Geometric medians in reconciliation spaces of phylogenetic trees

A Linear Time Solution to the Labeled Robinson-Foulds Distance Problem

MOTIVATION

A large variety of pairwise measures of similarity or dissimilarity have been developed for comparing phylogenetic trees, e.g. species trees or gene trees. Due to its intuitive definition in terms of tree clades and bipartitions and its computational efficiency, the Robinson-Foulds (RF) distance is the most widely used for trees with unweighted edges and labels restricted to leaves (representing the genetic elements being compared). However, in the case of gene trees, an important information revealing the nature of the homologous relation between gene pairs (orthologs, paralogs, xenologs) is the type of event associated to each internal node of the tree, typically speciations or duplications, but other types of events may also be considered, such as horizontal gene transfers. This labeling of internal nodes is usually inferred from a gene tree/species tree reconciliation method. Here, we address the problem of comparing such event-labeled trees. The problem differs from the classical problem of comparing uniformly labeled trees (all labels belonging to the same alphabet) that may be done using the Tree Edit Distance (TED) mainly due to the fact that, in our case, two different alphabets are considered for the leaves and internal nodes of the tree, and leaves are not affected by edit operations.

RESULTS

We propose an extension of the RF distance to event-labeled trees, based on edit operations comparable to those considered for TED: node insertion, node deletion and label substitution. We show that this new Labeled Robinson Foulds (LRF) distance can be computed in linear time, in addition of maintaining other desirable properties: being a metric, reducing to RF for trees with no labels on internal nodes and maintaining an intuitive interpretation. The algorithm for computing the LRF distance enables novel analyses on event-label trees such as reconciled gene trees. Here, we use it to study the impact of taxon sampling on labeled gene tree inference, and conclude that denser taxon sampling yields trees with better topology but worse labeling.

Efficiently sparse listing of classes of optimal cophylogeny reconciliations

Background

Cophylogeny reconciliation is a powerful method for analyzing host-parasite (or host-symbiont) co-evolution. It models co-evolution as an optimization problem where the set of all optimal solutions may represent different biological scenarios which thus need to be analyzed separately. Despite the significant research done in the area, few approaches have addressed the problem of helping the biologist deal with the often huge space of optimal solutions.

Results

In this paper, we propose a new approach to tackle this problem. We introduce three different criteria under which two solutions may be considered biologically equivalent, and then we propose polynomial-delay algorithms that enumerate only one representative per equivalence class (without listing all the solutions).

Conclusions

Our results are of both theoretical and practical importance. Indeed, as shown by the experiments, we are able to significantly reduce the space of optimal solutions while still maintaining important biological information about the whole space.

Reconciliation Reconsidered: In Search of a Most Representative Reconciliation in the Duplication-Transfer-Loss Model

Maximum parsimony reconciliation is a fundamental technique for studying the evolutionary histories of pairs of entities such as genes and species, parasites and hosts, and species and their biogeographical habitats. In these contexts, reconciliation is generally performed using the duplication-transfer-loss (DTL) model in a maximum parsimony framework. While efficient maximum parsimony reconciliation algorithms are known for the DTL model, the number of such reconciliations can grow exponentially with the sizes of the two phylogenetic trees. Choosing a maximum parsimony reconciliation arbitrarily may lead to conclusions that are not supported, and may even be contradicted, by other equally optimal reconciliations. This paper addresses the fundamental problem of how well a single reconciliation can represent the entire space of optimal reconciliations.

eMPRess: a systematic cophylogeny reconciliation tool

SUMMARY

We describe eMPRess, a software program for phylogenetic tree reconciliation under the duplication-transfer-loss model that systematically addresses the problems of choosing event costs and selecting representative solutions, enabling users to make more robust inferences.

AVAILABILITY AND IMPLEMENTATION

eMPRess is freely available at http://www.cs.hmc.edu/empress.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Capybara: equivalence ClAss enumeration of coPhylogenY event-BAsed ReconciliAtions

MOTIVATION

Phylogenetic tree reconciliation is the method of choice in analyzing host-symbiont systems. Despite the many reconciliation tools that have been proposed in the literature, two main issues remain unresolved: (i) listing suboptimal solutions (i.e. whose score is 'close' to the optimal ones) and (ii) listing only solutions that are biologically different 'enough'. The first issue arises because the optimal solutions are not always the ones biologically most significant; providing many suboptimal solutions as alternatives for the optimal ones is thus very useful. The second one is related to the difficulty to analyze an often huge number of optimal solutions. In this article, we propose Capybara that addresses both of these problems in an efficient way. Furthermore, it includes a tool for visualizing the solutions that significantly helps the user in the process of analyzing the results.

AVAILABILITY AND IMPLEMENTATION

The source code, documentation and binaries for all platforms are freely available at https://capybara-doc.readthedocs.io/.

CONTACT

yishu.wang@univ-lyon1.fr or blerina.sinaimeri@inria.fr.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

An efficient exact algorithm for computing all pairwise distances between reconciliations in the duplication-transfer-loss model

BACKGROUND

Maximum parsimony reconciliation in the duplication-transfer-loss model is widely used in studying the evolutionary histories of genes and species and in studying coevolution of parasites and their hosts and pairs of symbionts. While efficient algorithms are known for finding maximum parsimony reconciliations, the number of reconciliations can grow exponentially in the size of the trees. An understanding of the space of maximum parsimony reconciliations is necessary to determine whether a single reconciliation can adequately represent the space or whether multiple representative reconciliations are needed.

RESULTS

We show that for any instance of the reconciliation problem, the distribution of pairwise distances can be computed exactly by an efficient polynomial-time algorithm with respect to several different distance metrics. We describe the algorithm, analyze its asymptotic worst-case running time, and demonstrate its utility and viability on a large biological dataset.

CONCLUSIONS

This result provides new insights into the structure of the space of maximum parsimony reconciliations. These insights are likely to be useful in the wide range of applications that employ reconciliation methods.

Hierarchical clustering of maximum parsimony reconciliations

BACKGROUND

Maximum parsimony reconciliation in the duplication-transfer-loss model is a widely-used method for analyzing the evolutionary histories of pairs of entities such as hosts and parasites, symbiont species, and species and genes. While efficient algorithms are known for finding maximum parsimony reconciliations, the number of such reconciliations can be exponential in the size of the trees. Since these reconciliations can differ substantially from one another, making inferences from any one reconciliation may lead to conclusions that are not supported, or may even be contradicted, by other maximum parsimony reconciliations. Therefore, there is a need to find small sets of best representative reconciliations when the space of solutions is large and diverse.

RESULTS

We provide a general framework for hierarchical clustering the space of maximum parsimony reconciliations. We demonstrate this framework for two specific linkage criteria, one that seeks to maximize the average support of the events found in the reconciliations in each cluster and the other that seeks to minimize the distance between reconciliations in each cluster. We analyze the asymptotic worst-case running times and provide experimental results that demonstrate the viability and utility of this approach.

CONCLUSIONS

The hierarchical clustering algorithm method proposed here provides a new approach to find a set of representative reconciliations in the potentially vast and diverse space of maximum parsimony reconciliations.