Which body condition index is best?

Body condition indices are widely used by ecologists, but many indices are used without empirical validation. To test the validity of a variety of indices, we compared how well a broad range of body condition indices predicted body fat mass, percent body fat and residual fat mass in mice Mus musculus. We also compared the performance of these condition indices with the multiple regression of several morphometric variables on body fat mass, percent body fat and residual fat mass. In our study population, two ratio based condition indices – body mass/body length and log body mass/log body length – predicted body fat mass as well as or better than other ratio and residual indices of condition in females. In males one ratio based condition index (log body mass/log body length) and one residual index (residuals from a regression of pelvic circumference on body length) were best at predicting body fat mass. All indices were better at estimating body fat mass, and residual fat mass than at estimating percent body fat. The predictions of body fat were much better for females than for males. Multiple regressions incorporating pelvic circumference (i.e. girth at the iliac crests) were the best predictors of body fat mass, residual fat mass, and percent body fat, and these multiple regressions were better than any of the condition indices. We recommend 1) that condition be precisely defined, 2) that predictors of condition be empirically validated, 3) that pelvic circumference be considered as a potential predictor of fat content, and 4) that, in general, multiple regression be considered as an alternative to condition indices.     

Method of predicting reference condition biota affects the performance and interpretation of ecological indices

1. The statistical rigour and interpretability of ecological assessments is strongly affected by how well we predict the biological assemblages expected to occur in the absence of human‐caused stress, i.e. the reference condition. In this study, we examined how the specific method used to predict the reference condition affected the performance of two commonly used types of ecological index: RIVPACS‐based O/E indices and multimetric indices (MMIs). 2. These two types of index have generally relied on different approaches to predicting the reference condition. For MMIs, some type of regionalisation is typically used to describe the range of metric values among reference sites and hence the expected range at assessed sites. For O/E indices, continuous modelling is used to predict how the biota varies among sites both among and within regions. Because the prediction method differs for these two types of index, it has been impossible to judge if differences in index performance (accuracy, precision, responsiveness and sensitivity) are caused by differences in the way reference condition biota are predicted or by differences in what the indices measure. 3. We used a common data set of 94 reference sites and 255 managed sites and the same potential set of predictor variables to compare the performance of five different MMIs and three O/E indices that were derived from different prediction methods: null models, multiple linear regression (MLR), classification and regression trees, Random Forests (RF) and linear discriminant functions models (LDM). We then calculated values of these indices for samples collected from the managed catchments as well as samples collected from 13 reference sites that were progressively altered in known ways by a simulation programme. 4. Both the type of predictor used and the type of index affected overall index performance. Modelled indices generally had the greatest sensitivity in assessing managed sites as biologically different from reference. Index sensitivity was determined by both an aspect of index precision (10th percentile of reference condition values) and responsiveness. The O/E indices showed the best scope of response to known biological alteration. All three O/E indices decreased linearly in response to simulated alteration in both overall assemblage structure (Bray‐Curtis dissimilarity) and taxa loss. The MMIs declined linearly from low to intermediate levels of assemblage alteration but were less responsive between intermediate and high levels of biological alteration. 5. Insights gained from simulations can aid in testing assumptions regarding index response to stress and help ensure that we select indices that are ecologically interpretable and most useful to resource managers.     

Evaluating the validity of using unverified indices of body condition

Condition indices are commonly used in an attempt to link body condition of birds to ecological variables of interest, including demographic attributes such as survival and reproduction. Most indices are based on body mass adjusted for structural body size, calculated as simple ratios or residuals from regressions. However, condition indices are often applied without confirming their predictive value (i.e., without being validated against measured values of fat and protein), which we term 'unverified' use. We evaluated the ability of a number of unverified indices frequently found in the literature to predict absolute and proportional levels of fat and protein across five species of waterfowl. Among indices we considered, those accounting for body size never predicted absolute protein more precisely than body mass, however, some indices improved predictability of fat, although the form of the best index varied by species. Further, the gain in precision by using a condition index to predict either absolute or percent fat was minimal (rise in r²≤0.13), and in many cases model fit was actually reduced. Our data agrees with previous assertions that the assumption that indices provide more precise indicators of body condition than body mass alone is often invalid. We strongly discourage the use of unverified indices, because subjectively selecting indices likely does little to improve precision and might in fact decrease predictability relative to using body mass alone.     

