Distance-Based Functional Diversity Measures and Their Decomposition: A Framework Based on Hill Numbers

Hill numbers (or the “effective number of species”) are increasingly used to characterize species diversity of an assemblage. This work extends Hill numbers to incorporate species pairwise functional distances calculated from species traits. We derive a parametric class of functional Hill numbers, which quantify “the effective number of equally abundant and (functionally) equally distinct species” in an assemblage. We also propose a class of mean functional diversity (per species), which quantifies the effective sum of functional distances between a fixed species to all other species. The product of the functional Hill number and the mean functional diversity thus quantifies the (total) functional diversity, i.e., the effective total distance between species of the assemblage. The three measures (functional Hill numbers, mean functional diversity and total functional diversity) quantify different aspects of species trait space, and all are based on species abundance and species pairwise functional distances. When all species are equally distinct, our functional Hill numbers reduce to ordinary Hill numbers. When species abundances are not considered or species are equally abundant, our total functional diversity reduces to the sum of all pairwise distances between species of an assemblage. The functional Hill numbers and the mean functional diversity both satisfy a replication principle, implying the total functional diversity satisfies a quadratic replication principle. When there are multiple assemblages defined by the investigator, each of the three measures of the pooled assemblage (gamma) can be multiplicatively decomposed into alpha and beta components, and the two components are independent. The resulting beta component measures pure functional differentiation among assemblages and can be further transformed to obtain several classes of normalized functional similarity (or differentiation) measures, including N-assemblage functional generalizations of the classic Jaccard, Sørensen, Horn and Morisita-Horn similarity indices. The proposed measures are applied to artificial and real data for illustration.     

Methods for diversity and overlap analysis in T-cell receptor populations

The paper presents some novel approaches to the empirical analysis of diversity and similarity (overlap) in biological or ecological systems. The analysis is motivated by the molecular studies of highly diverse mammalian T-cell receptor (TCR) populations, and is related to the classical statistical problem of analyzing two-way contingency tables with missing cells and low cell counts. The new measures of diversity and overlap are proposed, based on the information-theoretic as well as geometric considerations, with the capacity to naturally up-weight or down-weight the rare and abundant population species. The consistent estimates are derived by applying the Good–Turing sample-coverage correction. In particular, novel consistent estimates of the Shannon entropy function and the Morisita–Horn index are provided. Data from TCR populations in mice are used to illustrate the empirical performance of the proposed methods vis a vis the existing alternatives.     

Multisite and multispecies measures of overlap,co‐occurrence,and co‐diversity

Several indices measure the association or segregation between two species and the similarity or differentiation between two sets of species. These indices are based on the overlap in the distribution of species (measured with the number of co‐occurrences) or on the overlap in species composition of sites (measured with the number of species that are shared between two sites). This paper shows that when evaluating more than two species the number of overlaps and the number of pairwise co‐occurrences are not equal, as it is the case for two species. Equivalently, when comparing more than two species assemblages, the number of overlaps differ from the number of instances of species sharing by pairs of sites (the ‘co‐diversities’). Considering this distinction, two different types of multispecies and multisite indices can be derived: indices of general overlap and indices of co‐occurrence or co‐diversity. Here I present a complete series of the two types of indices that correspond to the popular Jaccard, Sørensen, and Simpson two‐species or two‐site indices. Indices of general overlap are defined by three parameters (the total number of species, the total number of sites, and the total number of occurrences), whereas indices of co‐occurrence or co‐diversity depend on those parameters plus an additional one that is defined by the values of species richness or range size. Consequently, the two types of indices respond differently to null models, depending on the parameters that are fixed or randomized. All indices correlate well with the mean of the traditional indices calculated pair by pair, and the correspondence is extremely close for the new indices of co‐occurrence and co‐diversity. These properties should be useful in clarifying some of the confusion that exists in the current discussion about the advantages and disadvantages of pairwise vs community‐wide approaches in the analysis of diversity.     

