Multivariate analysis of variance, based on randomization (permutation) test, has become an important tool for ecological data analyses. However, a comprehensive evaluation of the accuracy and power of available methods is still lacking. This is a thorough examination of randomization tests for multivariate group mean differences. With simulated data, the accuracy and power of randomization tests were evaluated using different test statistics in one-factor multivariate analysis of variance (MANOVA). The evaluations span a wide spectrum of data types, including specified and unspecified (field data) distributional properties, correlation structures, homogeneous to very heterogeneous variances, and balanced an unbalanced group sizes. The choice of test statistic strongly affected the results. Sums of squares between groups (Qb) computed on Euclidean distances (Qb-EUD) gave better accuracy. Qb on Bray-Curtis, Manhattan or Chord distances, the multiresponse permutation procedure (MRPP) and the sum of univariate ANOVA F produced severely inflated type I errors under increasing variance heterogeneity among groups, a common scenario in ecological data. Despite pervasive claims in the ecological literature, the evidence thus suggests caution when using test statistics other than Qb-EUD.
We assess the performance of a new clustering method for Hierarchical Factor Classification of variables, which is based on the evaluation of the least differences among representative variables of groups, as defined by a set of two-dimensional Principal Components Analysis. As an additional feature the method gives at each step a principal plane where both grouped variables and units, as seen only by these variables, can be projected. We compare the method results with both single and complete linkage clustering, applied to simulated data with known correlation structure and we evaluate the results with a coherence measure based on the entropy between the expected partitions and those found by the methods. We found that the Hierarchical Factor Classification method performed as good as, and in some cases better than, both single and complete linkage clustering in detecting the known group structures in simulated data, with the advantage that the groups of variables and the units can be viewed on principal planes where usual interpretations apply.
Palynological records helped to illuminate the past, but we show the take can be made much sharper when statistical analysis recognises the records' scale dependence. The latter is an unavoidable consequence of site selection, sediment sampling, and the samples' arrangement into time series by dating. To make provision for this in statistical analysis, scale has to be incorporated as one of the intrinsic variables. But by incorporating scale, the analysis will render the outcome not to be a single conclusion, the usual case in conventional statistics, but a multitude of conclusions each regarding the same set of response and forcing variables and each as valid at its own scale as any of the other conclusions at theirs. Thus, the central question for a usable Statistics is this: how to incorporate scale into the analysis and still have a unique conclusion. We address the methodological aspects and illustrate them by worked examples. We use 14 sites scattered across the globe. Interestingly, the analysis of these brought forth hitherto hidden aspects of the temporal synchronicity of change in palynological composition and concomitant atmospheric temperature oscillations that should greatly interest Ecology, as one critique put it, in the age of Global Change. The examples testify to a conceptual advance in laying open a very basic principle: the synchronicity's statistically strong formation specificity, dominantly positive (in frequency terms) for climate warming at sites in the currently humid, micro- and mesothermal zones, and negative in the currently arid and semi-arid zones. Our paper begins with an introduction to the terminology of multiscale analysis in Ecology, followed by data sources, the method we call canonical serial scaling, and objectives. A detailed discussion of data properties with special attention to error sources in palynology is provided. The method components discussed include the scalars of compositional transition and synchronicity, error dampening, stabilisation of the synchronicity scalar and its sign distribution, analysis of time shifted series, the use of deviation graphs, and pointers to help detect hotspots and other characteristic points of change on the time axis.
We offer a new framework for cellular automata modeling to describe and predict vegetation dynamics. The model can simulate community composition and spatial patterns by following a set of probabilistic rules generated from empirical data on plant neighborhood dynamics. Based on published data (Lippe et al. 1985), we apply the model to simulate Atlantic Heathland vegetation dynamics and compare the outcome with previous models described for the same site. Our results indicate reasonable agreement between simulated and real data and with previous models based on Markov chains or on mechanistic spatial simulation, and that spatial models may detect similar species dynamics given by non-spatial models. We found evidence that a directional vegetation dynamics may not correspond to a monotonic increase in community spatial organization. The model framework may as well be applied to other systems.
In the analysis of multidimensional ecological data, it is often relevant to identify groups of variables since these groups may reflect similar ecological processes. The usual approach, the application of well-known clustering procedures using an appropriate similarity measure among the variables, may be criticized, but specific methods for clustering variables are neither investigated in detail nor used broadly. Here we introduce a new clustering method, the Hierarchical Factor Classification of variables, which is based on the evaluation of the least differences among representative variables of groups, as revealed by a two-dimensional Principal Components Analysis. As an additional feature, the method gives at each step a principal plane where both the grouped variables and the units, considered only according to these variables, can be projected. This method can be adapted to count data, so that it may be used for classifying both rows and columns of a contingency data table, by using the chi-square metric. In an example, we apply both methods to vegetation and soil data from the Campos in Southern Brazil.
