An efficiently computed lower bound on the number of recombinations in phylogenetic networks: Theory and empirical study

AbstractPhylogenetic networks are models of sequence evolution that go beyond trees, allowing biological operations that are not tree-like. One of the most important biological operations is recombination between two sequences. An established problem [J. Hein, Reconstructing evolution of sequences subject to recombination using parsimony, Math. Biosci. 98 (1990) 185–200; J. Hein, A heuristic method to reconstruct the history of sequences subject to recombination, J. Molecular Evoluation 36 (1993) 396–405; Y. Song, J. Hein, Parsimonious reconstruction of sequence evolution and haplotype blocks: finding the minimum number of recombination events, in: Proceedings of 2003 Workshop on Algorithms in Bioinformatics, Berlin, Germany, 2003, Lecture Notes in Computer Science, Springer, Berlin; Y. Song, J. Hein, On the minimum number of recombination events in the evolutionary history of DNA sequences, J. Math. Biol. 48 (2003) 160–186; L. Wang, K. Zhang, L. Zhang, Perfect phylogenetic networks with recombination, J. Comput. Biol. 8 (2001) 69–78; S.R. Myers, R.C. Griffiths, Bounds on the minimum number of recombination events in a sample history, Genetics 163 (2003) 375–394; V. Bafna, V. Bansal, Improved recombination lower bounds for haplotype data, in: Proceedings of RECOMB, 2005; Y. Song, Y. Wu, D. Gusfield, Efficient computation of close lower and upper bounds on the minimum number of needed recombinations in the evolution of biological sequences, Bioinformatics 21 (2005) i413–i422. Bioinformatics (Suppl. 1), Proceedings of ISMB, 2005, D. Gusfield, S. Eddhu, C. Langley, Optimal, efficient reconstruction of phylogenetic networks with constrained recombination, J. Bioinform. Comput. Biol. 2(1) (2004) 173–213; D. Gusfield, Optimal, efficient reconstruction of root-unknown phylogenetic networks with constrained and structured recombination, J. Comput. Systems Sci. 70 (2005) 381–398] is to find a phylogenetic network that derives an input set of sequences, minimizing the number of recombinations used. No efficient, general algorithm is known for this problem. Several papers consider the problem of computing a lower bound on the number of recombinations needed. In this paper we establish a new, efficiently computed lower bound. This result is useful in methods to estimate the number of needed recombinations, and also to prove the optimality of algorithms for constructing phylogenetic networks under certain conditions [D. Gusfield, S. Eddhu, C. Langley, Optimal, efficient reconstruction of phylogenetic networks with constrained recombination, J. Bioinform. Comput. Biol. 2(1) (2004) 173–213; D. Gusfield, Optimal, efficient reconstruction of root-unknown phylogenetic networks with constrained and structured recombination, J. Comput. Systems Sci. 70 (2005) 381–398; D. Gusfield, Optimal, efficient reconstruction of root-unknown phylogenetic networks with constrained recombination, Technical Report, Department of Computer Science, University of California, Davis, CA, 2004]. The lower bound is based on a structural, combinatorial insight, using only the site conflicts and incompatibilities, and hence it is fundamental and applicable to many biological phenomena other than recombination, for example, when gene conversions or recurrent or back mutations or cross-species hybridizations cause the phylogenetic history to deviate from a tree structure. In addition to establishing the bound, we examine its use in more complex lower bound methods, and compare the bounds obtained to those obtained by other established lower bound methods

SPRIT: Identifying horizontal gene transfer in rooted phylogenetic trees

<p>Abstract</p> <p>Background</p> <p>Phylogenetic trees based on sequences from a set of taxa can be incongruent due to horizontal gene transfer (HGT). By identifying the HGT events, we can reconcile the gene trees and derive a taxon tree that adequately represents the species' evolutionary history. One HGT can be represented by a rooted Subtree Prune and Regraft (<smcaps>R</smcaps>SPR) operation and the number of <smcaps>R</smcaps>SPRs separating two trees corresponds to the minimum number of HGT events. Identifying the minimum number of <smcaps>R</smcaps>SPRs separating two trees is NP-hard, but the problem can be reduced to fixed parameter tractable. A number of heuristic and two exact approaches to identifying the minimum number of <smcaps>R</smcaps>SPRs have been proposed. This is the first implementation delivering an exact solution as well as the intermediate trees connecting the input trees.</p> <p>Results</p> <p>We present the SPR Identification Tool (SPRIT), a novel algorithm that solves the fixed parameter tractable minimum <smcaps>R</smcaps>SPR problem and its GPL licensed Java implementation. The algorithm can be used in two ways, exhaustive search that guarantees the minimum <smcaps>R</smcaps>SPR distance and a heuristic approach that guarantees finding a solution, but not necessarily the minimum one. We benchmarked SPRIT against other software in two different settings, small to medium sized trees i.e. five to one hundred taxa and large trees i.e. thousands of taxa. In the small to medium tree size setting with random artificial incongruence, SPRIT's heuristic mode outperforms the other software by always delivering a solution with a low overestimation of the <smcaps>R</smcaps>SPR distance. In the large tree setting SPRIT compares well to the alternatives when benchmarked on finding a minimum solution within a reasonable time. SPRIT presents both the minimum <smcaps>R</smcaps>SPR distance and the intermediate trees.</p> <p>Conclusions</p> <p>When used in exhaustive search mode, SPRIT identifies the minimum number of <smcaps>R</smcaps>SPRs needed to reconcile two incongruent rooted trees. SPRIT also performs quick approximations of the minimum <smcaps>R</smcaps>SPR distance, which are comparable to, and often better than, purely heuristic solutions. Put together, SPRIT is an excellent tool for identification of HGT events and pinpointing which taxa have been involved in HGT.</p

