A comparison of species diversity estimators

Although having been much criticized, diversity indices are still widely used in animal and plant ecology to evaluate, survey, and conserve ecosystems. It is possible to quantify biodiversity by using estimators for which statistical characteristics and performance are, as yet, poorly defined. In the present study, four of the most frequently used diversity indices were compared: the Shannon index, the Simpson index, the Camargo eveness index, and the Pielou regularity index. Comparisons were performed by simulating the Zipf–Mandelbrot parametric model and estimating three statistics of these indices, i.e., the relative bias, the coefficient of variation, and the relative root-mean-squared error. Analysis of variance was used to determine which of the factors contributed most to the observed variation in the four diversity estimators: abundance distribution model or sample size. The results have revealed that the Camargo eveness index tends to demonstrate a high bias and a large relative root-mean-squared error whereas the Simpson index is least biased and the Shannon index shows a smaller relative root-mean-squared error, regardless of the abundance distribution model used and even when sample size is small. Shannon and Pielou estimators are sensitive to changes in species abundance pattern and present a nonnegligible bias for small sample sizes (<1000 individuals). Received: May 8, 1998 / Accepted: May 6, 1999     

A conceptual guide to measuring species diversity

Three metrics of species diversity – species richness, the Shannon index and the Simpson index – are still widely used in ecology, despite decades of valid critiques leveled against them. Developing a robust diversity metric has been challenging because, unlike many variables ecologists measure, the diversity of a community often cannot be estimated in an unbiased way based on a random sample from that community. Over the past decade, ecologists have begun to incorporate two important tools for estimating diversity: coverage and Hill diversity. Coverage is a method for equalizing samples that is, on theoretical grounds, preferable to other commonly used methods such as equal-effort sampling, or rarefying datasets to equal sample size. Hill diversity comprises a spectrum of diversity metrics and is based on three key insights. First, species richness and variants of the Shannon and Simpson indices are all special cases of one general equation. Second, richness, Shannon and Simpson can be expressed on the same scale and in units of species. Third, there is no way to eliminate the effect of relative abundance from estimates of any of these diversity metrics, including species richness. Rather, a researcher must choose the relative sensitivity of the metric towards rare and common species, a concept which we describe as ‘leverage.' In this paper we explain coverage and Hill diversity, provide guidelines for how to use them together to measure species diversity, and demonstrate their use with examples from our own data. We show why researchers will obtain more robust results when they estimate the Hill diversity of equal-coverage samples, rather than using other methods such as equal-effort sampling or traditional sample rarefaction.     

Simultaneous confidence intervals for comparing biodiversity indices estimated from overdispersed count data

Diversity indices might be used to assess the impact of treatments on the relative abundance patterns in species communities. When several treatments are to be compared, simultaneous confidence intervals for the differences of diversity indices between treatments may be used. The simultaneous confidence interval methods described until now are either constructed or validated under the assumption of the multinomial distribution for the abundance counts. Motivated by four example data sets with background in agricultural and marine ecology, we focus on the situation when available replications show that the count data exhibit extra‐multinomial variability. Based on simulated overdispersed count data, we compare previously proposed methods assuming multinomial distribution, a method assuming normal distribution for the replicated observations of the diversity indices and three different bootstrap methods to construct simultaneous confidence intervals for multiple differences of Simpson and Shannon diversity indices. The focus of the simulation study is on comparisons to a control group. The severe failure of asymptotic multinomial methods in overdispersed settings is illustrated. Among the bootstrap methods, the widely known Westfall–Young method performs best for the Simpson index, while for the Shannon index, two methods based on stratified bootstrap and summed count data are preferable. The methods application is illustrated for an example.     

