Abstract.-In this paper we present mathematical notation and formulae relating a number of indices of the biodiversity pattern of an aggregate of species, one index of phylogenetic similarity, and an implementation of them as linked maps or phylogenies in a plug-in for the increasingly popular open source geographic information system Quantum GIS. We provide detailed formulae relating three indices of beta diversity, two of pattern of nestedness, one of checkerboard pattern, and two of ratios of variances. The above synthesis is achieved by deriving six vectors from the full presence-absence matrix. Our GIS implementation is done via web services, tapping the LifeMapper platform for estimating potential distributions of species.