Lognormal Distributions and the Concept of Community Equilibrium

Abstract

The lognormal distribution of individuals among species fits many sets of ecological data remarkably well. Dispute exists however, as to whether this distribution is a mathematical artifact of large numbers or whether it has a biological meaning. In analysing general lognormal curves we argue that the characteristics discovered by Preston relating to the canonical lognormal are in fact merely mathematical properties of the whole family of lognormal curves. We develop a model that assumes that a community is composed of groups of species each differently adapted to a habitat. By integrating the distributions of these groups a lognormal distribution results if the community is in equilibrium. If the community is disturbed however, many species change their abundance and then species abundance curves show multiple maxima and no longer conform to a single lognormal curve.