Analyzing the (mis)behavior of Shannon index in eutrophication studies using field and simulated phytoplankton assemblages

The Shannon index of diversity H′ is a commonly used metric in ecology. The tendency of this index to show a unimodal relationship with productivity has been the subject of several studies. In the present work, the behavior of H′ and three related ecological indices (Simpson, Hill, and Evenness) was investigated using phytoplankton assemblages along a eutrophication gradient. We used both natural and simulated assemblages, whereby the comparison enabled us to assess the role of environmental ‘noise’ on index behavior. We developed simulated assemblages based on phytoplankton distributions predicted by two model types: the log series statistical model and the random fraction niche-based model. Using field data, H′ and the related Simpson index showed expected unimodal relationships with eutrophication. The same unimodal relationships were reproduced with simulated assemblages. Comparing the simulations with natural assemblages along a eutrophication gradient showed that there was much unexplained variance in the real-world data, suggesting that these diversity indices are sensitive to stochastic processes. An analysis of the simulated assemblages using relative abundance distributions suggested that increasing H′ and Simpson index values in the low range of the eutrophication gradient were due to increasing species richness, and that decreasing index values in the high range of the eutrophication gradient were due to decreasing evenness. In addition, this analysis revealed how assemblages of identical H′ values arose from contrasting community structures found in the low- and high-range of eutrophication. The high variability and non-linearity of the Shannon and Simpson indices along a eutrophication gradient suggests that these measures of diversity are inappropriate for use as water quality monitoring assessment tools. Indeed, when calculating ecological quality ratios that are employed by the European Water Framework Directive, unreliable (non-monotonic) predictions of water quality resulted.     

青藏高原高寒草甸物种多样性的海拔梯度分布格局及对地上生物量的影响

植物物种多样性在海拔梯度上的变化规律以及物种多样性与生产力的关系是生态学研究的热点, 至今还没有得出一般性规律。本文以青海省海南藏族自治州贵德县的拉脊山(36°21′ N, 101°27′ E, 海拔3,389-3,876 m)和果洛藏族自治州的玛沁县军牧场山体(34°22′ N, 100°30′ E, 海拔4,121-4,268 m)为研究对象, 对植物高度、盖度、地上生物量和物种多样性随海拔高度的变化进行调查和统计分析, 以探讨青藏高原高寒草甸的物种多样性和地上生物量在海拔梯度上的变化规律及两者的关系。结果表明: (1)两条山体样带上地上生物量与物种多样性随海拔的变化规律一致: 随着海拔的升高, 地上生物量线性降低; Shannon-Wiener指数、Simpson指数和物种丰富度都呈单峰曲线, 在中间海拔最大, 而Pielou指数随海拔的升高线性增加。结合目前针对青藏高原高寒草甸的研究数据, 发现物种丰富度随海拔高度的变化均呈单峰曲线, 说明随着海拔的升高物种多样性先升高后降低可能是青藏高原物种多样性分布的普遍规律。(2)地上生物量与物种多样性的关系在两条山体样带上表现一致: 地上生物量随Shannon- Wiener指数、Simpson指数和Pielou指数的升高而线性降低, 但与物种丰富度不相关。综合两条山体样带所有样方数据, 发现地上生物量与Shannon-Wiener指数、Simpson指数不相关, 而随物种丰富度的升高线性增加。结合目前在青藏高原的相关研究数据, 发现地上生物量与物种丰富度呈S型曲线(logistic model)。     

澜沧江流域水生昆虫群落分类多样性和功能多样性海拔格局的空间尺度依赖性

群落分类多样性和功能多样性的海拔格局研究, 是了解生物多样性空间分布现状、揭示多样性维持和变化机制的重要途径。当前对水生昆虫分类多样性和功能多样性沿海拔梯度分布格局, 及其尺度依赖性依旧缺乏深入研究。本文基于2013-2018年在云南澜沧江流域500-3,900 m海拔梯度共149个溪流点位的水生昆虫群落调查数据, 利用线性或二次回归模型探索并比较了局部尺度(点位尺度)和不同区域尺度(100 m、150 m、200 m、250 m海拔段)的分类多样性指数(物种丰富度指数、Simpson多样性指数和物种均匀度指数)和功能多样性指数(树状图功能多样性指数(dbFD)、Rao二次熵指数(RaoQ)和功能均匀度指数(FEve))的海拔格局。结果表明, 在局部尺度, 物种丰富度指数和dbFD指数沿海拔梯度均无显著分布特征, Simpson多样性指数、RaoQ指数、物种均匀度指数和FEve指数沿海拔梯度呈现U型或者单调递减趋势。在区域尺度, 随着区域海拔带宽度的增加, 物种丰富度指数沿海拔呈不显著的单调递减格局, 但dbFD指数沿海拔分布由U型转变为单调递减趋势; Simpson多样性指数和RaoQ指数沿海拔梯度由显著U型趋势转变为无显著分布特征; 物种均匀度指数沿海拔梯度无显著分布特征, 但FEve指数呈显著增加的海拔格局。综上, 群落分类多样性指数和功能多样性指数沿海拔梯度分布存在局部和区域尺度的空间差异, 但区域尺度下二者海拔格局随海拔带宽度的增加存在一定程度的一致性。     

