Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness

Species richness is a fundamental measurement of community and regional diversity, and it underlies many ecological models and conservation strategies. In spite of its importance, ecologists have not always appreciated the effects of abundance and sampling effort on richness measures and comparisons. We survey a series of common pitfalls in quantifying and comparing taxon richness. These pitfalls can be largely avoided by using accumulation and rarefaction curves, which may be based on either individuals or samples. These taxon sampling curves contain the basic information for valid richness comparisons, including category–subcategory ratios (species-to-genus and species-to-individual ratios). Rarefaction methods – both sample-based and individual-based – allow for meaningful standardization and comparison of datasets. Standardizing data sets by area or sampling effort may produce very different results compared to standardizing by number of individuals collected, and it is not always clear which measure of diversity is more appropriate. Asymptotic richness estimators provide lower-bound estimates for taxon-rich groups such as tropical arthropods, in which observed richness rarely reaches an asymptote, despite intensive sampling. Recent examples of diversity studies of tropical trees, stream invertebrates, and herbaceous plants emphasize the importance of carefully quantifying species richness using taxon sampling curves.     

Incorporating spatial autocorrelation may invert observed patterns

Though still often neglected, spatial autocorrelation can be a serious issue in ecology because the presence of spatial autocorrelation may alter the parameter estimates and error probabilities of linear models. Here I re-analysed data from a previous study on the relationship between plant species richness and environmental correlates in Germany. While there was a positive relationship between native plant species richness and an altitudinal gradient when ignoring the presence of spatial autocorrelation, the use of a spatial simultaneous liner error model revealed a negative relationship. This most dramatic effect where the observed pattern was inverted may be explained by the environmental situation in Germany. There the highest altitudes are in the south and the lowlands in the north that result in some locally or regionally inverted patterns of the large-scale environmental gradients from the equator to the north. This study therefore shows the necessity to consider spatial autocorrelation in spatial analyses.     

Functional rarefaction: estimating functional diversity from field data

Studies in biodiversity-ecosystem function and conservation biology have led to the development of diversity indices that take species' functional differences into account. We identify two broad classes of indices: those that monotonically increase with species richness (MSR indices) and those that weight the contribution of each species by abundance or occurrence (weighted indices). We argue that weighted indices are easier to estimate without bias but tend to ignore information provided by rare species. Conversely, MSR indices fully incorporate information provided by rare species but are nearly always underestimated when communities are not exhaustively surveyed. This is because of the well-studied fact that additional sampling of a community may reveal previously undiscovered species. We use the rarefaction technique from species richness studies to address sample-size-induced bias when estimating functional diversity indices. Rarefaction transforms any given MSR index into a family of unbiased weighted indices, each with a different level of sensitivity to rare species. Thus rarefaction simultaneously solves the problem of bias and the problem of sensitivity to rare species. We present formulae and algorithms for conducting a functional rarefaction analysis of the two most widely cited MSR indices: functional attribute diversity (FAD) and Petchey and Gaston's functional diversity (FD). These formulae also demonstrate a relationship between three seemingly unrelated functional diversity indices: FAD, FD and Rao's quadratic entropy. Statistical theory is also provided in order to prove that all desirable statistical properties of species richness rarefaction are preserved for functional rarefaction.     

Models and estimators linking individual-based and sample-based rarefaction,extrapolation and comparison of assemblages

Aims In ecology and conservation biology, the number of species counted in a biodiversity study is a key metric but is usually a biased underestimate of total species richness because many rare species are not detected. Moreover, comparing species richness among sites or samples is a statistical challenge because the observed number of species is sensitive to the number of individuals counted or the area sampled. For individual-based data, we treat a single, empirical sample of species abundances from an investigator-defined species assemblage or community as a reference point for two estimation objectives under two sampling models: estimating the expected number of species (and its unconditional variance) in a random sample of (i) a smaller number of individuals (multinomial model) or a smaller area sampled (Poisson model) and (ii) a larger number of individuals or a larger area sampled. For sample-based incidence (presence–absence) data, under a Bernoulli product model, we treat a single set of species incidence frequencies as the reference point to estimate richness for smaller and larger numbers of sampling units.Methods The first objective is a problem in interpolation that we address with classical rarefaction (multinomial model) and Coleman rarefaction (Poisson model) for individual-based data and with sample-based rarefaction (Bernoulli product model) for incidence frequencies. The second is a problem in extrapolation that we address with sampling-theoretic predictors for the number of species in a larger sample (multinomial model), a larger area (Poisson model) or a larger number of sampling units (Bernoulli product model), based on an estimate of asymptotic species richness. Although published methods exist for many of these objectives, we bring them together here with some new estimators under a unified statistical and notational framework. This novel integration of mathematically distinct approaches allowed us to link interpolated (rarefaction) curves and extrapolated curves to plot a unified species accumulation curve for empirical examples. We provide new, unconditional variance estimators for classical, individual-based rarefaction and for Coleman rarefaction, long missing from the toolkit of biodiversity measurement. We illustrate these methods with datasets for tropical beetles, tropical trees and tropical ants.Important findings Surprisingly, for all datasets we examined, the interpolation (rarefaction) curve and the extrapolation curve meet smoothly at the reference sample, yielding a single curve. Moreover, curves representing 95% confidence intervals for interpolated and extrapolated richness estimates also meet smoothly, allowing rigorous statistical comparison of samples not only for rarefaction but also for extrapolated richness values. The confidence intervals widen as the extrapolation moves further beyond the reference sample, but the method gives reasonable results for extrapolations up to about double or triple the original abundance or area of the reference sample. We found that the multinomial and Poisson models produced indistinguishable results, in units of estimated species, for all estimators and datasets. For sample-based abundance data, which allows the comparison of all three models, the Bernoulli product model generally yields lower richness estimates for rarefied data than either the multinomial or the Poisson models because of the ubiquity of non-random spatial distributions in nature.     

