Species distributions and area relationships

•Show a new, concise, derivation of Yule׳s equilibrium distribution.•Derive the species-area relationship based on the evolution of species through mutations.•Calculate the exponent of the species-area relationship for four different data sets.•Confirm that the exponent term, based on mutation rates, agrees with previously observed values.

The well-known species-area relationship is one of many scaling laws, or allometries, in ecology and biology that have received much attention over the years. We present a new derivation of this relationship based on Yule׳s theory of evolution of species. Using definitions of mutation rates, our analysis yields species-area exponents that are in close agreement with previously observed values.