A unified index to measure ecological diversity and species rarity

Several indices have been created to measure diversity, and the most frequently used are the Shannon-Wiener (H) and Simpson (D) indices along with the number of species (S) and evenness (E). Controversies about which index should be used are common in literature. However, a generalized entropy (Tsallis entropy) has the potential to solve part of these problems. Here we explore a family of diversity indices (S_q; where q is the Tsallis index) and evenness (E_q), based on Tsallis entropy that incorporates the most used indices. It approaches S when q=0, H when q→1 and gives D when q=2. In general, varying the value of the Tsallis index (q), S_q varies from emphasis on species richness (q<1) to emphasis on dominance (q>1). Similarly, E_q also works as a tool to investigate diversity. In particular, for a given community, its minimum value represents the maximum deviation from homogeneity (E_q=1) for a particular q (herein named q*). It is remarkable that our analysis indicates that q* and its corresponding evenness, E_q*, are negatively affected by S when using simulated data. They may represent an index related to species rarity. Furthermore, S_q* (i.e. the value of S_q for a specific q*) is positively affected by richness that is an important property of any diversity index. In general, our findings indicate that the indices H, D, S, S_q*, E and E_q* are only part of a whole set of possibilities. In addition, the ecological properties of E_q* and S_q*, proposed here for the first time, show promise in ecology.     

Choosing and using diversity indices: insights for ecological applications from the German Biodiversity Exploratories

Biodiversity, a multidimensional property of natural systems, is difficult to quantify partly because of the multitude of indices proposed for this purpose. Indices aim to describe general properties of communities that allow us to compare different regions, taxa, and trophic levels. Therefore, they are of fundamental importance for environmental monitoring and conservation, although there is no consensus about which indices are more appropriate and informative. We tested several common diversity indices in a range of simple to complex statistical analyses in order to determine whether some were better suited for certain analyses than others. We used data collected around the focal plant Plantago lanceolata on 60 temperate grassland plots embedded in an agricultural landscape to explore relationships between the common diversity indices of species richness (S), Shannon's diversity (H'), Simpson's diversity (D₁), Simpson's dominance (D₂), Simpson's evenness (E), and Berger–Parker dominance (BP). We calculated each of these indices for herbaceous plants, arbuscular mycorrhizal fungi, aboveground arthropods, belowground insect larvae, and P. lanceolata molecular and chemical diversity. Including these trait‐based measures of diversity allowed us to test whether or not they behaved similarly to the better studied species diversity. We used path analysis to determine whether compound indices detected more relationships between diversities of different organisms and traits than more basic indices. In the path models, more paths were significant when using H', even though all models except that with E were equally reliable. This demonstrates that while common diversity indices may appear interchangeable in simple analyses, when considering complex interactions, the choice of index can profoundly alter the interpretation of results. Data mining in order to identify the index producing the most significant results should be avoided, but simultaneously considering analyses using multiple indices can provide greater insight into the interactions in a system.     

喀斯特天然林植物多样性指数和土壤理化指标的相关性

植物多样性的土壤生态系统功能是喀斯特生态学研究的热点之一。在贵州省茂兰国家级自然保护区不同功能区(干扰等级)内采用野外样地调查和实验室分析相结合的方法,分析了41个喀斯特森林样地的植物多样性指数和土壤理化指标值的变化规律与相关性。结果表明:(1)依据乔木层物种重要值聚类法划分的5个喀斯特森林类型包括小叶栾树-青冈栎林、香叶树-枫香林、香椿-香叶树林、灯台-小花梾木林和檵木-马尾松林,由核心区、缓冲区、实验区至外缘区,乔木层植物多样性指数、林地岩石裸露率、土壤蓄水量、肥力及养分指标呈降低趋势。(2)因子分析表明不同层片植物多样性和不同土层土壤理化因子的相关趋势性各异。相关显著的因子对数量率呈乔木灌木草本的趋势,乔木植物多样性因子起主导作用。(3)喀斯特森林乔木层植物多样性指数和土壤理化指标的相关性分3种类型。直线型是植物多样性指数和土壤理化指标值相关性中较普遍的一类,相应指标对数量率为39.84%;曲线型是植物多样性指数和土壤理化指标值相关性中机理较复杂的一类,相应指标对数量率为46.10%,其中植物多样性指数有拐点值无生态意义的指标对数量率为11.72%,有拐点值有生态意义且呈先降后升、或先升后降趋势的指标对数量率分别为17.19%;无关型是植物多样性指数和土壤理化指标值相关性不显著,相应指标对数量率为54.69%。(4)喀斯特地区水土资源管理为目标的营林措施中,天然林乔木层植物多样性指数对土壤物理、肥力和养分指标响应的拐点值可成为人工造林中物种数量与株数比例选择的参考依据之一。     

