Application of fundamental equations to species-area theory.

Xubin Pan

doi:10.1186/s12898-016-0097-5

Abstract

BackgroundSpecies−area relationship (SAR), endemics-area relationship (EAR) and overlap-area relationship (OAR) are three important concepts in biodiversity study. The application of fundamental equations linking the SAR, EAR and OAR, can enrich the axiomatic framework of the species−area theory and deepen our understanding of the mechanisms of community assembly.ResultsTwo fundamental equations are derived and extended to power law model and random replacement model of species−area distribution. Several important parameters, including the overlap index and extinction rate, are defined and expressed to enrich the species−area theory. For power law model, both EAR and OAR have three parameters, with one more parameter of the total area than SAR does. The EAR equation is a monotonically increasing function for parameter c and z, and a monotonically decreasing function for parameter A. The extinction rate, with two parameters, is a monotonically increasing function for parameter z, and a monotonically decreasing function for parameter A. The overlap index is a monotonically increasing function for parameter A, and a monotonically decreasing function for parameter z, independent of parameter c.ConclusionsThe general formats of SAR, EAR, OAR, overlap index, overlap rate, sampling rate and extinction rate, are derived and extended to power law model and random replacement model as the axiomatic framework of species−area theory. In addition, if the total area is underestimated, the extinction rate will be overestimated.Electronic supplementary materialThe online version of this article (doi:10.1186/s12898-016-0097-5) contains supplementary material, which is available to authorized users.

Highlights

Species−area relationship (SAR), endemics-area relationship (EAR) and overlap-area relationship (OAR) are three important concepts in biodiversity study
The relationships among SAR, EAR and OAR have been shown in Fig. 1, where Sa is the number of species in area a, Ea is the number of species that will disappear when habitat area a is cleared, Oa, A−a is the number of overlap species in two areas a and A − a, SA(= EA)
Application of two fundamental equations to power law model Power law model has been widely used for species−area relationship: Sa = caz, (4)

Summary

Introduction

Species−area relationship (SAR), endemics-area relationship (EAR) and overlap-area relationship (OAR) are three important concepts in biodiversity study. Species−area relationship (SAR) is a core concept in biodiversity and species distribution [1], and endemics-area relationship (EAR) is a useful tool in biodiversity conservation and habitat preservation [2,3,4,5]. Besides SAR and EAR, overlap-area relationship (OAR), which refers to the number of overlap species in two areas, is a relevant and important concept [6,7,8]. To link SAR and EAR and develop a complete species−area theory, two fundamental equations are established to describe species distribution and interrelation between two compensatory areas [7]. The impact of total area on the extinction rate is still unknown without the specific species−area model and sensitivity analysis

Methods

Results

Discussion

Conclusion