Braun‐Blanquet's legacy and data analysis in vegetation science

Abstract. This article investigates whether the Braun‐Blanquet abundance/dominance (AD) scores that commonly appear in phytosociological tables can properly be analysed by conventional multivariate analysis methods such as Principal Components Analysis and Correspondence Analysis. The answer is a definite NO. The source of problems is that the AD values express species performance on a scale, namely the ordinal scale, on which differences are not interpretable. There are several arguments suggesting that no matter which methods have been preferred in contemporary numerical syntaxonomy and why, ordinal data should be treated in an ordinal way. In addition to the inadmissibility of arithmetic operations with the AD scores, these arguments include interpretability of dissimilarities derived from ordinal data, consistency of all steps throughout the analysis and universality of the method which enables simultaneous treatment of various measurement scales. All the ordination methods that are commonly used, for example, Principal Components Analysis and all variants of Correspondence Analysis as well as standard cluster analyses such as Ward's method and group average clustering, are inappropriate when using AD data. Therefore, the application of ordinal clustering and scaling methods to traditional phytosociological data is advocated. Dissimilarities between relevés should be calculated using ordinal measures of resemblance, and ordination and clustering algorithms should also be ordinal in nature. A good ordination example is Non‐metric Multidimensional Scaling (NMDS) as long as it is calculated from an ordinal dissimilarity measure such as the Goodman & Kruskal γ coefficient, and for clustering the new OrdClAn‐H and OrdClAn‐N methods.     

Does Ordinal Cover Estimation Offer Reliable Quality Data Structures in Vegetation Ecological Studies?

Using visual estimation of species cover in ordinal interval classes may reduce costs in vegetation studies. In phytosociology, species cover within plots is usually estimated according to the well-known Braun-Blanquet scale and ordinal data from this scale are usually treated using common exploratory analysis tools that are adequate for ratio-scale variables only. This paper addresses whether the visual estimation of ordinal cover data and the treatment of these data with multivariate procedures tailored for ratio-scale data would lead to a significant loss of information with respect to the use of more accurate methods of data collection and analysis. To answer these questions we used three data sets sampled by different authors in different sites of Tuscany (central Italy) in which the species cover is measured with the point quadrat method. For each data set we used a Mantel test to compare the dissimilarity matrices obtained from the original point-quadrat cover data with those obtained from the corresponding ordinal interval classes. The results suggest that the ordinal data are suitable to represent the plot-to-plot dissimilarity structure of all data sets in a reasonable way and that in using such data there is no need to apply dissimilarity coefficients specifically tailored for ordinal scales.     

Extended dissimilarity: a method of robust estimation of ecological distances from high beta diversity data

It is widely accepted that reliable ordination of ecological data requires a strong linear or ordinal relationship between the dissimilarity of sites, based on species composition, and the ecological distance between them. Certain dissimilarity measures, having the property that they take a fixed maximum value when sites have no species in common, have been shown to be strongly correlated with ecological distance. For ecological gradients of moderate length (moderate beta diversity), such measures, in conjunction with non-metric multidimensional scaling, will reliably yield successful ordinations. However, as beta diversity increases, more sites have no species in common, and such measures invariably under-estimate ecological distance for such sites. Thus ordinations of data with high species turnover (high beta diversity) may fail.Extended dissimilarities are defined using an iterative adaptation of flexible shortest path adjustment applied to the matrix of dissimilarities with fixed maximum values. By means of theoretical argument and simulations, this is shown to lead to far stronger correlations between the adjusted site dissimilarity and ecological distance for ecological gradients of greater length than previously considered. Hence ordinations of extended dissimilarities, by means of either metric or non-metric scaling techniques, are shown to outperform corresponding ordinations of unadjusted dissimilarities, with the difference increasing with increasing beta diversity.     

