AIM: The variation in species composition among sites, or beta diversity, can be decomposed into replacement and richness difference. A debate is ongoing in the literature concerning the best ways of ...computing and interpreting these indices. This paper first reviews the historical development of the formulae for decomposing dissimilarities into replacement, richness difference and nestedness indices. These formulae are presented for species presence–absence and abundance using a unified algebraic framework. The indices decomposing beta play different roles in ecological analysis than do beta‐diversity indices. INNOVATION: Replacement and richness difference indices can be interpreted and related to ecosystem processes. The pairwise index values can be summed across all pairs of sites; these sums form a valid decomposition of total beta diversity into total replacement and total richness difference components. Different communities and study areas can be compared: some may be dominated by replacement, others by richness/abundance difference processes. Within a region, differences among sites measured by these indices can then be analysed and interpreted using explanatory variables or experimental factors. The paper also shows that local contributions of replacement and richness difference to total beta diversity can be computed and mapped. A case study is presented involving fish communities along a river. MAIN CONCLUSIONS: The different forms of indices are based upon the same functional numerators. These indices are complementary; they can help researchers understand different aspects of ecosystem functioning. The methods of analysis used in this paper apply to any of the indices recently proposed. Further work, based on ecological theory and numerical simulations, is required to clarify the precise meaning and domain of application of the different forms. The forms available for presence–absence and quantitative data are both useful because these different data types allow researchers to answer different types of ecological or biogeographic questions.
Aim
This paper presents the statistical bases for temporal beta‐diversity analysis, a method to study changes in community composition through time from repeated surveys at several sites. Surveys of ...that type are presently done by ecologists around the world. A temporal beta‐diversity Index (TBI) is computed for each site, measuring the change in species composition between the first (T1) and second surveys (T2). TBI indices can be decomposed into losses and gains; they can also be tested for significance, allowing one to identify the sites that have changed in composition in exceptional ways. This method will be of value to identify exceptional sites in space–time surveys carried out to study anthropogenic impacts, including climate change.
Innovation
The null hypothesis of the TBI test is that a species assemblage is not exceptionally different between T1 and T2, compared to assemblages that could have been observed at this site at T1 and T2 under conditions corresponding to H0. Tests of significance of coefficients in a dissimilarity matrix are usually not possible because the values in the matrix are interrelated. Here, however, the dissimilarity between T1 and T2 for a site is computed with different data from the dissimilarities used for the T1–T2 comparison at other sites. It is thus possible to compute a valid test of significance in that case. In addition, the paper shows how TBI dissimilarities can be decomposed into loss and gain components (of species, or abundances‐per‐species) and how a B–C plot can be produced from these components, which informs users about the processes of biodiversity losses and gains through time in space–time survey data.
Main conclusion
Three applications of the method to different ecological communities are presented. This method is applicable worldwide to all types of communities, marine, and terrestrial. R software is available implementing the method.
This paper describes a new method, temporal beta‐diversity analysis, to study the changes in community composition through time from repeated surveys at several sites. (a) A temporal beta‐diversity Index (TBI) is computed for each site, measuring the change in species composition between the first and second surveys. TBI indices can be tested for significance, allowing one to identify the sites that have changed in composition in exceptional ways. (b) It is often of interest to examine the species loss and gain components of the TBI indices because change through time is directional. Graphical procedures are demonstrated. Several examples from the ecological literature are provided.
The Ward error sum of squares hierarchical clustering method has been very widely used since its first description by Ward in a 1963 publication. It has also been generalized in various ways. Two ...algorithms are found in the literature and software, both announcing that they implement the Ward clustering method. When applied to the same distance matrix, they produce different results. One algorithm preserves Ward’s criterion, the other does not. Our survey work and case studies will be useful for all those involved in developing software for data analysis using Ward’s hierarchical clustering method.
This review focuses on the analysis of temporal beta diversity, which is the variation in community composition along time in a study area. Temporal beta diversity is measured by the variance of the ...multivariate community composition time series and that variance can be partitioned using appropriate statistical methods. Some of these methods are classical, such as simple or canonical ordination, whereas others are recent, including the methods of temporal eigenfunction analysis developed for multiscale exploration (i.e. addressing several scales of variation) of univariate or multivariate response data, reviewed, to our knowledge for the first time in this review. These methods are illustrated with ecological data from 13 years of benthic surveys in Chesapeake Bay, USA. The following methods are applied to the Chesapeake data: distance-based Moran's eigenvector maps, asymmetric eigenvector maps, scalogram, variation partitioning, multivariate correlogram, multivariate regression tree, and two-way MANOVA to study temporal and space–time variability. Local (temporal) contributions to beta diversity (LCBD indices) are computed and analysed graphically and by regression against environmental variables, and the role of species in determining the LCBD values is analysed by correlation analysis. A tutorial detailing the analyses in the R language is provided in an appendix.