The use of incidence-based species richness estimators,species accumulation curves and similarity measures to appraise ethnobotanical inventories from South Africa

The incorporation of suitable quantitative methods into ethnobotanical studies enhances the value of the research and the interpretation of the results. Prediction of sample species richness and the use of species accumulation functions have been addressed little in applied ethnobotany. In this paper, incidence-based species richness estimators, species accumulation curves and similarity measures are used to compare and predict species richness, evaluate sampling effort and compare the similarity of species inventories for ethnobotanical data sets derived from the trade in traditional medicine in Johannesburg and Mpumalanga, South Africa. EstimateS was used to compute estimators of species richness (e.g. Jackknife), rarefaction curves, species accumulation curves and complimentarity. Results showed that while the Michaelis–Menten Means estimator appeared to be the best estimator because the curve approached a horizontal asymptote, it was not able to accurately predict species richness for one of the data sets when two of its subsamples were individually tested. Instead, the first-order Jackknife estimator best approximated the known richness.     

Assessing the diversity pattern of cryophilous plant species in high elevation habitats

This study aimed to better document the diversity and distribution patterns of vascular cryophilous species across major habitat types in a high-elevation Mediterranean system in central Italy. The research addressed the following questions: (a) whether different habitats support similar levels of biodiversity in terms of total vascular plants richness and cryophilous species richness, and (b) how each habitat contributes to the total cryophilous species diversity. A random stratified sampling approach based on a habitat map was applied to construct rarefaction curves for overall cryophilous species richness and habitat type-specific cryophilous richness. Rarefaction curves were also constructed for all-species and exclusive species. To determine whether the targeted species represented a constant proportion of all species, the ratio between the rarefaction curves of the cryophilous species and all species was also calculated. The results highlight the importance of the different habitat types in overall and cryophilous species conservation because these different habitat types had progressively higher richness values. At the regional scale, steep slopes had the highest species diversity, the greatest exclusive species richness and a steep rarefaction curve. The diversity pattern of cryophilous taxa was not related to the general pattern of total species richness, with these species being more common in three habitat types with extreme environmental conditions: ridges, cliffs, and screes. For the establishment of successful biodiversity conservation programs, it is imperative to include species-poor habitats containing a high proportion of cryophilous species, which are considered to be threatened by climate warming.     

Modelling geographical patterns in species richness using eigenvector-based spatial filters

Aim To test the mechanisms driving bird species richness at broad spatial scales using eigenvector‐based spatial filtering. Location South America. Methods An eigenvector‐based spatial filtering was applied to evaluate spatial patterns in South American bird species richness, taking into account spatial autocorrelation in the data. The method consists of using the geographical coordinates of a region, based on eigenanalyses of geographical distances, to establish a set of spatial filters (eigenvectors) expressing the spatial structure of the region at different spatial scales. These filters can then be used as predictors in multiple and partial regression analyses, taking into account spatial autocorrelation. Autocorrelation in filters and in the regression residuals can be used as stopping rules to define which filters will be used in the analyses. Results Environmental component alone explained 8% of variation in richness, whereas 77% of the variation could be attributed to an interaction between environment and geography expressed by the filters (which include mainly broad‐scale climatic factors). Regression coefficients of environmental component were highest for AET. These results were unbiased by short‐scale spatial autocorrelation. Also, there was a significant interaction between topographic heterogeneity and minimum temperature. Conclusion Eigenvector‐based spatial filtering is a simple and suitable statistical protocol that can be used to analyse patterns in species richness taking into account spatial autocorrelation at different spatial scales. The results for South American birds are consistent with the climatic hypothesis, in general, and energy hypothesis, in particular. Habitat heterogeneity also has a significant effect on variation in species richness in warm tropical regions.     