Subsampling Herbarium Collections to Assess Geographic Diversity Gradients: A Case Study with Endemic Orchidaceae and Rubiaceae in Cameroon

We compiled herbarium specimen data to provide an improved characterization of geographic patterns of diversity using indices of species diversity and floristic similarity based on rarefaction principles. A dataset of 3650 georeferenced plant specimens belonging to Orchidaceae and Rubiaceae endemic to Atlantic Central Africa was assembled to assess species composition per half‐degree or one‐degree grid cells. Local diversity was measured by the expected number of species (S_k) per grid cell found in subsamples of increasing size and compared with raw species richness (S_R). A nearly unbiased estimator of the effective number of species per grid cell was also used, allowing quantification of ratios of ‘true diversity’ between grid cells. Species turnover was measured using a presence/absence‐based similarity index (Sørensen) and an abundance‐based index that corrects for sampling bias (NNESS). Our results confirm that the coastal region of Cameroon is more diverse in endemic species than those more inland. The southern part of this coastal forest is, however, as diverse as the more intensively inventoried northern part, and should also be recognized as an important center of endemism. A strong congruence between Sørensen and NNESS similarity matrices lead to similar delimitations of floristic units. Hence, heterogeneous sampling seems to confer more bias when measuring patterns of local diversity using raw species richness than species turnover using Sørensen index. Overall, we argue that subsampling methods represent a useful way to assess diversity gradients using herbarium specimens while correcting for heterogeneous sampling effort. Abstract in French is available in the online version of this article.     

Characterization of feeding habits,prey diversity and diet overlap of two sympatric species: Bronze catfish,Netuma bilineata (Valenciennes, 1840) and blacktip sea catfish,Plicofollis dussumieri (Valenciennes, 1840) in the northern Arabian Sea

This study describes the diet composition, diet overlap and prey diversity in two economically and ecologically important marine catfish species: the bronze catfish (Netuma bilineata) and the blacktip sea catfish (Plicofollis dussumieri) collected between January and December 2015 from the northern Arabian Sea coast of Pakistan. Stomach data of 342 bronze catfish and 283 blacktip sea catfish were examined. Diet composition and feeding strategy of each species by identification of stomach contents were weighed and enumerated. Both species primarily consumed teleosts, Brachyura and small amounts of a wide variety of prey items; however, specialization was a more common trait for the bronze catfish than for the black tip sea catfish. The Morisita‐Horn index showed considerable diet overlap in percentage of mean weights (0.847) than in numbers (0.612) between co‐prey pairs of both species. The highest Bray‐Curtis similarity between the southwest monsoon (SWM) and south inter monsoon (SIM) was observed in bronze catfish and lowest between autumn inter monsoon (AIM) seasons in both species. While Bray‐Curtis dissimilarity was observed, both species share diet niches and diet overlap. The present study evaluation of the feeding strategy and potential competition between two sympatric species of marine catfishes can provide the framework for their conservation and management in the region.     

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.     

广州市不同城市化发展区域蝶类多样性

2005～2006年,对广州地区4个不同城市化发展区域(森林区、农田区、城市区、沿海湿地区)的蝶类进行6次调查,共统计到10科46属73种.森林区科、属、物种和个体数目都最多,沿海湿地区各项数量指标都最小,农田区的个体数量大于城市区,但科、属和物种数却与城市区差异不大.多样性分析结果表明,森林区的种类丰度、多样性指数最高,沿海湿地区的种类丰度和多样性指数最低;均匀度大小依次为沿海湿地区﹥农田区﹥森林区﹥城市区;优势度指数大小依次为沿海湿地区﹥城市区﹥农田区﹥森林区.相似性分析结果表明,森林区和农田区具有的相同物种数最多,相似性系数最高;沿海湿地区和森林区、农田区、城市区具有的相同物种数都较少,相似性系数也较低.     