Indices for monitoring biodiversity change: Are some more effective than others?

Statistically rigorous methods for summarizing and reporting trends in the intactness of biodiversity are a key element of effective biodiversity monitoring programs. There are four major approaches for translating complex monitoring data into easily communicated summary statistics: (1) traditional diversity indices such as species richness and Simpson's diversity, (2) species intactness indices based on occurrence, (3) species intactness indices based on abundance, and (4) multivariate community indices. We use simulated data to evaluate the effectiveness of 13 indices from these four categories based on statistical robustness, sensitivity to errors and noise in the data, ecological relevance, and ease of communication. We show that indices that calculate species intactness using equations like Buckland's arithmetic mean index are the most effective for use in large-scale biodiversity intactness monitoring programs. Traditional diversity indices are unsuitable for monitoring of biodiversity intactness, and multivariate indices can be highly sensitive to errors and noise in the data. Finally, we provide guidelines for the application of these indices in biodiversity intactness monitoring.     

Multiple Comparisons of Biodiversity

A common goal in statistical ecology is to compare several communities and or time points with respect to taxonomic diversity (usually species diversity). For this purpose, the current literature recommends the application of traditional ANOVA techniques to “replicates” of diversity indices. This approach is not even asymptotically correct because diversity index estimates have unequal variances, even when sample sizes are equal and even when the hypothesis of equality of diversity indices is true. It is shown that transformations of the data can not be used to remedy this situation. We construct an asymptotically correct method and illustrate its implementation using dinosaur extinction data.     

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.     

Entropy and diversity

Entropies such as the Shannon–Wiener and Gini–Simpson indices are not themselves diversities. Conversion of these to effective number of species is the key to a unified and intuitive interpretation of diversity. Effective numbers of species derived from standard diversity indices share a common set of intuitive mathematical properties and behave as one would expect of a diversity, while raw indices do not. Contrary to Keylock, the lack of concavity of effective numbers of species is irrelevant as long as they are used as transformations of concave alpha, beta, and gamma entropies. The practical importance of this transformation is demonstrated by applying it to a popular community similarity measure based on raw diversity indices or entropies. The standard similarity measure based on untransformed indices is shown to give misleading results, but transforming the indices or entropies to effective numbers of species produces a stable, easily interpreted, sensitive general similarity measure. General overlap measures derived from this transformed similarity measure yield the Jaccard index, Sørensen index, Horn index of overlap, and the Morisita–Horn index as special cases.     

Recommendations for the use of species diversity indices with reference to a recently published article as an example

There are some recommendations for the use of species diversity indices in a paper recently published in this journal by M. Ohsawa on the species richness and composition of weevils in five forest types in the middle region of Japan. Because several factors, such as small sample size, calculation of Simpson’s diversity index by the use of the original equation of Simpson’s measure of concentration D, and a weak point in the Shannon–Wiener diversity index H′, may have led to biased estimates, I recalculated these indices using combined species diversity values of the five forest types. As the general tendencies of 1−D and H′ values calculated here were similar to those in Ohsawa’s paper, there is no need to propose any change to his view. However, these recalculated diversity indices indicated that they are values which are more suitable for use. It should be noted that the characteristics and weak point associated with the diversity indices need to be taken into account in future studies.     