Museum collections, species distributions, and rarefaction

Biological specimens in museums and herbaria are sometimes used to compare the geographical distribution of different species. In doing so, it is necessary to account for differences in the numbers of specimens. We show how rarefaction can be used for this purpose. Rarefaction is a simple mathematical method originally designed to compare species richness in communities that differed in the number of sampled individuals. We present an example involving two Phragmipedium orchid species. In this case, rarefaction suggests that the apparent difference in range can be explained by the difference in the numbers of specimens.     

Methods to account for spatial autocorrelation in the analysis of species distributional data: a review

Species distributional or trait data based on range map (extent‐of‐occurrence) or atlas survey data often display spatial autocorrelation, i.e. locations close to each other exhibit more similar values than those further apart. If this pattern remains present in the residuals of a statistical model based on such data, one of the key assumptions of standard statistical analyses, that residuals are independent and identically distributed (i.i.d), is violated. The violation of the assumption of i.i.d. residuals may bias parameter estimates and can increase type I error rates (falsely rejecting the null hypothesis of no effect). While this is increasingly recognised by researchers analysing species distribution data, there is, to our knowledge, no comprehensive overview of the many available spatial statistical methods to take spatial autocorrelation into account in tests of statistical significance. Here, we describe six different statistical approaches to infer correlates of species’ distributions, for both presence/absence (binary response) and species abundance data (poisson or normally distributed response), while accounting for spatial autocorrelation in model residuals: autocovariate regression; spatial eigenvector mapping; generalised least squares; (conditional and simultaneous) autoregressive models and generalised estimating equations. A comprehensive comparison of the relative merits of these methods is beyond the scope of this paper. To demonstrate each method's implementation, however, we undertook preliminary tests based on simulated data. These preliminary tests verified that most of the spatial modeling techniques we examined showed good type I error control and precise parameter estimates, at least when confronted with simplistic simulated data containing spatial autocorrelation in the errors. However, we found that for presence/absence data the results and conclusions were very variable between the different methods. This is likely due to the low information content of binary maps. Also, in contrast with previous studies, we found that autocovariate methods consistently underestimated the effects of environmental controls of species distributions. Given their widespread use, in particular for the modelling of species presence/absence data (e.g. climate envelope models), we argue that this warrants further study and caution in their use. To aid other ecologists in making use of the methods described, code to implement them in freely available software is provided in an electronic appendix.     

Disparity between range map- and survey-based analyses of species richness: patterns, processes and implications

Species richness patterns are characterized either by overlaying species range maps or by compiling geographically extensive survey data for multiple local communities. Although, these two approaches are clearly related, they need not produce identical richness patterns because species do not occur everywhere in their geographical range. Using North American breeding birds, we present the first continent‐wide comparison of survey and range map data. On average, bird species were detected on 40.5% of the surveys within their range. As a result of this range porosity, the geographical richness patterns differed markedly, with the greatest disparity in arid regions and at higher elevations. Environmental productivity was a stronger predictor of survey richness, while elevational heterogeneity was more important in determining range map richness. In addition, range map richness exhibited greater spatial autocorrelation and lower estimates of spatial turnover in species composition. Our results highlight the fact that range map richness represents species coexistence at a much coarser scale than survey data, and demonstrate that the conclusions drawn from species richness studies may depend on the data type used for analyses.     

Spatial autocorrelation and red herrings in geographical ecology

Aim Spatial autocorrelation in ecological data can inflate Type I errors in statistical analyses. There has also been a recent claim that spatial autocorrelation generates ‘red herrings’, such that virtually all past analyses are flawed. We consider the origins of this phenomenon, the implications of spatial autocorrelation for macro‐scale patterns of species diversity and set out a clarification of the statistical problems generated by its presence. Location To illustrate the issues involved, we analyse the species richness of the birds of western/central Europe, north Africa and the Middle East. Methods Spatial correlograms for richness and five environmental variables were generated using Moran's I coefficients. Multiple regression, using both ordinary least‐squares (OLS) and generalized least squares (GLS) assuming a spatial structure in the residuals, were used to identify the strongest predictors of richness. Autocorrelation analyses of the residuals obtained after stepwise OLS regression were undertaken, and the ranks of variables in the full OLS and GLS models were compared. Results Bird richness is characterized by a quadratic north–south gradient. Spatial correlograms usually had positive autocorrelation up to c. 1600 km. Including the environmental variables successively in the OLS model reduced spatial autocorrelation in the residuals to non‐detectable levels, indicating that the variables explained all spatial structure in the data. In principle, if residuals are not autocorrelated then OLS is a special case of GLS. However, our comparison between OLS and GLS models including all environmental variables revealed that GLS de‐emphasized predictors with strong autocorrelation and long‐distance clinal structures, giving more importance to variables acting at smaller geographical scales. Conclusion Although spatial autocorrelation should always be investigated, it does not necessarily generate bias. Rather, it can be a useful tool to investigate mechanisms operating on richness at different spatial scales. Claims that analyses that do not take into account spatial autocorrelation are flawed are without foundation.     

