Bayes estimators for phylogenetic reconstruction

Deep mitochondrial DNA phylogeographic divergence in the threatened aoudad Ammotragus lervia (Bovidae, Caprini)

The aoudad or Barbary sheep (Ammotragus lervia) is a threatened ungulate emblematic of North Africa, whose population structure and subspecific taxonomy have not been examined genetically. This knowledge is essential and urgently needed to inform ongoing conservation and management efforts. We analysed the mitochondrial cytochrome b gene and four nuclear genes (casein kappa, spectrin beta nonerythrocytic 1, thyroglobulin, thyrotropin subunit beta) for the first phylogeographic survey of the aoudad, and uncovered a deep Mediterranean-Saharan mitochondrial split separating two highly distinct evolutionary lineages. Their level of divergence is greater than or comparable to those observed between several pairs of congeneric species of different caprine genera. The split was estimated to have occurred in the Early Pleistocene, about 1.3 million years ago. None of the four nuclear genes surveyed, chosen because they have been used in phylogeographic and species-level phylogenetic studies of bovids, allowed us to detect, likely due to their slow evolutionary rate, the substantial and geographically coherent subdivision revealed by mitochondrial DNA. This study is evidence and testament to the ability of mitochondrial DNA, probably unrivalled by any other single-locus marker, as an exploratory tool for investigating population genealogy and history and identifying potential evolutionarily significant units for conservation in animals.

Mean and Variance of Phylogenetic Trees

We describe the use of the Fréchet mean and variance in the Billera–Holmes–Vogtmann (BHV) treespace to summarize and explore the diversity of a set of phylogenetic trees. We show that the Fréchet mean is comparable to other summary methods, and, despite its stickiness property, is more likely to be binary than the majority-rule consensus tree. We show that the Fréchet variance is faster and more precise than commonly used variance measures. The Fréchet mean and variance are more theoretically justified, and more robust, than previous estimates of this type and can be estimated reasonably efficiently, providing a foundation for building more advanced statistical methods and leading to applications such as mean hypothesis testing and outlier detection.

Fish diversification at the pace of geomorphological changes: evolutionary history of western Iberian Leuciscinae (Teleostei: Leuciscidae) inferred from multilocus sequence data

The evolutionary history of western Iberian Leuciscinae, obligatory freshwater fish, is directly linked to the evolution of the hydrographic network of the Iberian Peninsula after its isolation from the rest of Europe, which involved dramatic rearrangements such as the transition from endorheic lakes to open basins draining to the Atlantic. Previous phylogenetic research on western Iberian leuciscines, using mainly mitochondrial DNA and more recently one or two nuclear genes, has found contradictory results and there remain many unresolved issues regarding species relationships, taxonomy, and evolutionary history. Moreover, there is a lack of integration between phylogenetic and divergence time estimates and information on the timing of geomorphological changes and paleobasin rearrangements in the Iberian Peninsula. This study presents the first comprehensive fossil-calibrated multilocus coalescent species tree of western Iberian Leuciscinae (including 14 species of Achondrostoma, Iberochondrostoma, Pseudochondrostoma and Squalius endemic to the Iberian Peninsula, seven of which endemic to Portugal) based on seven nuclear genes, and from which we infer their biogeographic history by comparing divergence time estimates to known dated geological events. The phylogenetic pattern suggests slow-paced evolution of leuciscines during the Early-Middle Miocene endorheic phase of the main Iberian river basins, with the shift to exorheism in the late Neogene-Quaternary allowing westward dispersals that resulted in many cladogenetic events and a high rate of endemism in western Iberia. The results of this study also: (i) confirm the paraphyly of S. pyrenaicus with respect to S. carolitertii, and thus the possible presence of a new taxon in the Portuguese Tagus currently assigned to S. pyrenaicus; (ii) support the taxonomic separation of the Guadiana and Sado populations of S. pyrenaicus; (iii) show the need for further population sampling and taxonomic research to clarify the phylogenetic status of A. arcasii from the Minho basin and of the I. lusitanicum populations in the Sado and Tagus basins; and (iv) indicate that A. occidentale, I. olisiponensis and P. duriensis are the most ancient lineages within their respective genera.

The space of ultrametric phylogenetic trees

The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data. Hence the question of statistical consistency of such methods is equivalent to the consistency of the summary of the sample. More generally, statistical consistency is ensured by the tree space used to analyse the sample. In this paper, we consider two standard parameterisations of phylogenetic time-trees used in evolutionary models: inter-coalescent interval lengths and absolute times of divergence events. For each of these parameterisations we introduce a natural metric space on ultrametric phylogenetic trees. We compare the introduced spaces with existing models of tree space and formulate several formal requirements that a metric space on phylogenetic trees must possess in order to be a satisfactory space for statistical analysis, and justify them. We show that only a few known constructions of the space of phylogenetic trees satisfy these requirements. However, our results suggest that these basic requirements are not enough to distinguish between the two metric spaces we introduce and that the choice between metric spaces requires additional properties to be considered. Particularly, that the summary tree minimising the square distance to the trees from the sample might be different for different parameterisations. This suggests that further fundamental insight is needed into the problem of statistical consistency of phylogenetic inference methods.