Assessing the multicomponent aspect of coral fish diversity: The impact of sampling unit dimensions

The influence of variations in sampling unit dimensions on the assessment of fish species structuring has been widely documented. However, this issue has been restricted to a very limited range of community and population indices (mainly species richness and density). Here, we have investigated this issue through the analysis of 13 diversity indices related to 3 diversity components (number of species, evenness and functional diversity). We analyzed a large set of 257 standardized underwater visual census (UVC) transects dealing with 254 coral fish species. The sensitivity of the indices to the variation in sampling unit dimensions was studied by comparing a range of 55 couples of transect length and width representing 34 sampling surfaces. We found that the extent and profile of the sensitivity to changes in transect dimensions strongly varied both from one index to another and from one dimension to another (length and width). The most sensitive indices were more strongly impacted by variation in length than width. We also showed that for a fixed transect surface, the couple of chosen length and width may alter the assessment of indices related to each of the three main diversity components studied. Some widely used diversity indices, such as species richness and Shannon index, appeared to be very sensitive to changes in transect length and width. In contrast, while still very little used in coral fish studies, two functional diversity indices (FDiv, FEve), and to a lesser extent an evenness index (Berger–Parker), remained robust in the face of change in sampling dimensions. By showing that the variation in sampling dimensions (length, width and surface) may impact diversity indices in a contrasting manner, we stress the need to take into account the sensitivity of the indices to this criterion in the process of selection of the indices to be analyzed in diversity studies. Finally, we found that 30 m long*5 m wide transects might be a suitable compromise size for assessing the patterns of each of the three major complementary components of coral fish diversity.     

DER: An algorithm for comparing species diversity between assemblages

There is no single diversity index that adequately summarises species diversity, since this is a multidimensional concept and hence should be quantified using a compound statistical measure. Here, we present the DER algorithm, available as an R package on CRAN and as an RWizard application on http://www.ipez.es/RWizard. This algorithm provides tools for differentiating assemblages on the basis of five compounds of diversity: rarity, heterogeneity, evenness, taxonomic/phylogenetic diversity and functional diversity. For all the samples, the algorithm calculates a total of 39 of the indices most often used. All indices of all samples are transformed to a scale range of between 0 and 1, and the algorithm calculates the polar coordinates of all samples with all possible combinations for all five groups of indices. Thus, for each combination, an index of rarity, heterogeneity (species richness is included in this group), evenness, taxonomic/phylogenetic diversity and functional diversity is used for each group to calculate the polar coordinates of all samples. When the polar coordinates of the samples are obtained for each combination, the convex hull and the mean Euclidean distance between samples are calculated. The algorithm selects the combination of indices with the highest value of the mean between convex hull and mean Euclidean distance between samples; priority is therefore given to maximising dispersion between the samples. The polar coordinates of the selected combination are depicted using a diagram from which it is possible to determine the differences in terms of rarity, heterogeneity, evenness, taxonomic/phylogenetic diversity and functional diversity between assemblages.     

火干扰对大兴安岭北部原始林下层植物多样性的影响

在景观尺度自然火干扰历史研究的基础上,采用1个物种丰富度指数（物种数 S）、2个均匀度指数（Pielou均匀度指数Eh＇和Alatalo均匀度指数E）、3个物种多样性指数（Shannon-Wiener指数H＇,Hill多样性指数N1和N2）共6个？多样性指数,研究了长期火干扰与最近一次火干扰对大兴安岭北部原始林下木层、草本层及下层总体的植物多样性的影响.研究结果表明,本区下层植物的物种数、均匀度指数和多样性指数都以下木层显著大于草本层,因而下木层对下层植物总体生物多样性的贡献最大,也是主要影响因子.火干扰对下木层、草本层和下层总体的物种丰富度和物种多样性有显著影响,而对均匀度的影响不显著.长期的火干扰影响下,下木层、草本层和下层总体的物种数、各类均匀度指数和物种多样性指数都呈现如下格局：高频类＞中频类＞低频类,低强类＞中强类＞高强类.最近一次火干扰影响下,各个生物多样性指数都表现为一致的趋势：低强类＞中强类＞高强类;短期类＞长期类＞中期类.下层植物多样性与火干扰的关系是长期适应的结果.     

