A multifractal model for spatial variation in species richness

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 p1p1, the proportion of species that occur in the richer half, and p2p2, the proportion of species that occur in the poorer half. An equivalent parameterisation is a=(p1+p2)/2a=(p1+p2)/2 and b=p2/p1b=p2/p1. 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.