On non-linear species response models in ordination

Ordination techniques are plagued by the non-linearity of vegetation data. The purpose of ordination is discussed and considered to be the process of arranging samples (or species) in relation to one or more environmental gradients or abstract axes that may represent such gradients, the arrangement to be ecologically significant. The appropriateness of various models of vegetation to current ordination techniques is considered, particularly the gaussian species response curve. Two alternatives are suggested based on -functions and an ecological response curve model incorporating competition between species.     

Multivariate analysis of benthic invertebrate communities: the implication of choosing particular data standardizations,measures of association,and ordination methods

Benthic invertebrate data from thirty-nine lakes in south-central Ontario were analyzed to determine the effect of choosing particular data standardizations, resemblance measures, and ordination methods on the resultant multivariate summaries. Logarithmic-transformed, 0–1 scaled, and ranked data were used as standardized variables with resemblance measures of Bray-Curtis, Euclidean distance, cosine distance, correlation, covariance and chi-squared distance. Combinations of these measures and standardizations were used in principal components analysis, principal coordinates analysis, non-metric multidimensional scaling, correspondence analysis, and detrended correspondence analysis. Correspondence analysis and principal components analysis using a correlation coefficient provided the most consistent results irrespective of the choice in data standardization. Other approaches using detrended correspondence analysis, principal components analysis, principal coordinates analysis, and non-metric multidimensional scaling provided less consistent results. These latter three methods produced similar results when the abundance data were replaced with ranks or standardized to a 0–1 range. The log-transformed data produced the least consistent results, whereas ranked data were most consistent. Resemblance measures such as the Bray-Curtis and correlation coefficient provided more consistent solutions than measures such as Euclidean distance or the covariance matrix when different data standardizations were used. The cosine distance based on standardized data provided results comparable to the CA and DCA solutions. Overall, CA proved most robust as it demonstrated high consistency irrespective of the data standardizations. The strong influence of data standardization on the other ordination methods emphasizes the importance of this frequently neglected stage of data analysis.     

Maximum-likelihood ordination — some improvements and further tests

A modification to a previously described maximum likelihood approach to non-linear ordination is presented. It involves weighting quantitative measures of species importance to ensure that changes in values along a gradient are given equal weight irrespective of their magnitude. The maximum likelihood method was tested with artificial data based on a model incorporating various types of non-linear species responses. Symmetrical and asymmetrical response surfaces, with and without central depression, were used and the method was shown to be reasonably robust. In tests on both real and artificial data it proved superior to other methods.     

广西英罗港红树植物群落的非线性排序

采用主分量分析 (PCA)、无偏主分量 (DPC)和非度量多维调节 (NMDS)等方法对广西英罗港 2 2个红树植物群落样地进行了排序。PCA和 DPC分析结果表明 ,取样数据具有明显的非线性结构。通过 NMDS分析 ,得到二维 NMDS排序格局 ,它能较好地反映了红树植物群落与环境因子之间的相互关系。     

Reconstructing community relationships: the impact of sampling error, ordination approach, and gradient length

Effectively summarizing complex community relationships is an important feature in studies such as biodiversity, global change, and invasion ecology. The reliability of such community summaries depends on the degree of sampling variability that is present in the data, the structure of the data, and the choice of ordination method, but the relative importance of these factors is not understood. We compared the validity of results from different ordination methods by applying five levels of sampling error to a simulated coenoplane model at two gradient lengths using two types of data (abundance and presence–absence). The multivariate methods we compared were correspondence analysis (CA), detrended correspondence analysis (DCA), non-metric multidimensional scaling (NMDS), principal component analysis (PCA) and principal coordinates analysis (PCoA). Our results showed CA and PCA using presence–absence data were the most successful methods regardless of sampling error and gradient length, closely followed by the other methods using presence–absence data. With abundance data, PCA and CA were the most successful approaches with the short and long gradients, respectively. Approaches based on PCoA and NMDS using abundance data did not perform well regardless of the choice of distance measure used in the analysis. Both of these methods, along with the PCA using abundance data, were strongly affected by the longer gradient, leading to more distorted results.     

