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.

Highlights

  • The rapidly growing abundance of genomic sequence data has revealed extensive incongruence among gene trees (e.g., [1,2]) that may be caused by processes such as deep coalescence, gene duplication and loss, or lateral gene transfer

  • Our contributions We prove that the deep coalescence consensus tree problem satisfies the Pareto property for clusters

  • In three cases with the 14-taxon gene trees, we found that the subtree pruning and regrafting (SPR) heuristic did not return a result that contained the consensus cluster

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Summary

Introduction

The rapidly growing abundance of genomic sequence data has revealed extensive incongruence among gene trees (e.g., [1,2]) that may be caused by processes such as deep coalescence (incomplete lineage sorting), gene duplication and loss, or lateral gene transfer (see [3,4,5]) In these cases, phylogenetic methods must account for and explain the patterns of variation among gene tree topologies, rather than assuming the gene tree topology reflects the relationships among species. 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. 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

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