Asymmetric Cluster-Based Measures for Comparative Phylogenetics

Phylogenetic inference and reconstruction methods generate hypotheses on evolutionary history. Competing inference methods are frequently used, and the evaluation of the generated hypotheses is achieved using tree comparison costs. The Robinson-Foulds (RF) distance is a widely used cost to compare the topology of two trees, but this cost is sensitive to tree error and can overestimate tree differences. To overcome this limitation, a refined version of the RF distance called the Cluster Affinity (CA) distance was introduced. However, CA distances are symmetric and cannot compare different types of trees. These asymmetric comparisons occur when gene trees are compared with species trees, when disparate datasets are integrated into a supertree, or when tree comparison measures are used to infer a phylogenetic network. In this study, we introduce a relaxation of the original Affinity distance to compare heterogeneous trees called the asymmetric CA cost. We also develop a biologically interpretable cost, the Cluster Support cost that normalizes by cluster size across gene trees. The characteristics of these costs are similar to the symmetric CA cost. We describe efficient algorithms, derive the exact diameters, and use these to standardize the cost to be applicable in practice. These costs provide objective, fine-scale, and biologically interpretable values that can assess differences and similarities between phylogenetic trees.

Unifying duplication episode clustering and gene-species mapping inference

We present a novel problem, called MetaEC, which aims to infer gene-species assignments in a collection of partially leaf-labeled gene trees labels by minimizing the size of duplication episode clustering (EC). This problem is particularly relevant in metagenomics, where incomplete data often poses a challenge in the accurate reconstruction of gene histories. To solve MetaEC, we propose a polynomial time dynamic programming (DP) formulation that verifies the existence of a set of duplication episodes from a predefined set of episode candidates. In addition, we design a method to infer distributions of gene-species mappings. We then demonstrate how to use DP to design an algorithm that solves MetaEC. Although the algorithm is exponential in the worst case, we introduce a heuristic modification of the algorithm that provides a solution with the knowledge that it is exact. To evaluate our method, we perform two computational experiments on simulated and empirical data containing whole genome duplication events, showing that our algorithm is able to accurately infer the corresponding events.

Embedding gene trees into phylogenetic networks by conflict resolution algorithms

BACKGROUND

Phylogenetic networks are mathematical models of evolutionary processes involving reticulate events such as hybridization, recombination, or horizontal gene transfer. One of the crucial notions in phylogenetic network modelling is displayed tree, which is obtained from a network by removing a set of reticulation edges. Displayed trees may represent an evolutionary history of a gene family if the evolution is shaped by reticulation events.

RESULTS

We address the problem of inferring an optimal tree displayed by a network, given a gene tree G and a tree-child network N, under the deep coalescence and duplication costs. We propose an O(mn)-time dynamic programming algorithm (DP) to compute a lower bound of the optimal displayed tree cost, where m and n are the sizes of G and N, respectively. In addition, our algorithm can verify whether the solution is exact. Moreover, it provides a set of reticulation edges corresponding to the obtained cost. If the cost is exact, the set induces an optimal displayed tree. Otherwise, the set contains pairs of conflicting edges, i.e., edges sharing a reticulation node. Next, we show a conflict resolution algorithm that requires [Formula: see text] invocations of DP in the worst case, where r is the number of reticulations. We propose a similar [Formula: see text]-time algorithm for level-k tree-child networks and a branch and bound solution to compute lower and upper bounds of optimal costs. We also extend the algorithms to a broader class of phylogenetic networks. Based on simulated data, the average runtime is [Formula: see text] under the deep-coalescence cost and [Formula: see text] under the duplication cost.

CONCLUSIONS

Despite exponential complexity in the worst case, our algorithms perform significantly well on empirical and simulated datasets, due to the strategy of resolving internal dissimilarities between gene trees and networks. Therefore, the algorithms are efficient alternatives to enumeration strategies commonly proposed in the literature and enable analyses of complex networks with dozens of reticulations.