A new framework for measuring functional diversity (FD) from multiple traits has recently been proposed. This framework was mostly limited to quantitative traits without missing values and to ...situations in which there are more species than traits, although the authors had suggested a way to extend their framework to other trait types. The main purpose of this note is to further develop this suggestion. We describe a highly flexible distance‐based framework to measure different facets of FD in multidimensional trait space from any distance or dissimilarity measure, any number of traits, and from different trait types (i.e., quantitative, semi‐quantitative, and qualitative). This new approach allows for missing trait values and the weighting of individual traits. We also present a new multidimensional FD index, called functional dispersion (FDis), which is closely related to Rao's quadratic entropy. FDis is the multivariate analogue of the weighted mean absolute deviation (MAD), in which the weights are species relative abundances. For unweighted presence–absence data, FDis can be used for a formal statistical test of differences in FD. We provide the “FD” R language package to easily implement our distance‐based FD framework.
The Mantel correlogram is an elegant way to compute a correlogram for multivariate data. However, recent papers raised concerns about the power of the Mantel test itself. Hence the question: Is the ...Mantel correlogram powerful enough to be useful? To explore this issue, we compared the performances of the Mantel correlogram to those of other methods, using numerical simulations based on random, normally distributed data. For a single response variable, we compared it to the Moran and Geary correlograms. Type I error rates of the three methods were correct. Power of the Mantel correlogram was nearly as high as that of the univariate methods. For the multivariate case, the test of the multivariate variogram developed in the context of multiscale ordination is in fact a Mantel test, so that the power of the two methods is the same by definition. We devised an alternative permutation test based on the variance, which yielded similar results. Overall, the power of the Mantel test was high, the method successfully detecting spatial correlation at rates similar to the permutation test of the variance statistic in multivariate variograms. We conclude that the Mantel correlogram deserves its place in the ecologist's toolbox.
This article presents a new implementation of hierarchical clustering for the R language that allows one to apply spatial or temporal contiguity constraints during the clustering process. The need ...for contiguity constraint arises, for instance, when one wants to partition a map into different domains of similar physical conditions, identify discontinuities in time series, group regional administrative units with respect to their performance, and so on. To increase computation efficiency, we programmed the core functions in plain C. The result is a new R function, constr.hclust, which is distributed in package adespatial. The program implements the general agglomerative hierarchical clustering algorithm described by Lance and Williams (1966; 1967), with the particularity of allowing only clusters that are contiguous in geographic space or along time to fuse at any given step. Contiguity can be defined with respect to space or time. Information about spatial contiguity is provided by a connection network among sites, with edges describing the links between connected sites. Clustering with a temporal contiguity constraint is also known as chronological clustering. Information on temporal contiguity can be implicitly provided as the rank positions of observations in the time series. The implementation was mirrored on that found in the hierarchical clustering function hclust of the standard R package stats (R Core Team 2022). We transcribed that function from Fortran to C and added the functionality to apply constraints when running the function. The implementation is efficient. It is limited mainly by input/output access as massive amounts of memory are potentially needed to store copies of the dissimilarity matrix and update its elements when analyzing large problems. We provided R computer code for plotting results for numbers of clusters.
Ecologists often face the task of studying the association between single species and one or several groups of sites representing habitat types, community types, or other categories. Besides ...characterizing the ecological preference of the species, the strength of the association usually presents a lot of interest for conservation biology, landscape mapping and management, and natural reserve design, among other applications. The indices most frequently employed to assess these relationships are the phi coefficient of association and the indicator value index (IndVal). We compare these two approaches by putting them into a broader framework of related measures, which includes several new indices. We present permutation tests to assess the statistical significance of species–site group associations and bootstrap methods for obtaining confidence intervals. Correlation measures, such as the phi coefficient, are more context‐dependent than indicator values but allow focusing on the preference of the species. In contrast, the two components of an indicator value index directly assess the value of the species as a bioindicator because they can be interpreted as its positive predictive value and sensitivity. Ecologists should select the most appropriate index of association strength according to their objective and then compute confidence intervals to determine the precision of the estimate.
Indicator species are species that are used as ecological indicators of community or habitat types, environmental conditions, or environmental changes. In order to determine indicator species, the ...characteristic to be predicted is represented in the form of a classification of the sites, which is compared to the patterns of distribution of the species found at the sites. Indicator species analysis should take into account the fact that species have different niche breadths: if a species is related to the conditions prevailing in two or more groups of sites, an indicator species analysis undertaken on individual groups of sites may fail to reveal this association. In this paper, we suggest improving indicator species analysis by considering all possible combinations of groups of sites and selecting the combination for which the species can be best used as indicator. When using a correlation index, such as the point-biserial correlation, the method yields the combination where the difference between the observed and expected abundance/frequency of the species is the largest. When an indicator value index (IndVal) is used, the method provides the set of site-groups that best matches the observed distribution pattern of the species. We illustrate the advantages of the method in three different examples. Consideration of combinations of groups of sites provides an extra flexibility to qualitatively model the habitat preferences of the species of interest. The method also allows users to cross multiple classifications of the same sites, increasing the amount of information resulting from the analysis. When applied to community types, it allows one to distinguish those species that characterize individual types from those that characterize the relationships between them. This distinction is useful to determine the number of types that maximizes the number of indicator species.
PDF