On the evaluation of ordinal data with conventional multivariate procedures

In a recent Forum paper, it is argued that, in most studies, ordinal data such as the Braun‐Blanquet abundance/dominance scale are not properly treated by multivariate methods. This is because conventional multivariate methods are generally adequate for ratio‐scale variables only, while for ordinal variables differences between states and their ratios are not interpreted. Conversely, in this paper it is shown that using conventional multivariate procedures for evaluating ordinal data should imply a shift from a metric space to a topological data space; as such the use of ordinal data does not represent a serious methodological error, provided that results are interpreted accordingly.     

A family of functional dissimilarity measures for presence and absence data

Plot‐to‐plot dissimilarity measures are considered a valuable tool for understanding the complex ecological mechanisms that drive community composition. Traditional presence/absence coefficients are usually based on different combinations of the matching/mismatching components of the 2 × 2 contingency table. However, more recently, dissimilarity measures that incorporate information about the degree of functional differences between the species in both plots have received increasing attention. This is because such “functional dissimilarity measures” capture information on the species' functional traits, which is ignored by traditional coefficients. Therefore, functional dissimilarity measures tend to correlate more strongly with ecosystem‐level processes, as species influence these processes via their traits. In this study, we introduce a new family of dissimilarity measures for presence and absence data, which consider functional dissimilarities among species in the calculation of the matching/mismatching components of the 2 × 2 contingency table. Within this family, the behavior of the Jaccard coefficient, together with its additive components, species replacement, and richness difference, is examined by graphical comparisons and ordinations based on simulated data.     

A comparison of patch connectivity measures using data on invertebrates in hollow oaks

This study aimed at comparing six patch connectivity measures by fitting them to field data. We used occupancy data for eight beetle and two pseudoscorpion species from 281 hollow oaks in southeast Sweden. Species occupancy was modelled in relation to tree characteristics and one measure of patch connectivity at a time. For each connectivity measure we searched for the spatial scale that generated the best fit to field data. Connectivity measures that only include occupied patches provided better model fits than those that include all patches. When occupancy data are absent for surrounding habitat patches, information that reflects occurrence probabilities can be included in the connectivity measure. However, in this study incorporation of such information resulted in only a slight improvement of model fit. A frequently used connectivity measure based on the negative exponential function was relatively poor in explaining species’ occurrence; for eight species out of nine a buffer measure was better. A better fit was obtained when the negative exponential function was modified to take into account that habitat patches may “compete” for the immigrants. The spatial scale with the best fit tended to be larger when we used connectivity measures in which dispersal sources are identified with lower precision. Thus, the outcomes from different multiple‐scale studies are not directly comparable if the density of dispersal sources is not measured in the same way. Overall we conclude that buffer measures are useful, as they give good predictions and are easy to understand and use. If a biologically more realistic measure is needed, one that up‐weights the closest patches should be used. Finally, the possibility that habitat patches may compete with each other for immigrants should be considered when selecting a connectivity measure.     

A multiple-site dissimilarity measure for species presence/absence data and its relationship with nestedness and turnover

Multiple-site dissimilarity may be caused by two opposite processes of meta-community organization, such as species nestedness and turnover. Therefore, discriminating among these contributions is necessary for linking multiple-site dissimilarity to ecosystem functioning. This paper introduces a measure of multiple-site dissimilarity or beta diversity for presence/absence data that is based on information on species absences from the species × sites matrix. It is also shown that the newly proposed dissimilarity index can be additively partitioned into species nestedness and turnover.     

Enhancing the dissimilarity-based classification of birdsong recordings

Classification of birdsong recordings can be naturally formulated as a multiple instance problem, where bags of instances are represented by either features or dissimilarities. In bioacoustics, bags typically correspond to regions of interest in spectrograms, which are detected after a segmentation stage of the audio recordings. In this paper, we use different dissimilarity measures between bags and explore whether the subsequent application of metric learning/adaptation methods and the construction of dissimilarity spaces allow increasing the classification performance of birdsong recordings. A publicly available bioacoustic data set is used for the experiments. Our results suggest, in the first place, that appropriate dissimilarity measures are those which capture most of the overall differences between bags, such as the modified Hausdorff distance and the mean minimum distance; in the second place, they confirm the benefit from adapting the applied dissimilarity measure as well as the potential further enhancement of the classification performance by building dissimilarity spaces and increasing training set sizes.     

