Spectral analysis of a Plio-Pleistocene multispecies time series using the Mantel periodogram

A simple method for the spectral analysis of multispecies microfossil data through time or stratigraphic level is presented. The method is based on the Mantel correlogram, allowing any ecological similarity measure to be used. The method can therefore be applied to binary (presence-absence) data as well as raw or normalized species counts. In contrast with spectral analysis of univariate ordination scores, this approach does not explicitly discard information. The method, referred to as the Mantel periodogram, is exemplified with a data set from the literature, demonstrating several astronomically forced periodicities in microfaunal data from the Plio-Pleistocene.     

Community pattern analysis: A method for quantifying community mosaic structure

A method of quantifying community spatial patterns, community pattern analysis, is described. It is proposed that ordination analysis is used to obtain an integrated score for each quadrat from transect data. For the data presented here, separate ordinations were made of both floristic and environmental (soils) data. The ordination axis scores are then analysed using two or three-term local variance analysis to quantify the scales of community pattern. Correlation analyses allow the relationship between the vegetation and soils data (as represented by ordination axis scores), and other environmental data to be investigated at defined scales. The advantages of this method, that employs the joint application of conventional methods, are that it includes the influence of all species in the analysis, and that multiple uncorrelated scales of pattern within a community are identified.     

宜昌百里荒草山草坡群落物种分布的空间趋势分析

通过基于CCA的趋势面分析和空间插值方法,研究了宜昌百里荒山地草场的群落结构空间变化,以及群落结构空间趋势与主要环境因子的相关性。结果表明,该群落物种空间中的群落结构面和物理空间中的空间趋势面可以很好地吻合,说明该群落的结构由一种具有强烈空间结构化特征的机制控制。对群落结构和空间趋势影响最显著的环境因素是土壤有效磷。     

A new approach to the discrimination of chirotherioid ichnospecies by means of multivariate statistics. Triassic eastern border of the French Massif Central

Rotated principal components analysis is used to clarify the morphology and taxonomy of Chirotheriod footprints. It reveals that the best characteristic for separating out the footprints is a combination of increasing size of the prints and increasing spread of the digits. Reasonably coherent neighbourhoods of the traditionally recognised species are displayed by the component scores. The resulting ordination of the species reflects an evolutionary trend through the Triassic.     

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.     

Ordination and classification of operational geographic units in Southwest Sweden

The vascular plant distributions of Dalsland and northern Bohuslän (Southwest Sweden) were subjected to multivariate analyses in order to delimit geographically coherent floristic zones. 271 squares of 5×5 km were the Operational Geographic Units; the data matrix comprises presence/absence species records for each OGU. Different ordination and classification methods were tested and detailed results are presented for detrended correspondence analysis (DCA), UPGMA and ordination space partitioning (OSP). A weighting procedure, neighbour-weighting, which gives pseudo-frequency scores along the nominal scale 0–9 depending on the species' distribution patterns, is introduced. The superior method for delimiting geographically coherent floristic zones was judged to be ordination space partitioning, using DCA and neighbour-weighted species scores.Abbreviations DCA Detrended Correspondence Analysis - OGU Operational Geographical Unit - OSP Ordination Space Partitioning - UPGMA Unweighted Pair-Group Method using Arithmetic Averages     

Analyzing floristic inventories with multiple maps

Spatial observations of plant occurrences contain a wealth of information on relations among species and on the relation between species and environmental conditions. Typically, inventory data of this kind are large co-occurrence matrices, and hence, direct ecological interpretations based on expert knowledge are often very difficult. Hitherto, ordination approaches have been used to construct a virtual ordination space (represented as one or multiple scatter plots) in which species that often co-occur are situated close together, whereas species that hardly co-occur are found far apart. In this study, we investigate a recently proposed ordination approach, multiple maps t-SNE, that constructs multiple, independent ordination spaces in order to reveal and visualize complementary structure in the data. We compare multiple maps t-SNE to several conventional ordination approaches, exploring a large inventory of vascular plant occurrences (FLORKART). Our results reveal that multiple maps t-SNE is well suited for the analysis of floristic inventories. In particular, multiple maps t-SNE uncovers the major dependencies of species co-occurrences on climate and soil biogeochemical preconditions.     

草海国家级自然保护区水生植物群落的数量分类与排序分析

在群落样方调查的基础之上,采用双向指示种分析法（TW INSPAN）和除趋势对应分析（DCA）对草海国家级自然保护区水生植物群落进行分类和排序。TW INSPAN将50个样方分为17组,根据植被分类的原则划分为17个群丛,论述了各个群丛的群落学特征。50个样方的DCA排序结果反映了植物群落类型与环境梯度之间的关系,表明影响群落分布格局的主导生态因子为水分条件,第一轴反映了各个群落类型所在的水分条件梯度。排序结果与分类结果较吻合,反映出植物群落类型和物种分布随环境因子梯度变化的趋势。     

