Community assessment techniques and the implications for rarefaction and extrapolation with Hill numbers

Diversity estimates play a key role in ecological assessments. Species richness and abundance are commonly used to generate complex diversity indices that are dependent on the quality of these estimates. As such, there is a long‐standing interest in the development of monitoring techniques, their ability to adequately assess species diversity, and the implications for generated indices. To determine the ability of substratum community assessment methods to capture species diversity, we evaluated four methods: photo quadrat, point intercept, random subsampling, and full quadrat assessments. Species density, abundance, richness, Shannon diversity, and Simpson diversity were then calculated for each method. We then conducted a method validation at a subset of locations to serve as an indication for how well each method captured the totality of the diversity present. Density, richness, Shannon diversity, and Simpson diversity estimates varied between methods, despite assessments occurring at the same locations, with photo quadrats detecting the lowest estimates and full quadrat assessments the highest. Abundance estimates were consistent among methods. Sample‐based rarefaction and extrapolation curves indicated that differences between Hill numbers (richness, Shannon diversity, and Simpson diversity) were significant in the majority of cases, and coverage‐based rarefaction and extrapolation curves confirmed that these dissimilarities were due to differences between the methods, not the sample completeness. Method validation highlighted the inability of the tested methods to capture the totality of the diversity present, while further supporting the notion of extrapolating abundances. Our results highlight the need for consistency across research methods, the advantages of utilizing multiple diversity indices, and potential concerns and considerations when comparing data from multiple sources.     

On the use of sample indices to reflect changes in benthic fauna biodiversity

This paper focuses on the difference between the value of some commonly used diversity indices (Simpson, Shannon, abundance, richness) calculated from benthic grab samples and their value in the population or region from which the samples are taken. The ability of the sample indices, as well as a recently derived relative Shannon index, to reflect change in biodiversity is examined in a short simulation study based on changing one of the diversity parameters (abundance, richness and evenness) in the population, whilst keeping the other two components constant. Our results suggest that, whilst their population equivalents do not always reflect biodiversity changes, the sample Simpson, Shannon and Richness indices perform well. We note that this will be true for any surveys where the sampling programme fails to detect many species in a population, and hence will be applicable for most benthic surveys. The use of sample indices to detect changes in biodiversity from long-running time series in the Thames and Tyne estuaries is illustrated.     

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。     

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.     

Cellular automata and ecology

Many indices for measuring species diversity have been proposed. In this article, a link is noted between a common family of diversity indices and non-additive statistical mechanics. This makes the Shannon index and the Simpson diversity (or Gini coefficient) special cases of a more general index. The general index includes a parameter q that can be interpreted from a statistical mechanics perspective for systems with an underlying (multi)fractal structure. A q - generalised version of the Zipf–Mandelbrot distribution sometimes used to characterise rank–abundance relationships may be obtained by maximising this entropy.     

亚高寒草甸植物群落的中性理论验证

 该文以物种组成较为复杂的青藏高原东部亚高寒草甸为背景,结合最新的群落中性理论,以解释亚高寒草甸草本植物群落的物种分布格局和生物多样性的维持机制。通过对阴坡、阳坡和滩地3个生境进行随机取样调查,用中性模型对所得多样性数据进行拟合,并分别应用置信区间检验、拟合优度检验和多样性指数检验3种方法对拟合效果进行检验。研究结果表明,在拟合优度检验中,3个生境中中性理论预测和实际物种多度分布之间没有显著差异(p>0.05);实际观测值基本全部落入模型预测分布的95%的置信区间之内（仅滩地草本植物群落的63个物种中的1个以及阴坡草本植物群落75个物种中的2个偏离95%的置信区间）;对群落多样性的预测也和实际观测没有显著差异,其中丰富度预测拟合得最好(0.49相似文献   

The Role of Landscape Patterns of Habitat Types on Plant Species Diversity of a Tropical Forest in Mexico

The relationships among landscape characteristics and plant diversity in tropical forests may be used to predict biodiversity. To identify and characterize them, the number of species, as well as Shannon and Simpson diversity indices were calculated from 157 sampling quadrats (17,941 individuals sampled) while the vegetation classes were obtained from multi-spectral satellite image classification in four landscapes located in the southeast of Quintana Roo, Mexico. The mean number of species of trees, shrubs and vines as well as the mean value of the total number of species and the other two diversity indices were calculated for four vegetation classes in every one of the four landscapes. In addition, the relationships between landscape patterns metrics of patch types and diversity indices were explored. The multiple statistical analyses revealed significant predictor variables for the three diversity indices. Moreover, the shape, similarity and edge contrast metrics of patch types might serve as useful indicators for the number of species and the other two diversity variables at the landscape scale. Although the association between the three diversity indices and patch types metrics showed similar behavior, some differences were appreciated. The Shannon diversity index, with its greater sensitivity to rare species, should be considered as having a greater importance in interpretation analysis than Simpson index.     

