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.     

Response of ecological indices to nutrient and chemical contaminant stress factors in Eastern Mediterranean coastal waters

Environmental data produced throughout monitoring activities in the framework of the implementation of Water Framework Directive 2000/60/EC (WFD) in Eastern Mediterranean (Greece) were used to assess the sensitivity and response of ecological indices against trace metals, eutrophication and multiple stress factors. The applied ecological indices include multi-metric eutrophication indices, a physicochemical status index applied for the first time in the Greek marine area, benthic indices, phytoplankton biomass index, and integrated status indices assessed through the application of the decision tree integration scheme. To investigate the exceedances in the eco-stoichiometric relationship between nutrients, considered a stressing factor, all physicochemical elements influenced directly or indirectly by eutrophication, such as nutrient concentrations, water transparency, oxygen saturation, particulates concentration, and sediment organic content, were related to ecological indices. Also, chemical contaminant stress factors represented by heavy metal concentrations in the water, as well as multiple stress factors represented by a pressure index, were related to ecological indices. A graphical visualization multivariate tool and statistical correlations were used to evaluate the sensitivity or explanatory power of the tested ecological indices against single and multiple stress factors. Results showed a strong response of all ecological indices to stress factors, although a diversification of sensitivity was evident. Primary production-related indices, i.e., macroalgae and chlorophyll-a indices, are more sensitive to particulates and nitrogen, while secondary production-related indices, i.e., benthic macroinvertebrates indices and eutrophication indices, including nutrients, are more sensitive to phosphates in the water column. The macroalgae index shows the strongest sensitivity to multiple stress factors. Among metals, mostly cadmium seems to match all indices⿿ performance. Nutrient relationships were shown as critical to eutrophication and ecological status.     

Stratification of a population of intracranial aneurysms using blood flow metrics

Indices of the intra-aneurysm hemodynamic environment have been proposed as potentially indicative of their longitudinal outcome. To be useful, the indices need to be used to stratify large study populations and tested against known outcomes. The first objective was to compile the diverse hemodynamic indices reported in the literature. Furthermore, as morphology is often the only patient-specific information available in large population studies, the second objective was to assess how the ranking of aneurysms in a population is affected by the use of steady flow simulation as an approximation to pulsatile flow simulation, even though the former is clearly non-physiological. Sixteen indices of aneurysmal hemodynamics reported in the literature were compiled and refined where needed. It was noted that, in the literature, these global indices of flow were always time-averaged over the cardiac cycle. Steady and pulsatile flow simulations were performed on a population of 198 patient-specific and 30 idealised aneurysm models. All proposed hemodynamic indices were estimated and compared between the two simulations. It was found that steady and pulsatile flow simulations had a strong linear dependence (r ≥ 0.99 for 14 indices; r ≥ 0.97 for 2 others) and rank the aneurysms in an almost identical fashion (ρ ≥ 0.99 for 14 indices; ρ ≥ 0.96 for other 2). When geometry is the only measured piece of information available, stratification of aneurysms based on hemodynamic indices reduces to being a physically grounded substitute for stratification of aneurysms based on morphology. Under such circumstances, steady flow simulations may be just as effective as pulsatile flow simulation for estimating most key indices currently reported in the literature.     

Hyperspectral indices based on first derivative spectra closely trace canopy transpiration in a desert plant

A clear understanding of transpiration of arid ecosystems and its underlying mechanisms is critical for accurate prediction of long-term water and energy fluxes in such ecosystems, which have gradually been recognized to play major roles on a global scale. Unlike traditional measurements of transpiration that are generally time-consuming, expensive, and often unfeasible, remote sensing techniques such as hyperspectral indices are widely utilized as the only approach to obtain such information on a large scale. However, compared with other biochemical and biophysical parameters, few studies on hyperspectral indices have been applied to estimate canopy transpiration. In this study, we focused on a native dominant plant in the arid land of central Asia, Haloxylon ammodendron, to explore the featured spectra and to develop proper hyperspectral indices for estimating transpiration. This was based on a simultaneous dataset of original canopy-reflectance spectra as well as its first derivatives with transpiration estimated from sap flow. The results indicated that the derivative spectra-based indices are more effective for tracing canopy transpiration compared with its counterpart that was based on the original reflectance. The identified best index for estimating canopy transpiration was dSR(660,1040) based on the first-derivative spectra, which had a coefficient of determination (R²) of 0.54. The index is also relatively stable concerning spectral resolutions. Results obtained in this study should help lay the basis for using remote sensing data to estimate transpiration.     

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.     

