Species-area relation and self-similarity in a biogeographical model of speciation and extinction

We introduce a generic model for the population growth and dispersal of individuals in species with heterogeneous, fluctuating environments. New species originate with a probability inversely proportional to the abundance of the parent species. The model generates an average number of species which depends on the domain area in agreement with the species-area relation for islands. The model also generates self-similar radiations characterized by a power-law distribution for the number of subtaxa with the same parent taxon and a 1/f power spectrum for the time series of extinctions and originations.