A New Multivariate Approach to Studying Temporal Changes of Vegetation

We emphasize the necessity of a complex approach to evaluating vegetation change at various levels of abstraction. The analytical steps include comparisons at the data, derived variable, distance, ordination and classification levels. A variety of data randomization methods incorporated in testing the significance of changes in raw data are introduced and compared. It is shown that these are true alternatives to Procrustean comparisons, which offer an apparently unfortunate choice in the presence/absence case. We propose to evaluate nearest neighbor relationships among quadrats in a new method, called adjacency analysis, to detect temporal trends that may remain unrevealed, should our attention be paid to full distance structures only. As an illustration, compositional and structural changes in the rock grassland vegetation of the Sas-hegy Nature Reserve (Budapest, Hungary), intensively sampled by quadrats in 1977 and 2000, are evaluated. Permutation tests show that differences between the 2 years are much smaller than expected by chance alone. Such an overall stability in community structure, however, does not mean that minor aspects of vegetation pattern are invariant over the years. Changes in life form and seed mass spectra are explained by the fluctuation of hemicryptophytes and the slight but detectable expansion of annuals and woody species. Classification is slightly rearranged in time, with clearly detectable within-cluster changes, also depicted in ordination scattergrams.     

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。     

Elements of metacommunity structure of Paraguayan bats: multiple gradients require analysis of multiple ordination axes

Techniques to evaluate elements of metacommunity structure (EMS; coherence, species turnover and range boundary clumping) have been available for several years. Such approaches are capable of determining which idealized pattern of species distribution best describes distributions in a metacommunity. Nonetheless, this approach rarely is employed and such aspects of metacommunity structure remain poorly understood. We expanded an extant method to better investigate metacommunity structure for systems that respond to multiple environmental gradients. We used data obtained from 26 sites throughout Paraguay as a model system to demonstrate application of this methodology. Using presence–absence data for bats, we evaluated coherence, species turnover and boundary clumping to distinguish among six idealized patterns of species distribution. Analyses were conducted for all bats as well as for each of three feeding ensembles (aerial insectivores, frugivores and molossid insectivores). For each group of bats, analyses were conducted separately for primary and secondary axes of ordination as defined by reciprocal averaging. The Paraguayan bat metacommunity evinced Clementsian distributions for primary and secondary ordination axes. Patterns of species distribution for aerial insectivores were dependent on ordination axis, showing Gleasonian distributions when ordinated according to the primary axis and Clementsian distributions when ordinated according to the secondary axis. Distribution patterns for frugivores and molossid insectivores were best described as random. Analysis of metacommunities using multiple ordination axes can provide a more complete picture of environmental variables that mold patterns of species distribution. Moreover, analysis of EMS along defined gradients (e.g., latitude, elevation and depth) or based on alternative ordination techniques may complement insights based on reciprocal averaging because the fundamental questions addressed in analyses are contingent on the ordination technique that is employed.     

The ecology of Araucaria species in New Guinea. I. Ordination studies of forest types and environments

Previous studies of the ecology and regeneration strategies of Araucaria cunninghamii and A. hunsteinii in New Guinea rainforests have treated these species as ecologically identical and disagree concerning their ability to maintain a stable population size in forest communities dominated by angiosperms. Vegetation data from a number of 0.5 ha forest sites in New Guinea are analysed in order to characterize forest types and their environmental regimes in the altitudinal zone from 700 to 1500 m a.s.l. Particular attention is paid to forests containing Araucaria species. Nodal component analysis identifies a number of distinct forest types or ‘series’, each dominated by a different species. Continuity analysis displays the location of sites and species in non-linear ordination space. Subsequent regression of environmental data on the position of sites in ordination space shows that forest types are separated along gradients related to altitude and rainfall on the one hand, and soil nutrient concentrations on the other. A. cunninghamii is generally found in wetter and less nutrient-rich sites than A. hunsteinii. The analysis of species presence data, as opposed to quantitative data, shows that whilst forest types are easily differentiated according to their dominant species, changes in floristic composition are subtle along the altitudinal and other gradients recognized.     

Bayesian correlation between temperature and blossom onset data

The recent quantification of changes in time series of phenology data with Bayesian methods has provided compelling evidence for changes during the last 20 years. In this paper we correlate the phenological observations with spring temperature time series. We provide quantitative answers to the question whether changes in temperature and phenological time series should be regarded as coherent or independent. For the three considered species snowdrops, cherry and lime tree we find factors of 1.05, 2.19 and 3.26, respectively, in favor of coherence. The functional behavior and the trend in the temperature time series are presented. They amount to 0.15°C yr^?1 for the January–March average, 0.09°C yr^?1 for February–April and 0.1°C yr^?1 for March–May in 2002. In addition, we compare blossom trends for the coherent and independent hypotheses and find that the transition from trend values slightly positive before 1970 to strongly negative at present becomes sharper as the temperature data are included in the analysis.     