A novel representation of RNA secondary structure based on element-contact graphs

Background  

Depending on their specific structures, noncoding RNAs (ncRNAs) play important roles in many biological processes. Interest in developing new topological indices based on RNA graphs has been revived in recent years, as such indices can be used to compare, identify and classify RNAs. Although the topological indices presented before characterize the main topological features of RNA secondary structures, information on RNA structural details is ignored to some degree. Therefore, it is necessity to identify topological features with low degeneracy based on complete and fine-grained RNA graphical representations.     

A field comparison of lime requirement indices for maize

Due, in part, to the relative paucity of published comparisons based on field generated data, there is still poor agreement regarding the relative merits of lime requirement indices based on exchangeable Al and those based on pH. The objective of this study was to compare such indices using results obtained from long-term field experiments. Data were obtained over 22 site-years from lime trials conducted on clay (Typic Haplorthox) and sandy loam (Plinthic Paleudult) soils differing widely in organic carbon content. Relative maize (Zea mays L.) yields were used to compare the prognostic value of soil pH with indices obtained using exchangeable Al and exchangeable acidity (Al+H). Both within and across soils, pH proved to be markedly inferior to Al based indices. Exchangeable acid saturation of the effective cation exchange capacity, a readily obtained and popular index of lime requirement in some countries, proved as effective as less easily acquired indices based on exchangeable Al per se. The findings reported are consistent with those of many glasshouse studies and support the viewpoint that indices based on Al or acid saturation should replace pH as a measure of lime requirement.     

山西七里峪茶条槭群落特征及物种多样性研究

运用TWINSPAN对山西七里峪茶条槭群落类型进行划分,并采用Patrick指数、Simpson指数、Shannon-Wiener指数、Alatalo指数研究群落的物种多样性。结果表明:TWINSPAN将茶条槭群落的73个样方划分为10个群丛;各群丛的物种丰富度指数、多样性指数和均匀度指数之间存在差异,群丛Ⅲ和Ⅶ的丰富度指数和多样性指数较高,群丛Ⅰ的多样性指数较低;各群丛乔木层、灌木层和草本层之间的物种多样性也存在差异,多样性指数大致表现为草本层高于灌木层高于乔木层。土壤中的有机质、速效钾、含水量是影响茶条槭群落物种多样性的主要因素。     

Krill (<Emphasis Type="Italic">Euphausia superba</Emphasis>) recruitment indices from the western Antarctic Peninsula: are they representative of larger regions?

This study presents data on krill demography west of the Antarctic Peninsula covering many years since 1982. The recruitment indices are compared with those for other mesoscale study regions collected over the last 25 years. We use these data to investigate whether results from such mesoscale surveys are representative of large-scale stocks or regional populations. Generally, the proportional recruitment indices for 1- (R₁) and 2-year-old (R₂) krill differ substantially between years for a given area. However, indices were in conformity with the results from other regional scientific surveys. Recruitment indices showed a significant correlation for age-class 1 krill between scientific surveys from the northern Bellingshausen Sea, the Elephant Island area and South Georgia. The correlation becomes weaker for R₂ recruitment indices. There was no correlation between krill recruitment indices from Atlantic and Indian Ocean survey sites. Problems of single-year outliers from Elephant Island are discussed, as well as the problem of "undersized" length classes of the age-1 group that occur in the samples of some years.     

Body Condition Indices Predict Reproductive Success but Not Survival in a Sedentary,Tropical Bird

Body condition may predict individual fitness because those in better condition have more resources to allocate towards improving their fitness. However, the hypothesis that condition indices are meaningful proxies for fitness has been questioned. Here, we ask if intraspecific variation in condition indices predicts annual reproductive success and survival. We monitored a population of Neochmia phaeton (crimson finch), a sedentary, tropical passerine, for reproductive success and survival over four breeding seasons, and sampled them for commonly used condition indices: mass adjusted for body size, muscle and fat scores, packed cell volume, hemoglobin concentration, total plasma protein, and heterophil to lymphocyte ratio. Our study population is well suited for this research because individuals forage in common areas and do not hold territories such that variation in condition between individuals is not confounded by differences in habitat quality. Furthermore, we controlled for factors that are known to impact condition indices in our study population (e.g., breeding stage) such that we assessed individual condition relative to others in the same context. Condition indices that reflect energy reserves predicted both the probability of an individual fledging young and the number of young produced that survived to independence, but only during some years. Those that were relatively heavy for their body size produced about three times more independent young compared to light individuals. That energy reserves are a meaningful predictor of reproductive success in a sedentary passerine supports the idea that energy reserves are at least sometimes predictors of fitness. However, hematological indices failed to predict reproductive success and none of the indices predicted survival. Therefore, some but not all condition indices may be informative, but because we found that most indices did not predict any component of fitness, we question the ubiquitous interpretation of condition indices as surrogates for individual quality and fitness.     