Inference of Ancestral Recombination Graphs through Topological Data Analysis

The recent explosion of genomic data has underscored the need for interpretable and comprehensive analyses that can capture complex phylogenetic relationships within and across species. Recombination, reassortment and horizontal gene transfer constitute examples of pervasive biological phenomena that cannot be captured by tree-like representations. Starting from hundreds of genomes, we are interested in the reconstruction of potential evolutionary histories leading to the observed data. Ancestral recombination graphs represent potential histories that explicitly accommodate recombination and mutation events across orthologous genomes. However, they are computationally costly to reconstruct, usually being infeasible for more than few tens of genomes. Recently, Topological Data Analysis (TDA) methods have been proposed as robust and scalable methods that can capture the genetic scale and frequency of recombination. We build upon previous TDA developments for detecting and quantifying recombination, and present a novel framework that can be applied to hundreds of genomes and can be interpreted in terms of minimal histories of mutation and recombination events, quantifying the scales and identifying the genomic locations of recombinations. We implement this framework in a software package, called TARGet, and apply it to several examples, including small migration between different populations, human recombination, and horizontal evolution in finches inhabiting the Gal\'apagos Islands.Comment: 33 pages, 12 figures. The accompanying software, instructions and example files used in the manuscript can be obtained from https://github.com/RabadanLab/TARGe

Phylogenetic Detection of Recombination with a Bayesian Prior on the Distance between Trees

Genomic regions participating in recombination events may support distinct topologies, and phylogenetic analyses should incorporate this heterogeneity. Existing phylogenetic methods for recombination detection are challenged by the enormous number of possible topologies, even for a moderate number of taxa. If, however, the detection analysis is conducted independently between each putative recombinant sequence and a set of reference parentals, potential recombinations between the recombinants are neglected. In this context, a recombination hotspot can be inferred in phylogenetic analyses if we observe several consecutive breakpoints. We developed a distance measure between unrooted topologies that closely resembles the number of recombinations. By introducing a prior distribution on these recombination distances, a Bayesian hierarchical model was devised to detect phylogenetic inconsistencies occurring due to recombinations. This model relaxes the assumption of known parental sequences, still common in HIV analysis, allowing the entire dataset to be analyzed at once. On simulated datasets with up to 16 taxa, our method correctly detected recombination breakpoints and the number of recombination events for each breakpoint. The procedure is robust to rate and transition∶transversion heterogeneities for simulations with and without recombination. This recombination distance is related to recombination hotspots. Applying this procedure to a genomic HIV-1 dataset, we found evidence for hotspots and de novo recombination

Bridging trees for posterior inference on Ancestral Recombination Graphs

We present a new Markov chain Monte Carlo algorithm, implemented in software Arbores, for inferring the history of a sample of DNA sequences. Our principal innovation is a bridging procedure, previously applied only for simple stochastic processes, in which the local computations within a bridge can proceed independently of the rest of the DNA sequence, facilitating large-scale parallelisation.Comment: 23 pages, 9 figures, accepted for publication in Proceedings of the Royal Society

A general and efficient representation of ancestral recombination graphs

As a result of recombination, adjacent nucleotides can have different paths of genetic inheritance and therefore the genealogical trees for a sample of DNA sequences vary along the genome. The structure capturing the details of these intricately interwoven paths of inheritance is referred to as an ancestral recombination graph (ARG). Classical formalisms have focused on mapping coalescence and recombination events to the nodes in an ARG. However, this approach is out of step with some modern developments, which do not represent genetic inheritance in terms of these events or explicitly infer them. We present a simple formalism that defines an ARG in terms of specific genomes and their intervals of genetic inheritance, and show how it generalizes these classical treatments and encompasses the outputs of recent methods. We discuss nuances arising from this more general structure, and argue that it forms an appropriate basis for a software standard in this rapidly growing field.</p