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

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

A comparison of rarefaction and bayesian methods for predicting the allelic richness of future samples on the basis of currently available samples

Rarefaction methods have been introduced into population genetics (from ecology) for predicting and comparing the allelic richness of future samples (or sometimes populations) on the basis of currently available samples, possibly of different sizes. Here, we focus our attention on one such problem: Predicting which population is most likely to yield the future sample having the highest allelic richness. (This problem can arise when we want to construct a core collection from a larger germplasm collection.) We use extensive simulations to compare the performance of the Monte Carlo rarefaction (repeated random subsampling) method with a simple Bayesian approach we have developed-which is based on the Ewens sampling distribution. We found that neither this Bayesian method nor the (Monte Carlo) rarefaction method performed uniformly better than the other. We also examine briefly some of the other motivations offered for these methods and try to make sense of them from a Bayesian point of view.     

Efficiency of a Rapid Assessment of the Diversity of Ground Beetles and Ants, in Natural and Disturbed Habitats of the Nahuel Huapi Region (NW Patagonia, Argentina)

We use sample-based rarefaction curves to evaluate the efficiency of a rapid species richness assay of ground beetles and ants captured in pitfall traps in the Nahuel Huapi National Park (NW Patagonia, Argentina). We ask whether ant species richness patterns show some concordance with those of beetles, and use several extrapolation indices for estimating the expected number of species at a regional scale. A total of 342 pitfall traps were spread in groups, at an intensity of 9 traps/100 m², with two collection stations, at each of 19 sites representative of burned and unburned habitats in the forest, scrub and steppe, along a west-to-east transect of 63 km long. The high regional habitat heterogeneity along the west-to-east gradient is paralleled by a turnover of beetle and ant species, although different families of Coleoptera show idiosyncratic responses across habitat types. Spatial stratification of sampling over three major habitats along with the inclusion of burned and unburned environments may improve sampling efficiency. The observed and extrapolated species richness suggests that we captured a high proportion of the total number of species of beetles and ants known for the region. However, trends in species richness of ants may not indicate similar trends in beetles. Ants and beetles cannot be used as surrogate taxa for the analysis of species richness patterns. Instead, both taxa should be considered as focal as they may offer complementary information for the analysis of the effect of disturbance and regional habitat heterogeneity on species diversity patterns at a regional scale.     

The relationship between psyllid leaf galls and redbay (Persea borbonia) fitness traits in sun and shade

Spatial autocorrelation in vegetation has been discussed extensively, but little is yet known about how standard plant sampling methods perform when confronted with varying levels of patchiness. Simulated species maps with a range of total abundance and spatial autocorrelation (patchiness) were sampled using four methods: strip transect, randomly located quadrats, the non-nested multiscale modified Whittaker plot and the nested multiscale North Carolina Vegetation Survey (NCVS) plot. Cover and frequency estimates varied widely within and between methods, especially in the presence of high patchiness and for species with moderate abundances. Transect sampling showed the highest variability, returning estimates of 19–94% cover for a species with an actual cover of 50%. Transect and random methods were likely to miss rare species entirely unless large numbers of quadrats were sampled. NCVS plots produced the most accurate cover estimates because they sampled the largest area. Total species richness calculated using semilog species-area curves was overestimated by transect and random sampling. Both multiscale methods, the modified Whittaker and the NCVS plots, overestimated species richness when patchiness was low, and underestimated it when patchiness was high. There was no clear distinction between the nested NCVS or the non-nested modified Whittaker plot for any of the measures assessed. For all sampling methods, cover and especially frequency estimates were highly variable, and depended on both the level of autocorrelation and the sampling method used. The spatial structure of the vegetation must be considered when choosing field sampling protocols or comparing results between studies that used different methods.     

