Modeling species-area and endemic species-area relationships have been
broadly focused. However, little attention has been paid to rare species-area relationship
and common species-area relationship. Also, there were few studies revealing the shape
patterns among the curves. In the present study, we quantified the relationships among
species-area (SAR), commonness-area (CAR), rarity-area (RAR) and endemism-area
(EAR) relationships by investigating different probability functions of species distribution
(including negative binomial distribution, finite negative binomial distribution, Poisson
distribution, geometric distribution and He-Legendre extension of negative binomial
distribution). Results showed that RAR could be used as a robust indicator of SAR,
because the curve patterns are identical between RAR and SAR in most cases. CAR could
easily become saturated for all probability models in that common species are readily
detectable. Finally, EAR curves have convex patterns compared to other relationships. The
influences of species aggregation and abundance on SAR and EAR typically showed
opposite patterns: increasing aggregation and reducing abundance would lower SAR
curves, while uplift EAR curves. Interestingly, varying aggregation and abundance of
species could not change the flat patterns of CAR and predict the curve shapes of RAR
among different probability models.
Keywords: Aggregation, commonness, ecological universal rules, endemism,
flagship species, geometric constraint, indicator species, power law, rarity,
sampling bias, species distribution, species-area relationship.