virDTL: Viral Recombination Analysis Through Phylogenetic Reconciliation and Its Application to Sarbecoviruses and SARS-CoV-2

An accurate understanding of the evolutionary history of rapidly-evolving viruses like SARS-CoV-2, responsible for the COVID-19 pandemic, is crucial to tracking and preventing the spread of emerging pathogens. However, viruses undergo frequent recombination, which makes it difficult to trace their evolutionary history using traditional phylogenetic methods. In this study, we present a phylogenetic workflow, virDTL, for analyzing viral evolution in the presence of recombination. Our approach leverages reconciliation methods developed for inferring horizontal gene transfer in prokaryotes and, compared to existing tools, is uniquely able to identify ancestral recombinations while accounting for several sources of inference uncertainty, including in the construction of a strain tree, estimation and rooting of gene family trees, and reconciliation itself. We apply this workflow to the Sarbecovirus subgenus and demonstrate how a principled analysis of predicted recombination gives insight into the evolution of SARS-CoV-2. In addition to providing confirming evidence for the horseshoe bat as its zoonotic origin, we identify several ancestral recombination events that merit further study.

Improved Duplication-Transfer-Loss Reconciliation with Extinct and Unsampled Lineages

Duplication-Transfer-Loss (DTL) reconciliation is a widely used computational technique for understanding gene family evolution and inferring horizontal gene transfer (transfer for short) in microbes. However, most existing models and implementations of DTL reconciliation cannot account for the effect of unsampled or extinct species lineages on the evolution of gene families, likely affecting their accuracy. Accounting for the presence and possible impact of any unsampled species lineages, including those that are extinct, is especially important for inferring and studying horizontal transfer since many genes in the species lineages represented in the reconciliation analysis are likely to have been acquired through horizontal transfer from unsampled lineages. While models of DTL reconciliation that account for transfer from unsampled lineages have already been proposed, they use a relatively simple framework for transfer from unsampled lineages and cannot explicitly infer the location on the species tree of each unsampled or extinct lineage associated with an identified transfer event. Furthermore, there does not yet exist any systematic studies to assess the impact of accounting for unsampled lineages on the accuracy of DTL reconciliation. In this work, we address these deficiencies by (i) introducing an extended DTL reconciliation model, called the DTLx reconciliation model, that accounts for unsampled and extinct species lineages in a new, more functional manner compared to existing models, (ii) showing that optimal reconciliations under the new DTLx reconciliation model can be computed just as efficiently as under the fastest DTL reconciliation model, (iii) providing an efficient algorithm for sampling optimal DTLx reconciliations uniformly at random, (iv) performing the first systematic simulation study to assess the impact of accounting for unsampled lineages on the accuracy of DTL reconciliation, and (v) comparing the accuracies of inferring transfers from unsampled lineages under our new model and the only other previously proposed parsimony-based model for this problem.

Indirect identification of horizontal gene transfer

Several implicit methods to infer horizontal gene transfer (HGT) focus on pairs of genes that have diverged only after the divergence of the two species in which the genes reside. This situation defines the edge set of a graph, the later-divergence-time (LDT) graph, whose vertices correspond to genes colored by their species. We investigate these graphs in the setting of relaxed scenarios, i.e., evolutionary scenarios that encompass all commonly used variants of duplication-transfer-loss scenarios in the literature. We characterize LDT graphs as a subclass of properly vertex-colored cographs, and provide a polynomial-time recognition algorithm as well as an algorithm to construct a relaxed scenario that explains a given LDT. An edge in an LDT graph implies that the two corresponding genes are separated by at least one HGT event. The converse is not true, however. We show that the complete xenology relation is described by an rs-Fitch graph, i.e., a complete multipartite graph satisfying constraints on the vertex coloring. This class of vertex-colored graphs is also recognizable in polynomial time. We finally address the question “how much information about all HGT events is contained in LDT graphs” with the help of simulations of evolutionary scenarios with a wide range of duplication, loss, and HGT events. In particular, we show that a simple greedy graph editing scheme can be used to efficiently detect HGT events that are implicitly contained in LDT graphs.

An Integrated Reconciliation Framework for Domain, Gene, and Species Level Evolution

The majority of genes in eukaryotes consists of one or more protein domains that can be independently lost or gained during evolution. This gain and loss of protein domains, through domain duplications, transfers, or losses, has important evolutionary and functional consequences. Yet, even though it is well understood that domains evolve inside genes and genes inside species, there do not exist any computational frameworks to simultaneously model the evolution of domains, genes, and species and account for their inter-dependency. Here, we develop an integrated model of domain evolution that explicitly captures the interdependence of domain-, gene-, and species-level evolution. Our model extends the classical phylogenetic reconciliation framework, which infers gene family evolution by comparing gene trees and species trees, by explicitly considering domain-level evolution and decoupling domain-level events from gene-level events. In this paper, we (i) introduce the new integrated reconciliation framework, (ii) prove that the associated optimization problem is NP-hard, (iii) devise an efficient heuristic solution for the problem, (iv) apply our algorithm to a large biological dataset, and (v) demonstrate the impact of using our new computational framework compared to existing approaches. The implemented software is freely available from http://compbio.engr.uconn.edu/software/seadog/.