Taming the Duplication-Loss-Coalescence Model with Integer Linear Programming

The duplication-loss-coalescence (DLC) parsimony model is invaluable for analyzing the complex scenarios of concurrent duplication loss and deep coalescence events in the evolution of gene families. However, inferring such scenarios for already moderately sized families is prohibitive owing to the computational complexity involved. To overcome this stringent limitation, we make the first step by describing a flexible integer linear programming (ILP) formulation for inferring DLC evolutionary scenarios. Then, to make the DLC model more scalable, we introduce four sensibly constrained versions of the model and describe modified versions of our ILP formulation reflecting these constraints. Our simulation studies showcase that our constrained ILP formulations compute evolutionary scenarios that are substantially larger than scenarios computable under our original ILP formulation and the original dynamic programming algorithm by Wu et al. Furthermore, scenarios computed under our constrained DLC models are remarkably accurate compared with corresponding scenarios under the original DLC model, which we also confirm in an empirical study with thousands of gene families.

Exact median-tree inference for unrooted reconciliation costs

Background

Solving median tree problems under tree reconciliation costs is a classic and well-studied approach for inferring species trees from collections of discordant gene trees. These problems are NP-hard, and therefore are, in practice, typically addressed by local search heuristics. So far, however, such heuristics lack any provable correctness or precision. Further, even for small phylogenetic studies, it has been demonstrated that local search heuristics may only provide sub-optimal solutions. Obviating such heuristic uncertainties are exact dynamic programming solutions that allow solving tree reconciliation problems for smaller phylogenetic studies. Despite these promises, such exact solutions are only suitable for credibly rooted input gene trees, which constitute only a tiny fraction of the readily available gene trees. Standard gene tree inference approaches provide only unrooted gene trees and accurately rooting such trees is often difficult, if not impossible.

Results

Here, we describe complex dynamic programming solutions that represent the first nonnaïve exact solutions for solving the tree reconciliation problems for unrooted input gene trees. Further, we show that the asymptotic runtime of the proposed solutions does not increase when compared to the most time-efficient dynamic programming solutions for rooted input trees.

Conclusions

In an experimental evaluation, we demonstrate that the described solutions for unrooted gene trees are, like the solutions for rooted input gene trees, suitable for smaller phylogenetic studies. Finally, for the first time, we study the accuracy of classic local search heuristics for unrooted tree reconciliation problems.

Minimizing genomic duplication episodes

BACKGROUND

The genomic duplication study is fundamental to understand the process of evolution. In evolutionary molecular biology, many approaches focus on discovering the occurrences of gene duplications and multiple gene duplication episodes and their locations in the Tree of Life. To reconstruct such episodes, one can cluster single gene duplications inferred by reconciling a set of gene trees with a species tree.

RESULTS

We propose an efficient quadratic time algorithm to solve the problem of genomic duplication clustering, in which input gene trees are rooted, episode locations are restricted to preserve the minimal number of single gene duplications, clustering rules are described by minimum episodes method, and the goal is based on the recently introduced new approach to minimize the maximal number of duplication episodes on a single path, called here the MP score. Based on our theoretical results, we show new algorithmic relationships between the MP score and the minimum episodes (ME) score, defined as the minimal number of duplication episodes.

CONCLUSIONS

Our evaluation analysis on three empirical datasets demonstrates, that under the model in which the minimal number of duplications is preserved, the duplication clusterings with minimal MP score support the clusterings with the minimal total number of duplication episodes.

AVAILABILITY

The software is available at https://bitbucket.org/pgor17/rmp.

Minimizing the deep coalescence cost

Metagenomic studies identify the species present in an environmental sample usually by using procedures that match molecular sequences, e.g. genes, with the species taxonomy. Here, we first formulate the problem of gene-species matching in the parsimony framework using binary phylogenetic gene and species trees under the deep coalescence cost and the assumption that each gene is paired uniquely with one species. In particular, we solve the problem in the cases when one of the trees is a caterpillar. Next, we propose a dynamic programming algorithm, which solves the problem exactly, however, its time and space complexity is exponential. Next, we generalize the problem to include non-binary trees and show the solution for caterpillar trees. We then propose time and space-efficient heuristic algorithms for solving the gene-species matching problem for any input trees. Finally, we present the results of computational experiments on simulated and empirical datasets consisting of binary tree pairs.

Locus-aware decomposition of gene trees with respect to polytomous species trees

Background

Horizontal gene transfer (HGT), a process of acquisition and fixation of foreign genetic material, is an important biological phenomenon. Several approaches to HGT inference have been proposed. However, most of them either rely on approximate, non-phylogenetic methods or on the tree reconciliation, which is computationally intensive and sensitive to parameter values.

