Two major accretion epochs in M31 from two distinct populations of globular clusters.

Large galaxies grow through the accumulation of dwarf galaxies1,2. In principle it is possible to trace this growth history via the properties of a galaxy's stellar halo3-5. Previous investigations of the galaxy Messier 31 (M31, Andromeda) have shown that outside a galactocentric radius of 25 kiloparsecs the population of halo globular clusters is rotating in alignment with the stellar disk6,7, as are more centrally located clusters8,9. The M31 halo also contains coherent stellar substructures, along with a smoothly distributed stellar component10-12. Many of the globular clusters outside a radius of 25 kiloparsecs are associated with the most prominent substructures, but some are part of the smooth halo13. Here we report an analysis of the kinematics of these globular clusters. We find two distinct populations rotating perpendicular to each other. The rotation axis for the population associated with the smooth halo is aligned with the rotation axis for the plane of dwarf galaxies14 that encircles M31. We interpret these separate cluster populations as arising from two major accretion epochs, probably separated by billions of years. Stellar substructures from the first epoch are gone, but those from the more recent second epoch still remain.

Model Selection and Parameter Inference in Phylogenetics Using Nested Sampling.

Bayesian inference methods rely on numerical algorithms for both model selection and parameter inference. In general, these algorithms require a high computational effort to yield reliable estimates. One of the major challenges in phylogenetics is the estimation of the marginal likelihood. This quantity is commonly used for comparing different evolutionary models, but its calculation, even for simple models, incurs high computational cost. Another interesting challenge relates to the estimation of the posterior distribution. Often, long Markov chains are required to get sufficient samples to carry out parameter inference, especially for tree distributions. In general, these problems are addressed separately by using different procedures. Nested sampling (NS) is a Bayesian computation algorithm, which provides the means to estimate marginal likelihoods together with their uncertainties, and to sample from the posterior distribution at no extra cost. The methods currently used in phylogenetics for marginal likelihood estimation lack in practicality due to their dependence on many tuning parameters and their inability of most implementations to provide a direct way to calculate the uncertainties associated with the estimates, unlike NS. In this article, we introduce NS to phylogenetics. Its performance is analysed under different scenarios and compared to established methods. We conclude that NS is a competitive and attractive algorithm for phylogenetic inference. An implementation is available as a package for BEAST 2 under the LGPL licence, accessible at https://github.com/BEAST2-Dev/nested-sampling.