Cultural Importance Indices: A Comparative Analysis Based on the Useful Wild Plants of Southern Cantabria (Northern Spain)<Superscript>1</Superscript>

Cultural Importance Indices: A Comparative Analysis Based on the Useful Wild Plants of Southern Cantabria (Northern Spain). This paper compares four indices based on informant consensus. Each index aims to assess the cultural significance of plant species and is suitable for statistical testing of different hypotheses. For the comparison, we used data concerning plants traditionally used in the Campoo area of southern Cantabria in northern Spain. Our results show a positive and significant correlation between the number of uses (NU) and the frequency of citation (FC) of the species. It seems to be a general rule that the more versatile a plant, the more widespread its usefulness. In addition, NU is highly influenced by the number of use-categories in the study. Consequently, an objective index must rely on FC more than NU. We propose the use of the cultural importance index (CI), which is defined as the summation of the informants’ proportions that mention each of the uses of the species. The CI index is highly correlated with FC and, although it also considers diversity of use, each use-category is conveniently weighted by the number of informants mentioning it. Despite the use of cultural significance indices being questioned, we believe that indices based on in-depth, semi-structured interviews are still very useful for compilation studies of passive knowledge, such as most ethnobotanical works conducted in the last three decades in Europe.     

白龙江上游地区森林植物群落物种多样性的研究

 白龙江上游地区属长江防护林工程重点地区之一。根据36个样地的调查资料,分析了该地区森林植物群落物种多样性的特征：群落内各层物种丰富度指数的大小顺序为“灌木层>草本层>乔木层”;均匀度指数变化比较复杂,在杜鹃巴山冷杉（Rhododendron fastigiatum-Abies fargesii）林中为“草本层>灌木层>乔木层”,在苔藓巴山冷杉林中为“乔木层>灌木层>草本层”,其余群落中为“灌木层>草本层>乔木层”;多样性指数的大小顺序为“乔木层<灌木层和草本层”,而灌木层与草本层的多样性指数随林分郁闭度变化而变化,在郁闭度30%的杜鹃巴山冷杉林中,草本层大于灌木层,在郁闭度47%的箭竹巴山冷杉林中,草本层和灌木层相当,在郁闭度55%以上的各个群落内,灌木层大于草本层。同一海拔不同坡向群落的物种多样性表现为分布于阳坡的油松（Pinus tabulaeformis）林大于分布于阴坡的草类云杉（Picea asperata）林。物种多样性沿海拔梯度的变化表现为随海拔升高先降低后增加,从海拔2 400 m的栎类阔叶林,2 600 m的草类云杉林,2 800 m的箭竹(Sinarundinaria nitida)巴山冷杉林,到3 000 m的苔藓巴山冷杉林和3 200 m的杜鹃巴山冷杉林,物种多样性依次下降,到海拔3 400 m的高山杜鹃（Rhododendron fastigiatum）灌丛,物种多样性增加。物种多样性在紫果云杉(Picea purpurea)林的演替系列中表现为随群落演替发展而增加,后降低,在针阔混交林阶段达到最大。     

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.     

多山城市遗存山体植物多样性斑块效应研究

为探讨城市遗存山体植物多样性的斑块效应,以贵阳市建成区城市遗存山体为研究对象,采用单因素方差分析和最小显著性差异法(LSD),比较不同山体以及坡向、坡位的植物多样性差异,通过Spearman相关分析法,分析城市遗存山体植物多样性指数与城市遗存山体斑块指数之间的关系。结果表明：除地表粗糙度(SR)和分维数(Fd)指数外,23个城市遗存山体的斑块特征指标斑块面积(Pa)、表面积(Sa)、斑块形状指数(PSI)、破碎度(F)、相对高度(Rh)、平均坡度(As)、平面曲率(Hc)和剖面曲率(Pc)等指数差异比较大;不同城市遗存山体的植物群落整体植物、乔木层、灌木层和草本层的多样性指数均有显著差异。植物多样性各指数均与城市遗存山体的斑块特征指数F、Hc、Pc、Hc、Pa和Sa有相关性,与Rh、Fd、SR、PSI和As指数相关性不显著;不同坡位植物多样性各指数与城市遗存山体斑块指数响应强度由高到低顺序为山顶>山脚>山腰。不同坡向的植物多样性指数与城市遗存山体斑块指数响应强度由高到低顺序为西坡>北坡>南坡>东坡。总体而言,城市遗存山体的植物群落物种多样性存在斑块效应,城...     

