Research Article: The generalized Simpson’s entropy is a measure of biodiversity

Date Published: March 7, 2017

Publisher: Public Library of Science

Author(s): Michael Grabchak, Eric Marcon, Gabriel Lang, Zhiyi Zhang, Stefan J. Green.

http://doi.org/10.1371/journal.pone.0173305

Abstract

Modern measures of diversity satisfy reasonable axioms, are parameterized to produce diversity profiles, can be expressed as an effective number of species to simplify their interpretation, and come with estimators that allow one to apply them to real-world data. We introduce the generalized Simpson’s entropy as a measure of diversity and investigate its properties. We show that it has many useful features and can be used as a measure of biodiversity. Moreover, unlike most commonly used diversity indices, it has unbiased estimators, which allow for sound estimation of the diversity of poorly sampled, rich communities.

Partial Text

Many indices of biodiversity have been proposed based on different definitions of diversity and different visions of the biological aspects to address [1]. Indeed, measuring diversity requires both a robust theoretical framework [2] and empirical techniques to effectively estimate it [3]. We focus on species-neutral diversity, i.e. the diversity of the distribution of species, ignoring their features. Such measures only make sense when applied to a single taxocene, i.e. a subset of species in the community under study that belong to the same taxon (e.g. butterflies) or, more loosely, to a meaningful group (e.g. trees). Classical measures of this type include richness (the number of species), Shannon’s entropy [4], and Simpson’s index [5].

In this section we apply our methodology to estimate and compare the diversities of two 1-ha plots (#6 and #18) of tropical forest in the experimental forest of Paracou, French Guiana [27]. Respectively 641 and 483 trees with diameter at breast height over 10 cm were inventoried. The data is available in the entropart package for R.

Generalized Simpson’s entropy is a measure of diversity respecting the classical axioms when r < S and has a simple formula to transform it into an effective number of species. It faces several issues that limit its use. Specifically, it only makes sense when applied to a single taxocene and its estimator has nice properties only under the assumption of random sampling. However, these issues are shared with all of the other measures of diversity discussed here and many, if not most, of the ones available in the literature. Further, generalized Simpson’s entropy has a decisive advantage over other such measures: it has an easy-to-calculate uniformly minimum variance unbiased estimator, which is consistent and asymptotically normal. These properties make it a useful tool for estimating diversity and for comparing hyper-diverse, poorly sampled communities. R code to reproduce the examples in the paper, based on the packages EntropyEstimation and entropart [22], is given in S2 Appendix. All data are available in the entropart package.   Source: http://doi.org/10.1371/journal.pone.0173305