A Comparative Analysis of Evenness Index Sensitivity

Evenness indices are numerous but the lack of knowledge of their properties is a limitation to their biological usefulness. 15 evenness indices, two of them being recently proposed, were studied in this work. We investigated the sensitivity of each index using (1) 189 macroinvertebrate communities sampled in the field, and (2) a set of communities modified in a controlled way. There is no single way to measure evenness. We demonstrated that a measure should be chosen considering (1) the kind of data analysed and, (2) the index properties wanted by users. Depending on the ecological data set the index should be more sensitive to variations in rare, median or abundant species. For most of macroinvertebrate community analyses, a convenient evenness index requirs to be symmetric, unsensitive to variation on rare taxa, with a large range of variation and can be compared with a diversity index. Depending on diversity measure used, five indices correspond to these criteria: E_Pielou, E_Hurlbert, E_–ln(D), E_1–D, E_MI. Our results were summarized in a table which may help users to select a convenient evenness measure according to their specific data. Concerning index properties, three main features that an evenness index should meet are briefly discussed: dependence with richness, symmetry criteria and variation range. A revue of this controversial subject allowed a best understanding of values obtained with evenness measures depending on their own features.     

Development and Applications of Five New Water Quality Indices

Two indices, P₁ and I, employing ranked data and following the beta distribution, are described. These indices, which are true statistical measures of water quality, can be used with any set of parameters. Further, these indices correlate highly with biological and subjective-engineering assessments of water quality. Three indices, employing raw data and based on the chi-square distribution, are described. Two of these, B₁ and B₂, do not have sufficient discrimination to serve as general measures of water quality, although they have use in specific circumstances. The index C has been found to be a measure of excessive variability (at a station), and can be used to quantitatively compare the (data) variability among stations. The five indices described here are evaluated against a set of operational criteria which a mathematically sound index should meet.     

Phylogenetic indices for measuring the diet breadths of phytophagous insects

Prevailing methods of measuring diet breadth of phytophagous insects are not consistent between studies and generally rely on counts of a variety of higher plant taxa (e.g. genera, families, orders). Results derived from them can be inconsistent if different taxonomic levels are used between studies. In any case, such indices do not include information from the whole branching structure of the host plant phylogeny, and do not address the fact that higher taxa are not necessarily phylogenetically equivalent. Here we present novel phylogeny-based methods which address these shortcomings. Although a previously proposed index (the Phylogenetic Diversity index) may be employed, it cannot be used to measure diets of strictly monophagous insects (i.e. those which utilise a single host species). We therefore introduce a modification of this index (the Root Phylogenetic Diversity index) which may be applied to all diets. In addition, we propose a Clade Dispersion index as a branch-length-independent measure of the degree to which hosts are scattered across the host phylogeny. We describe how these indices could be employed in studies of insect diet breadth and discuss potential problems which may be encountered in their use. Received: 16 November 1998 / Accepted: 10 February 1999     

On the challenge of treating various types of variables: application for improving the measurement of functional diversity

Functional diversity is at the heart of current research in the field of conservation biology. Most of the indices that measure diversity depend on variables that have various statistical types (e.g. circular, fuzzy, ordinal) and that go through a matrix of distances among species. We show how to compute such distances from a generalization of Gower's distance, which is dedicated to the treatment of mixed data. We prove Gower's distance can be extended to include new types of data. The impact of this generalization is illustrated on a real data set containing 80 plant species and 13 various traits. Gower's distance allows an efficient treatment of missing data and the inclusion of variable weights. An evaluation of the real contribution of each variable to the mixed distance is proposed. We conclude that such a generalized index will be crucial for analyzing functional diversity at small and large scales.     

Hyperspectral indices for estimating leaf biochemical properties in temperate deciduous forests: Comparison of simulated and measured reflectance data sets

This study aimed at finding efficient hyperspectral indices for estimating three leaf biochemical parameters: chlorophyll content (CHL, μg cm⁻²), leaf water thickness (EWT, g cm⁻²), and leaf mass per area (LMA, g cm⁻²) in typical temperate deciduous forests. These parameters are required by most biogeochemical models that describe ecosystem functions. We have identified the most efficient hyperspectral indices (both the index types and the wavelength domains) based on both a simulated data set (produced with the calibrated leaf reflectance model PROSPECT) and with data sets (I, II, and III) from measurement of field-collected leaves. Results indicated that CHL, EWT, and LMA can be estimated with high precision using a two-waveband vegetation index (Double Deference index, DDn) for all parameters, with an overall root mean square error (RMSE) of 6.87 μg cm⁻² for CHL, 0.0011 g cm⁻² for EWT, and 0.0015 g cm⁻² for LMA. The best overall indices for temperate deciduous forests were DDn (715, 185) for CHL, DDn (1530, 525) for EWT, and DDn (1235, 25) for LMA, although these indices were not necessarily the best for every specific data set (especially for the simulated data set). Moreover, discrepancies were obvious when the identified indices were applied to different data sets. Even if the wavelengths of calibrated indices have been accurately determined through the simulated data set, the regressions between the indices and the biochemical parameters must be calibrated with field-based measurements. The indices identified in this study are applicable to various species (data set III), various phenological stages and locations (data set I), and various leaf anatomies (data set II) and may therefore be widely applicable for temperate deciduous forests and possibly for other plant communities.     

A causal examination of the effects of confounding factors on multimetric indices

The development of multimetric indices (MMIs) as a means of providing integrative measures of ecosystem condition is becoming widespread. An increasingly recognized problem for the interpretability of MMIs is controlling for the potentially confounding influences of environmental covariates. Most common approaches to handling covariates are based on simple notions of statistical control, leaving the causal implications of covariates and their adjustment unstated. In this paper, we use graphical models to examine some of the potential impacts of environmental covariates on the observed signals between human disturbance and potential response metrics. Using simulations based on various causal networks, we show how environmental covariates can both obscure and exaggerate the effects of human disturbance on individual metrics. We then examine from a causal interpretation standpoint the common practice of adjusting ecological metrics for environmental influences using only the set of sites deemed to be in reference condition. We present and examine the performance of an alternative approach to metric adjustment that uses the whole set of sites and models both environmental and human disturbance effects simultaneously. The findings from our analyses indicate that failing to model and adjust metrics can result in a systematic bias towards those metrics in which environmental covariates function to artificially strengthen the metric–disturbance relationship resulting in MMIs that do not accurately measure impacts of human disturbance. We also find that a “whole-set modeling approach” requires fewer assumptions and is more efficient with the given information than the more commonly applied “reference-set” approach.     

A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement

Nestedness has been widely reported for both metacommunities and networks of interacting species. Even though the concept of this ecological pattern has been well-defined, there are several metrics by which it can be quantified. We noted that current metrics do not correctly quantify two major properties of nestedness: (1) whether marginal totals (i.e. fills) differ among columns and/or among rows, and (2) whether the presences (1's) in less-filled columns and rows coincide, respectively, with those found in the more-filled columns and rows. We propose a new metric directly based on these properties and compare its behavior with that of the most used metrics, using a set of model matrices ranging from highly-nested to alternative structures in which no nestedness should be detected. We also used an empirical dataset to explore possible biases generated by the metrics as well as to evaluate correlations between metrics. We found that nestedness has been quantified by metrics that inappropriately detect this pattern, even for matrices in which there is no nestedness. In addition, the most used metrics are prone to type I statistical errors while our new metric has better statistical properties and consistently rejects a nested pattern for different types of random matrices. The analysis of the empirical data showed that two nestedness metrics, matrix temperature and the discrepancy measure, tend to overestimate the degrees of nestedness in metacommunities. We emphasize and discuss some implications of these biases for the theoretical understanding of the processes shaping species interaction networks and metacommunity structure.     

Evaluating indices of body condition in two cricket species

Body mass components (dry mass, lean dry mass, water mass, fat mass) in each sex correlate strongly with body mass and pronotum length in Gryllus texensis and Acheta domesticus. Ordinary least squares (OLS) regression underestimates the scaling relationship between body mass and structural size (i.e., pronotum length) in both cricket species compared with standard major axis (SMA) regression. Standardized mass components correlate more strongly with scaled mass index () than with residual body mass (R_i). R_i represents the residuals from an OLS regression of log body mass against log pronotum length. Neither condition index predicts energy stores (i.e., fat content) in G. texensis. R_i is not correlated with energy stores in A. domesticus whereas is negatively correlated. A comparison of condition index methods using published data showed that neither sex nor diet quality affected body condition at adulthood in G. texensis when using the scaled mass index. However, the residual index suggested that sex had a significant effect on body condition. Further, analysis of covariance (ANCOVA) suggested that diet quality significantly affects body mass while statistically controlling for body size (i.e., body condition). We conclude that the statistical assumptions of condition index methods must be met prior to use and urge caution when using methods that are based on least squares in the y‐plane (i.e., residual index ANCOVA).     

Sensitivity of lod scores to changes in diagnostic status.

This paper investigates effects on lod scores when one individual in a data set changes diagnostic or recombinant status. First we examine the situation in which a single offspring in a nuclear family changes status. The nuclear-family situation, in addition to being of interest in its own right, also has general theoretical importance, since nuclear families are "transparent"; that is, one can track genetic events more precisely in nuclear families than in complex pedigrees. We demonstrate that in nuclear families log10 [(1-theta)/theta] gives an upper limit on the impact that a single offspring's change in status can have on the lod score at that recombination fraction (theta). These limits hold for a fully penetrant dominant condition and fully informative marker, in either phase-known or phase-unknown matings. Moreover, log10 [(1-theta)/theta] (where theta denotes the value of theta at which Zmax occurs) gives an upper limit on the impact of a single offspring's status change on the maximum lod score (Zmax). In extended pedigrees, in contrast to nuclear families, no comparable limit can be set on the impact of a single individual on the lod score. Complex pedigrees are subject to both stabilizing and destabilizing influences, and these are described. Finally, we describe a "sensitivity analysis," in which, after all linkage analysis is completed, every informative individual in the data set is changed, one at a time, to see the effect which each separate change has on the lod scores. The procedure includes identifying "critical individuals," i.e., those who would have the greatest impact on the lod scores, should their diagnostic status in fact change. To illustrate use of the sensitivity analysis, we apply it to the large bipolar pedigree reported by Egeland et al. and Kelsoe et al. We show that the changes in lod scores observed there, on the order of 1.1-1.2 per person, are not unusual. We recommend that investigators include a sensitivity analysis as a standard part of reporting the results of a linkage analysis.     

Conceptual and statistical problems with the use of the Shannon-Weiner entropy index in bioacoustic analyses