On the impact of uncertain gene tree rooting on duplication-transfer-loss reconciliation

Background

Duplication-Transfer-Loss (DTL) reconciliation is a powerful and increasingly popular technique for studying the evolution of microbial gene families. DTL reconciliation requires the use of rooted gene trees to perform the reconciliation with the species tree, and the standard technique for rooting gene trees is to assign a root that results in the minimum reconciliation cost across all rootings of that gene tree. However, even though it is well understood that many gene trees have multiple optimal roots, only a single optimal root is randomly chosen to create the rooted gene tree and perform the reconciliation. This remains an important overlooked and unaddressed problem in DTL reconciliation, leading to incorrect evolutionary inferences. In this work, we perform an in-depth analysis of the impact of uncertain gene tree rooting on the computed DTL reconciliation and provide the first computational tools to quantify and negate the impact of gene tree rooting uncertainty on DTL reconciliation.

Results

Our analysis of a large data set of over 4500 gene families from 100 species shows that a large fraction of gene trees have multiple optimal rootings, that these multiple roots often, but not always, appear closely clustered together in the same region of the gene tree, that many aspects of the reconciliation remain conserved across the multiple rootings, that gene tree error has a profound impact on the prevalence and structure of multiple optimal rootings, and that there are specific interesting patterns in the reconciliation of those gene trees that have multiple optimal roots.

Conclusions

Our results show that unrooted gene trees can be meaningfully reconciled and high-quality evolutionary information can be obtained from them even after accounting for multiple optimal rootings. In addition, the techniques and tools introduced in this paper make it possible to systematically avoid incorrect evolutionary inferences caused by incorrect or uncertain gene tree rooting. These tools have been implemented in the phylogenetic reconciliation software package RANGER-DTL 2.0, freely available from http://compbio.engr.uconn.edu/software/RANGER-DTL/.

On the Complexity of Duplication-Transfer-Loss Reconciliation with Non-Binary Gene Trees

Duplication-Transfer-Loss (DTL) reconciliation has emerged as a powerful technique for studying gene family evolution in the presence of horizontal gene transfer. DTL reconciliation takes as input a gene family phylogeny and the corresponding species phylogeny, and reconciles the two by postulating speciation, gene duplication, horizontal gene transfer, and gene loss events. Efficient algorithms exist for finding optimal DTL reconciliations when the gene tree is binary. However, gene trees are frequently non-binary. With such non-binary gene trees, the reconciliation problem seeks to find a binary resolution of the gene tree that minimizes the reconciliation cost. Given the prevalence of non-binary gene trees, many efficient algorithms have been developed for this problem in the context of the simpler Duplication-Loss (DL) reconciliation model. Yet, no efficient algorithms exist for DTL reconciliation with non-binary gene trees and the complexity of the problem remains unknown. In this work, we resolve this open question by showing that the problem is, in fact, NP-hard. Our reduction applies to both the dated and undated formulations of DTL reconciliation. By resolving this long-standing open problem, this work will spur the development of both exact and heuristic algorithms for this important problem.

Fast algorithm for the reconciliation of gene trees and LGT networks

In phylogenomics, reconciliations aim at explaining the discrepancies between the evolutionary histories of genes and species. Several reconciliation models are available when the evolution of the species of interest is modelled via phylogenetic trees; the most commonly used are the DL model, accounting for duplications and losses in gene evolution and yielding polynomially-solvable problems, and the DTL model, which also accounts for gene transfers and implies NP-hard problems. However, when dealing with non-tree-like evolutionary events such as hybridisations, phylogenetic networks - and not phylogenetic trees - should be used to model species evolution. Reconciliation models involving phylogenetic networks are still at their early days. In this paper, we propose a new reconciliation model in which the evolution of species is modelled by a special kind of phylogenetic networks - the LGT networks. Our model considers duplications, losses and transfers of genes, but restricts transfers to happen through some specific arcs of the network, called secondary arcs. Moreover, we provide a polynomial algorithm to compute the most parsimonious reconciliation between a gene tree and an LGT network under this model. Our method, when combined with quartet decomposition methods to detect putative "highways" of transfers, permits to refine their analyses by allowing to examine the two possible directions of a highway and even consider combinations of highways.

