Assessing the use of forest islands by parrot species in a neotropical savanna

Understanding the effect of habitat fragmentation is a fundamental yet complicated aim of many ecological studies. Beni savanna is a naturally fragmented forest habitat, where forest islands exhibit variation in resources and threats. To understand how the availability of resources and threats affect the use of forest islands by parrots, we applied occupancy modeling to quantify use and detection probabilities for 12 parrot species on 60 forest islands. The presence of urucuri (Attalea phalerata) and macaw (Acrocomia aculeata) palms, the number of tree cavities on the islands, and the presence of selective logging,and fire were included as covariates associated with availability of resources and threats. The model-selection analysis indicated that both resources and threats variables explained the use of forest islands by parrots. For most species, the best models confirmed predictions. The number of cavities was positively associated with use of forest islands by 11 species. The area of the island and the presence of macaw palm showed a positive association with the probability of use by seven and five species, respectively, while selective logging and fire showed a negative association with five and six species, respectively. The Blue-throated Macaw (Ara glaucogularis), the critically endangered parrot species endemic to our study area, was the only species that showed a negative association with both threats. Monitoring continues to be essential to evaluate conservation and management actions of parrot populations. Understanding of how species are using this natural fragmented habitat will help determine which fragments should be preserved and which conservation actions are needed.

Power properties if invariant tests for spatial autocorrelation in linear regression

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included

Non-testability of equal weights spatial dependence

We show that any invariant test for spatial autocorrelation in a spatial error or spatial lag model with equal weights matrix has power equal to size. This result holds under the assumption of an elliptical distribution. Under Gaussianity, we also show that any test whose power is larger than its size for at least one point in the parameter space must be biased.

Testing for spatial autocorrelation: the regressors that make the power disappear

We show that for any sample size, any size of the test, and any weights matrix outside a small class of exceptions, there exists a positive measure set of regression spaces such that the power of the Cli-Ord test vanishes as the autocorrelation increases in a spatial error model. This result extends to the tests that dene the Gaussian power envelope of all invariant tests for residual spatial autocorrelation. In most cases, the regression spaces such that the problem occurs depend on the size of the test, but there also exist regression spaces such that the power vanishes regardless of the size. A characterization of such particularly hostile regression spaces is provided.