When trees grow too long: Investigating the causes of highly inaccurate bayesian branch-length estimates

A surprising number of recent Bayesian phylogenetic analyses contain branch-length estimates that are several orders of magnitude longer than corresponding maximum-likelihood estimates. The levels of divergence implied by such branch lengths are unreasonable for studies using biological data and are known to be false for studies using simulated data. We conducted additional Bayesian analyses and studied approximate-posterior surfaces to investigate the causes underlying these large errors. We manipulated the starting parameter values of the Markov chain Monte Carlo (MCMC) analyses, the moves used by the MCMC analyses, and the prior-probability distribution on branch lengths. We demonstrate that inaccurate branch-length estimates result from either 1) poor mixing of MCMC chains or 2) posterior distributions with excessive weight at long tree lengths. Both effects are caused by a rapid increase in the volume of branch-length space as branches become longer. In the former case, both an MCMC move that scales all branch lengths in the tree simultaneously and the use of overdispersed starting branch lengths allow the chain to accurately sample the posterior distribution and should be used in Bayesian analyses of phylogeny. In the latter case, branch-length priors can have strong effects on resulting inferences and should be carefully chosen to reflect biological expectations. We provide a formula to calculate an exponential rate parameter for the branch-length prior that should eliminate inference of biased branch lengths in many cases. In any phylogenetic analysis, the biological plausibility of branch-length output must be carefully considered

The importance of data partitioning and the utility of bayes factors in bayesian phylogenetics

As larger, more complex data sets are being used to infer phylogenies, accuracy of these phylogenies increasingly requires models of evolution that accommodate heterogeneity in the processes of molecular evolution. We investigated the effect of improper data partitioning on phylogenetic accuracy, as well as the type I error rate and sensitivity of Bayes factors, a commonly used method for choosing among different partitioning strategies in Bayesian analyses. We also used Bayes factors to test empirical data for the need to divide data in a manner that has no expected biological meaning. Posterior probability estimates are misleading when an incorrect partitioning strategy is assumed. The error was greatest when the assumed model was underpartitioned. These results suggest that model partitioning is important for large data sets. Bayes factors performed well, giving a 5% type I error rate, which is remarkably consistent with standard frequentist hypothesis tests. The sensitivity of Bayes factors was found to be quite high when the across-class model heterogeneity reflected that of empirical data. These results suggest that Bayes factors represent a robust method of choosing among partitioning strategies. Lastly, results of tests for the inclusion of unexpected divisions in empirical data mirrored the simulation results, although the outcome of such tests is highly dependent on accounting for rate variation among classes. We conclude by discussing other approaches for partitioning data, as well as other applications of Bayes factors. Copyright © Society of Systematic Biologists

Neutron Transfer Studied with a Radioactive beam of 24Ne, using TIARA at SPIRAL

A general experimental technique for high resolution studies of nucleon transfer reactions using radioactive beams is briefly described, together with the first new physics results that have been obtained with the new TIARA array. These first results from TIARA are for the reaction 24Ne(d,p)25Ne, studied in inverse kinematics with a pure radioactive beam of 100,000 pps from the SPIRAL facility at GANIL. The reaction probes the energies of neutron orbitals relevant to very neutron rich nuclei in this mass region and the results highlight the emergence of the N=16 magic number for neutrons and the associated disappearance of the N=20 neutron magic number for the very neutron rich neon isotopes.Comment: Proceedings of the Carpathian Summer School of Physics, Mamaia-Constanta, Romania, 13-24 June 200

Flow probe of symmetry energy in relativistic heavy-ion reactions

Flow observables in heavy-ion reactions at incident energies up to about 1 GeV per nucleon have been shown to be very useful for investigating the reaction dynamics and for determining the parameters of reaction models based on transport theory. In particular, the elliptic flow in collisions of neutron-rich heavy-ion systems emerges as an observable sensitive to the strength of the symmetry energy at supra-saturation densities. The comparison of ratios or differences of neutron and proton flows or neutron and hydrogen flows with predictions of transport models favors an approximately linear density dependence, consistent with ab-initio nuclear-matter theories. Extensive parameter searches have shown that the model dependence is comparable to the uncertainties of existing experimental data. Comprehensive new flow data of high accuracy, partly also through providing stronger constraints on model parameters, can thus be expected to improve our knowledge of the equation of state of asymmetric nuclear matter.Comment: 20 pages, 24 figures, review to appear in EPJA special volume on nuclear symmetry energ

Gaussian-Charge Polarizable Interaction Potential for Carbon Dioxide

A number of simple pair interaction potentials of the carbon dioxide molecule are investigated and found to underestimate the magnitude of the second virial coefficient in the temperature interval 220 K to 448 K by up to 20%. Also the third virial coefficient is underestimated by these models. A rigid, polarizable, three-site interaction potential reproduces the experimental second and third virial coefficients to within a few percent. It is based on the modified Buckingham exp-6 potential, an anisotropic Axilrod-Teller correction and Gaussian charge densities on the atomic sites with an inducible dipole at the center of mass. The electric quadrupole moment, polarizability and bond distances are set to equal experiment. Density of the fluid at 200 and 800 bars pressure is reproduced to within some percent of observation over the temperature range 250 K to 310 K. The dimer structure is in passable agreement with electronically resolved quantum-mechanical calculations in the literature, as are those of the monohydrated monomer and dimer complexes using the polarizable GCPM water potential. Qualitative agreement with experiment is also obtained, when quantum corrections are included, for the relative stability of the trimer conformations, which is not the case for the pair potentials.Comment: Error in the long-range correction fixed and three-body dispersion introduced. 32 pages (incl. title page), 7 figures, 9 tables, double-space

QCD Viscosity to Entropy Density Ratio in the Hadronic Phase

Shear viscosity (eta) of QCD in the hadronic phase is computed by the coupled Boltzmann equations of pions and nucleons in low temperatures and low baryon number densities. The eta to entropy density ratio eta/s maps out the nuclear gas-liquid phase transition by forming a valley tracing the phase transition line in the temperature-chemical potential plane. When the phase transition turns into a crossover, the eta/s valley gradually disappears. We suspect the general feature for a first-order phase transition is that eta/s has a discontinuity in the bottom of the eta/s valley. The discontinuity coincides with the phase transition line and ends at the critical point. Beyond the critical point, a smooth eta/s valley is seen. However, the valley could disappear further away from the critical point. The eta/s measurements might provide an alternative to identify the critical points.Comment: 16 pages, 4 figures. Minor typos corrected and references adde

Multiple chromosomal rearrangements in a hybrid zone between Littorina saxatilis ecotypes

Both classical and recent studies suggest that chromosomal inversion polymorphisms are important in adaptation and speciation. However, biases in discovery and reporting of inversions make it difficult to assess their prevalence and biological importance. Here, we use an approach based on linkage disequilibrium among markers genotyped for samples collected across a transect between contrasting habitats to detect chromosomal rearrangements de novo. We report 17 polymorphic rearrangements in a single locality for the coastal marine snail, Littorina saxatilis. Patterns of diversity in the field and of recombination in controlled crosses provide strong evidence that at least the majority of these rearrangements are inversions. Most show clinal changes in frequency between habitats, suggestive of divergent selection, but only one appears to be fixed for different arrangements in the two habitats. Consistent with widespread evidence for balancing selection on inversion polymorphisms, we argue that a combination of heterosis and divergent selection can explain the observed patterns and should be considered in other systems spanning environmental gradients. This article is protected by copyright. All rights reserved

From Display to Labelled Proofs for Tense Logics

We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt