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Phylogenetic trees illustrate the evolutionary history of genes and species. In most cases, although genes evolve along with the species they belong to, a species tree and gene tree are not identical, because of evolutionary events at the gene level like duplication or transfer. These differences are handled by phylogenetic reconciliation, which formally is a mapping between gene tree nodes and species tree nodes and branches. We investigate models of reconciliation with a gene transfer that replaces existing gene, which is a biological important event but never included in reconciliation models. Also the problem is close to a dated version of the classical subtree prune and regraft (SPR) distance problem, where a pruned subtree has to be regrafted only on a branch closer to the root. We prove that the reconciliation problem including transfer and replacement is NP-hard, and that if speciations and transfers with replacement are the only allowed evolutionary events, then it is fixed-parameter tractable (FPT) with respect to the reconciliation's weight. We prove that the results extend to the dated SPR problem., Comment: 34 pages, 11 figures. J Comb Optim (2019)

Gene tree/species tree reconciliation is a recent decisive progress in phylo-genetic methods, accounting for the possible differences between gene histories and species histories. Reconciliation consists in explaining these differences by gene-scale events such as duplication, loss, transfer, which translates mathematically into a mapping between gene tree nodes and species tree nodes or branches. Gene conversion is a very frequent biological event, which results in the replacement of a gene by a copy of another from the same species and in the same gene tree. Including this event in reconciliations has never been attempted because this changes as well the solutions as the methods to construct reconciliations. Standard algorithms based on dynamic programming become ineffective. We propose here a novel mathematical framework including gene conversion as an evolutionary event in gene tree/species tree reconciliation. We describe a randomized algorithm giving in polynomial running time a reconciliation minimizing the number of duplications, losses and conversions. We show that the space of reconciliations includes an analog of the Last Common Ancestor reconciliation, but is not limited to it. Our algorithm outputs any optimal reconciliation with non null probability. We argue that this study opens a wide research avenue on including gene conversion in reconciliation, which can be important for biology.

Although the role of lateral gene transfer is well recognized in the evolution of bacteria, it is generally assumed that it has had less influence among eukaryotes. To explore this hypothesis we compare the dynamics of genome evolution in two groups of organisms: Cyanobacteria and Fungi. Ancestral genomes are inferred in both clades using two types of methods. First, Count, a gene tree unaware method that models gene duplications, gains and losses to explain the observed numbers of genes present in a genome. Second, ALE, a more recent gene tree-aware method that reconciles gene trees with a species tree using a model of gene duplication, loss, and transfer. We compare their merits and their ability to quantify the role of transfers, and assess the impact of taxonomic sampling on their inferences. We present what we believe is compelling evidence that gene transfer plays a significant role in the evolution of Fungi.

Molecular phylogeny has focused mainly on improving models for the reconstruction of gene trees based on sequence alignments. Yet, most phylogeneticists seek to reveal the history of species. Although the histories of genes and species are tightly linked, they are seldom identical, because genes duplicate, are lost or horizontally transferred, and because alleles can co-exist in populations for periods that may span several speciation events. Building models describing the relationship between gene and species trees can thus improve the reconstruction of gene trees when a species tree is known, and vice-versa. Several approaches have been proposed to solve the problem in one direction or the other, but in general neither gene trees nor species trees are known. Only a few studies have attempted to jointly infer gene trees and species trees. In this article we review the various models that have been used to describe the relationship between gene trees and species trees. These models account for gene duplication and loss, transfer or incomplete lineage sorting. Some of them consider several types of events together, but none exists currently that considers the full repertoire of processes that generate gene trees along the species tree. Simulations as well as empirical studies on genomic data show that combining gene tree-species tree models with models of sequence evolution improves gene tree reconstruction. In turn, these better gene trees provide a better basis for studying genome evolution or reconstructing ancestral chromosomes and ancestral gene sequences. We predict that gene tree-species tree methods that can deal with genomic data sets will be instrumental to advancing our understanding of genomic evolution., Comment: Review article in relation to the "Mathematical and Computational Evolutionary Biology" conference, Montpellier, 2013

The genome of a 650 year old Yersinia pestis bacteria, responsible for the medieval Black Death, was recently sequenced and assembled into 2,105 contigs from the main chromosome. According to the point mutation record, the medieval bacteria could be an ancestor of most Yersinia pestis extant species, which opens the way to reconstructing the organization of these contigs using a comparative approach. We show that recent computational paleogenomics methods, aiming at reconstructing the organization of ancestral genomes from the comparison of extant genomes, can be used to correct, order and complete the contig set of the Black Death agent genome, providing a full chromosome sequence, at the nucleotide scale, of this ancient bacteria. This sequence suggests that a burst of mobile elements insertions predated the Black Death, leading to an exceptional genome plasticity and increase in rearrangement rate., Comment: Extended abstract of a talk presented at the conference JOBIM 2013, https://colloque.inra.fr/jobim2013_eng/. Full paper submitted