西双版纳热带雨林树种多样性的尺度效应

基于西双版纳20hm2森林动态监测样地内直径≥1cm的树种资料,分析了该样地树种香农多样性指数和辛普森多样性指数及其方差和变异系数在7个取样尺度(5m×5m、10m×10m、20m×20m、25m×25m、50m×50m、100m×100m、200m×250m)的变化规律,结果表明:(1)香农指数-面积曲线在尺度100m×100m有一个峰值,而辛普森指数-面积曲线在尺度为20m×20m有一个峰值。(2)香农指数和辛普森指数的方差随尺度的增加而减小,其中香农指数的方差在尺度100m×100m上最小,辛普森指数在尺度20m×20m方差最小,表明香农多样性指数在100m×100m的尺度上所获得的多样性信息比较可靠,而辛普森指数在20m×20m的尺度上所获得信息比较可靠。(3)多样性指数的方差和变异系数远大于随机模型拟合的数值,说明样地内树种不是随机分布。     

戴云山物种多样性与系统发育多样性海拔梯度分布格局及驱动因子

生物多样性的海拔分布格局是生态学研究的热点。海拔作为综合性因子驱动着植物群落的物种、系统发育与功能多样性的空间分布。以戴云山南坡900-1600 m森林植物群落为研究对象,探讨物种多样性、系统发育指数与环境驱动因子的相互关系以及环境因子在群落构建与多样性维持中的重要意义。结果表明：（1）森林植物群落的系统发育多样性与物种多样性沿海拔均呈现中间高度膨胀格局。（2）物种多样性Margalef指数、Shannon-Wiener指数与系统发育多样性指数呈显著正相关,表明物种多样性越高,系统发育多样性也越高。Shannon-Wiener指数与物种多样性指数（Margalef、Pielou、Simpson指数）、系统发育多样性及系统发育结构都存在显著相关性,一定程度上Shannon-Wiener指数可以代替其他指数。Pielou指数、Simpson指数、Shannon-Wiener指数与系统发育结构NRI （Net relatedness index）指数、NTI （Net nearest taxa index）指数存在显著正相关,表明群落优势度、均匀度与系统发育结构相关性较强。（3）土壤全磷含量是影响系统发育多样性和物种多样性的主要驱动因子,土壤含水量是影响Shannon-Wiener、Pielou、Simpson指数的最显著因子,海拔是影响群落系统发育结构的主要因素。海拔是影响系统发育结构变化的主要环境因子,而土壤因子是影响物种多样性与系统发育多样性的主要因素,进一步验证了物种多样性与系统发育多样性的高度相关,结果旨在揭示物种群落空间分布规律。     

遥感植被指数与植物多样性的相关性及空间分布特征研究——以海口市主城区为例

植物多样性监测是开展物种保护与植被景观规划的重要基础,对实施生物多样性的优先区域保护具有重要意义.该文以海口市主城区为例,利用Landsat 8遥感数据与样方实测数据分析了植被指数与植物多样性指数之间的相关性,根据相关性分析结果构建植物多样性遥感监测数学模型,并筛选出最优模型用于监测研究区植物多样性的空间分布状况.结果...     