Measuring beta‐diversity from taxonomic similarity

Question: The utility of beta (β‐) diversity measures that incorporate information about the degree of taxonomic (dis)similarity between species plots is becoming increasingly recognized. In this framework, the question for this study is: can we define an ecologically meaningful index of β‐diversity that, besides indicating simple species turnover, is able to account for taxonomic similarity amongst species in plots? Methods: First, the properties of existing measures of taxonomic similarity measures are briefly reviewed. Next, a new measure of plot‐to‐plot taxonomic similarity is presented that is based on the maximal common subgraph of two taxonomic trees. The proposed measure is computed from species presences and absences and include information about the degree of higher‐level taxonomic similarity between species plots. The performance of the proposed measure with respect to existing coefficients of taxonomic similarity and the coefficient of Jaccard is discussed using a small data set of heath plant communities. Finally, a method to quantify β‐diversity from taxonomic dissimilarities is discussed. Results: The proposed measure of taxonomic β‐diversity incorporates not only species richness, but also information about the degree of higher‐order taxonomic structure between species plots. In this view, it comes closer to a modern notion of biological diversity than more traditional measures of β‐di‐versity. From regression analysis between the new coefficient and existing measures of taxonomic similarity it is shown that there is an evident nonlinearity between the coefficients. This nonlinearity demonstrates that the new coefficient measures similarity in a conceptually different way from previous indices. Also, in good agreement with the findings of previous authors, the regression between the new index and the Jaccard coefficient of similarity shows that more than 80% of the variance of the former is explained by the community structure at the species level, while only the residual variance is explained by differences in the higher‐order taxonomic structure of the species plots. This means that a genuine taxonomic approach to the quantification of plot‐to‐plot similarity is only needed if we are interested in the residual system's variation that is related to the higher‐order taxonomic structure of a pair of species plots.     

Properties of similarity indices under niche-based and dispersal-based processes in communities

Little is known about the combined impact of habitat filtering and dispersal limitation on species turnover patterns. To gain new insights, we constructed a spatially explicit community model wherein we controlled dispersal distances, the strength of habitat filtering, and the grain of habitat heterogeneity to study the distance decay of several (dis)similarity indices. The impact of habitat filtering is dependent on the ratio between the grain of habitats and the mean dispersal distance. The behavior of (dis)similarity indices varies. First, incidence-based measures of species overlap are less affected by habitat filtering than are abundance-based indices. Second, species identity-based indices, derived from population genetics' F(ST), show interesting capacities to infer dispersal processes under neutrality but are also highly sensitive to habitat filtering. All indices except F(ST)-related indices under neutrality are very sensitive to overall species richness. Hence, community patterns showing contrasted diversity levels should be compared with caution. Partitioning similarity indices within and between habitats appears to be an efficient approach to assess the strength of habitat filtering, and we show that a torus-translation test is powerful for this purpose. We finally highlight the need for further analytical studies to achieve theoretical expectations of similarity decay under dispersal and niche processes.     

石门台自然保护区蝴蝶特种多样性研究

1999年6月～2003年4月间,对广东石门台自然保护区的蝴蝶进行了调查,共记录到蝴蝶361种,分隶于11科190属。其中中国特有种51 种,占总数的14.1%;国家保护种10种,占我国两次颁布（1989和2000年）的保护物种名录中蝴蝶总数量（83种）的12.0%。通过以人工林生境为主的试验区、次生林生境为主的缓冲区和原生林生境为主的核心区等3个功能区中选择样点进行的蝴蝶多样性分析表明,缓冲区的物种多样性及科、属多样性均较高,且有众多的珍稀物种,是一个重要的蝴蝶生息地,应加强管制。进一步说明了保护蝶类的根本在于护林,进而为保护好广东省目前面积最大的自然保护区——石门台自然保护区的生物多样性及不可多得的自然遗产——热带亚热带低地森林提供依据。此外,本文将科、属多样性与物种多样性综合起来考虑,同时使用Shannon-Wiener指数与G-F指数,较为全面地评价了该保护区蝴蝶的群落多样性。     

Diatom Model Affinity (DMA), a New Index for Water Quality Assessment

A new index, diatom model affinity (DMA) was erected as a reference-based community metric, derived from generic and species composition. DMA provides an assessment of water quality by the calculation of percent similarity to a model community, which can be viewed as a reference standard. High similarity to the model indicates communities that are minimally disturbed, while lower similarity suggests water quality problems. The index is similar to that developed for macroinvertebrate communities by Novak & Bode (1992, Journal of the North American Benthological Society 11: 80-85). The index correlated well with environmental factors operating on hierarchical scales. Compared to other commonly used diatom indices, DMA-based community assessments demonstrated high correspondence to patterns derived from multivariate statistics.     