Information theory and its indices were developed for human communication to predict the amount of information transferred in a message. One such index, the Shannon-Weiner index (SWI), has often been used to analyse information from other fields in which its application may not be appropriate. In ecoacoustics, SWI is used to compare acoustic diversity (i.e. a measure derived by integrating the richness and abundance of animal sounds) between locations. In animal communication, SWI is used to quantify repertoire complexity (i.e. a measure derived by integrating the number and abundance of sound types produced by individuals or species) as an approach to understanding signal evolution. We discuss problems associated with using the SWI in ecoacoustics and animal communication. Specifically, we discuss conceptual and statistical problems associated with the SWI and then illustrate these problems using hypothetical data. In ecoacoustics, the SWI’s assumptions of random variables and independent samples are often violated. In animal communication, the SWI fails to distinguish among repertoires in which the number of sound types and the abundance of each sound type differ. We also show that other methods do capture these differences. We conclude that the SWI does not adequately represent acoustic diversity or repertoire complexity due to the multiple conceptual and statistical issues associated with its use. We recommend other analytical methods to more fully describe these biological systems, including goodness of fit, Morisita similarity index and Markov chain analysis. These methods provide more information for future comparisons and permit researchers to test hypotheses more directly.     

Transferability of bioassessment indices among water body types and ecoregions: A California experiment in wetland assessment

Biological assessment of aquatic resources requires the availability of bioassessment tools that work in all waterbody types and regions of interest. Developing new assessment tools may require several years of data collection and substantial investment of resources, which may not be an option for some aquatic resource managers. Adapting tools developed for different regions or wetland types may be an attractive alternative to developing new indices, provided they work well in the novel setting. In this study, we explore the transferability of two bioassessment indices for application to depressional wetlands in California, which are wetland type of management concern but for which bioassessment tools don’t currently exist. We tested the applicability of a depressional wetland invertebrate index of biotic integrity (IBI) developed in the San Francisco Bay region of northern California for application in the drier regions of southern California (i.e. geographic transferability), and the ability to apply a riverine benthic diatom IBI to benthic diatoms in depressional wetlands (i.e. water body type transferability). We evaluated the accuracy and responsiveness of the existing Indices for use in depressional wetlands and refined reference definitions and recalibrated thresholds relative to stressor gradients to maximize index performance. Performance of the adapted indices was compared to that of an existing habitat assessment tool (the California Rapid Assessment Method; CRAM) that has been developed for statewide application of depressional wetlands. Finally, we demonstrate application of the revised indices for ambient assessment of depressional wetland condition in southern California. Recalibrating both the macroinvertebrate and diatom indices to reference thresholds based on nutrient concentrations resulted in lower coefficient of variation among reference sites, greater differentiation between reference and non-reference and stronger relationship with stressors than when reference thresholds were based on landscape disturbance. Overall, the simple adjustment of the reference definition allowed us to transfer the indices with no structural changes to the metrics. This approach can facilitate future index adaptations that allow practitioners to include waterbody types for which there is no current index into routine biomonitoring programs.     

Topological modelling of analgesia

Analgesic activity (log IC) of a large series of 97 analgesics was modelled topologically using a series of distance-based topological indices. The results show that analgesic activity (log IC) exhibit inter familial correlation and these can only be modelled by splitting 97 analgesics into five different categories. The regression analyses of the data show that the Wiener (W)-, Branching (B)- and first-order connectivity (chi)- indices are the better topological indices for modelling the activity (log IC), and that W index gave the excellent results.     

闽北地区森林群落物种多样性的测定

采用8个物种多样性指数对闽北地区的8个森林群落类型物种多样性进行测定,并选用4个种一多度关系模型(对数正态分布、Weibull分布、对数级数分布、生态位优先占领模型)分析其物种-多度关系,把多样性指数与对数正态分布、Weibull分布和生态位优先占领模型的有关参数进行线性回归,以分析多度模型参数描述物种多样性的可行性。结果表明：(1)多数物种多样性指数对群落的测度是一致的,(2)对数正态分布、Weibull分布和生态位优先占领模型对8个群落的物种多度拟合效果很好;(3)对数正态分布、Weibull分布和生态位优先占领模型有关模型参数与部分物种多样性指数的线性关系达显著或极显著水平。通过闽北地区8个类型森林群落物种多样性指数测定,使生物多样性较准确地数量化,同时还说明采用改进单纯形法进行非线性分布函数的拟合是简单有效的,可推广应用。     

The assessment of DNA-synthetic activity

Summary A method is described by which a numerical value can be assigned to the amount of DNA-synthesis shown graphically by population-histograms obtained by Feulgen cytophotometry. The index appeared to give a reasonable measure of DNA-synthetic activity in populations having very low, moderate and high mitotic indices and closely followed labelling indices obtained by autoradiography. Thus the advantage of a numerical value is that the DNA-synthetic activities in different populations can be compared for statistical analysis.     

