal processes; i.e., they are in a near-equilibrium state. The hypotheses will therefore be ones which yield an equilibrium or near-equilibrium population. Hypothesis 1: Nonoverlapping Niches. The environment is compared with a stick of unit length on which n 1 points are thrown at random. The stick is broken at these points, and the lengths of the n resulting segments are proportional to the abundances of the n species. This comparison is legitimate, since the mathematical part of the derivation can be used unchanged for spaces of higher dimension. The most complete discussion of the resulting distribution is given by Barton and David.4 The expected length of the rth shortest interval is given by