Consensus properties for the deep coalescence problem and their application for scalable tree search

Abstract

BackgroundTo infer a species phylogeny from unlinked genes, phylogenetic inference methods must confront the biological processes that create incongruence between gene trees and the species phylogeny. Intra-specific gene variation in ancestral species can result in deep coalescence, also known as incomplete lineage sorting, which creates incongruence between gene trees and the species tree. One approach to account for deep coalescence in phylogenetic analyses is the deep coalescence problem, which takes a collection of gene trees and seeks the species tree that implies the fewest deep coalescence events. Although this approach is promising for phylogenetics, the consensus properties of this problem are mostly unknown and analyses of large data sets may be computationally prohibitive.ResultsWe prove that the deep coalescence consensus tree problem satisfies the highly desirable Pareto property for clusters (clades). That is, in all instances, each cluster that is present in all of the input gene trees, called a consensus cluster, will also be found in every optimal solution. Moreover, we introduce a new divide and conquer method for the deep coalescence problem based on the Pareto property. This method refines the strict consensus of the input gene trees, thereby, in practice, often greatly reducing the complexity of the tree search and guaranteeing that the estimated species tree will satisfy the Pareto property.ConclusionsAnalyses of both simulated and empirical data sets demonstrate that the divide and conquer method can greatly improve upon the speed of heuristics that do not consider the Pareto consensus property, while also guaranteeing that the proposed solution fulfills the Pareto property. The divide and conquer method extends the utility of the deep coalescence problem to data sets with enormous numbers of taxa.

Phylogeny, systematics, and trait evolution of Carex section Glareosae

“…Barring the conflation of paralogy and orthology (Doyle, 1992; Álvarez and Wendel, 2003), gene‐tree incongruence is most commonly due to interspecific gene flow or incomplete lineage sorting (Doyle, 1992; de Queiroz and Gatesy, 2007; Pelser et al, 2010; Záveská Drábková and Vlček, 2010), both of which have been detected in Carex (Escudero and Luceño, 2009; Jiménez‐Mejías et al, 2012a; Escudero et al, 2013, 2014). However, lineage sorting is perhaps the more prevalent source of gene‐tree incongruence generally (Edwards, 2009; Knowles, 2009; Lin et al, 2012), and it is most likely the most common in Carex (King and Roalson, 2008; Escudero et al, 2014) (but cf. Cayouette and Catling, 1992; Luceño, 1994; Dragon and Barrington, 2009; Gehrke et al, 2010; Jiménez‐Mejías et al, 2014).…”

Are the Duplication Cost and Robinson-Foulds Distance Equivalent?

“…The deep coalescence cost has the Pareto property (Lin et al, 2012), meaning that a node cluster that appears in every input gene tree must also appear in the parsimony species tree. Than and Rosenberg (2013) report the formulas for the number of trees that achieve the maximum deep coalescence cost for a fixed gene or species tree.…”

Manhattan Path-Difference Median Trees

“…While most median tree problems are NP-hard [4], they have been effectively addressed by local search heuristics [1,10,21,22,41], which have provided credible estimates of large-scale species trees [22,41]. Such a search heuristic starts with some initial candidate species tree, and finds a tree with the minimum overall distance to the given input trees in the local neighborhood of the initial tree.…”