DNA reassociation kinetics and diversity indices: richness is not rich enough

DNA reassociation kinetics, also known as Cot curves, were recently used by Gans and co-workers to estimate the number of bacterial species present in soil samples. By reanalysing the mathematical model we show that rather than the number of species, Simpson and Shannon diversity indices are encoded in the experimental data. Our main tool to establish this result are the so-called Rényi diversities, closely related to Hill numbers, illustrating the power of these concepts in interpreting ecological data. We argue that the huge diversity encountered in microbial ecology can be quantified more informatively by diversity indices than by number of species.     

Estimation of spectra of multiple molecular forms of enzymes using the index of system internal diversity level

Comparative analysis of the most widely used indexes of system diversity is carried out using model electrophoretic spectra. The basic requirements for the diversity index of electrophoretiñ spectra are formulated. A formula for estimating the level of spectra diversity of multiple forms on the basis of synthesis of the Ashby system complexity index and Simpson index is offered.     

重庆四面山5种不同配置模式人工林生物多样性研究

应用物种多样性指数(Shannon-Wiener指数、Simpson指数)、均匀度指数(Pielou)和物种丰富度指数对重庆四面山地区5种人工水土保持林群落进行多样性分析.结果显示:(1)5种人工林群落以枫香+木荷+石栎+香樟+灌木混交林的物种多样性最为丰富,纯杉木林最次.(2)各多样性指数在不同群落间的变化以乔木层的枫香+木荷+石栎+香樟+灌木混交林、灌木层的石栎+木荷混交林、草本层的纯杉木林等的生物多样性最为丰富.(3)不同林型的物种多样性不同,其生态效益、环境效益也有较大差异.建议在四面山地区以及类似生态区的退耕还林过程中选择以常绿阔叶林和针阔混交林为主的乔一灌结合混交林模式,以提高人工林群落的物种多样性,实现理想的水土保持林功能.     

On the measurement of species diversity incorporating species differences

When pairwise differences (relatedness) between species are numerically given, the average of the species differences weighted by relative frequencies can be used as a species diversity index. This paper first theoretically develops the indices of this type, then applies them to forestry data. As examples of diversity indices, this paper explores the taxonomic diversity and the newly introduced amino acid diversity, which is a modification of the nucleotide diversity in genetics. The first, mathematical part shows that both indices can be decomposed into three inner factors; evenness of relative frequencies (=the Simpson index), the simple average over species differences regardless of relative frequencies, and the taxonomic or genetic balance in relative frequencies. The taxonomic diversity has another decomposition: the sum over the Simpson indices at all the taxonomic levels. The second part examines the effects of different forest management techniques on diversity. It is shown that a thinning operation for promoting survival of specific desirable species also contributed to increasing the taxonomic diversity. If we calculated only conventional indices that do not incorporate species relatedness, we would simply conclude that the thinning did not significantly affect the diversity. The theoretical developments of the first part complement the result, leading us to a better interpretation about contrasting vegetation structures. The mathematical results also reveal that the amino acid diversity involves redundant species, which is undesirable when measuring diversity; hence, this index is used to demonstrates crucial points when we introduce species relatedness. The results suggest further possibilities of applying diversity indices incorporating species differences to a variety of ecological studies.     

城市乔木树种多样性遥感反演方法研究

量化城市乔木树种多样性是定量研究其生态系统服务的前提和基础。目前,城市树种多样性水平的定量研究以地面调查方法为主,存在效率低、成本高的问题。针对上述问题,首先验证了光谱变异性假说和生产力假说在城市中的适用性,进而提出了快速量化城市树种多样性水平的方法。该方法基于神经网络刻画了乔木斑块多样性与光谱异质性之间的关系,能够较准确地反演城市乔木的香浓维纳指数和辛普森指数。为城市乔木树种多样性的调查提供了新的思路,并将为定量研究城市乔木多样性的生态系统服务提供基础数据。     

