Effect of biogeographic history on population vulnerability in European amphibians.

The genetic diversity of populations, which contributes greatly to their adaptive potential, is negatively affected by anthropogenic habitat fragmentation and destruction. However, continental-scale losses of genetic diversity also resulted from the population expansions that followed the end of the last glaciation, an element that is rarely considered in a conservation context. We addressed this issue in a meta-analysis in which we compared the spatial patterns of vulnerability of 18 widespread European amphibians in light of phylogeographic histories (glacial refugia and postglacial routes) and anthropogenic disturbances. Conservation statuses significantly worsened with distances from refugia, particularly in the context of industrial agriculture; human population density also had a negative effect. These findings suggest that features associated with the loss of genetic diversity in post-glacial amphibian populations (such as enhanced fixation load or depressed adaptive potential) may increase their susceptibility to current threats (e.g., habitat fragmentation and pesticide use). We propose that the phylogeographic status of populations (i.e., refugial vs. post-glacial) should be considered in conservation assessments for regional and national red lists.

Towards automated derivation in the theory of allegories

We provide an algorithm that automatically derives many provable theorems in the equational theory of allegories. This was accomplished by noticing properties of an existing decision algorithm that could be extended to provide a derivation in addition to a decision certificate. We also suggest improvements and corrections to previous research in order to motivate further work on a complete derivation mechanism. The results presented here are significant for those interested in relational theories, since we essentially have a subtheory where automatic proof-generation is possible. This is also relevant to program verification since relations are well-suited to describe the behaviour of computer programs. It is likely that extensions of the theory of allegories are also decidable and possibly suitable for further expansions of the algorithm presented here.

Simulation-Based Finite and Large Sample Tests in Multivariate Regressions.

In the context of multivariate linear regression (MLR) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. In this paper, we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of MLR systems. For the case of uniform linear hypotheses, we present exact distributional invariance results concerning several standard test criteria. These include Wilks' likelihood ratio (LR) criterion as well as trace and maximum root criteria. The normality assumption is not necessary for most of the results to hold. Implications for inference are two-fold. First, invariance to nuisance parameters entails that the technique of Monte Carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses. Second, the invariance property of the latter statistic is exploited to derive general nuisance-parameter-free bounds on the distribution of the LR statistic for arbitrary hypotheses. Even though it may be difficult to compute these bounds analytically, they can easily be simulated, hence yielding exact bounds Monte Carlo tests. Illustrative simulation experiments show that the bounds are sufficiently tight to provide conclusive results with a high probability. Our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation-based test methods (e.g., the parametric bootstrap) which may be applied when the bounds are not conclusive.