  There has been a considerable effort to understand and quantify the spatial
distribution of species across different ecosystems. Relative species abundance
(RSA), beta diversity and species area relationship (SAR) are among the most
used macroecological measures to characterize plants communities in forests. In
this article we introduce a simple phenomenological model based on Poisson
cluster processes which allows us to exactly link RSA and beta diversity to
SAR. The framework is spatially explicit and accounts for the spatial
aggregation of conspecific individuals. Under the simplifying assumption of
neutral theory, we derive an analytical expression for the SAR which reproduces
tri-phasic behavior as sample area increases from local to continental scales,
explaining how the tri-phasic behavior can be understood in terms of simple
geometric arguments. We also find an expression for the endemic area
relationship (EAR) and for the scaling of the RSA.
