Institute of Statistics, National Tsing Hua University, Hsin-Chu, 30043, Taiwan.
Department of Environmental Biology, University of Rome, "La Sapienza," Piazzale Aldo Moro 5, Rome, 0185, Italy.
Ecology. 2019 Dec;100(12):e02852. doi: 10.1002/ecy.2852. Epub 2019 Sep 19.
An enormous number of measures based on different criteria have been proposed to quantify evenness or unevenness among species relative abundances in an assemblage. However, a unified approach that can encompass most of the widely used indices is still lacking. Here, we first present some basic requirements for an evenness measure. We then propose that unevenness among species relative abundances in an assemblage can be measured by a normalized divergence between the vector of species relative abundances and the mean vector, where the mean vector represents the species relative abundances of a completely even assemblage. Thus, evenness among species relative abundances is measured by the corresponding normalized extent of closeness between these two vectors. We consider five divergence measures, leading to five classes of evenness indices. All our evenness measures are in terms of diversity (Hill number) of order q > 0 (here q controls the weighting of species relative abundances) and species richness (diversity of order q = 0). We propose quantifying evenness through a continuous profile that depicts evenness as a function of diversity order q > 0. The profiles can be easily and visually compared across multiple assemblages. Our evenness indices satisfy all the requirements presented in this paper and encompass many widely used evenness measures as special cases. When there are multiple assemblages, the abundance-based Jaccard- and Sørensen-type dissimilarity measures (which are monotonic functions of beta diversity) can be expressed as weighted averages of the individual species' compositional unevenness values; here, each individual species' compositional unevenness is calculated based on that species' abundances among assemblages. The contribution of a species to each dissimilarity measure can be clearly disentangled and quantified in terms of this single species' compositional unevenness among assemblages. Thus, our framework links the concepts of evenness, diversity, beta diversity, and similarity. Moreover, the framework can be readily extended to a phylogenetic version. A real data example is used to illustrate our approach. We also discuss some criteria and other measures that were previously proposed in the literature.
已经提出了大量基于不同标准的方法来量化群落中物种相对丰度的均匀度或不均匀度。然而，仍然缺乏一种可以包含大多数广泛使用的指数的统一方法。在这里，我们首先提出了均匀度度量的一些基本要求。然后，我们建议可以通过群落中物种相对丰度向量与平均值向量之间的归一化差异来测量物种相对丰度的不均匀度，其中平均值向量代表完全均匀群落的物种相对丰度。因此，物种相对丰度的均匀度通过这两个向量之间相应的归一化接近程度来衡量。我们考虑了五种分歧度量方法，从而产生了五类均匀度指数。我们所有的均匀度度量都是以阶数 q>0 的多样性（Hill 数）（此处 q 控制物种相对丰度的权重）和物种丰富度（阶数 q=0 的多样性）来表示的。我们建议通过连续的分布来量化均匀度，该分布将均匀度描绘为阶数 q>0 的函数。这些分布可以很容易地在多个群落之间进行直观比较。我们的均匀度指数满足本文中提出的所有要求，并包含许多广泛使用的均匀度度量作为特例。当存在多个群落时，基于丰度的 Jaccard 和 Sørensen 型不相似性度量（它们是β多样性的单调函数）可以表示为个体物种组成不均匀度值的加权平均值；这里，每个个体物种的组成不均匀度是根据该物种在群落中的丰度计算的。物种对每个不相似性度量的贡献可以根据该物种在群落之间的单一组成不均匀度清楚地分解和量化。因此，我们的框架将均匀度、多样性、β多样性和相似性的概念联系起来。此外，该框架可以很容易地扩展到一个系统发育版本。一个真实数据的例子被用来举例说明我们的方法。我们还讨论了文献中以前提出的一些标准和其他度量。