停止人为去除植物功能群后的高寒草甸多样性恢复过程与群落构建

已有大量研究利用功能性状或系统发育来推断群落构建机制, 然而不同过程可能会导致相似的格局。本文基于对甘南高寒草甸植物功能群去除处理后群落恢复过程的跟踪调查, 对比了物种多样性、功能多样性和系统发育多样性的动态变化, 并分析了物种定殖与消失过程对功能多样性和系统发育多样性变化的影响。结果表明: 去除不同数量功能群的群落中: (1)包括物种丰富度(SR)、Shannon-Wiener指数(H°)和Simpson指数(D)在内的传统物种多样性均随时间快速上升并与自然群落趋同, 不同群落的均匀度指数(J)随时间呈增加趋势并趋于相似; 功能多样性(FD)与系统发育多样性(PD)呈现出与物种多样性相似的动态变化趋势, 而平均配对距离(MPD/MPD_a、MFD/MFD_a)则向中等程度聚集。(2)不同群落的功能群和物种组成在短期内均恢复到与自然群落非常相似的程度。(3)物种定殖与消失过程的功能格局是群落恢复过程中趋同效应的主要驱动力。本研究揭示了高寒草甸植物功能群去除停止后群落短期内快速恢复的过程, 说明在小尺度且周边具有大范围未退化草甸的情况下, 无论物种多样性、功能多样性还是系统发育多样性都具有较快的恢复能力, 同时说明了利用群落系统发育多样性格局来推断群落构建机制的局限性。     

生物多样性和均匀度显著性的随机化检验及计算软件

多样性指数和均匀度以其简单易用而被广泛应用于群落生物学和生物多样性等研究中,然而由于缺乏合适的统计检验方法等原因,其分析的可信性往往较低,因而限制了其应用。鉴于生物多样性研究中广泛应用主观和直接的比较不,有必要建立和使用较为严格的多样性统计检验。本研究建立和应用了如下随机化检验方法：单群落多样性指数和均匀度的显著性检验,单群落多样性指数和均匀度的置认区间,群落间多群样和均匀度的差异显著性检验。随机化方法已被成功地应用于群落生态学研究,其原理是：随机排序某一向量中的元素,或随机交换两向量中的对应元素。计算该随机化数据的多样性和均匀度,重复该过程多次,统计和计算显著性检验的p值,由向量中的对应元素。计算该随机化数据的多样性和均匀度,重复该过程多次,统计和显著性检验的p值。由此可确定多样性和差异的统计显著性。同时,研制了相应的Internet计算软件BiodiverisytTest。该软件由7个Java类和1个HTML文件组成,可运行于多种操作系统和网络浏览器上,可读取多种类型的ODBC数据库文件如Access,Excel,FoxPro,Dbase等。该软件中包括Shannon-Wiener多样性指数,Simpson多样性指数,McIntosh多样性指数,Berger-Parker多样性指数,Hrlbert多样性指数以及Brillouin多样性指数。基于Shannon-Wiener多样性指数和Berger-Parker多样性指数,用BiodiversityTest软件对水稻田节肢动物群落多样性（15个地点,17个功能群,125个节肢动物种）进行了比较和分析。结果显示,两组结果可较好地反映水稻节肢动物群落多样性的差异显著性,这些检验方法可有效地反映多样性指数和均匀度的变化。与水稻田节肢动物群落间多样性的直接比较法相比,该随机化检验方法获得更客观的结果。本算法与软件有助于改进生物多样性研究中使用的某些不甚严格的分析方法,为随机化检验方法在生物多样性研究中的进一步应用提供了一种可用的工具。     

林木分布格局多样性测度方法: 以阔叶红松林为例

林木分布格局是森林结构的重要组成部分, 直接影响森林生态系统的健康与稳定, 维持森林结构多样性被认为是保护生物多样性的最佳途径。本研究探讨了林木分布格局多样性的测度方法, 以期为揭示森林结构多样性提供理论依据。格局多样性研究的关键在于选择合适的生物多样性测度方法和具有分布属性的格局指数。本研究通过统计角尺度分布频率和Voronoi多边形边数分布频率, 运用Simpson指数分别计算角尺度多样性和Voronoi多边形边数分布多样性, 作为表达林木分布格局多样性指数的方法, 并以我国东北吉林蛟河的3个100 m × 100 m的阔叶红松(Pinus koreansis)林长期定位监测标准地为例, 分析了林木分布格局的多样性。结果表明: 无论是角尺度分布还是Voronoi多边形的边数分布都接近正态分布, 角尺度分布中随机分布林木的频数最多, 占55%以上; Voronoi多边形的类型多达10个以上, 50%以上的林木有5-6株最近相邻木。利用Simpson指数衡量林木格局多样性, 角尺度分布与Voronoi多边形的边数分布都显示出聚集分布的林分比随机分布林分的格局多样性高。研究还发现, 两种格局判定方法得出的Simpson指数值有所不同, 角尺度分布的多样性数值明显低于Voronoi多边形的边数分布的多样性数值, 主要原因是二者的等级数量不同。可见, 林木分布格局多样性研究应选择具有分布属性的格局指数, 但由于各指数反映的角度不同, 所以在分析比较不同林分格局多样性时应采用相同的分析方法。     

