A multifractal model for spatial variation in species richness

Abstract

MFp1p2 is a self-similar multifractal that generalises the model of scaling in species richness due to Harte et al. [Harte, J., Kinzig, A., Green, J., 1999. Self-similarity in the distribution and abundance of species. Science 284, 334–336]. It quantifies the scaling in the variation as well as the mean of species richness. The construction is based on a cascade of bisections of a rectangle. The two parameters of the model are p 1 , the proportion of species that occur in the richer half, and p 2 , the proportion of species that occur in the poorer half. An equivalent parameterisation is a = ( p 1 + p 2 ) / 2 and b = p 2 / p 1 . These parameters are interpreted as follows: a gives the scaling of mean richness, b gives the scaling of spatial variation around that mean. Several properties of MFp1p2 are derived, a generalisation is noted and some applications are suggested.