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Reconstruct Species-Area Theory Using Set Theory

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Abstract

The species-area theory (SAT) is an important research platform for ecology and biodiversity conservation. Traditionally, the SAT is described using the algebra method, without considering taxonomic characteristic differences between species. Here, we use the branch of mathematics known as set theory to reformulate the SAT, including the species-area relationship, endemic-area relationship, overlap-area relationship, and alpha, beta, and gamma diversity. Then fundamental equations are derived by this method: (1) the number of species in one area can be divided into two parts: species (endemic species) in only this area, and species (overlapping species) in both the focal and neighboring area. The total number of species in these two areas is equal to the sum of the number of species in one of the two areas and the number of species existing only in the other area. (2) A new definition of beta diversity is proposed to describe the overlapping species distribution among the local alpha diversity in the whole gamma diversity. Therefore, gamma diversity is the union of all alpha diversity or the union of all beta diversity.

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Acknowledgments

I warmly thank Xuejun Dong, Bob Patton, and Fengqiao Liu for the helpful suggestions for the manuscript revision. The work is supported by the Basic Scientific Research Foundation of Chinese Academy of Inspection and Quarantine (No. 2014JK014 and 2014JK015) and Public Welfare Project for Quality Supervision, Inspection and Quarantine (No. 201310091 and 201410080). Pan X. also thanks for personal financial support from Scientific Research Foundations for the Returned Overseas Chinese Scholars, Ministry of Labour and Social Security and Ministry of Education, the People's Republic of China.

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Authors and Affiliations

  1. Institute of Plant Quarantine, Chinese Academy of Inspection and Quarantine, Beijing, 100029, China

    Xubin Pan

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  1. Xubin Pan
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Correspondence to Xubin Pan.

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Pan, X. Reconstruct Species-Area Theory Using Set Theory. Natl. Acad. Sci. Lett. 38, 173–177 (2015). https://doi.org/10.1007/s40009-014-0319-3

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  • DOI: https://doi.org/10.1007/s40009-014-0319-3

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