Background. Models of ancestral gene order reconstruction have progressively integrated different evolutionary patterns and processes such as unequal gene content, gene duplications, and implicitly sequence evolution via reconciled gene trees. In unicellular organisms, these models have so far ignored lateral gene transfer, even though it can have an important confounding effect on such models, as well as a rich source of information on the function of genes through the detection of transfers of entire clusters of genes. Result. We report an algorithm together with its implementation, DeCoLT, that reconstructs ancestral genome organization based on reconciled gene trees which summarize information on sequence evolution, gene origination, duplication, loss, and lateral transfer. DeCoLT finds in polynomial time the minimum number of rearrangements, computed as the number of gains and breakages of adjacencies between pairs of genes. We apply DeCoLT to 1099 gene families from 36 cyanobacteria genomes. Conclusion. DeCoLT is able to reconstruct adjacencies in 35 ancestral bacterial genomes with a thousand genes families in a few hours, and detects clusters of co-transferred genes. As there is no constraint on genome organization, adjacencies can be generalized to any relationship between genes to reconstruct ancestral interactions, functions or complexes with the same framework., Comment: submitted for RECOMB CG 2013

Gene trees record the combination of gene level events, such as duplication, transfer and loss, and species level events, such as speciation and extinction. Gene tree-species tree reconciliation methods model these processes by drawing gene trees into the species tree using a series of gene and species level events. The reconstruction of gene trees based on sequence alone almost always involves choosing between statistically equivalent or weakly distinguishable relationships that could be much better resolved based on a putative species tree. To exploit this potential for accurate reconstruction of gene trees the space of reconciled gene trees must be explored according to a joint model of sequence evolution and gene tree-species tree reconciliation. Here we present amalgamated likelihood estimation (ALE), a probabilistic approach to exhaustively explore all reconciled gene trees that can be amalgamated as a combination of clades observed in a sample of trees. We implement ALE in the context of a reconciliation model, which allows for the duplication, transfer and loss of genes. We use ALE to efficiently approximate the sum of the joint likelihood over amalgamations and to find the reconciled gene tree that maximizes the joint likelihood. We demonstrate using simulations that gene trees reconstructed using the joint likelihood are substantially more accurate than those reconstructed using sequence alone. Using realistic topologies, branch lengths and alignment sizes, we demonstrate that ALE produces more accurate gene trees even if the model of sequence evolution is greatly simplified. Finally, examining 1099 gene families from 36 cyanobacterial genomes we find that joint likelihood-based inference results in a striking reduction in apparent phylogenetic discord, with 24%, 59% and 46% percent reductions in the mean numbers of duplications, transfers and losses., Comment: Manuscript accepted pending revision in Systematic Biology

The Single Cut or Join (SCJ) operation on genomes, generalizing chromosome evolution by fusions and fissions, is the computationally simplest known model of genome rearrangement. While most genome rearrangement problems are already hard when comparing three genomes, it is possible to compute in polynomial time a most parsimonious SCJ scenario for an arbitrary number of genomes related by a binary phylogenetic tree. Here we consider the problems of sampling and counting the most parsimonious SCJ scenarios. We show that both the sampling and counting problems are easy for two genomes, and we relate SCJ scenarios to alternating permutations. However, for an arbitrary number of genomes related by a binary phylogenetic tree, the counting and sampling problems become hard. We prove that if a Fully Polynomial Randomized Approximation Scheme or a Fully Polynomial Almost Uniform Sampler exist for the most parsimonious SCJ scenario, then RP = NP. The proof has a wider scope than genome rearrangements: the same result holds for parsimonious evolutionary scenarios on any set of discrete characters.

In phylogenetic studies, the evolution of molecular sequences is assumed to have taken place along the phylogeny traced by the ancestors of extant species. In the presence of lateral gene transfer (LGT), however, this may not be the case, because the species lineage from which a gene was transferred may have gone extinct or not have been sampled. Because it is not feasible to specify or reconstruct the complete phylogeny of all species, we must describe the evolution of genes outside the represented phylogeny by modelling the speciation dynamics that gave rise to the complete phylogeny. We demonstrate that if the number of sampled species is small compared to the total number of existing species, the overwhelming majority of gene transfers involve speciation to, and evolution along extinct or unsampled lineages. We show that the evolution of genes along extinct or unsampled lineages can to good approximation be treated as those of independently evolving lineages described by a few global parameters. Using this result, we derive an algorithm to calculate the probability of a gene tree and recover the maximum likelihood reconciliation given the phylogeny of the sampled species. Examining 473 near universal gene families from 36 cyanobacteria, we find that nearly a third of transfer events -- 28% -- appear to have topological signatures of evolution along extinct species, but only approximately 6% of transfers trace their ancestry to before the common ancestor of the sampled cyanobacteria., Comment: published in Systematic Biology http://sysbio.oxfordjournals.org/content/early/2013/01/25/sysbio.syt003.abstract.html