Plant-environment relationships on the Montlake wildlife area,Seattle, Washington,USA

Grassland vegetation on the Montlake fill was analyzed using TWINSPAN. Eight herb communities were recognized. Moisture, proximity to gas vents, and disturbance are the main factors that control species and community distributions. Binary discriminant analysis (BDA) and detrended correspondence analysis (DCA) were used to study species-environment relationships. BDA revealed complex species response patterns and the resultant indicator values were used to interpret the ordination axes. Species distributions are controlled primarily by moisture, but also influenced by soil pH. Multiple regressions revealed little about plant-environment relationships not discovered by BDA. Before robust nonlinear methods are available, BDA, metric ordination with data stratification and nonmetric ordination are methods that can yield satisfactory results in exploratory plant-environment studies. BDA alone is an efficient, useful first approach where response patterns of species are initially unknown.Abbreviations BDA Binary Discriminant Analysis - DCA Detrended Correspondence Analysis     

西藏阿里植物群落的间接梯度分析、数量分类与环境解释

根据对西藏阿里地区163个植物群落样地资料进行的多元分析——排序、数量分类与环境解释,给出了该地区植被的基本类型、生态梯度及其与环境因子的定量关系。基本分析方法包括3个步骤：1)通过无倾向对应分析(DCA)的两个排序向量揭示了阿里植被的两个主要生态梯度;2)由该梯度的二维散点图及二元指示种分析(TWINSPAN)分别产生非等级制与等级制的植物群落分类系统;3)以多元回归分析将排序值与环境及地理参数相联系而给出各类型的环境指标——定量环境解释。分析表明,阿里植被类型及其分布主要取决于热量与湿度梯度,前者可通过地理参数,后者则通过土壤特征的数学表达式来定量地确定。两梯度包含的类型、种类与生境差异颇大,由低山暖性荒漠直到高山冰缘植被,从隐带性沼泽与盐生草甸到高原地带性荒漠与草原均各得其位,各有其值。表明该数量分析法对于处理高度生态多样性的植物群落生态信息是十分有效的。     

A brute‐force approach to vegetation classification

Aim: Introduction of a novel approach to the classification of vegetation data (species by plot matrices). This approach copes with a large amount of noise, groups irregularly shaped in attribute space and species turnover within groups. Method: The proposed algorithm (Isopam) is based on the classification of ordination scores from isometric feature mapping. Ordination and classification are repeated in a search for either high overall fidelity of species to groups of sites, or high quantity and quality of indicator species for groups of sites. The classification is performed either as a hierarchical, divisive method or as non‐hierarchical partitioning. In divisive clustering, resulting groups are subdivided until a stopping criterion is met. Isopam was tested on 20 real‐world data sets. The resulting classifications were compared with solutions from eight widely used clustering algorithms. Results: When looking at the significance of species fidelities to groups of sites, and at quantity and quality of indicator species, Isopam often achieved high ranks as compared with other algorithms.     

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.     

Principal components analysis and trend surface analysis of a small-scale pattern in a transition mire

Principal components analysis and trend surface analysis have been applied to a transition mire with the aim to characterize the vegetation pattern and reveal the major trends of variation. The first three PCA axes were ecologically interpretable, viz. the 1 st and 2nd as a complex soil moisture gradient and the 3rd axis as a gradient in the amount of peat in the soil. The ecological interpretability of the 1st axis of PCA after VARIMAX rotation, is unclear because some outlier samples caused a reorientation of the axis. TSA appeared to be useful for the clarification of joint patterns of species groups, which were major contributors to ordination axes in terms of component loadings. The smooth effect of TSA was briefly discussed in connection with the influence of extremes upon the outcoming trend structure. The use of four-variable TSA including a time series is emphasized for the study of spatial-temporal relations and ecological succession.     

Mapping the floristic continuum: Ordination space position estimated from imaging spectroscopy

Objective: To present a non‐classificatory technique of map representation of compositional patterns of vegetation as no two plant species assemblages are completely alike and gradations often occur. Variation is depicted as continuous fields instead of classes. Location: Murnauer Moos, Bavaria. Methods: The study combined vegetation ecology and remote sensing methods. The gradual representation of compositional patterns was based on techniques of ordination and regression, instead of mapping class fractions. The floristic field data were collected in relevés and subjected to three‐dimensional non‐metric multidimensional scaling (NMS). The reflectance information corresponding to plots was gathered from remotely sensed imagery with a high spectral resolution. Reflectance values in numerous wavelengths were related to NMS axes scores by partial least squares regression analysis. The regression equations were applied to the imagery and yielded three grey‐scale images, one for each ordination axis. These three images were transformed into a red, green, and blue colour map with a specific colour for each position in the ordination space. Similar colours corresponded to similar species compositions. Results: Compositional variation was mapped accurately (R²= 0.79), using continuous fields. The results took account of various types of stand transitions and of heterogeneities within stands. The map representation featured relatively homogeneous stands and abrupt transitions between stands as well as within‐stand heterogeneity and gradual transitions. Conclusions: The use of NMS in combination with imaging spectroscopy proved to be an expedient approach for non‐classificatory map representations of compositional patterns. Ordination is efficiently extended into the geographic domain. The approach in abandoning pre‐defined plant communities is able to reconcile mapping practice and complex reality.     

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.