A comparison between diversity, similarity and biotic indices applied to the macroinvertebrate community of a small stream: the Ravella river (Como Province, Northern Italy)

This study aimed at comparing the results obtained by processing a series of data according to several diversity indices (Simpson, Berger-Parker, Margalef, Menhinick, McIntosh, Shannon) and one similarity index (Jaccard) with those obtained from two biotic indices (Trent River Biotic Index, Extended Biotic Index). In addition, Cody's index was adopted to measure the species turnover along the stream gradient. The source of the data was a study of the seasonal variations of macroinvertebrates from the Ravella stream (Como Province, Northern Italy). The conclusions are the following. There is clearly a certain connection between the organic debris in the habitat, the abundance of individuals and the decrease in the diversity value of the macroinvertebrate association. The species turnover along the stream gradient is rapid which is due, in addition to birth and death rates, to the fact that most of the insects emerge as terrestrial adults. The species abundance distribution is a very simple and powerful tool for describing and comparing the species diversity from different sampling stations. Any type of monitoring (e.g., biotic indices, diversity indices) is useful in comparing non-polluted and heavily polluted environments. Conversely, small differences between species associations are better highlighted if diversity indices with high discriminant ability (e.g., Simpson's index) or species abundance distribution are used rather than biotic indices.     

Species-area curves, diversity indices, and species abundance distributions: a multifractal analysis

Although fractals have been applied in ecology for some time, multifractals have, in contrast, received little attention. In this article, we apply multifractals to the species-area relationship and species abundance distributions. We highlight two results: first, species abundance distributions collected at different spatial scales may collapse into a single curve after appropriate renormalization, and second, the power-law form of the species-area relationship and the Shannon, Simpson, and Berger-Parker diversity indices belong to a family of equations relating the species number, species abundance, and area through the moments of the species abundance-probability density function. Explicit formulas for these diversity indices, as a function of area, are derived. Methods to obtain the multifractal spectra from a data set are discussed, and an example is shown with data on tree and shrub species collected in a 50-ha plot on Barro Colorado Island, Panama. Finally, we discuss the implications of the multifractal formalism to the relationship between species range and abundance and the relation between the shape of the species abundance distribution and area.     

天童国家森林公园树种多样性的加性分配

根据物种丰富度、Shannon指数和Simpson指数建立的物种多样性分配方法,提出分异度系数,对天童森林公园内不同森林类型的树种多样性进行了分析.结果表明,基于物种丰富度指数,总体的多样性只有小部分归功于样方内多样性,而多样性大多分配在样方间、亚群丛间或群丛间,例如在木荷-栲树群丛中,样方内只贡献了20.3%的物种丰富度.而在Shannon指数和Simpson指数中,多样性大多分配在样方内.这种差异主要是由于后两种指数不仅考虑了物种的存在与否,也考虑了其在样方内的多度.同时比较分析了加性分配与传统方法的结果.     

长白山北坡阔叶红松林及其次生白桦林高等植物物种多样性比较

应用Ｓｉｍｐｓｏｎ和Ｓｈａｎｎｏｎ多样性指数及其相应的均匀度,对阔叶红松林及其次生白桦林的高等植物物种多样性进行了对比研究．结果表明,对于木本植物,次生白桦林物种多样性高于阔叶红松林;而对于草本植物,情况正好相反．但在次生白桦林中,无论木本植物还是草本植物,占优势的物种都是一些常见种,而许多阔叶红松林中的珍稀或特有物种在次生白桦林中数量很少,有些甚至完全消失．对群落各种群多度分布的检验表明,２种森林类型中,无论木本植物还是草本植物,各种群的多度分布都遵从对数级数分布．     

海南岛吊罗山山地雨林物种多样性

在海南岛吊罗山热带山地雨林设置两５０００ｍ＾２的样地,分别从物种多样性指数,种－多度曲线,空间格局多样性,时间格局多样性,组成格局多样性对其进行了研究。结果表明海南岛吊罗山山地雨林物种多样性指数Ｓｈａｎｎｏｎ－Ｗｅａｖｅｒ和Ｓｉｍｐｓｏｎ指数分别为４．１９５和０．０２１,均匀度为０．８８０和２．９６２。     

辽东山区次生林物种多样性的空间分布及尺度效应

以辽东山区次生林为研究对象,分析4 hm²样地Gleason丰富度指数、Simpson优势度指数、Shannon多样性指数和Pielou均匀度指数的空间分布特征及其与尺度的关系.结果表明: 4个多样性指数的空间分布均表现出较高的空间异质性;4个多样性指数的方差随尺度的增加其变化趋势有所差异;4个多样性指数的变异系数随尺度的增加呈下降趋势;乔木层的4个多样性指数值高于灌木层,且随尺度增加其变化趋势有所差异.在分析辽东山区次生林物种多样性时应考虑尺度效应.     