A new method for evaluating flowering synchrony to support the temporal isolation of genetically modified crops from their wild relatives

Hybridization between crops and their wild relatives potentially threatens the genetic identity of the wild plants, particularly in the case of genetically modified crops. Only a few studies have examined the use of temporal isolation to prevent hybridization, and the indices used in those studies, (e.g., the days of flowering overlap), are not precise to evaluate the degree of synchrony in flowering. Here we propose a flowering similarity index that can compare the degree of flowering synchrony between two relevant species and measure the efficiency of temporal isolation. The results showed that the flowering similarity index predicts the likelihood of hybridization much better than the number of flowering-overlap days, regardless of different flowering patterns among cultivars. Thus, temporal isolation of flowering or flowering asynchrony is the most effective means in preventing hybridization between crops and their wild relatives.     

Body size and measurement of species diversity in large grazing mammals

Species are by definition different from each other. This fact favours ranking rather than additive indices. However, ecologists have measured species diversity in terms of species richness, or by combining species richness with the relative abundance of species within an area. Both methods raise problems: species richness treats all species equally, while relative abundance is not a fixed property of species but varies widely temporally and spatially, and requires a massive sampling effort. The functional aspect of species diversity measurement may be strengthened by incorporating differences between species such as body size as a component of diversity. An index of diversity derived from a measure of variation in body size among species is proposed for large grazing mammals. The proposed diversity index related positively to species abundance, indicating that the use of body size as a surrogate for diversity is adequate. Because the proposed index is based on presence or absence data, the expensive and time consuming counting of individuals per species in each sampling unit is not necessary.     

Finding the Minimum Sample Richness (MSR) for multivariate analyses: implications for palaeoecology

Many techniques have been developed to estimate species richness and beta diversity. Those techniques, dependent on sampling, require abundance or presence/absence data. Palaeontological data is by nature incomplete, and presence/absence data is often the only type of data that can be used to provide an estimate of ancient biodiversity. We used a simulation approach to investigate the behaviour of commonly used similarity indices, and the reliability of classifications derived from these indices, when working with incomplete data. We drew samples, of varying number and richness, from artificial species lists, which represented original life assemblages, and calculated error rates for classifications of the parent lists and samples. Using these results, we estimated the Minimum Sample Richness (MSR) needed to achieve 95% classification accuracy. Results were compared for classifications derived from several commonly used similarity indexes (Dice, Jaccard, Simpson and Raup–Crick). MSR was similar for the Dice, Jaccard and Simpson indices. MSR for the Raup–Crick index was often much lower, suggesting that it is preferable for classifying patchy data, however the performance of this index was less stable than the other three in the simulations, which required an even lower MSR. MSR can be found for all presence/absence data from the contour graphs and equations as long as the absolute species richness and the beta diversity can be estimated.     

Diversity partitioning of Rao’s quadratic entropy

Many applications of diversity indices are only valid if they are first transformed into their equivalent number of species. These equivalent numbers of species can be multiplicatively partitioned into independent alpha, beta and gamma components, and can be formed into mathematically consistent similarity measures. The utility of beta diversity and similarity measures that incorporate information about the degree of ecological dissimilarity between species is becoming increasingly recognized. The concept of equivalent number of species is here extended to Rao’s quadratic entropy, opening the way to methods of diversity partitioning that take into account taxonomic or ecological differences between species.     

Spatial variation in species diversity and composition of flea assemblages in small mammalian hosts: geographical distance or faunal similarity?

Aim Spatial variation in the diversity of fleas parasitic on small mammals was examined to answer three questions. (1) Is the diversity of flea assemblages repeatable among populations of the same host species? (2) Does similarity in the composition of flea assemblages among populations of the same host species decay with geographical distance, with decreasing similarity in the composition of local host faunas, or with both? (3) Does the diversity of flea assemblages correlate with climatic variables? Location The study used previously published data on 69 species of small mammals and their fleas from 24 different regions of the Holarctic. Methods The diversity of flea assemblages was measured as both species richness and the average taxonomic distinctness of their component species. Similarity between flea assemblages was measured using both the Jaccard and Morisita–Horn indices, whereas similarity in the composition of host faunas between regions (host ‘faunal’ distance) was quantified using the Jaccard index. Where appropriate, a correction was made for the potentially confounding influence of phylogeny using the independent contrasts method. Results Flea species richness varied less within than among host species, and is thus a repeatable host species character; the same was not true of the taxonomic distinctness of flea assemblages. In almost all host species found in at least five regions, similarity in flea assemblages decreased with increases in either or both geographical and faunal distance. In most host species, the diversity of flea assemblages correlated with one or more climatic variable, in particular mean winter temperature. Main conclusions Spatial variation in flea diversity among populations of the same mammal species is constrained by the fact that it appears to be a species character, but is also driven by local climatic conditions. The results highlight how ecological processes interact with co‐evolutionary history to determine local parasite biodiversity.     

