A multifractal model for spatial variation in species richness

Models for species-area relationships up to now have focused on the mean richness as a function of area. We present MFp1p2, a self-similar multifractal. It explicitly models both trend and variation in richness as a function of area, and is a generalisation of the model of scaling of mean species richness due to Harte et al (1999). The construction is based on a cascade of bisections of a rectangle. The two parameters of the model are p1, the proportion of species that occur in the richer half, and p2, the proportion of species that occur in the poorer half. Equivalent parameterisations are a = (p1 + p2)/2 and b = p1/p2. These parameters are interpreted as follows: a gives the scaling of mean density, b gives the scaling of spatial variability. Several properties of MFp1p2 are derived, a generalisation is noted and some applications are suggested.