Simultaneous small-sample multivariate Bernoulli confidence intervals

A technique based on the bootstrap is presented for assessing the simultaneous confidence level of k small-sample confidence intervals for multivariate Bernoulli marginal frequencies. The small-sample intervals used are those of Clopper and Pearson (1934, Biometrika 26, 404-413) and require iterative computation. To estimate the simultaneous confidence level, the multivariate Bernoulli vectors are resampled via the bootstrap and the Clopper-Pearson intervals recomputed on each pseudosample. The bootstrap estimate is then the proportion of times (computed via Monte Carlo) that all the k intervals computed by resampling contain the original sample frequencies. The technique is applied to single-sample HLA data.     

渤海中、南部大型底栖动物物种多样性的研究

以1997年 6月、1998年9月和1999年4月共3个航次,覆盖渤海中、南部大部分海区的大型底栖动物丰度、生物量和生产力的研究为基础,进一步对其物种多样性进行了分析。结果表明：研究海域的大型底栖动物物种多样性没有明显的平面分布规律;物种多样性指数与沉积物因子的相关性高于其与底层水因子的相关性;沉积物中污染物含量的确会对大型底栖动物的多样性造成影响。通过对3个航次中3个相同站位的比较,发现不同年份之3个季节的平均Shannon Wiener指数无显著差异（P>0.05）;而1998年9月和1999年4月2个航次中20个相同站位的平均Shannon Wiener指数同样也未表现出明显的差异（P>0.05）。此外,渤海的物种数量要明显地高于胶州湾。     

Only Simpson Diversity can be Estimated Accurately from Microbial Community Fingerprints

Lalande et al. (Microb. Ecol. 66(3):647–658, 2013) introduced a promising approach to quantify microbial diversity from fingerprinting profiles. Their analysis is based on extrapolating the abundance of the phylotypes detectable in a fingerprint towards the rare phylotypes of the community. By considering a set of reconstructed communities, Lalande et al. obtained a range of estimates for phylotype richness, Shannon diversity and Simpson diversity. They reported narrow ranges indicating accurate estimation, especially for Shannon and Simpson diversities. Here, we show that a much larger set of reconstructed communities than the one considered by Lalande et al. is consistent with the fingerprint. We find that the estimates for phylotype richness and Shannon diversity vary over orders of magnitude, but that the estimates for Simpson diversity are restricted to a narrow range (around 10 %). We conclude that only Simpson diversity can be estimated accurately from fingerprints.     

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.     

农药污染对土壤微生物群落功能多样性的影响

根据95种不同的单一联底物上的BIOLOGGN微平板系统的反应所构造的多样性指数，结果表明农药严重污染的土壤微生物群落的Shannon指数和均度、Simpson指数、Mclntosh指数和均度均显著低于无污染的对照。说明农药严重污染导致土壤微生物群落功能多样性的下降，减少了能利用有关碳底物的微生物的数量，降低微生物对单一碳底物的利用能力。     

火灾恢复年限对大兴安岭森林乔灌草多样性及优势种影响

林火是大兴安岭地区森林生态系统的重要影响因子,研究火灾对植物多样性和优势种多度长期影响,有助于火灾区域森林生态系统重建与管理。本研究以大兴安岭不同火烧年限（1~5、5~10、10~20、20~30、30~40和40~50年）48对配对样地（火烧样地与邻近未火烧对照样地）为研究对象,利用二者差值变化来探讨森林恢复年限对植物多样性指数影响,通过对乔灌草相对多度变化确认火灾恢复对优势种的影响。研究结果表明：（1）火烧与对照间乔木多样性和丰富度差值先降后升趋势,在10年左右最低,而恢复30~40年后与对照样地相当或更高。灌木与乔木变化趋势相似,但是变化趋势多达到统计学显著（P<0.05）,灌木Shannon-wiener多样性指数和丰富度差值随年限增加而线性上升。草本Simpson多样性指数随火烧年限增加而直线下降,但是均匀度与丰富度没有出现线性变化。（2）乔灌草优势种变化趋势为：乔木层白桦（Betula platyphylla）在火烧5~30年占比均超过30%,在30年后占比不超过15%,同时兴安落叶松（Larix gmelinii）在30~40年占比超过50%;灌木层在0~30年均是越桔（Vaccinium vitis-idaea）占比最大,30年之后变为榛子（Corylus heterophylla）,草本层5~30年均是小叶章（Deyeuxia angustifolia）占比最大,30年之后变为其他物种。对照样地乔木层主要是兴安落叶松,占比超过50%,灌木层主要是越桔（Vaccinium vitis-idaea）,草本层主要是小叶章（Deyeuxia angustifolia）。整体来看,乔木火后恢复需要更长的时间,而灌木和草本火后恢复更快。植物多样性及优势种变化是研究其对生态服务功能（如碳汇）影响的基础,我们研究结果为天保工程后续实施及科学管理大兴安岭森林生态系统提供数据支撑。