An assembly rule could explain the canonical property of the lognormal species-abundance distribution

Background: The lognormal distribution of species abundances is a classic model of ecology whose canonical property consists of the fact that the individuals curve tends to peak at the rightmost species-abundance class. Currently ecology lacks any compelling biological or mathematical explanation of the canonical property. Goal: Propose a hypothesis for the canonical property by comparing the results of a maximum entropy niche-assembly model to the patterns obtained from the canonical relationship in empirical data. Data: Published data of the numbers of species in lognormal communities, and their standard deviations. Method: Let a niche dimension be any independent characteristic of the habitat that can be subdivided by species to reduce competition. Obtain relative species abundances as the product of randomly assigned species occupancies along multiple niche dimensions. Plot the standard deviation of the resulting lognormal-like species histogram for different niche dimensions and numbers of species. Estimate the number of species added with each niche dimension by interpolation along the line representing the canonical property and the regression line of empirical data. Results: Randomly assigning species occupancies along multiple niche dimensions produces lognormal-like distributions. Each added niche dimension roughly doubles the number of species in the community. Conclusions: The canonical property may originate from the doubling of the number of species with each added niche dimension. This assembly rule is supported by analyses on the relationship between bird species and habitat complexity.