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