Results

We investigate the locus tree inference problem as a possible alternative that combines the advantages of both approaches. We present several algorithms to solve the problem in the parsimony framework. We introduce a novel tree mapping, which allows us to obtain a heuristic solution to the problems of locus tree inference and duplication classification.

Conclusions

Our approach allows for faster comparisons of gene and species trees and improves known algorithms for duplication inference in the presence of polytomies in the species trees. We have implemented our algorithms in a software tool available at https://github.com/mciach/LocusTreeInference.

Inferring duplication episodes from unrooted gene trees

Background

One of evolutionary molecular biology fundamental issues is to discover genomic duplication events and their correspondence to the species tree. Such events can be reconstructed by clustering single gene duplications inferred by reconciling a set of gene trees with a species tree.

Results

Here we propose the first solutions to the genomic duplication problem in which every reconciliation with the minimal number of single gene duplications is allowed and the method of clustering called minimum episodes under the assumption that input gene trees are unrooted.

Conclusions

We showed new theoretical properties of unrooted reconciliation for the duplication cost and apply them to design several exact and heuristic algorithms for solving the problem. Our evaluation study on empirical dataset confirmed several genomic duplication events from the literature and demonstrate that algorithms can be successfully applied.

Genomic duplication problems for unrooted gene trees

BACKGROUND

Discovering the location of gene duplications and multiple gene duplication episodes is a fundamental issue in evolutionary molecular biology. The problem introduced by Guigó et al. in 1996 is to map gene duplication events from a collection of rooted, binary gene family trees onto theirs corresponding rooted binary species tree in such a way that the total number of multiple gene duplication episodes is minimized. There are several models in the literature that specify how gene duplications from gene families can be interpreted as one duplication episode. However, in all duplication episode problems gene trees are rooted. This restriction limits the applicability, since unrooted gene family trees are frequently inferred by phylogenetic methods.

RESULTS

In this article we show the first solution to the open problem of episode clustering where the input gene family trees are unrooted. In particular, by using theoretical properties of unrooted reconciliation, we show an efficient algorithm that reduces this problem into the episode clustering problems defined for rooted trees. We show theoretical properties of the reduction algorithm and evaluation of empirical datasets.

CONCLUSIONS

We provided algorithms and tools that were successfully applied to several empirical datasets. In particular, our comparative study shows that we can improve known results on genomic duplication inference from real datasets.

Gene Tree Diameter for Deep Coalescence

The deep coalescence cost accounts for discord caused by deep coalescence between a gene tree and a species tree. It is a major concern that the diameter of a gene tree (the tree's maximum deep coalescence cost across all species trees) depends on its topology, which can largely obfuscate phylogenetic studies. While this bias can be compensated by normalizing the deep coalescence cost using diameters, obtaining them efficiently has been posed as an open problem by Than and Rosenberg. Here, we resolve this problem by describing a linear time algorithm to compute the diameter of a gene tree. In addition, we provide a complete classification of the species trees yielding this diameter to guide phylogenetic analyses.

Maximizing Deep Coalescence Cost

The minimizing deep coalescence (MDC) problem seeks a species tree that reconciles the given gene trees with the minimum number of deep coalescence events, called deep coalescence (DC) cost. To better assess MDC species trees we investigate into a basic mathematical property of the DC cost, called the diameter. Given a gene tree, a species tree, and a leaf labeling function that assigns leaf-genes of the gene tree to a leaf-species in the species tree from which they were sampled, the DC cost describes the discordance between the trees caused by deep coalescence events. The diameter of a gene tree and a species tree is the maximum DC cost across all leaf labelings for these trees. We prove fundamental mathematical properties describing precisely these diameters for bijective and general leaf labelings, and present efficient algorithms to compute the diameters and their corresponding leaf labelings. In particular, we describe an optimal, i.e., linear time, algorithm for the bijective case. Finally, in an experimental study we demonstrate that the average diameters between a gene tree and a species tree grow significantly slower than their naive upper bounds, suggesting that our exact bounds can significantly improve on assessing DC costs when using diameters.