A paired-quadrat method for use in multiscale ordination

Multiscale ordination is a technique for examining spatial patterns of several species at several scales. We present a paired-quadrat method (paired quadrat covariance; PQC) to be used in multiscale ordination and test it with artificial data. Multiscale ordination with PQC successfully extracted the salient features of the data set. The method appears to be more sensitive than blocked-quadrat techniques for extracting small-scale patterns. We suggest that PQC will be useful as a complement to existing procedures or as a tool for analysing data from scattered quadrat arrangements.Abbreviations PQC = Paired Quadrat Covariance - PQV = Paired Quadrat Variance - TTLC = Two-Term Local Covariance - TTLQV = Two-Term Local Quadrat Variance     

排序和广义线性模型与广义可加模型在植物种与环境关系研究中的应用

排序和广义线性模型(Generalized Linear Model,GLM)与广义可加模型(Goneralized Additive Model,GAM)是研究植物种与环境间关系的重要方法。基于线性模型的排序方法应限定于环境梯度较短的植被数据。而基于单峰模型的排序方法更适用于梯度较长的情况。PCA、CA／RA系列和CCA系列是常用的排序方法。同时进行环境数据和植被数据分析的CCA系列,能清楚地得出植物种与环境间的关系。CCA改进后的DCCA和PCCA,是现今较理想的排序方法。GLM和GAM实质上是用环境变量的高阶多项式来拟合植物种与环境变量的关系。GLM和GAM扩展了植物种与环境变量之间的关系模型,能深入地探讨植物种与环境间的关系。GLM主要是模型决定的,而GAM主要取决于原始数据。一般来说,排序能得出研究区域的主要环境梯度,提供了物种聚集和植物群落的概略描述。GLM与GAM对于深入研究单个植物种与环境间的关系具有优势。在实际研究中,两种方法结合使用能互补不足。     

Finding a common ordination for several data sets by individual differences scaling

Individual differences scaling is a multidimensional scaling method for finding a common ordination for several data sets. An individual ordination for each data set can then be derived from the common ordination by adjusting the axis lengths so as to maximize the correlations between observed proximities and individual ordination distances. The importance of the various axes for each data set and the mutual similarities and goodness of fit for the individual data sets are described by weight plots. As an example, 46 soft-water lakes in eastern Finland are ordinated on two dimensions according to 3 chemical data sets (water in summer and autumn, sediment) and 4 biological sets (major phytoplankton groups, phytoplankton, surface sediment diatom and cladoceran assemblages). The method seems to be effective as a means of ordination for obtaining the common ordination for the data sets. The major taxonomic groups gave the ordination which differed most clearly from the ordinations of the other data sets. Phytoplankton was most poorly ordinated in all the analyses. The other data sets were fairly coherent. When only biological data sets were ordinated, the diatoms and cladocerans showed rather different patterns. It seems that the cladocerans are best correlated with water chemistry, both according to weights in the joint analysis, and according to correlation between the axes from the biological data sets and the chemical variables.Abbreviations CCA = Canonical correspondence analysis - IDS = Individual differences scaling - MDS = multidimensional scaling - PCA = Principal components analysis     

Detrended correspondence analysis: An improved ordination technique

Summary Detrended correspondence analysis (DCA) is an improvement upon the reciprocal averaging (RA) ordination technique. RA has two main faults: the second axis is often an arch or horseshoe distortion of the first axis, and distances in the ordination space do not have a consistent meaning in terms of compositional change (in particular, distances at the ends of the first RA axis are compressed relative to the middle). DCA corrects these two faults. Tests with simulated and field data show DCA superior to RA and to nonmetric multidimensional sealing in giving clear, interpretable results. DCA has several advantages. (a) Its performance is the best of the ordination techniques tested, and both species and sample ordinations are produced simultaneously. (b) The axes are scaled in standard deviation units with a definite meaning, (c) As implemented in a FORTRAN program called DECORANA, computing time rises only linearly with the amount of data analyzed, and only positive entries in the data matrix are stored in memory, so very large data sets present no difficulty. However, DCA has limitations, making it best to remove extreme outliers and discontinuities prior to analysis. DCA consistently gives the most interpretable ordination results, but as always the interpretation of results remains a matter of ecological insight and is improved by field experience and by integration of supplementary environmental data for the vegetation sample sites.This research was supported by the Institute of Terrestrial Ecology, Bangor, Wales, and by a grant from the National Science Foundation to R.H. Whittaker. We thank R.H. Whittaker for encouragement and comments, S.B. Singer for assistance with the Cornell computer, and H.J.B. Birks, S.R. Sabo, T.C.E. Wells, and R.H. Whittaker for data sets used for ordination tests.     