A Bayesian Supertree Model for Genome-Wide Species Tree Reconstruction

Current phylogenomic data sets highlight the need for species tree methods able to deal with several sources of gene tree/species tree incongruence. At the same time, we need to make most use of all available data. Most species tree methods deal with single processes of phylogenetic discordance, namely, gene duplication and loss, incomplete lineage sorting (ILS) or horizontal gene transfer. In this manuscript, we address the problem of species tree inference from multilocus, genome-wide data sets regardless of the presence of gene duplication and loss and ILS therefore without the need to identify orthologs or to use a single individual per species. We do this by extending the idea of Maximum Likelihood (ML) supertrees to a hierarchical Bayesian model where several sources of gene tree/species tree disagreement can be accounted for in a modular manner. We implemented this model in a computer program called guenomu whose inputs are posterior distributions of unrooted gene tree topologies for multiple gene families, and whose output is the posterior distribution of rooted species tree topologies. We conducted extensive simulations to evaluate the performance of our approach in comparison with other species tree approaches able to deal with more than one leaf from the same species. Our method ranked best under simulated data sets, in spite of ignoring branch lengths, and performed well on empirical data, as well as being fast enough to analyze relatively large data sets. Our Bayesian supertree method was also very successful in obtaining better estimates of gene trees, by reducing the uncertainty in their distributions. In addition, our results show that under complex simulation scenarios, gene tree parsimony is also a competitive approach once we consider its speed, in contrast to more sophisticated models.

Molecular Evolution of Aralkylamine N-Acetyltransferase in Fish: A Genomic Survey

All living organisms synchronize biological functions with environmental changes; melatonin plays a vital role in regulating daily and seasonal variations. Due to rhythmic activity of the timezyme aralkylamine N-acetyltransferase (AANAT), the blood level of melatonin increases at night and decreases during daytime. Whereas other vertebrates have a single form of AANAT, bony fishes possess various isoforms of aanat genes, though the reasons are still unclear. Here, we have taken advantage of multiple unpublished teleost aanat sequences to explore and expand our understanding of the molecular evolution of aanat in fish. Our results confirm that two rounds of whole-genome duplication (WGD) led to the existence of three fish isoforms of aanat, i.e., aanat1a, aanat1b, and aanat2; in addition, gene loss led to the absence of some forms from certain special fish species. Furthermore, we suggest the different roles of two aanat1s in amphibious mudskippers, and speculate that the loss of aanat1a, may be related to terrestrial vision change. Several important sites of AANAT proteins and regulatory elements of aanat genes were analyzed for structural comparison and functional forecasting, respectively, which provides insights into the molecular evolution of the differences between AANAT1 and AANAT2.

Point estimates in phylogenetic reconstructions

Motivation: The construction of statistics for summarizing posterior samples returned by a Bayesian phylogenetic study has so far been hindered by the poor geometric insights available into the space of phylogenetic trees, and ad hoc methods such as the derivation of a consensus tree makeup for the ill-definition of the usual concepts of posterior mean, while bootstrap methods mitigate the absence of a sound concept of variance. Yielding satisfactory results with sufficiently concentrated posterior distributions, such methods fall short of providing a faithful summary of posterior distributions if the data do not offer compelling evidence for a single topology.

Results: Building upon previous work of Billera et al., summary statistics such as sample mean, median and variance are defined as the geometric median, Fréchet mean and variance, respectively. Their computation is enabled by recently published works, and embeds an algorithm for computing shortest paths in the space of trees. Studying the phylogeny of a set of plants, where several tree topologies occur in the posterior sample, the posterior mean balances correctly the contributions from the different topologies, where a consensus tree would be biased. Comparisons of the posterior mean, median and consensus trees with the ground truth using simulated data also reveals the benefits of a sound averaging method when reconstructing phylogenetic trees.

Availability and implementation: We provide two independent implementations of the algorithm for computing Fréchet means, geometric medians and variances in the space of phylogenetic trees. TFBayes: https://github.com/pbenner/tfbayes, TrAP: https://github.com/bacak/TrAP.

Contact:philipp.benner@mis.mpg.de

Looking for trees in the forest: summary tree from posterior samples

Background

Bayesian phylogenetic analysis generates a set of trees which are often condensed into a single tree representing the whole set. Many methods exist for selecting a representative topology for a set of unrooted trees, few exist for assigning branch lengths to a fixed topology, and even fewer for simultaneously setting the topology and branch lengths. However, there is very little research into locating a good representative for a set of rooted time trees like the ones obtained from a BEAST analysis.

Results

We empirically compare new and known methods for generating a summary tree. Some new methods are motivated by mathematical constructions such as tree metrics, while the rest employ tree concepts which work well in practice. These use more of the posterior than existing methods, which discard information not directly mapped to the chosen topology. Using results from a large number of simulations we assess the quality of a summary tree, measuring (a) how well it explains the sequence data under the model and (b) how close it is to the “truth”, i.e to the tree used to generate the sequences.

Conclusions

Our simulations indicate that no single method is “best”. Methods producing good divergence time estimates have poor branch lengths and lower model fit, and vice versa. Using the results presented here, a user can choose the appropriate method based on the purpose of the summary tree.

Statistical phylogenetic tree analysis using differences of means

We propose a statistical method to test whether two phylogenetic trees with given alignments are significantly incongruent. Our method compares the two distributions of phylogenetic trees given by two input alignments, instead of comparing point estimations of trees. This statistical approach can be applied to gene tree analysis for example, detecting unusual events in genome evolution such as horizontal gene transfer and reshuffling. Our method uses difference of means to compare two distributions of trees, after mapping trees into a vector space. Bootstrapping alignment columns can then be applied to obtain p-values. To compute distances between means, we employ a "kernel method" which speeds up distance calculations when trees are mapped in a high-dimensional feature space, e.g., splits or quartets feature space. In this pilot study, first we test our statistical method on data sets simulated under a coalescence model, to test whether two alignments are generated by congruent gene trees. We follow our simulation results with applications to data sets of gophers and lice, grasses and their endophytes, and different fungal genes from the same genome. A companion toolkit, Phylotree, is provided to facilitate computational experiments.