Rarefaction does not eliminate the species richness‐biomass relationship in calcareous blackland prairies

Abstract. Relationships between species richness and biomass are common, but the causes remain controversial. It has been suggested that a hump‐shaped relationship may be an artifact of few individuals in both low and high biomass samples. We used rarefaction to standardize species richness to a constant number of individuals in 99 quadrat samples from relict calcareous prairies. Animal ecologists have long used rarefaction to standardize species richness to a constant number of individuals. The expected species richness of each quadrat was determined for 10, 25, 50, 100 and 150 individual plant ramets using the EcoSim program which resampled the data in each quadrat 1000 times. Because we had few samples with biomass over 300 g/m², our data showed a positive relationship between species richness and biomass. The relationship was largely unaffected by rarefaction. Even at the most extreme case of rarefying to 10 individual ramets, the relationship was clear. Monte Carlo covariance tests did not change the shape of the richness‐biomass relationship and significant correlations between observed species richness and rarified species richness suggest that the number of individuals had negligible effects on richness patterns. Because the data had no strong declining phase, these results may not apply to the declining phase of a humped relationship. The results are discussed with reference to other methods of standardizing species richness. Most importantly, we suggest that expressing species richness per number of individuals is inappropriate and may lead to incorrect conclusions.     

Additive partitioning of rarefaction curves and species-area relationships: unifying alpha-, beta- and gamma-diversity with sample size and habitat area

Additive partitioning of species diversity is widely applicable to different kinds of sampling regimes at multiple spatial and temporal scales. In additive partitioning, the diversity within and among samples ( α and β ) is expressed in the same units of species richness, thus allowing direct comparison of α and β . Despite its broad applicability, there are few demonstrated linkages between additive partitioning and other approaches to analysing diversity. Here, we establish several connections between diversity partitions and patterns of habitat occupancy, rarefaction, and species–area relationships. We show that observed partitions of species richness are equivalent to sample-based rarefaction curves, and expected partitions from randomization tests are approximately equivalent to individual-based rarefaction. Additive partitions can also be applied to species–area relationships to determine the relative contributions of factors influencing the β -diversity among habitat fragments.     

Analysis of determinants of mammalian species richness in South America using spatial autoregressive models

Classically, hypotheses concerning the distribution of species have been explored by evaluating the relationship between species richness and environmental variables using ordinary least squares (OLS) regression. However, environmental and ecological data generally show spatial autocorrelation, thus violating the assumption of independently distributed errors. When spatial autocorrelation exists, an alternative is to use autoregressive models that assume spatially autocorrelated errors. We examined the relationship between mammalian species richness in South America and environmental variables, thereby evaluating the relative importance of four competing hypotheses to explain mammalian species richness. Additionally, we compared the results of ordinary least squares (OLS) regression and spatial autoregressive models using Conditional and Simultaneous Autoregressive (CAR and SAR, respectively) models. Variables associated with productivity were the most important at determining mammalian species richness at the scale analyzed. Whereas OLS residuals between species richness and environmental variables were strongly autocorrelated, those from autoregressive models showed less spatial autocorrelation, particularly the SAR model, indicating its suitability for these data. Autoregressive models also fit the data better than the OLS model (increasing R² by 5–14%), and the relative importance of the explanatory variables shifted under CAR and SAR models. These analyses underscore the importance of controlling for spatial autocorrelation in biogeographical studies.     

Effects of disturbance frequency,intensity, and area on assemblages of stream macroinvertebrates

Disturbance frequency, intensity, and areal extent may influence the effects of disturbance on biological communities. Furthermore, these three factors may have interacting effects on biological diversity. We manipulated the frequency, intensity, and area of disturbance in a full-factorial design on artificial substrates and measured responses of benthic macroinvertebrates in a northern Vermont stream. Macroinvertebrate abundance was lower in all disturbance treatments than in the undisturbed control. As in most other studies in streams, species density (number of species/sample) was lower in disturbed treatments than in undisturbed controls. However, species density is very sensitive to total abundance of a sample, which is usually reduced by disturbance. We used a rarefaction method to compare species richness based on an equivalent number of individuals. In rarefied samples, species richness was higher in all eight disturbed treatments than in the undisturbed control, with significant increases in species richness for larger areas and greater intensities of disturbance. Increases in species richness in response to disturbance were consistent within patches, among patches with similar disturbance histories, and among patches with differing disturbance histories. These results provide some support for Huston’s dynamic-equilibrium model but do not support the intermediate-disturbance hypothesis. Our analyses demonstrate that species richness and species density can generate opposite patterns of community response to disturbance. The interplay of abundance, species richness, and species density has been neglected in previous tests of disturbance models. Received: 20 July 1999 / Accepted: 26 January 2000