We investigated the influence of position on a slope (plot relative elevation) and vegetation disturbance (the tallest tree height per plot) on community composition and diversity in a SE Brazilian Seasonal Semideciduous Forest (46°55¢ W, 22°50¢ S). Trees with dbh ‡5 cm were sampled in one hundred 10 · 10 m plots randomly placed in a 6.5-ha stand. Through partial Mantel test, floristic dissimilarities among plots (Jaccard index computed with species abundance in each plot) were correlated with environmental distances among plots (Euclidian distance index computed with relative elevation and the tallest tree height values in each plot). Relative elevation and the tallest tree per plot height were individually correlated with floristic gradients expressed by PCA axes scores using Pearson's correlation coefficient. Through resampling, we compared diversity (richness, Berger-Parker D and Shannon H¢) among plots in the drier (up) and moister (low) ends of the slope. Floristic dissimilarities were significantly correlated with environmental distances even after geographic distances among plots have been partialled out (r m = 0.1274, p < 0.001). The first two PCA axes accounted for 22% of the total variance. After Bonferroni and Dutilleul's corrections, axis 1 showed a marginally significant correlation with plot relative elevation (r = -0.4097, p = 0.0309), and axis 2 was significantly correlated with the tallest tree height per plot (r = 0.2953, p = 0.0106). Position on the slope and vegetation disturbance were reliable predictors of community composition, thus suggesting the operation of niche assembly organizing processes. Richness and diversity (H¢) decreased and dominance (D) increased with elevation on the slope. Dominance increase from D (300) = 0.11 (confidence interval = 0.091-0.131) to D (300) = 0.19 (CI = 0.165-0.210) surpassed the expected dominance increase based on the reduction of richness alone: D (300) = 0.13 (CI = 0.110-0.140), thus highlighting the niche partitioning assembly of the community, especially among abundant species. Given the great amount of floristic variability remaining unexplained, stochastic processes, such 2006 as those related to dispersal limitation, may also have influence on the community composition. Therefore, both niche assembly and chance events can operate even on a fine local scale.

The species abundance distribution of ecological communities has been represented through several mathematical models, of which the most common are: geometric series, logseries, lognormal, and a type of broken stick, this latter found only in animal communities. There is no consensus on the underlying biological processes, but initial observations on plant communities related these models to equilibrium and high richness (lognormal), stress or disturbance and low richness (logseries and geometric series). Recently the value of these relationships was challenged, and other descriptors were considered better predictors of richness, disturbance and stress. We aimed at investigating how these models and their parameters, as well as dominance and evenness are related with species richness, stress and disturbance in six tropical forest communities, SE Brazil: two well-conserved fragments, two disturbed by fire, and two swampy forests (anoxic stress). The models did not show consistent relationships with richness, disturbance or stress. The parameters and indices of diversity α (logseries) and λ (lognormal) varied closely with richness, and the dominance was larger in the communities submitted to stress or disturbance. Our results indicate the need of further studies in order to validate (or refute) the use of abundance distribution models for detection of patterns related to richness, stress or disturbance in tropical arboreal communities. On the other hand, richness and dominance did respond to disturbance and stress.

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Sugiura [11] gives an asymptotic expansion of the modified likelihood ratio criteria for testing the hypothesis that a covariance matrix is equal to a given matrix. An improvement of this expansion is presented here. Numerical comparisons via simulation with the original approximation to the criteria's distribution confirm the superiority of our expansion. This enable us to use the proposed method in usual hypotheses testing and in applications where extreme tail quantiles are necessary, as for instance, for monitoring dispersion in multivariate processes quality control charts.