Species abundance distributions result from body size-energetics relationships

Abundance distributions are a central characteristic of ecosystems. Certain distributions have been derived from theoretical models of community organization, and therefore the fit of data to these distributions has been proposed as a test of these theories. However, it is shown here that the geometric sequence distribution can be derived directly from the empirical relationship between population density and body size, with the assumption of random or uniform body size distributions on a log scale (as holds at local scales). The geometric sequence model provides a good to excellent fit to empirical data. The presence of noise in the relationship between population density and body size creates a curve that begins to approximate a lognormal species abundance distribution as the noise term increases. For continental-scale data in which the body size distribution is not flat, the result of sampling tends again toward the lognormal. Repeat sampling over time smooths out species population fluctuations and damps out the noise, giving a more precise geometric sequence abundance distribution. It is argued that the direct derivation of this distribution from empirical relationships gives it priority over distributions derived from complex theoretical community models.