Ordination methods and chironomid species in stony bottom streams

Stony bottom streams in Italy were sampled in 369 sites in different years, and 174 chironomid species (or species groups) were identified.The species by sites matrix was submitted to different ordination methods, with the aim of outlining the major factors that are responsible of the observed species composition.The methods considered were principal component analysis (PCA), detrended correspondence analysis (DCA) and non-metric multidimensional scaling (MDSCAL). These methods assume different models describing the species-responses to the environmental gradients.PCA gave poor results, the best species ordination was given by MDSCAL. DCA gave results in agreement with MDSCAL. DCA results were useful as a starting point to perform MDSCAL. MDSCAL was performed with different options. At last Procrustean analysis was carried out to have a single fitted configuration, that summarized the results given by the different MDSCAL methods.All multivariate analyses emphasized that the first ordination axis can be interpreted as a crenonrithron-potamon gradient, probably an oxygen availability and/or a water temperature gradient, whereas the second axis can be considered a water speed gradient, separating lotic from lentic sites.The 3rd and 4th ordination axes had apparently no ecological meaning.Separated clusters of species were never evident, so well defined chironomid species assemblages could not be outlined in this analysis.     

A seriation method for summarizing vegetation-environment relationships

A computer program is described for producing site-species tables termed seriation arrays. Sites can be ordered according to sequences in direct habitat gradients, indirect site ordination axes, and trends oblique to the axes of an indirect site ordination. A ² technique is used to filter species for restriction to segments of each site sequence, retaining only accepted species in the construction of arrays.     

Modelling the potential effects of climate change on calcareous grasslands in Atlantic Europe

Aim This study aims to assess the sensitivity of calcareous grassland vegetation to climate change and to indicate the most probable direction of change. Location The study area was a region of Britain, Ireland, France and Spain, centred on the Bay of Biscay, which was defined using a land classification based on climatic criteria. Methods Vegetation was sampled in the field, with additional data collected on soils, climate, management and land cover. The vegetation samples were ordinated by detrended correspondence analysis in order to explore the main gradients present and as a basis for modelling changes. Environmental data were summarized by ordination techniques, with the scores generated used to predict the current vegetation score on the first two ordination axes by multiple regression. The model was then manipulated to represent a 2 °C increase in temperature and resulting shifts in the vegetation samples in terms of their species composition assessed. Results There was a good general agreement between the original vegetation ordination axis scores and those predicted by the model, the latter of which were based on environmental data alone. Following a 2 °C increase in temperature, the predicted changes in the ordination space were demonstrated to be subtle, consisting of small shifts towards vegetation associated with warmer conditions, representing distances 100 km or less on the ground. Main conclusions The models are simple but nevertheless provide a useful basis for the investigation of potential vegetation change. The shifts in the ordination space represent more minor changes than those predicted in previous studies. This suggests that the potential for major change is lower when environmental factors such as soil and management are considered in addition to climate. The potential for change is also reduced when vegetation is considered as a whole rather than on an individual species basis, due to both interspecific interactions and interactions with environmental factors acting as constraints.     