Weighted clustering of called array CGH data

Array comparative genomic hybridization (aCGH) is a laboratory technique to measure chromosomal copy number changes. A clear biological interpretation of the measurements is obtained by mapping these onto an ordinal scale with categories loss/normal/gain of a copy. The pattern of gains and losses harbors a level of tumor specificity. Here, we present WECCA (weighted clustering of called aCGH data), a method for weighted clustering of samples on the basis of the ordinal aCGH data. Two similarities to be used in the clustering and particularly suited for ordinal data are proposed, which are generalized to deal with weighted observations. In addition, a new form of linkage, especially suited for ordinal data, is introduced. In a simulation study, we show that the proposed cluster method is competitive to clustering using the continuous data. We illustrate WECCA using an application to a breast cancer data set, where WECCA finds a clustering that relates better with survival than the original one.     

Statistical Measures of DNA Sequence Dissimilarity under Markov Chain Models of Base Composition

In molecular biology, the issue of quantifying the similarity between two biological sequences is very important. Past research has shown that word-based search tools are computationally efficient and can find some new functional similarities or dissimilarities invisible to other algorithms like FASTA. Recently, under the independent model of base composition, Wu, Burke, and Davison (1997, Biometrics 53, 1431 1439) characterized a family of word-based dissimilarity measures that defined distance between two sequences by simultaneously comparing the frequencies of all subsequences of n adjacent letters (i.e., n-words) in the two sequences. Specifically, they introduced the use of Mahalanobis distance and standardized Euclidean distance into the study of DNA sequence dissimilarity. They showed that both distances had better sensitivity and selectivity than the commonly used Euclidean distance. The purpose of this article is to extend Mahalanobis and standardized Euclidean distances to Markov chain models of base composition. In addition, a new dissimilarity measure based on Kullback-Leibler discrepancy between frequencies of all n-words in the two sequences is introduced. Applications to real data demonstrate that Kullback-Leibler discrepancy gives a better performance than Euclidean distance. Moreover, under a Markov chain model of order kQ for base composition, where kQ is the estimated order based on the query sequence, standardized Euclidean distance performs very well. Under such a model, it performs as well as Mahalanobis distance and better than Kullback-Leibler discrepancy and Euclidean distance. Since standardized Euclidean distance is drastically faster to compute than Mahalanobis distance, in a usual workstation/PC computing environment, the use of standardized Euclidean distance under the Markov chain model of order kQ of base composition is generally recommended. However, if the user is very concerned with computational efficiency, then the use of Kullback-Leibler discrepancy, which can be computed as fast as Euclidean distance, is recommended. This can significantly enhance the current technology in comparing large datasets of DNA sequences.     

Similarity measures for structured data: a general framework and some applications to vegetation data

Although there are many measures of similarity existing in the phytosociological literature, these almost all apply to data for which the describing attributes have only single values. In many cases, however, there can be a richer structure in the attribute values, either directly from the nature of the attributes or derived from relationships between the stands. In this paper, I first examine a range of possible sources of such structure in phytosociological data, and then propose a similarity measure sufficiently general to be applicable to all the variant types. Finally I present some examples of applying such measures to frequency data from tropical grasslands and to successional data from subtropical rain forest.     

