Species Tree Inference by Minimizing Deep Coalescences

Cuong Than,Wen-Hsiung Li,Luay Nakhleh

doi:10.1371/journal.pcbi.1000501

Abstract

In a 1997 seminal paper, W. Maddison proposed minimizing deep coalescences, or MDC, as an optimization criterion for inferring the species tree from a set of incongruent gene trees, assuming the incongruence is exclusively due to lineage sorting. In a subsequent paper, Maddison and Knowles provided and implemented a search heuristic for optimizing the MDC criterion, given a set of gene trees. However, the heuristic is not guaranteed to compute optimal solutions, and its hill-climbing search makes it slow in practice. In this paper, we provide two exact solutions to the problem of inferring the species tree from a set of gene trees under the MDC criterion. In other words, our solutions are guaranteed to find the tree that minimizes the total number of deep coalescences from a set of gene trees. One solution is based on a novel integer linear programming (ILP) formulation, and another is based on a simple dynamic programming (DP) approach. Powerful ILP solvers, such as CPLEX, make the first solution appealing, particularly for very large-scale instances of the problem, whereas the DP-based solution eliminates dependence on proprietary tools, and its simplicity makes it easy to integrate with other genomic events that may cause gene tree incongruence. Using the exact solutions, we analyze a data set of 106 loci from eight yeast species, a data set of 268 loci from eight Apicomplexan species, and several simulated data sets. We show that the MDC criterion provides very accurate estimates of the species tree topologies, and that our solutions are very fast, thus allowing for the accurate analysis of genome-scale data sets. Further, the efficiency of the solutions allow for quick exploration of sub-optimal solutions, which is important for a parsimony-based criterion such as MDC, as we show. We show that searching for the species tree in the compatibility graph of the clusters induced by the gene trees may be sufficient in practice, a finding that helps ameliorate the computational requirements of optimization solutions. Further, we study the statistical consistency and convergence rate of the MDC criterion, as well as its optimality in inferring the species tree. Finally, we show how our solutions can be used to identify potential horizontal gene transfer events that may have caused some of the incongruence in the data, thus augmenting Maddison's original framework. We have implemented our solutions in the PhyloNet software package, which is freely available at: http://bioinfo.cs.rice.edu/phylonet.

Highlights

Accurate species trees, which model the evolutionary histories of sets of species, play a central role in comparative genomics, conservation studies, and analyses of population divergence, among many other applications
We address the problem of efficient inference of accurate species trees from multiple loci, when the gene trees are assumed to be correct, and their incongruence is assumed to be exclusively due to lineage sorting
The traditional approach to accomplishing this task from molecular sequences entails sequencing a gene in the set of species under consideration, reconstructing the gene’s evolutionary history, and declaring it to be the species tree

Summary

Introduction

Accurate species trees, which model the evolutionary histories of sets of species, play a central role in comparative genomics, conservation studies, and analyses of population divergence, among many other applications. The availability of such data has allowed for analyzing multiple loci in various groups of species These analyses have in many cases uncovered widespread incongruence among the gene trees of the same set of organisms. Barring any recombination, the evolutionary history of a set of genomes would be depicted by a tree that is the same tree that models the evolution of each gene in these genomes Events such as recombination break ‘‘linkage’’ among the different parts of the genome, and those unlinked parts may take different paths through the phylogeny, which results in gene trees that differ from the species tree as well as from each other, due to lineage sorting. Widespread gene tree incongruence due to lineage sorting has been shown recently in several groups of closely related organisms, including

Author Summary

Findings

Methods