Development and assessment of a landscape-scale ecological threat index for the Lower Colorado River Basin

Anthropogenic disturbances impact freshwater biota but are rarely incorporated into conservation planning due to the difficulties in quantifying threats. There is currently no widely accepted method to quantify disturbances, and determining how to measure threats to upstream catchments using disturbance metrics can be time consuming and subjective. We compared four watershed-scale ecological threat indices for the Lower Colorado River Basin (LCRB) using landscape-level threats of land use (e.g., agricultural and urban lands), waterway development and diversions (e.g., number of canals, dams), and human development (e.g., road and railroads density, pollution sites). The LCRB is an ideal region to assess ecological threat indices because of the increasing need for conservation to ensure the persistence of native fishes in highly altered habitat. Each threat was measured for severity (i.e., level of influence on the upstream watershed) and frequency throughout each watershed; both severity and frequency were measured using two different methods. Severity values were based either on peer-reviewed literature and weighted in accordance to their published ecological impact, or assumed equal severity across stressors. Threat frequency was calculated according to either the presence/absence of each stressor, or on the relative density of each stressor in the watershed. Each measure of severity was combined with a measure of frequency, creating four ecological threat indices, and transformed to a 0–100 scale. Threat indices were highly correlated (slopes of 0.94–1.63; R² of 0.82–0.98), and were highest for watersheds close to urban centers, including Phoenix, Tucson, and Flagstaff, Arizona, and Las Vegas, Nevada. Road crossings and density appeared to be the most influential stressors in the index, but the removal of any individual stressor only changed the index by <5.1 units. Our results indicate that a simpler index with less subjectivity (i.e., presence/absence of a stressor in a watershed) provides similar results to the more subjective measure of threats (i.e., peer-reviewed threat severity). Because these threats have been linked to ecological health, the development of the index should be a useful tool to identify regions of greatest potential threat to aquatic biota and can aid in conservation planning for the Lower Colorado River Basin.     

Statistical determination of diagnostic species for site groups of unequal size

Aim: Concentration of species occurrences in groups of classified sites can be quantified with statistical measures of fidelity, which can be used for the determination of diagnostic species. However, for most available measures fidelity depends on the number of sites within individual groups. As the classified data sets typically contain site groups of unequal size, such measures do not enable a comparison of numerical fidelity values of species between different site groups. We therefore propose a new method of measuring fidelity with presence/absence data after equalization of the size of the site groups. We compare the properties of this new method with other measures of statistical fidelity, in particular with the Dufrêne‐Legendre Indicator Value (IndVal) index. Methods: The size of site groups in the data set is equalized, while relative frequencies of species occurrence within and outside of these groups are kept constant. Then fidelity is calculated using the phi coefficient of association. Results: Fidelity values after equalization are independent of site group size, but their numerical values vary independently of the statistical significance of fidelity. By changing the size of the target site group relative to the size of the entire data set, the fidelity measure can be made more sensitive to either common or rare species. We show that there are two modifications of the IndVal index for presence/absence data, one of which is also independent of the size of site groups. Conclusion: The phi coefficient applied to site groups of equalized size has advantages over other statistical measures of fidelity based on presence/absence data. Its properties are close to an intuitive understanding of fidelity and diagnostic species in vegetation science. Statistical significance can be checked by calculation of another fidelity measure that is a function of statistical significance, or by direct calculation of the probability of observed species concentrations by Fisher's exact test. An advantage of the new method over IndVal is its ability to distinguish between positive and negative fidelity. One can also weight the relative importance of common and rare species by changing the equalized size of the site groups.