The ecology of south-east Tasmanian phytal animal communities. III. Patterns of species diversity

Diversity indices which have been widely used in ecological studies were calculated for each of 135 samples of phytal macrofauna. A comparison of the properties of these indices indicated that they could be grouped into those primarily influenced by dominance (such as Simpson's Index, McIntosh's Index and E(S₂)), those primarily influenced by the number of species (such as Menhinick's Index, Margalef's Index and Q), and those intermediate between the other two groups (such as the Shannon—Wiener Index and Brillouin's Index). Evenness indices were also calculated but were found to be highly dependent on sample size and consequently difficult to interpret.Environmental correlates of dominance and the number of species per plant indicated that these two community parameters were relatively independent. Dominance and animal density were related as both appeared to be monotonically increasing functions of the level of food resources. The number of species was dependent on the weight of sampled algae but was also strongly influenced by wave exposure and habitat complexity (sensu number of microhabitats rather than rugosity). The wave exposure effects were interrelated to habitat structure; elongate plants having the greatest animal species densities at the sheltered site and compact plants having the greatest species densities at the exposed site.     

Symmetry and range limits in importance indices

Recently, Mingo has analyzed the properties of I_imp, an importance index, and demonstrated that its range is not symmetrical. While agreeing with this comment, we believe that more light needs to be shed on the issue of symmetry in relation to such indices. Importance indices are calculated using three values: performance of the organism in the absence and in the presence of neighbors and maximum performance of the organism in ideal conditions. Because of this structure, importance indices can hardly ever achieve symmetry along the whole range of potential performances. We discuss the limitation of the symmetry range for different symmetry types and for both additive and multiplicative indices. We conclude that importance indices, as other interactions indices, are practical tools for interpreting ecological outcomes, especially while comparing between studies. Nevertheless, the current structure of importance indices prevents symmetry along their whole range. While the lack of “perfect” symmetry may call for the development of more sophisticated importance metrics, the current indices are still helpful for the understanding of biological systems and should not be discarded before better alternatives are well established. To prevent potential confusion, we suggest that ecologists present the relevant index symmetry range in addition to their results, thus minimizing the probability of misinterpretation.     

Dependency and independency among fish density and electivity indices in a stream fish assemblage

Habitat preferences can be identified from population density and electivity indices, which can be derived from either abundance or occurrence data. This study examined the preference detectability and independency of density and electivity indices from different data sources -- abundance and occurrence. Eight scenarios comprising four fish species along two environmental gradients (flow velocity and water depth) in an undisturbed mountain stream were used in this study. Fish density and seven electivity indices were calculated from abundance and occurrence data for the eight scenarios. The correlation analyses illustrated that abundance electivity indices were positively correlated with density in all eight scenarios while occurrence electivity indices were positively correlated with density in only three scenarios. Electivity indices were positively correlated with each other within the same data quality (abundance or occurrence) but not between. The Chesson’s L index was less correlated with other indices and should be used cautiously. Natural historical traits, such as social interactions among organisms, may affect the preference performance of density and electivity indices. In conclusion, density is a good preference indicator. Abundance electivity indices can represent density while occurrence electivity density should be used cautiously for fast assessment. Three electivity indices, Ivlev’s E and E′ and Jacobs’ D, were recommended for their ease of understanding.     

基于TM遥感影像的陕北黄土区结构化植被因子指数提取

根据结构化植被因子指数的概念,以TM影像为信息源,探讨了利用遥感技术提取陕北黄土区结构化植被因子指数（C_s）的途径与方法.结果表明：在陕北黄土区,C_s能更好地描述植被群落的水土保持效益,其与绿度植被指数（归一化植被指数NDVI、修正土壤调整植被指数MSAVI）和黄度植被指（归一化差异衰败指数NDSVI、归一化耕作指数NDTI）等单一的遥感植被指数虽然均存在良好的相关关系,但用绿度与黄度植被指数相结合可综合反映植被的水土保持功能,能较好地克服单一指数在描述植被控制水土流失中的不足;MSAVI、NDTI分别是基于遥感影像提取C_s较为理想的绿度和黄度植被指数;根据群落结构化植被因子指数与遥感植被指数的关系推算区域尺度上的结构化植被因子指数是可行的,但由于不同地区植物物候期的差异,要使该方法在其他地区适用,仍需开展相应的率定和验证工作.     