大豆田节肢动物群落优势种群时间生态位及营养关系分析

【目的】阐明大豆田节肢动物群落时间生态位及营养关系,为大豆害虫生态调控手段的实施提供坚实的理论依据。【方法】以大豆田节肢动物群落为研究对象,通过两年的田间系统调查分析。【结果】统计得到种类220余种,物种可分为天敌、害虫和中性昆虫3个类群,以天敌物种丰富度最高;害虫中以烟蓟马Thrips tabaci(0.36902)和大豆蚜Aphis glycines(0.13122)优势度最高,且有着较高的生态位重叠指数(0.8163),蚜小蜂Aphytis sp.和大草蛉Chrysopa septempunctata对害虫的时间生态位重叠指数很高,其他天敌如异色瓢虫Harmonia axyridis、龟纹瓢虫Propylaea japonica、黑带食蚜蝇Zyistrophe balteata和黑食蚜盲蝽Deraeocoris punctulatus等对害虫的重叠指数居中;大豆田中各类群构成错综复杂的食物网结构。【结论】综合考虑天敌的种群数量,确定捕食性天敌是控制害虫种群数量的有效天敌。研究可知不能单纯从时间生态位的重叠指数的高低来判断天敌的控制能力。     

A two-stage probabilistic approach to multiple-community similarity indices

SUMMARY: A traditional approach for assessing similarity among N (N > 2) communities is to use multiple pairwise comparisons. However, pairwise similarity indices do not completely characterize multiple-community similarity because the information shared by at least three communities is ignored. We propose a new and intuitive two-stage probabilistic approach, which leads to a general framework to simultaneously compare multiple communities based on abundance data. The approach is specifically used to extend the commonly used Morisita index and NESS (normalized expected species shared) index to the case of N communities. For comparing N communities, a profile of N- 1 indices is proposed to characterize similarity of species composition across communities. Based on sample abundance data, nearly unbiased estimators of the proposed indices and their variances are obtained. These generalized NESS and Morisita indices are applied to comparison of three size classes of plant data (seedling, saplings, and trees) within old-growth and secondary rain forest plots in Costa Rica.     

若尔盖不同生境植物多样性与植物竞争强度和生态位重叠度的关系

植物多样性与植物竞争强度和生态位重叠度的关系会随环境发生变化。为探究上述关系在若尔盖地区的表现形式,于2021年8月对若尔盖地区典型的水生、湿生、湿生-中生和中生植物群落进行调查,构建了新的植物竞争强度（Competition intensity,CI）公式并进行测算,计算了植物群落的植物多样性指数（包括物种丰富度、Shannon-Weiner指数、Simpson指数和Pielou均匀度指数）和生态位重叠度（Niche overlap of species,NOS）,分析了植物群落物种多样性指数与CI和NOS的关系。结果表明：1）从水生到中生生境,植物多样性指数均呈增加趋势（P<0.05）;2）湿生-中生生境的CI显著高于湿生生境（P<0.05）,湿生生境的NOS高于水生生境（P<0.05）;CI与NOS无显著相关性,但在湿生生境中两者呈倒抛物线关系（P<0.05）。3）整体来看,植物群落的物种丰富度与CI呈抛物线关系（P<0.05）,与NOS无显著关系（P>0.05）;Shannon-Weiner指数、Simpson指数和Pielou均匀度指数均与NOS呈线性正相关（P<0.05）,与CI无显著关系（P>0.05）;从单个生境看,湿生-中生生境的Simpson指数、Shannon-Weiner指数和Pielou均匀度指数与CI呈线性负相关（P<0.05）,其余生境的上述多样性指数与CI无显著关系（P>0.05）;各生境的植物多样性指数均与NOS无显著相关性（P>0.05）。本研究表明,从水生到中生生境,若尔盖地区的植物多样性呈增加趋势,但植物多样性与物种竞争强度和生态位重叠度的关系较复杂。本研究结果有助于理解若尔盖高原植物多样性的形成机制。