Potential Global-Local Inconsistency in Species-Area Relationships Fitting

The Species-Area Relationship (SAR) has been widely employed to assess species diversity and predict species extinction. Thus far, although many functions were proposed to fit SAR based on field observations or simulation results, the shape of SAR curve has been debated extensively over decades. Here we uncover a potential global-local inconsistency in SARs fitting simulation blocked by the limitation of large area sampling before. The results indicated that power and logarithm SAR formulas were good for the fitting if the sampling area range is not large which is also the practical sampling interval in the field. However, for the logarithm SAR fitting, a sigmoid curve occurred in the log10 Area-Number of Species plane, and for the power SAR fitting, the curve is convex instead of a straight line as assumed when linear regression was applied. In conclusion, neither the power SAR nor the logarithm SAR fitted to simulated data is linear at large sampling range as commonly assumed in previous studies, no matter the distribution of species abundance is log-normal or negative-binomial, which unmasks the global-local inconsistency in SARs fitting. Thus, misestimates of total number of species or other derivation parameters can occur if the fitted relationship is extrapolated beyond the range of the small and intermediate sampling size.