Problems in Measuring Bacterial Diversity and a Possible Solution

The indices of species diversity used by plant and animal ecologists are not appropriate for bacterial diversity because of the inherent difficulty of defining a bacterial species. Arbitrary cutoff points to define a species or biotype lead to severe statistical problems. We suggest in this paper that a mean dissimilarity-based index without any attempt to define a species provides a statistically sound measurement of bacterial diversity.     

Measurement of biological information with applications from genes to landscapes

Biological diversity is quantified for reasons ranging from primer design, to bioprospecting, and community ecology. As a common index for all levels, we suggest Shannon's (S)H, already used in information theory and biodiversity of ecological communities. Since Lewontin's first use of this index to describe human genetic variation, it has been used for variation of viruses, splice-junctions, and informativeness of pedigrees. However, until now there has been no theory to predict expected values of this index under given genetic and demographic conditions. We present a new null theory for (S)H at the genetic level, and show that this index has advantages including (i) independence of measures at each hierarchical level of organization; (ii) robust estimation of genetic exchange over a wide range of conditions; (iii) ability to incorporate information on population size; and (iv) explicit relationship to standard statistical tests. Utilization of this index in conjunction with other existing indices offers powerful insights into genetic processes. Our genetic theory is also extendible to the ecological community level, and thus can aid the comparison and integration of diversity at the genetic and community levels, including the need for measures of community diversity that incorporate the genetic differentiation between species.     

Effects of habitat fragmentation on the functional diversity of insects in Thousand Island Lake,China

Due to habitat fragmentation, the loss of species diversity has been extensively studied. On the contrary, the effects of habitat fragmentation on functional diversity is still poorly understood. In the Thousand Island Lake, we conducted studies of insect functional diversity on a set of 29 isolated islands. We used 10 functional diversity indices from three aspects (functional richness, functional evenness and functional divergence) to respectively describe functional diversity of insects on sample islands. We found the following results: (i) The functional indices selected could reflect the functional diversity of sample islands and it is further proved that in general, three components of functional diversity were independent of each other; (ii) Sample islands could be divided into two categories, island JSD and the remaining islands; (iii) Functional richness increased with island area and shape index, but had no significant correlation with isolation. Likewise, both functional evenness and functional divergence had no significant correlation with island attributes. The conclusion to emphasize from our research is that: (i) habitat fragmentation reduced the biological functional diversity to some extent, further demonstrating the importance of habitat continuity in biodiversity protection; and (ii) for functional diversity protection of insects in a fragmented landscape, an island which has high approximate shape index values of at least hundred hectare magnitude order has a critical promoting effect.     

Assessing tillage disturbance on assemblages of ground beetles (Coleoptera: Carabidae) by using a range of ecological indices

Many ecological studies have used diversity indices to assess the impact of environmental disturbance. In particular, ground beetles have been advocated as a good group for assessing disturbance. Most studies on various organisms have used only one or two indices. For our study of the impact of tillage disturbance on carabid beetles in farm fields in southern Ontario, Canada, we used seven different diversity indices (richness, Shannon–Wiener, Berger–Parker, Q-statistic, Margalef, and evenness). Few studies have used deviation from diversity abundance models as a measure of disturbance; however, we use three that are applicable to our data (geometric, log-normal and log-series). The indices and models were used to test the null hypothesis that there is no change in diversity with increasing tillage disturbance, and that there is no difference in diversity with different crops or years. We were not able to reject the null hypothesis that there is any diversity difference among farms. We also found that there was no single diversity index or model that was better than any other at detecting disturbance. These results are supplemented by a meta-analysis of 45 published data sets for the same taxon but in different habitats. The meta-analysis supports the conclusions from our field research that diversity indices and models are not useful for detecting the possible effect of disturbance on assemblages of carabid beetles.