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In community ecology, randomization tests with problem specific test statistics (e.g., nestedness, functional diversity, etc.) are often applied. Researchers in such studies may want not only to detect the significant departure from randomness, but also to measure the effect size (i.e., the magnitude of this departure). Measuring the effect size is necessary, for instance, when the roles of different assembly forces (e.g., environmental filtering, competition) are compared among sites. The standard method is to calculate standardized effect size (SES), i.e., to compute the departure from the mean of random communities divided by their standard deviations. Standardized effect size is a useful measure if the test statistic (e.g., nestedness index, phylogenetic or functional diversity) in the random communities follows a symmetric distribution. In this paper, I would like to call attention to the fact that SES may give us misleading information if the distribution is asymmetric (skewed). For symmetric distribution median and mean values are equal (i.e., SES = 0 indicates p = 0.5). However, this condition does not hold for skewed distributions. For symmetric distributions departure from the mean shows the extremity of the value, regardless of the sign of departure, while in asymmetric distributions the same deviation can be highly probable and extremely improbable, depending on its sign. To avoid these problems, I recommend checking symmetry of null-distribution before calculating the SES value. If the distribution is skewed, I recommend either log-transformation of the test statistic, or using probit-transformed p-value as effect size measure.

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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 (Q b) computed on Euclidean distances (Q b -EUD) gave better accuracy. Q b 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.

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Testing the ecological communities of different areas for convergence, in the sense of remarkable similarity in the characteristics of the species present, has a long history in biology. Recently, numerical methods have been developed for comparing community-level convergence to an explicit null model. No valid method has been known for testing the significance of texture convergence when the species are weighted by their abundance. Six combinations of method variants are tested on random datasets. A valid P value (i. e., with P . 0. 05 in no more than 5% of the cases) is obtained so long as for each species the distribution of abundances across sites is retained, and only the assignment of character values is randomised. Further restriction is not necessary for obtaining a valid P value, and can lead to a test with considerably lower power to detect convergence. The power of the test with free matching of character values to species is only moderate with 10 sites, though improved with larger numbers of sites. Previous methods for detecting texture convergence have examined convergence only in the mean value for any character. It is possible that the external environment might be reflected in the community mean of a character, leaving the imprint of convergence on the shape of the distribution, rather than the mean. A method for comparing the shape is described, and it is shown that the null model is valid also for this test statistic.  

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A most widespread technique in vegetation boundary detection is the Moving Split Window analysis. It is effective in single edge cases provided that the attributes are highly correlated. In dry grasslands with mosaic structure, boundary zones are frequent, they are rather close to one another, causing some uncertainty in edge detection. Artificial community patterns were used to reveal the response of dissimilarity/distance functions to the number and distance of edges and to window sizes. Dissimilarity functions are sensitive to the compositional difference of the adjacent patches, and the dissimilarity increases with window size. The usual significance test highly depends on the patch size and edge frequency, therefore additional analyses must be applied or other randomization methods should be found that can ignore the effect of patch size.

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Meta-analysis is used to compare the patterns of the tree and the herb layers in a Central-European deciduous hardwood forest. Vegetation patterns are represented by distance matrices and dendrograms. The significance of the relation between the patterns is evaluated through permutation (Mantel) tests and full randomization (Monte Carlo simulation) tests. The relationship between the two layers is significant but weak. When using ecological indicators as variables for characterising the herb layer, the relation is stronger. Distance matrices and dendrograms describe the vegetation pattern similarly. However, the results of pairwise tests of significance strongly depend on the “level” of comparisons, i.e., whether distance matrices or dendrograms are compared. This follows perhaps from the differences between permutation and full randomization tests.

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Tree species richness is remarkably high in many tropical forests, even at very fine spatial scales. However, the study of fine-scale richness is complicated by the rarefaction effect: that is, a trivial correlation between the number of individuals and the number of species. We developed null models to test whether fine-scale species richness differs from random expectation, and applied these models to a dataset of 1170 100 m2circular plots in the old-growth portion of La Selva Biological Station in the Atlantic Lowlands of Costa Rica. Although species richness in these plots was close to its theoretical maximum, we found that it was frequently lower than null expectation. This was a result of slightly clumped distributions within species. We found no relationships between species richness at the 100 m2scale and soil type or topography, after accounting for the effects of density

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Edgington, E.S. 1987. Randomization Tests . 2nd ed. Marcel Dekker, New York. Edgington E.S. Randomization

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Pillar, V.D. 2006. MULTIV: Multivariate Exploratory Analysis, Randomization Testing and Bootstrap Resampling, User’s Guide v. 2.4 . Universidade Federal do Rio Grande do Sul, Porto Alegre. Pillar V

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1051 Hunter, J. C. and McCoy, R. A. (2004): Applying randomization tests to cluster analyses. — J. Veg. Sci. 15 : 135–138. McCoy R. A

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Edgington, E.S. 1987. Randomization Tests. 2nd ed. Marcel Dekker, New York. Randomization Tests. Feller, W. 1957. An Introduction to

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