A method for analysing spatial scales of variation in composition of assemblages

In several areas of research on ecological assemblages, it is useful to be able to analyse patterns of spatial variation at various scales. Multivariate analyses of dissimilarity or similarity in assemblages of species are limited by problems of non-independence caused by repeated use of the sample-units. Where rank-order procedures are used, no comparative quantitative measurements of dissimilarity at different scales are produced. An alternative method is described that uses the sample's average assemblage (or centroid). These estimates are themselves averaged to give centroids for larger spatial scales. Dissimilarities from the centroids at each scale are then calculated using independent replicates for each scale from those in each sample. The dissimilarity measures can then be examined by analysis of variance to detect spatial scales of differences for each sample at every level of a hierarchy of scales. The method is illustrated using data from mangrove forests and rocky shores, involving up to 97 taxonomic groups (species, other taxa). Differences among assemblages at the scales of sites (tens of meters apart) or locations at shores (hundreds of meters apart) were identified. Consequences of different numbers of replicates are discussed, with some potential problems (and their solutions) in application. Received: 14 November 1997 / Accepted: 14 September 1998     

Joint species distribution modelling for spatio‐temporal occurrence and ordinal abundance data

Aim

Species distribution models are important tools used to study the distribution and abundance of organisms relative to abiotic variables. Dynamic local interactions among species in a community can affect abundance. The abundance of a single species may not be at equilibrium with the environment for spreading invasive species and species that are range shifting because of climate change. Innovation : We develop methods for incorporating temporal processes into a spatial joint species distribution model for presence/absence and ordinal abundance data. We model non‐equilibrium conditions via a temporal random effect and temporal dynamics with a vector‐autoregressive process allowing for intra‐ and interspecific dependence between co‐occurring species. The autoregressive term captures how the abundance of each species can enhance or inhibit its own subsequent abundance or the subsequent abundance of other species in the community and is well suited for a ‘community modules’ approach of strongly interacting species within a food web. R code is provided for fitting multispecies models within a Bayesian framework for ordinal data with any number of locations, time points, covariates and ordinal categories.

Main conclusions

We model ordinal abundance data of two invasive insects (hemlock woolly adelgid and elongate hemlock scale) that share a host tree and were undergoing northwards range expansion in the eastern U.S.A. during the period 1997–2011. Accounting for range expansion and high inter‐annual variability in abundance led to improved estimation of the species–environment relationships. We would have erroneously concluded that winter temperatures did not affect scale abundance had we not accounted for the range expansion of scale. The autoregressive component revealed weak evidence for commensalism, in which adelgid may have predisposed hemlock stands for subsequent infestation by scale. Residual spatial dependence indicated that an unmeasured variable additionally affected scale abundance. Our robust modelling approach could provide similar insights for other community modules of co‐occurring species.     

A guide through a family of phylogenetic dissimilarity measures among sites

Ecological studies have now gone beyond measures of species turnover towards measures of phylogenetic and functional dissimilarity. This change of perspective has a main objective: disentangling the processes that drive species distributions from local to broad scales. A fundamental difference between phylogenetic and functional analyses is that phylogeny is intrinsically dependent on a tree‐like structure whereas functional data can, most of time, only be forced to adhere a tree structure, not without some loss of information. When the branches of a phylogenetic tree have lengths, then each evolutionary unit on these branches can be considered as a basic entity on which dissimilarities among sites should be measured. Several of the recent measures of phylogenetic dissimilarities among sites thus are traditional dissimilarity indices where species are replaced by evolutionary units. The resulting indices were named PD‐dissimilarity indices, in reference to early work on the phylogenetic diversity (PD) measure. Here I review and compare indices and ordination approaches that, although first developed to analyse the differences in the species compositions of sites, can be adapted to describe PD‐dissimilarities among sites. Using simulations of species distributions along environmental gradients, I compare indices, associated with permutation tests and null models, in their ability to reveal existing phylogenetic patterns along the gradients. As an illustration, I show that the amount of bat PD‐dissimilarities along a disturbance gradient in Selva Lacandona of Chiapas, Mexico is dependent on whether species' abundance is considered, and on the PD‐dissimilarity index used. Overall, the family of PD‐dissimilarity indices has a critical potential for future analyses of phylogenetic diversity as it benefits from decades of research on the measure of species dissimilarity. I provide clues to help to choose among many potential indices, identifying which indices satisfy minimal basic properties, and analysing their sensitivity to abundance, size, diversity and joint absences.     

