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Sampled-based estimation of diversity sensu stricto by transforming Hurlbert diversities into effective number of species

Authors

  • Gilles Dauby,

    1. Evolutionary Biology and Ecology unit, Univ. Libre de Bruxelles, CP 160/12, Faculté des Sciences, Av. F.D. Roosevelt, 50, BE-1050 Brussels, Belgium
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  • Olivier J. Hardy

    1. Evolutionary Biology and Ecology unit, Univ. Libre de Bruxelles, CP 160/12, Faculté des Sciences, Av. F.D. Roosevelt, 50, BE-1050 Brussels, Belgium
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G. Dauby, Evolutionary Biology and Ecology unit, Univ. Libre de Bruxelles, CP 160/12, Faculté des Sciences, Av. F.D. Roosevelt, 50, BE-1050 Brussels, Belgium. E-mail: gildauby@gmail.com

Abstract

A theoretical framework based on Hill numbers has recently been advocated to measure and partition diversity sensu stricto. Hill numbers can be interpreted intuitively as effective number of species (ENS). They conform to the so-called replication principle allowing a mathematically coherent multiplicative partitioning of diversity. They form a family of ENS defined by the parameter q which controls the weight attributed to rare species. Despite its advantages, this framework was developed without considering its robustness when treating community samples. In this study, we first show that Hurlbert diversity indices (expected number of species among k individuals) can be transformed into ENS that conform asymptotically to the replication principle while controlling the weight given to rare species through parameter k. We investigate the statistical properties of Hill and Hurlbert ENS using simulated communities with contrasted diversity. The properties of multiplicative beta diversity estimators based on ENS are also characterized by simulating communities with different levels of differentiation. We show that Hurlbert ENS provides a better statistical performance than Hill numbers when dealing with small sample sizes. By contrast, Hill numbers and their estimators suffer from substantial bias except when rare species have a low weight (q= 2). An estimator of ENS estimating both Hill numbers for q= 2 and Hurlbert ENS for k= 2 is shown to give the best performance and is recommended for processing real datasets when rare species receive low weight. In order to better take account of rare species, current estimators of Hill numbers are not recommended when sample size is too low while Hurlbert’s ENS performs reliably. In conclusion, while Hill numbers possess some interesting mathematical properties that are not shared by Hurlbert’s ENS, the latter outperforms Hill numbers in terms of statistical properties and is well suited to processing community samples, as illustrated on a real dataset.

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