Fundamental equations for species-area theory

Species-area theory is an important concept in ecology. However, debates still surround the species-area relationship (SAR) or endemics-area relationship (EAR) and their relations to expected extinction rates. In this paper, I introduce the concept of overlap-area relationship (OAR) to link SAR and EAR. Two fundamental equations are derived from the relationship between the area and species number in a limited whole area A: 1) the sum of species number in area a and species number, here defined as endemics, in area A − a is the total species number in area A; 2) the number of species common to both areas a and A − a (overlapping species) equals the species number in area a minus the endemics number in area a. Thus, we should carefully consider the total area on which EAR depends, when estimating extinction rate based on SAR.