Algorithms for MDC-Based Multi-locus Phylogeny Inference

Abstract

Abstract. One of the criteria for inferring a species tree from a collection of gene trees, when gene tree incongruence is assumed to be due to incomplete lineage sorting (ILS), is minimize deep coalescence, or MDC. Exact algorithms for inferring the species tree from rooted, binary trees under MDC were recently introduced. Nevertheless, in phylogenetic analyses of biological data sets, estimated gene trees may differ from true gene trees, be incompletely resolved, and not necessarily rooted. In this paper, we propose new MDC formulations for the cases where the gene trees are unrooted/binary, rooted/non-binary, and unrooted/nonbinary. Further, we prove structural theorems that allow us to extend the algorithms for the rooted/binary gene tree case to these cases in a straightforward manner. Finally, we study the performance of these methods in coalescent-based computer simulations.

Computational approaches to species phylogeny inference and gene tree reconciliation

“…Indeed, this refinement concept was used in [68, 69, 70] for reconciling non-binary gene and species trees. While the number of refinements is exponential in the degrees of the polytomies (the number of children of a node), Yu et al recently devised polynomial-time, exact algorithms for finding the refinement that results in an optimal reconciliation under ILS [71, 72]. Further, the same ideas were extended to the problem of parsimonious reconciliation of a non-binary gene tree with a phylogenetic network [54].…”

Unrooted Tree Reconciliation: A Unified Approach

“…Another example of rooting problems related to model-based approaches shows that for many models including Yule generated unrooted gene trees some rootings are more likely than others [29]. Consequently, reconciliation costs have been naturally extended to reconcile an unrooted gene tree with a rooted species tree by seeking a rooting of the gene tree that invokes the minimum number of evolutionary events in the context of a given species tree [14], [32]. The plateau property has been shown independently for the unrooted reconciliation costs for the events gene duplication [14], gene duplication and loss [14], and deep coalescence [10], and provided the fundamental base of separate designs of linear-time algorithms to compute these costs.…”

Algorithms for constructing more accurate and inclusive phylogenetic trees

“…DupLoss (Bansal et al, 2010a) seek to minimize the number of duplications or duplications and losses. GeneTree (Page, 1998), Mesquite (Maddison, 1997), PhyloNet (Yu et al, 2011), and the method of (Bansal et al, 2010a) minimize deep coalescence events. The Subtree Prune and Regraft (SPR) supertree method (Whidden et al, 2012) is based on minimizing the number of LGT events, and thus it can be considered a type of gene tree parsimony.…”

“…5.9.) There has been recent work to develop GTP methods for unrooted trees (e.g., Yu et al (2011); Górecki et al (2012)), and rooted GTP methods have the added benefit of inferring rooted species trees, which cannot be done with MulRF (e.g., Katz et al (2012)). Still, uncertainty and error in the root of gene trees presents a potential liability and computational challenge to GTP that can be avoided using a method based on unrooted metrics.…”

“…First, questionable nodes in a gene tree or nodes with low support may be collapsed prior to gene tree reconciliation, and the resulting non-binary gene trees may be reconciled with species trees (Berglund-Sonnhammer et al (2006); Vernot et al (2007); Yu et al (2011)). Similarly, GT-ST reconciliations can use a distribution of gene tree topologies, such as bootstrap gene trees, rather than a single gene tree estimate (Burleigh et al (2009); Cotton and Page (2002); Joly and Bruneau (2009)).…”