Comparison of single and complete linkage clustering with the hierarchical factor classification of variables

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

Measures of precision for dissimilarity-based multivariate analysis of ecological communities

Ecological studies require key decisions regarding the appropriate size and number of sampling units. No methods currently exist to measure precision for multivariate assemblage data when dissimilarity-based analyses are intended to follow. Here, we propose a pseudo multivariate dissimilarity-based standard error (MultSE) as a useful quantity for assessing sample-size adequacy in studies of ecological communities. Based on sums of squared dissimilarities, MultSE measures variability in the position of the centroid in the space of a chosen dissimilarity measure under repeated sampling for a given sample size. We describe a novel double resampling method to quantify uncertainty in MultSE values with increasing sample size. For more complex designs, values of MultSE can be calculated from the pseudo residual mean square of a permanova model, with the double resampling done within appropriate cells in the design. R code functions for implementing these techniques, along with ecological examples, are provided

Dinâmica vegetacional em pastagem natural submetida a tratamentos de queima e pastejo Vegetation dynamics of natural grassland under treatments of burning and grazing

Foram avaliados durante três anos os efeitos de tratamentos de fogo e pastejo sobre a dinâmica da vegetação de uma pastagem natural localizada em Santa Maria, na região da Depressão Central, Rio Grande do Sul. Foi considerada a hipótese de resiliência, resultado das espécies componentes da pastagem terem evoluído sob influência de tais distúrbios. O experimento foi composto por oito parcelas experimentais submetidas a combinações de níveis de pastejo (pastejado, excluído) e de fogo (queimado, não-queimado), em duas posições de relevo (encosta, baixada). A análise multivariada dos dados de composição de espécies foi baseada em ordenação e testes de aleatorização. A vegetação sob efeito de pastejo, independente da queima, apresentou trajetórias direcionais, enquanto sob exclusão as trajetórias foram caóticas. O efeito do pastejo parece ser determinante da dinâmica vegetacional (P=0,077).<br>The effect of fire and grazing treatments on vegetation dynamics was evaluated during three years on a natural grassland located in Santa Maria, in the region of "Depressão Central", Rio Grande do Sul, Brazil. A hypothesis of resilience resulting from the fact that the species of the grassland evolved under the influence of these disturbances was considered. The experimental setup was formed by eight plots subjected to combinations of grazing (grazed, ungrazed) and fire (burned, unburned) levels, on two relief positions (convex, concave slope). Multivariate analysis of compositional data used ordination and randomization testing. Vegetation under grazing tended to show directional trajectories of floristic composition change, while under grazing exclusion the trajectories could be considered chaotic, independently from the plots being burned or not. Grazing effect seems to be determinant of vegetacional dynamics (P=0.077)