The Canonical Distribution of Commonness and Rarity: Part I

Abstract

In an earlier paper (Preston 1948) we found that, in a sufficiently large aggregation of individuals of many species, the individuals often tended to be distributed among the species according to a lognormal law. We plotted as abscissa equal increments in the logarithms of the number of individuals representing a species, and as ordinate the number of species falling into each of these increments. We found it convenient to use as such increments the octave, that is the interval in which representation doubled, so that our abscissae became simply a scale of octaves, but this choice of unit is arbitrary. Whatever logarithmic unit is used, the graph tended to take the form of a normal or Gaussian curve, so that the distribution was lognormal. \Ve called this the Species Curve. In the present paper we take up a point inerely mentioned in 1948 that not only is the distribution lognormal, but the constants or parameters seem to be restricted in a peculiar way. They are not fixed, but they are interlocked. The nature of this restriction and interlocking is the main theme of the present paper. In the earlier paper we graduated the experimental results with curves of the form