Influences of temporal independence of data on modelling species distributions

Modelling species distributions has been widely used to understand present and future potential distributions of species, and can provide adaptation and mitigation information as references for conservation and management under climate change. However, various methods of data splitting to develop and validate functions of the models do not get enough attention, which may mislead the interpretation of predicted results. We used the Taiwanese endemic birds to test the influences of temporal independence of datasets on model performance and prediction. Training and testing data were considered to be independent if they were collected during different survey periods (1993–2004 and 2009–2010). The results indicated no significant differences of six model performance measures (AUC, kappa, TSS, accuracy, sensitivity, and specificity) among the combinations of training and testing datasets. Both species- and grid cell-based assessments differed significantly between predictions by the annual and pooled training data. We also found an average of 85.8% similarity for species presences and absences in different survey periods. The remaining dissimilarity was mostly caused by species observed in the late survey period but not in the early one. The method of data splitting, yielding training and testing data, is critical for resulting model species distributions. Even if similar model performance exists, different methods can lead to different species distributional maps. More attention needs to be given to this issue, especially when amplifying these models to project species distributions in a changing world.     

Multivariate dispersion as a measure of beta diversity

Beta diversity can be defined as the variability in species composition among sampling units for a given area. We propose that it can be measured as the average dissimilarity from individual observation units to their group centroid in multivariate space, using an appropriate dissimilarity measure. Differences in beta diversity among different areas or groups of samples can be tested using this approach. The choice of transformation and dissimilarity measure has important consequences for interpreting results. For kelp holdfast assemblages from New Zealand, variation in species composition was greater in smaller holdfasts, while variation in relative abundances was greater in larger holdasts. Variation in community structure of Norwegian continental shelf macrobenthic fauna increased with increases in environmental heterogeneity, regardless of the measure used. We propose a new dissimilarity measure which allows the relative weight placed on changes in composition vs. abundance to be specified explicitly.     

Evaluating the use of pairwise dissimilarity metrics in paleoanthropology

Questions of alpha taxonomy are best addressed by comparing unknown specimens to samples of the taxa to which they might belong. However, analysis of the hominin fossil record is riddled with methods that claim to evaluate whether pairs of individual fossils belong to the same species. Two such methods, log se_m and the related STET method, have been introduced and used in studies of fossil hominins. Both methods attempt to quantify morphological dissimilarity for a pair of fossils and then evaluate a null hypothesis of conspecificity using the assumption that pairs of fossils that fall beneath a predefined dissimilarity threshold are likely to belong to the same species, whereas pairs of fossils above that threshold are likely to belong to different species. In this contribution, we address (1) whether these particular methods do what they claim to do, and (2) whether such approaches can ever reliably address the question of conspecificity. We show that log se_m and STET do not reliably measure deviations from shape similarity, and that values of these measures for any pair of fossils are highly dependent upon the number of variables compared. To address these issues we develop a measure of shape dissimilarity, the Standard Deviation of Logged Ratios (s_LR). We suggest that while pairwise dissimilarity metrics that accurately measure deviations from isometry (e.g., s_LR) may be useful for addressing some questions that relate to morphological variation, no pairwise method can reliably answer the question of whether two fossils are conspecific.     

Of beta diversity,variance, evenness,and dissimilarity

The amount of variation in species composition among sampling units or beta diversity has become a primary tool for connecting the spatial structure of species assemblages to ecological processes. Many different measures of beta diversity have been developed. Among them, the total variance in the community composition matrix has been proposed as a single‐number estimate of beta diversity. In this study, I first show that this measure summarizes the compositional variation among sampling units after nonlinear transformation of species abundances. Therefore, it is not always adequate for estimating beta diversity. Next, I propose an alternative approach for calculating beta diversity in which variance is substituted by a weighted measure of concentration (i.e., an inverse measure of evenness). The relationship between this new measure of beta diversity and so‐called multiple‐site dissimilarity measures is also discussed.