Reconciliation of gene and species trees

The first part of the paper briefly overviews the problem of gene and species trees reconciliation with the focus on defining and algorithmic construction of the evolutionary scenario. Basic ideas are discussed for the aspects of mapping definitions, costs of the mapping and evolutionary scenario, imposing time scales on a scenario, incorporating horizontal gene transfers, binarization and reconciliation of polytomous trees, and construction of species trees and scenarios. The review does not intend to cover the vast diversity of literature published on these subjects. Instead, the authors strived to overview the problem of the evolutionary scenario as a central concept in many areas of evolutionary research. The second part provides detailed mathematical proofs for the solutions of two problems: (i) inferring a gene evolution along a species tree accounting for various types of evolutionary events and (ii) trees reconciliation into a single species tree when only gene duplications and losses are allowed. All proposed algorithms have a cubic time complexity and are mathematically proved to find exact solutions. Solving algorithms for problem (ii) can be naturally extended to incorporate horizontal transfers, other evolutionary events, and time scales on the species tree.

Algorithms of ancestral gene length reconstruction

Ancestral sequence reconstruction is a well-known problem in molecular evolution. The problem presented in this study is inspired by sequence reconstruction, but instead of leaf-associated sequences we consider only their lengths. We call this problem ancestral gene length reconstruction. It is a problem of finding an optimal labeling which minimizes the total length's sum of the edges, where both a tree and nonnegative integers associated with corresponding leaves of the tree are the input. In this paper we give a linear algorithm to solve the problem on binary trees for the Manhattan cost function s(v, w) = |π(v) − π(w)|.

Cubic time algorithms of amalgamating gene trees and building evolutionary scenarios

BACKGROUND

A long recognized problem is the inference of the supertree S that amalgamates a given set {G(j)} of trees G(j), with leaves in each G(j) being assigned homologous elements. We ground on an approach to find the tree S by minimizing the total cost of mappings α(j) of individual gene trees G(j) into S. Traditionally, this cost is defined basically as a sum of duplications and gaps in each α(j). The classical problem is to minimize the total cost, where S runs over the set of all trees that contain an exhaustive non-redundant set of species from all input G(j).

RESULTS

We suggest a reformulation of the classical NP-hard problem of building a supertree in terms of the global minimization of the same cost functional but only over species trees S that consist of clades belonging to a fixed set P (e.g., an exhaustive set of clades in all G(j)). We developed a deterministic solving algorithm with a low degree polynomial (typically cubic) time complexity with respect to the size of input data. We define an extensive set of elementary evolutionary events and suggest an original definition of mapping β of tree G into tree S. We introduce the cost functional c(G, S, f) and define the mapping β as the global minimum of this functional with respect to the variable f, in which sense it is a generalization of classical mapping α. We suggest a reformulation of the classical NP-hard mapping (reconciliation) problem by introducing time slices into the species tree S and present a cubic time solving algorithm to compute the mapping β. We introduce two novel definitions of the evolutionary scenario based on mapping β or a random process of gene evolution along a species tree.

CONCLUSIONS

Developed algorithms are mathematically proved, which justifies the following statements. The supertree building algorithm finds exactly the global minimum of the total cost if only gene duplications and losses are allowed and the given sets of gene trees satisfies a certain condition. The mapping algorithm finds exactly the minimal mapping β, the minimal total cost and the evolutionary scenario as a minimum over all possible distributions of elementary evolutionary events along the edges of tree S. The algorithms and their effective software implementations provide useful tools in many biological studies. They facilitate processing of voluminous tree data in acceptable time still largely avoiding heuristics. Performance of the tools is tested with artificial and prokaryotic tree data.

REVIEWERS

This article was reviewed by Prof. Anthony Almudevar, Prof. Alexander Bolshoy (nominated by Prof. Peter Olofsson), and Prof. Marek Kimmel.

Efficient algorithms for the reconciliation problem with gene duplication, horizontal transfer and loss

MOTIVATION

Gene family evolution is driven by evolutionary events such as speciation, gene duplication, horizontal gene transfer and gene loss, and inferring these events in the evolutionary history of a given gene family is a fundamental problem in comparative and evolutionary genomics with numerous important applications. Solving this problem requires the use of a reconciliation framework, where the input consists of a gene family phylogeny and the corresponding species phylogeny, and the goal is to reconcile the two by postulating speciation, gene duplication, horizontal gene transfer and gene loss events. This reconciliation problem is referred to as duplication-transfer-loss (DTL) reconciliation and has been extensively studied in the literature. Yet, even the fastest existing algorithms for DTL reconciliation are too slow for reconciling large gene families and for use in more sophisticated applications such as gene tree or species tree reconstruction.

RESULTS

We present two new algorithms for the DTL reconciliation problem that are dramatically faster than existing algorithms, both asymptotically and in practice. We also extend the standard DTL reconciliation model by considering distance-dependent transfer costs, which allow for more accurate reconciliation and give an efficient algorithm for DTL reconciliation under this extended model. We implemented our new algorithms and demonstrated up to 100 000-fold speed-up over existing methods, using both simulated and biological datasets. This dramatic improvement makes it possible to use DTL reconciliation for performing rigorous evolutionary analyses of large gene families and enables its use in advanced reconciliation-based gene and species tree reconstruction methods.

AVAILABILITY

Our programs can be freely downloaded from http://compbio.mit.edu/ranger-dtl/.