We present new and improved approximation and FPT algorithms for computing rooted and unrooted maximum agreement forests (MAFs) of pairs of phylogenetic trees. Their sizes correspond to the subtree-prune-and-regraft distances and the tree-bisection-and-reconnection distances of the trees, respectively. We also provide the first bounded search tree FPT algorithm for computing rooted maximum acyclic agreement forests (MAAFs) of pairs of phylogenetic trees, whose sizes are the hybridization numbers of these pairs of trees. These distance metrics are essential tools for understanding reticulate evolution.
Background Lateral genetic transfer can lead to disagreements among phylogenetic trees comprising sequences from the same set of taxa. Where topological discordance is thought to have arisen through genetic transfer events, tree comparisons can be used to identify the lineages that may have shared genetic information. An 'edit path' of one or more transfer events can be represented with a series of subtree prune and regraft (SPR) operations, but finding the optimal such set of operations is NP-hard for comparisons between rooted trees, and may be so for unrooted trees as well. This paper develops a model for lateral gene transfer events (a.k.a. horizontal gene transfer events) between a set of gene trees T 1 , T 2 , …, T k and a species tree S. To the best of our knowledge, this model possesses a higher degree of biological and mathematical soundness than any other model proposed in the literature. Among other biological considerations, the model respects the partial order of evolution implied by S. Within our model, we identify an activity parameter that measures the number of genes that are allowed to be simultaneously active in the genome of a taxa and show that finding the most parsimonious scenario that reconciles the disagreeing gene trees with the species tree is doable in polynomial time when the activity level and number of transfers are small, but intractable in general. To the best of our knowledge, all other models proposed in the literature assume implicitly that the activity is one. Finally, using a dataset of bacterial gene sequences from [4], our implementations found 5 optimal scenarios; one of which is the scenario proposed by the authors in [4]. Horizontal gene transfer (HGT) plays a major role in microbial genome diversification, and is claimed to be rampant among various groups of genes in bacteria. Further, HGT is a major confounding factor for any attempt to reconstruct bacterial phylogenies. As a result, detecting and reconstructing HGT events in groups of organisms has become a major endeavor in biology. The problem of detecting HGT events based on incongruence between a species tree and a gene tree is computationally very hard (NP-hard). Efficient algorithms exist for solving restricted cases of the problem. We propose RIATA-HGT, the first polynomial-time heuristic to handle all HGT scenarios, without any restrictions. The method accurately infers HGT events based on analyzing incongruence among species and gene trees. Empirical performance of the method on synthetic and biological data is outstanding. Being a heuristic, RIATA-HGT may overestimate the optimal number of HGT events; empirical performance, however, shows that such overestimation is very mild. We have implemented our method and run it on biological and synthetic data. The results we obtained demonstrate very high accuracy of the method. Current version of RIATA-HGT uses the PAUP tool, and we are in the process of implementing a stand-alone version, with a graphical user interface, which will be made public. The tool, in its current implementation, is available from the authors upon request. Background When organismal phylogenies based on sequences of single marker genes are poorly resolved, a logical approach is to add more markers, on the assumption that weak but congruent phylogenetic signal will be reinforced in such multigene trees. Such approaches are valid only when the several markers indeed have identical phylogenies, an issue which many multigene methods (such as the use of concatenated gene sequences or the assembly of supertrees) do not directly address. Indeed, even when the true history is a mixture of vertical descent for some genes and lateral gene transfer (LGT) for others, such methods produce unique topologies.