Environmental diversity: on the best-possible use of surrogate data for assessing the relative biodiversity of sets of areas

The conservation goal of representation of biodiversity (in the broad sense of all species) in protected areas requires best-possible use of available surrogate information. One standard approach is based on indicator groups of taxa. A minimum set of areas having at least one representation of each indicator species is taken to be representative of other organisms. This same minimum-set approach is adapted to other attributes of biodiversity, for example, derived environmental clusters. A weakness of these approaches is that useful information is lost; for example, for environmental clusters, there is no distinction made either among or within clusters. A more powerful surrogate approach can use some expression of environmental and/or biotic pattern so that variation among areas is seen as part of a continuum rather than partitioned into arbitrary clusters/attributes. The challenge in using pattern effectively is to adopt a robust model for the relationship between pattern and the underlying units of biodiversity, i.e. species. An environmental space (a continuum or ordination pattern), combined with the standard ecological continuum model relating species to environmental space, has advantages over other patterns based on hierarchy or distance matrices. Because an environmental space can be estimated either directly (observed environmental data) or indirectly (data on indicator groups), the corresponding surrogate-measure of biodiversity, environmental diversity (ED) makes best-possible use of either kind of data. We conclude that the arbitrariness of the attribute approach can be replaced by a robust surrogate pattern approach that is flexible and avoids unwarranted assumptions.     

On non-metric multidimensional scaling ordination and interpretation of the matorral vegetation in lowland Murcía

The plant-environment relationships in a range of matorral communities, having different rainfall conditions in semi-arid lowland habitats in Murcía, S.E. Spain, were examined using the non-metric multidimensional scaling ordination technique. Hypotheses on floristic variations were derived based on an interpretative strategy which involved a site configuration rotation, followed by stepwise multiple regression analysis. An environmental data set was used to isolate variables associated with site co-ordinate trends. Results showed that floristic variation in these communities was mainly determined by aspect induced radiation receipt. Besides, most environmental trends in the study areas were found to be oblique to original site ordination axes and configuration rotation seemed to be a prerequisite in quantitative interpretation. The interpretative strategy introduced in this study was effective. It enhanced straightforward, quantitative and objective interpretation whereby inductive inferences on environmental trends could be readily formulated.Abbreviations ARAD radiation receipt surrogate - DEPTH soil depth - DISTURB disturbance index - NMDS non-metric multidimensional scaling - NUT nutrient scalar - SLOPE slope angle - TEXTIN texture index     

Evaluating and presenting uncertainty in model‐based unconstrained ordination

Variability in ecological community composition is often analyzed by recording the presence or abundance of taxa in sample units, calculating a symmetric matrix of pairwise distances or dissimilarities among sample units and then mapping the resulting matrix to a low‐dimensional representation through methods collectively called ordination. Unconstrained ordination only uses taxon composition data, without any environmental or experimental covariates, to infer latent compositional gradients associated with the sampling units. Commonly, such distance‐based methods have been used for ordination, but recently there has been a shift toward model‐based approaches. Model‐based unconstrained ordinations are commonly formulated using a Bayesian latent factor model that permits uncertainty assessment for parameters, including the latent factors that correspond to gradients in community composition. While model‐based methods have the additional benefit of addressing uncertainty in the estimated gradients, typically the current practice is to report point estimates without summarizing uncertainty. To demonstrate the uncertainty present in model‐based unconstrained ordination, the well‐known spider and dune data sets were analyzed and shown to have large uncertainty in the ordination projections. Hence to understand the factors that contribute to the uncertainty, simulation studies were conducted to assess the impact of additional sampling units or species to help inform future ordination studies that seek to minimize variability in the latent factors. Accurate reporting of uncertainty is an important part of transparency in the scientific process; thus, a model‐based approach that accounts for uncertainty is valuable. An R package, UncertainOrd , contains visualization tools that accurately represent estimates of the gradients in community composition in the presence of uncertainty.     