辽东半岛仙人洞自然保护区植物区系多样性分析

物种多样性分析与研究对于全球生物多样性保护具有重要的意义,运用植物地理学理论,结合外业调查、多样性指数、相关分析和聚类模型等方法,对辽宁仙人洞植物区系多样性进行定量分析,以揭示山地区系生物多样性的特点及规律。结果表明:(1)本区野生植物种类组成丰富,共有维管植物109科379属803种,其中蕨类植物13科17属39种,裸子植物5科12属18种,被子植物91科350属746种,优势科现象明显,单种属和少种属占比率较高,表现出一定古老残遗性;种的区系分布型多样,区系组成复杂,但特有现象不明显;温带成分占主体,表明本区温带植物区系历史起源。(2)仙人洞与邻近山地相比较,植物区系Shannon-Wiener指数差异明显(1.736~2.053),其中仙人洞和徂徕山较高,白石砬子和长白山较低,而Simpson指数差异并不明显(0.711 4~0.825 3)。(3)经相关性分析,不同山地植物区系之间相似程度显著(P0.01),相关系数达0.811~0.997,聚类分析显示仙人洞、凤凰山、千山、五台山及小五台山区系关系较近,支持仙人洞划归华北植物区系山地植物亚地区较为合适。     

Coexistence and competition in HIV infections.

In this paper we extend our explanation of a model for the dynamics of the interaction between HIV and the cells of the immune system (Nowak et al., 1990). We show that the Simpson index of viral diversity is a Lyapunov function for a simplified version of this model. We also present a more general mathematical characterization of the nature of the diversity threshold exhibited by the model, including for the first time heterogeneity in parameters like virus replication rate, cytopathicity and antigenicity. The more general diversity threshold condition includes the different contributions of strains with higher replication rates and cytopathicities or strains that are only weakly recognized by the immune system. This leads to some new insights and a more detailed understanding of why the viral diversity falls once the diversity threshold is exceeded.     

Partitioning diversity for conservation analyses

Aim  Differentiation of sites or communities is often measured by partitioning regional or gamma diversity into additive or multiplicative alpha and beta components. The beta component and the ratio of within-group to total diversity (alpha/gamma) are then used to infer the compositional differentiation or similarity of the sites. There is debate about the appropriate measures and partitioning formulas for this purpose. We test the main partitioning methods, using empirical and simulated data, to see if some of these methods lead to false conclusions, and we show how to resolve the problems that we uncover.
Location  South America, Ecuador, Orellana province, Rio Shiripuno.
Methods  We construct sets of real and simulated tropical butterfly communities that can be unambiguously ranked according to their degree of differentiation. We then test whether beta and similarity measures from the different partitioning approaches rank these datasets correctly.
Results  The ratio of within-group diversity to total diversity does not reflect compositional similarity, when the Gini–Simpson index or Shannon entropy are used to measure diversity. Additive beta diversity based on the Gini–Simpson index does not reflect the degree of differentiation between N sites or communities.
Main conclusions  The ratio of within-group to total diversity (alpha/gamma) should not be used to measure the compositional similarity of groups, if diversity is equated with Shannon entropy or the Gini–Simpson index. Conversion of these measures to effective number of species solves these problems. Additive Gini–Simpson beta diversity does not directly reflect the differentiation of N samples or communities. However, when properly transformed onto the unit interval so as to remove the dependence on alpha and N , additive and multiplicative beta measures yield identical normalized measures of relative similarity and differentiation.