The matrix-tolerance hypothesis: an empirical test with frogs in the Atlantic Forest

The matrix-tolerance hypothesis suggests that the most abundant species in the inter-habitat matrix would be less vulnerable to their habitat fragmentation. This model was tested with leaf-litter frogs in the Atlantic Forest where the fragmentation process is older and more severe than in the Amazon, where the model was first developed. Frog abundance data from the agricultural matrix, forest fragments and continuous forest localities were used. We found an expected negative correlation between the abundance of frogs in the matrix and their vulnerability to fragmentation, however, results varied with fragment size and species traits. Smaller fragments exhibited stronger matrix-vulnerability correlation than intermediate fragments, while no significant relation was observed for large fragments. Moreover, some species that avoid the matrix were not sensitive to a decrease in the patch size, and the opposite was also true, indicating significant differences with that expected from the model. Most of the species that use the matrix were forest species with aquatic larvae development, but those species do not necessarily respond to fragmentation or fragment size, and thus affect more intensively the strengthen of the expected relationship. Therefore, the main relationship expected by the matrix-tolerance hypothesis was observed in the Atlantic Forest; however we noted that the prediction of this hypothesis can be substantially affected by the size of the fragments, and by species traits. We propose that matrix-tolerance model should be broadened to become a more effective model, including other patch characteristics, particularly fragment size, and individual species traits (e. g., reproductive mode and habitat preference).

Empirical analysis of the Lieb-Oxford bound in ions and molecules

Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, in particular, are important for the construction of improved density functionals. Here we investigate one such universal property-the Lieb-Oxford lower bound-for ionic and molecular systems. In recent work [J Chem Phys 127, 054106 (2007)], we observed that for atoms and electron liquids this bound may be substantially tightened. Calculations for a few ions and molecules suggested the same tendency, but were not conclusive due to the small number of systems considered. Here we extend that analysis to many different families of ions and molecules, and find that for these, too, the bound can be empirically tightened by a similar margin as for atoms and electron liquids. Tightening the Lieb-Oxford bound will have consequences for the performance of various approximate exchange-correlation functionals. (C) 2008 Wiley Periodicals Inc.

Performance of balanced two-stage empirical predictors of realized cluster latent values from finite populations: A simulation study

Predictors of random effects are usually based on the popular mixed effects (ME) model developed under the assumption that the sample is obtained from a conceptual infinite population; such predictors are employed even when the actual population is finite. Two alternatives that incorporate the finite nature of the population are obtained from the superpopulation model proposed by Scott and Smith (1969. Estimation in multi-stage surveys. J. Amer. Statist. Assoc. 64, 830-840) or from the finite population mixed model recently proposed by Stanek and Singer (2004. Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 1119-1130). Predictors derived under the latter model with the additional assumptions that all variance components are known and that within-cluster variances are equal have smaller mean squared error (MSE) than the competitors based on either the ME or Scott and Smith`s models. As population variances are rarely known, we propose method of moment estimators to obtain empirical predictors and conduct a simulation study to evaluate their performance. The results suggest that the finite population mixed model empirical predictor is more stable than its competitors since, in terms of MSE, it is either the best or the second best and when second best, its performance lies within acceptable limits. When both cluster and unit intra-class correlation coefficients are very high (e.g., 0.95 or more), the performance of the empirical predictors derived under the three models is similar. (c) 2007 Elsevier B.V. All rights reserved.