Data transformation as a scaling operation in ordination of plankton

Data transformation is seen here as an aspect of scaling such that we are less interested in the quirks and properties of each transformation but are more concerned with the general scaling properties and trends of suites of transformations.Over two years of daily phytoplankton abundance data for 30 species from a temperate lake (Llyn Maelog, North Wales) were subjected to a series of scale-ordered transformations. Two major classes of transformation were systematically varied: binary and smoothing. Binary transformation scaled the cutoff threshold between presence and absence of a species to various levels of abundance.With successively smaller universes and smoothing windows and successive species exclusion, ordinations of sample dates revealed smaller scaled structures in the order: annual cycles of species turnover, seasonal areas of attraction and uniqueness of individual sample dates. Gradual increases in the length of the smoothing window resulted in gradual shifts in the positions of points in sample data ordination, but not necessarily in the species ordinations. Thus sample data structures are more stable with change in scale than are species data structures. These differences in stability are discussed in the context of filtering characteristics of data collection and data analysis. Transformations producing similar species statistics (means, variances and skews) did not generally give similar ordination results, while some transformations giving similar ordinations differed in species statistical parameters.Acknowledgement: The present research was supported by a grant from the National Science foundation (NSF DEB 78-07546) to the first author.     

Land-use influence on stream water quality and diatom communities in Victoria, Australia: a response to secondary salinization

Diatom communities were analyzed in 39 streams located in drainages with varied land-use practices throughout Victoria, Australia. Thirteen water quality parameters were also measured in each stream. Most streams had low HCO₃ ^1- concentrations (low buffering capacity) with >90% of the waters dominated by Na¹⁺ and Cl^1-. Phosphate concentrations ranged from 0.003 to 2.0 mg/L. Diatom communities (245 taxa) were strongly correlated with land-use practices, i.e. historic clear cutting, and secondary salinization. Streams influenced by heavy irrigation practices and dryland farming had reduced species diversity and richness compared to systems with low to moderate land use. A nonmetric multidimensional ordination of diatom communities in the 39 streams was conducted. An ANOSIM on the ordination showed that diatom communities in upland watersheds with native forest canopies and low salinization, lowland streams in watersheds with cleared forest canopies, moderate agricultural utilization and salinization, and lowland streams in areas with high irrigation and salinization were all significantly different (p<0.001) from one another. Community ordination techniques showed that both specific conductance (salinity) and phosphorus interacted to determine stream diatom community structure in drainages with high secondary salinization. Drainages with low to moderate agricultural activity and low nutrients, but with a wide range of salinities showed strong associations with the diatom taxa Amphora coffeaeformis, Cymbella pusilla and Entomoneis paludosa, whereas, streams in regions with heavy agricultural practices and high phosphorus had Bacillaria paradoxa, Nitzschia hungarica, N. frustulum and Aulacoseira granulata as numerically important diatoms. In contrast, Rhizosolenia eriensis, Frustulia rhomboides, Eunotia pectinatus and Tabellaria flocculosa were strongly associated with upland streams with fast current, relatively low O-PO₄ ^3- concentrations, low pH, low salinity, and low temperature. In general, the diatom communities in saline streams (3 mS) were similar to those previously reported in saline lakes in Victoria.     

A maximum likelihood approach to non-linear ordination

Summary A non-linear method of ordinating vegetation samples based on the fitting of bell-shaped response curves is lescribed. For each species two Gaussian curves were itted, one to quantitative values, where the species was present, the other to probabilities of absence. A maximum likelihood approach was then used to obtain a best approximation of the positions of the samples along a one-dimensional gradient. By an iterative process successively better approximations were obtained.The method was successful in recovering gradients based on hypothetical data. With two sets of real data the gradient produced was more ecologically satisfying and far less distorted than that revealed by principal component analysis.     

SYSTEMATICS AND BIOGEOGRAPHY OF THE AUSTRALIAN "GREEN ASH" EUCALYPTS (MONOCALYPTUS)

Abstract— A cladistic analysis of the "green ash" eucalypts, informal subgenus " Monocalyptus ", is presented- As a first step, ordination methods of principal coordinates analysis and multidimensional scaling delineated some terminal taxa. The cladistic analysis, applying parsimony methods to the unweighted data set, yielded 25 equally parsimonious trees, each with a consistency index of 0.57.
Farris' successive approximations approach to character weighting produced one tree with a consistency index of 0.74.
An informal classification of the group, superseries Eucalyptus , is based on that cladogram. The biogeographic history of superseries Eucalyptus is interpreted from the cladogram as having been caused by lour vicariant events in southeastern Australia, in combination with a suite of ecological features that overlie the biogeographic area-pattern.