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9 - Species Accumulation Curves and Extreme Value Theory

from Part III - Theoretical Advances in Species–Area Relationship Research

Published online by Cambridge University Press:  11 March 2021

By
Luís Borda-de-Água ,
Saeid Alirezazadeh ,
Manuela Neves ,
Stephen P. Hubbell ,
Paulo A. V. Borges ,
Pedro Cardoso ,
Francisco Dionísio  and
Henrique M. Pereira
Edited by
Thomas J. Matthews ,
Kostas A. Triantis  and
Robert J. Whittaker
Thomas J. Matthews
Affiliation:
University of Birmingham
Kostas A. Triantis
Affiliation:
National and Kapodistrian University of Athens
Robert J. Whittaker
Affiliation:
University of Oxford
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Summary

The species–area relationship (SAR) has been described as one of the few general patterns in ecology. Although there are many types of SAR, here we are concerned solely with the so-called species accumulation curve (SAC). The theoretical basis of this relationship is not well established. Here, we suggest that extreme value theory, also known as the statistics of extremes, provides a theoretical foundation for, as well as functions to fit, empirical species accumulation curves. Among the several procedures in extreme value theory, the appropriate way to deal with the species accumulation curve is the so-called block minima procedure. We first provide a brief description of this approach and the relevant formulas. We then illustrate the application of the block minima approach using data on tree species from a 50 ha plot in Barro Colorado Island, Panama. We conclude by discussing the extent to which the assumptions under which the extreme types theorem occurs are confirmed by the data. Although we recognize limitations to the present application of extreme value theory, we predict that it will provide fertile ground for future work on the theory of SARs and its application in the fields of ecology, biogeography and conservation.

Keywords

Species accumulation curveextreme value theorystatistics of extremesblock minima procedureBarro Colorado Island
Type
Chapter
Information
The Species–Area Relationship
Theory and Application
 , pp. 211 - 226
Publisher: Cambridge University Press
Print publication year: 2021

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