Visualizing phylogenetic tree landscapes.

BACKGROUND: Genomic-scale sequence alignments are increasingly used to infer phylogenies in order to better understand the processes and patterns of evolution. Different partitions within these new alignments (e.g., genes, codon positions, and structural features) often favor hundreds if not thousands of competing phylogenies. Summarizing and comparing phylogenies obtained from multi-source data sets using current consensus tree methods discards valuable information and can disguise potential methodological problems. Discovery of efficient and accurate dimensionality reduction methods used to display at once in 2- or 3- dimensions the relationship among these competing phylogenies will help practitioners diagnose the limits of current evolutionary models and potential problems with phylogenetic reconstruction methods when analyzing large multi-source data sets. We introduce several dimensionality reduction methods to visualize in 2- and 3-dimensions the relationship among competing phylogenies obtained from gene partitions found in three mid- to large-size mitochondrial genome alignments. We test the performance of these dimensionality reduction methods by applying several goodness-of-fit measures. The intrinsic dimensionality of each data set is also estimated to determine whether projections in 2- and 3-dimensions can be expected to reveal meaningful relationships among trees from different data partitions. Several new approaches to aid in the comparison of different phylogenetic landscapes are presented. RESULTS: Curvilinear Components Analysis (CCA) and a stochastic gradient decent (SGD) optimization method give the best representation of the original tree-to-tree distance matrix for each of the three- mitochondrial genome alignments and greatly outperformed the method currently used to visualize tree landscapes. The CCA + SGD method converged at least as fast as previously applied methods for visualizing tree landscapes. We demonstrate for all three mtDNA alignments that 3D projections significantly increase the fit between the tree-to-tree distances and can facilitate the interpretation of the relationship among phylogenetic trees. CONCLUSIONS: We demonstrate that the choice of dimensionality reduction method can significantly influence the spatial relationship among a large set of competing phylogenetic trees. We highlight the importance of selecting a dimensionality reduction method to visualize large multi-locus phylogenetic landscapes and demonstrate that 3D projections of mitochondrial tree landscapes better capture the relationship among the trees being compared.

TreeScaper: Visualizing and Extracting Phylogenetic Signal from Sets of Trees.

Modern phylogenomic analyses often result in large collections of phylogenetic trees representing uncertainty in individual gene trees, variation across genes, or both. Extracting phylogenetic signal from these tree sets can be challenging, as they are difficult to visualize, explore, and quantify. To overcome some of these challenges, we have developed TreeScaper, an application for tree set visualization as well as the identification of distinct phylogenetic signals. GUI and command-line versions of TreeScaper and a manual with tutorials can be downloaded from https://github.com/whuang08/TreeScaper/releases TreeScaper is distributed under the GNU General Public License.

Descent algorithms on oblique manifold for source-adaptive ICA contrast.

A Riemannian manifold optimization strategy is proposed to facilitate the relaxation of the orthonormality constraint in a more natural way in the course of performing independent component analysis (ICA) that employs a mutual information-based source-adaptive contrast function. Despite the extensive development of manifold techniques catering to the orthonormality constraint, only a limited number of works have been dedicated to oblique manifold (OB) algorithms to intrinsically handle the normality constraint, which has been empirically shown to be superior to other Riemannian and Euclidean approaches. Imposing the normality constraint implicitly, in line with the ICA definition, essentially guarantees a substantial improvement in the solution accuracy, by way of increased degrees of freedom while searching for an optimal unmixing ICA matrix, in contrast with the orthonormality constraint. Designs of the steepest descent, conjugate gradient with Hager-Zhang or a hybrid update parameter, quasi-Newton, and cost-effective quasi-Newton methods intended for OB are presented in this paper. Their performance is validated using natural images and systematically compared with the popular state-of-the-art approaches in order to assess the performance effects of the choice of algorithm and the use of a Riemannian rather than Euclidean framework. We surmount the computational challenge associated with the direct estimation of the source densities using the improved fast Gauss transform in the evaluation of the contrast function and its gradient. The proposed OB schemes may find applications in the offline image/signal analysis, wherein, on one hand, the computational overhead can be tolerated, and, on the other, the solution quality holds paramount interest.