Exact solutions for species tree inference from discordant gene trees

Phylogenetic analysis has to overcome the grant challenge of inferring accurate species trees from evolutionary histories of gene families (gene trees) that are discordant with the species tree along whose branches they have evolved. Two well studied approaches to cope with this challenge are to solve either biologically informed gene tree parsimony (GTP) problems under gene duplication, gene loss, and deep coalescence, or the classic RF supertree problem that does not rely on any biological model. Despite the potential of these problems to infer credible species trees, they are NP-hard. Therefore, these problems are addressed by heuristics that typically lack any provable accuracy and precision. We describe fast dynamic programming algorithms that solve the GTP problems and the RF supertree problem exactly, and demonstrate that our algorithms can solve instances with data sets consisting of as many as 22 taxa. Extensions of our algorithms can also report the number of all optimal species trees, as well as the trees themselves. To better asses the quality of the resulting species trees that best fit the given gene trees, we also compute the worst case species trees, their numbers, and optimization score for each of the computational problems. Finally, we demonstrate the performance of our exact algorithms using empirical and simulated data sets, and analyze the quality of heuristic solutions for the studied problems by contrasting them with our exact solutions.

DrML: probabilistic modeling of gene duplications

DrML is a software program for inferring evolutionary scenarios from a gene tree and a species tree with speciation time estimates that is based on a general maximum likelihood model. The program implements novel algorithms that efficiently infer most likely scenarios of gene duplication and loss events. Our comparative studies suggest that the general maximum likelihood model provides more credible estimates than standard parsimony reconciliation, especially when speciation times differ significantly. DrML is an open source project written in Python, and along with an on-line manual and sample data sets publicly available.

The Paleozoic origin of enzymatic lignin decomposition reconstructed from 31 fungal genomes

Wood is a major pool of organic carbon that is highly resistant to decay, owing largely to the presence of lignin. The only organisms capable of substantial lignin decay are white rot fungi in the Agaricomycetes, which also contains non-lignin-degrading brown rot and ectomycorrhizal species. Comparative analyses of 31 fungal genomes (12 generated for this study) suggest that lignin-degrading peroxidases expanded in the lineage leading to the ancestor of the Agaricomycetes, which is reconstructed as a white rot species, and then contracted in parallel lineages leading to brown rot and mycorrhizal species. Molecular clock analyses suggest that the origin of lignin degradation might have coincided with the sharp decrease in the rate of organic carbon burial around the end of the Carboniferous period.

Inferring phylogeny from whole genomes

MOTIVATION

Inferring species phylogenies with a history of gene losses and duplications is a challenging and an important task in computational biology. This problem can be solved by duplication-loss models in which the primary step is to reconcile a rooted gene tree with a rooted species tree. Most modern methods of phylogenetic reconstruction (from sequences) produce unrooted gene trees. This limitation leads to the problem of transforming unrooted gene tree into a rooted tree, and then reconciling rooted trees. The main questions are 'What about biological interpretation of choosing rooting?', 'Can we find efficiently the optimal rootings?', 'Is the optimal rooting unique?'.

RESULTS

In this paper we present a model of reconciling unrooted gene tree with a rooted species tree, which is based on a concept of choosing rooting which has minimal reconciliation cost. Our analysis leads to the surprising property that all the minimal rootings have identical distributions of gene duplications and gene losses in the species tree. It implies, in our opinion, that the concept of an optimal rooting is very robust, and thus biologically meaningful. Also, it has nice computational properties. We present a linear time and space algorithm for computing optimal rooting(s). This algorithm was used in two different ways to reconstruct the optimal species phylogeny of five known yeast genomes from approximately 4700 gene trees. Moreover, we determined locations (history) of all gene duplications and gene losses in the final species tree. It is interesting to notice that the top five species trees are the same for both methods.

AVAILABILITY

Software and documentation are freely available from http://bioputer.mimuw.edu.pl/~gorecki/urec

[Evaluation of prophylaxis and actual prevalence of HBV infection in twelve hemodialysis centers of Northern Poland]

The aim of the study was to estimate the HBV infection preventive measures used in the twelve dialysis centres in north Poland. In all of the centres hepatitis B vaccination and segregation of HBV infected patients (dedicated machines or separate rooms), which are the two basic HBV infection control methods, were introduced. Our results point out that in some of the centres certain modification of these methods would be possible, including universal predialysis vaccination programme, changes in hepatitis B vaccination schedules with most effective routes of vaccination only and dedication for HBV infected patients not only separate rooms but separate dialysis staff as well.