The paper responds to the question: How should one go about designing the statistical analysis of biodiversity if it had to be done across scales in time and space? The conceptual basis of the design is the definition of biodiversity as a convolution of two community components. One of the components is richness, the product of species evolution, and the other structure, the consequence of environmental sorting (biotic, physical). The method of choice takes information in the manner of frequency distributions, and decomposes the associated total diversity into additive components specific to the deemed sorting factors. Diversity quantities are supplied by the analysis by which the relative importance of sorting factors can be measured and the dynamic oscillations which they generate in diversity can be traced. Examples support the a priori idea that the velocity of compositional change in the community during the late quaternary period has co-varied closely with the specific components of Kolmogorov-type complexity, Anand's structural complexity and Rényi's entropy of order one. The paper explains what is involved and why is it important.
A mosaic of Campos grassland and Araucaria forest characterizes the vegetation of the Southern Brazilian highland plateau. Palaeoecological evidence indicates that forest expansion over grassland initiated after the mid Holocene, when climate changed towards present day cool and moist conditions. In this paper, we discuss landscape level changes that occurred on vegetation patterns after grazing and fire exclusion in a mosaic of Campos and Araucaria forest in Southern Brazil. The analysis of aerial photographs from 1974 and 1999 showed alterations on grassland communities under grazing and fire exclusion, especially pronounced shrub establishment near the edge of the forest. Considering the change in the cover of vegetation classes relative to the total altered cover in all classes from 1974 to 1999, the most prominent alterations were: 48% from grassland with tussock grasses dominance (GRA) to grassland with shrubs (GSR), 24% from GRA to grassland with tall shrubs (GTS), 16% from GSR to GTS and 9% from GTS to forest (FOR). Considering the alteration relatively to the vegetation cover in 1974, the most relevant changes were: 44% from GSR to GTS and 94% from GTS to FOR. These observations support a directional forest expansion over grassland under grazing and fire exclusion.
Gradients of physical conditions and biological interactions of species may generate assembly patterns of trait-convergence and trait-divergence in the structure of plant communities. Here we report evidence on the effect of canopy closure on non-random patterns in the functional structure of herbaceous plant communities in temperate forest. We evaluated SLA (specific leaf area), leaf area and shape, dry matter content, presence of rhizomes, and plant height and inclination. In one of the three sites surveyed we found clear patterns of both trait-convergence and trait-divergence. Along the canopy closure gradient we observed communities formed by species with large SLA and long and narrow leaves being replaced by communities formed by species with smaller SLA and rounded leaves, which we interpret as environmental filtering producing such a trait-convergence. Further, communities located in more open sites contained more distinct species in terms of SLA, leaf area and leaf shape, i.e., indicating a divergence pattern along the canopy closure gradient. The other study sites showed no significant patterns when analyzed alone. When the three sites were analyzed jointly, a significant pattern of convergence for plant inclination was found. Although subjected to local variation and historical agents, our study presents consistent patterns of both trait-convergence and divergence and evidence of assembly rules and non-random patterns in communities of herbaceous plants along a canopy closure gradient.
Authors:L. Orlóci, V.D. Pillar, M. Anand, and et al.
The characteristics discussed are measurable on the process “trajectory”, the path traced out by vegetation transitions in time. It is argued that since the trajectory is symptomatic of factor influences and governing principles, it has to be an object of central interest in dynamic studies. Theoretical points, scaling scenarios, and analytical tools are the main topics. Numerical examples illustrate the applications.
Two simulated coenoclines and a real data set were differently recoded with respect to the Braun-Blanquet coding (including presence/absence) and analysed through the most common multidimensional scaling methods. This way, we aim at contributing to the debate concerning the nature of the Braun-Blanquet coding and the consequent multidimensional scaling methods to be used. Procrustes, Pearson, and Spearman correlation matrices were computed to compare the resulting sets of coordinates and synthesized through their Principal Component Analyses (PCA). In general, both Procrustes and Pearson correlations showed high coherence of the obtained results, whereas Spearman correlation values were much lower. This proves that the main sources of variation are similarly identified by most of used methods/transformations, whereas less agreement results on the continuous variations along the detected gradients. The conclusion is that Correspondence Analysis on presence/absence data seems the most appropriate method to use. Indeed, presence/absence data are not affected by species cover estimation error and Simple Correspondence Analysis performs really well with this coding. As alternative, Multiple Correlation Analysis provides interesting information on the species distribution while showing a pattern of relevés very similar to that issued by PCA.