Indices of nonlinearity in finger force interaction

Experiments with force production by subsets of fingers within the human hand have shown that finger interaction may be significantly nonlinear. In particular, this nonlinearity is reflected in the phenomenon of force deficit, a drop of the peak force of a finger when several fingers act simultaneously. We describe nonlinear effects in force relations within finger pairs, triplets, etc. Finger forces are represented as the sums of components resulting from force interactions within all subsets of the explicitly involved (master) fingers. The values of these components computed at extreme values of control signals, zero and unity, are taken as indices of such elementary force interactions. Indices of the first order reflect purposeful force production by a single master finger and its effects on forces produced by other fingers (enslaving). Indices of the second order reflect additional influences from pairs of simultaneously recruited master fingers, etc. Force interaction indices were computed based on finger forces measured in earlier experiments. Signs of indices alternated with their order, being positive for the indices of the first order (enslaving), negative for the indices of the second order (force deficit), positive for the indices of the third order, and mostly negative for the indices of the fourth order. Indices of the third and fourth orders reflect phenomena of force interaction not reported earlier. The study emphasizes the importance of nonlinear interactions among finger forces and introduces a set of independent indices that can be used to quantify such interactions in different subpopulations and their possible changes with practice and/or rehabilitation of the hand function.     

Chronic toxicity of rare-earth elements on human beings

Blood analyses for rare-earth element (REE)-high background regions in South Jiangxi show that the population averages of many of the biochemical indices deviate markedly from normal values in the normal region. These deviations are thought to be caused by prolonged intake of REE through food chains in view of that the toxicity of other harmful metals such as Pb and Cd can be neglected because of their insignificant amounts in the environment. In comparison with the normal region, blood biochemical indices abnormal in the REE-high regions are manifested as low total serum protein (TSP), albumin, β-globulin, glutamic pyruvic transitanase, serium triglycerides, and immunoglobulin, but high cholesterol. These deviations may be related to the REE concentration and composition of food chains, and are sex dependent. Certain blood indices (such as TSP) of different age groups in the LREE-high region indicate that the influence of REE on males is a one-way irreversible process, whereas females show a strong ability of restoration.     

Mathematical convergences of biodiversity indices

Various indices are used in the scientific literature to describe biodiversity changes. Nevertheless, the appropriateness of an index rather than another to transcribe trends in biodiversity of plankton communities is not clearly established.So, starting from the definitions of the diversity indices of Simpson, Gleason-Margalef, Menhinick, Brillouin, Shannon, Patten, Piélou and Hurlbert, the aim of this work is to state, under the assumption that the total number of individual is great, a mathematical convergence between the indices of Brillouin, Shannon, Simpson's reciprocal, Hurlbert on the one hand and between the indices of Piélou and Patten on the other hand. More particularly, it will be also established that these last two indices are complementary provided that the total number of individual is greater than the number of species. Gleason-Margalef's and Menhinick's indices will be considered as independents.Thus, such a convergence will lead to propose a classification of these indices into three great groups reducing their number from eight to four. This theoretical result will be then applied on phytoplankton and zooplankton communities of two neighbouring bays differently affected by anthropogenic inputs in NW Mediterranean Sea (Toulon area, France) throughout three consecutive annual cycles. A strong statistical correlation between the indices belonging to the same group seems to confirm the validity of our classification.     

中国东部沿海中小型河流鱼类的整体遗传多样性评价——以曹娥江为例

研究将曹娥江作为东部沿海中小型河流代表, 基于线粒体细胞色素b基因(Cyt b)分子标记对其鱼类的整体遗传多样性水平进行了评估。结果表明, 21个种26个群体鱼类Cyt b基因的单倍型多样性指数(h)和核苷酸多样性指数(π)水平分别为0.074—0.987和0.00019—0.00520, 物种间遗传多样性水平差异较大; 比较不同江段鱼类遗传多样性水平发现, 曹娥江鱼类的单倍型多样性指数水平从河口到中下游再到上游逐渐降低(P<0.05)。比较同一物种的遗传多样性水平发现, 曹娥江鱼类的核苷酸多样性指数水平低于长江、珠江等大型河流鱼类的相应指数水平(P<0.05), 提示曹娥江鱼类的整体遗传多样性处于中等偏下水平, 鱼类资源亟需科学的保护和修复。进一步分析人为扰动因素对曹娥江鱼类遗传多样性水平的影响发现, 敏感型鱼类的单倍型多样性指数水平显著低于中等耐受型鱼类(P<0.05); 麦穗鱼(Pseudorasbora parva)、光泽黄颡鱼(Pelteobagrus nitidus)和刺鳅(Mastacembelus aculeatus)3种鱼类的上游镜岭群体单倍型多样性指数和核苷酸多样性指数水平均低于其中游仙岩群体的相应指数水平。结果提示, 水体污染、过度捕捞可能是造成目前曹娥江鱼类遗传多样性水平较低的主要原因。研究结果将为曹娥江乃至东部中小河流的鱼类资源的管理、保护和开发利用提供重要的理论依据。