  We studied the mathematical relations between species abundance distributions
(SADs) and species-area relationships (SARs) and found that a power-law SAR can
be generally derived from a power-law SAD without a special assumption such as
the ``canonical hypothesis''. In the present analysis, an SAR-exponent is
obtained as a function of an SAD-exponent for a finite number of species. We
also studied the inverse problem, from SARs to SADs, and found that a power-SAD
can be derived from a power-SAR under the condition that the functional form of
the corresponding SAD is invariant for changes in the number of species. We
also discuss general relationships among lognormal SADs, the broken-stick model
(exponential SADs), linear SARs and logarithmic SARs. These results suggest the
existence of a common mechanism for SADs and SARs, which could prove a useful
tool for theoretical and experimental studies on biodiversity and species
coexistence.
