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The properties of random gene tree topologies have recently been studied under a coalescent model that treats a species tree as a fixed parameter. Here we develop the analogous theory for random ranked gene tree topologies, in which both the topology and the sequence of coalescences for a random gene tree are considered. We derive the probability distribution of ranked gene tree topologies conditional on a fixed species tree. We then show that similar to the unranked case, ranked gene trees that do not match either the ranking or the topology of the species tree can have greater probability than the matching ranked gene tree., (Copyright © 2011 Elsevier Inc. All rights reserved.)

Given a gene tree and a species tree, a coalescent history is a list of the branches of the species tree on which coalescences in the gene tree take place. Each pair consisting of a gene tree topology and a species tree topology has some number of possible coalescent histories. Here we show that, for each n>or=7, there exist a species tree topology S and a gene tree topology G not equalS, both with n leaves, for which the number of coalescent histories exceeds the corresponding number of coalescent histories when the species tree topology is S and the gene tree topology is also S. This result has the interpretation that the gene tree topology G discordant with the species tree topology S can be produced by the evolutionary process in more ways than can the gene tree topology that matches the species tree topology, providing further insight into the surprising combinatorial properties of gene trees that arise from their joint consideration with species trees.

Although multiple gene sequences are becoming increasingly available for molecular phylogenetic inference, the analysis of such data has largely relied on inference methods designed for single genes. One of the common approaches to analyzing data from multiple genes is concatenation of the individual gene data to form a single supergene to which traditional phylogenetic inference procedures - e.g., maximum parsimony (MP) or maximum likelihood (ML) - are applied. Recent empirical studies have demonstrated that concatenation of sequences from multiple genes prior to phylogenetic analysis often results in inference of a single, well-supported phylogeny. Theoretical work, however, has shown that the coalescent can produce substantial variation in single-gene histories. Using simulation, we combine these ideas to examine the performance of the concatenation approach under conditions in which the coalescent produces a high level of discord among individual gene trees and show that it leads to statistically inconsistent estimation in this setting. Furthermore, use of the bootstrap to measure support for the inferred phylogeny can result in moderate to strong support for an incorrect tree under these conditions. These results highlight the importance of incorporating variation in gene histories into multilocus phylogenetics.

Motivation Consensus methods can be used for reconstructing a species tree from several gene trees, which exhibit incompatible topologies due to incomplete lineage sorting. Motivated by the fact that there are no anomalous rooted gene trees with three taxa and no anomalous unrooted gene trees with four taxa in the multispecies coalescent model, several contemporary methods form the gene tree consensus by finding the median tree with respect to the triplet or quartet distance—i.e. estimate the species tree as the tree which minimizes the sum of triplet or quartet distances to the input gene trees. These methods reformulate the solution to the consensus problem as the solution to a recursively solved dynamic programming (DP) problem. We present an iterative, easily parallelizable approach to finding the exact median triplet tree and implement it as an open source software package that can also find suboptimal consensus trees within a specified triplet distance to the gene trees. The most time-consuming step for methods of this type is the creation of a weights array for all possible subtree bipartitions. By grouping the relevant calculations and array update operations of different bipartitions of the same subtree together, this implementation finds the exact median tree of many gene trees faster than comparable methods, has better scaling properties with respect to the number of gene trees and has a smaller memory footprint. Results RTIST (Rooted Triple Inference of Species Trees) finds the exact median triplet tree of a set of gene trees. Its runtime and memory footprints scale better than existing algorithms. RTIST can resolve all the non-unique median trees, as well as sub-optimal consensus trees within a user-specified triplet distance to the median. Although it is limited in the number of taxa (≤20), its runtime changes little when the number of gene trees is changed by several orders of magnitude. Availability and implementation RTIST is written in C and Python. It is freely available at https://github.com/glebzhelezov/rtist [ABSTRACT FROM AUTHOR]

Species trees, which describe the evolutionary relationships between species, are often inferred from gene trees, which describe the ancestral relationships between sequences sampled at different loci from the species of interest. A common approach to inferring species trees from gene trees is motivated by supposing that gene tree variation is due to incomplete lineage sorting, also known as deep coalescence. One of the earliest methods motivated by deep coalescence is to find the species tree that minimizes the number of deep coalescent events needed to explain discrepancies between the species tree and input gene trees. This minimize deep coalescence (MDC) criterion can be applied in both rooted and unrooted settings. where either rooted or unrooted gene trees can be used to infer a rooted species tree. Previous work has shown that MDC is statistically inconsistent in the rooted setting, meaning that under a probabilistic model for deep coalescence, the multispecies coalescent, for some species trees, increasing the number of input gene trees does not make the method more likely to return a correct species tree. Here, we obtain analogous results in the unrooted setting, showing conditions leading to inconsistency of the MDC criterion using the multispecies coalescent model with unrooted gene trees for four taxa and five taxa. [ABSTRACT FROM AUTHOR]

Summary PRANC computes the Probabilities of RANked gene tree topologies under the multispecies coalescent. A ranked gene tree is a gene tree accounting for the temporal ordering of internal nodes. PRANC can also estimate the maximum likelihood (ML) species tree from a sample of ranked or unranked gene tree topologies. It estimates the ML tree with estimated branch lengths in coalescent units. Availability and implementation PRANC is written in C++ and freely available at github.com/anastasiiakim/PRANC. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

Background: The ancestries of genes form gene trees which do not necessarily have the same topology as the species tree due to incomplete lineage sorting. Available algorithms determining the probability of a gene tree given a species tree require exponential computational runtime. Results: In this paper, we provide a polynomial time algorithm to calculate the probability of a ranked gene tree topology for a given species tree, where a ranked tree topology is a tree topology with the internal vertices being ordered. The probability of a gene tree topology can thus be calculated in polynomial time if the number of orderings of the internal vertices is a polynomial number. However, the complexity of calculating the probability of a gene tree topology with an exponential number of rankings for a given species tree remains unknown. Conclusions: Polynomial algorithms for calculating ranked gene tree probabilities may become useful in developing methodology to infer species trees based on a collection of gene trees, leading to a more accurate reconstruction of ancestral species relationships. [ABSTRACT FROM AUTHOR]

Genome-wide patterns of variation across individuals provide a powerful source of data for uncovering the history of migration, range expansion, and adaptation of the human species. However, high-resolution surveys of variation in genotype, haplotype and copy number have generally focused on a small number of population groups. Here we report the analysis of high-quality genotypes at 525,910 single-nucleotide polymorphisms (SNPs) and 396 copy-number-variable loci in a worldwide sample of 29 populations. Analysis of SNP genotypes yields strongly supported fine-scale inferences about population structure. Increasing linkage disequilibrium is observed with increasing geographic distance from Africa, as expected under a serial founder effect for the out-of-Africa spread of human populations. New approaches for haplotype analysis produce inferences about population structure that complement results based on unphased SNPs. Despite a difference from SNPs in the frequency spectrum of the copy-number variants (CNVs) detected—including a comparatively large number of CNVs in previously unexamined populations from Oceania and the Americas—the global distribution of CNVs largely accords with population structure analyses for SNP data sets of similar size. Our results produce new inferences about inter-population variation, support the utility of CNVs in human population-genetic research, and serve as a genomic resource for human-genetic studies in diverse worldwide populations. [ABSTRACT FROM AUTHOR]

Under the coalescent model for population divergence, lineage sorting can cause considerable variability in gene trees generated from any given species tree. In this paper, we derive a method for computing the distribution of gene tree topologies given a bifurcating species tree for trees with an arbitrary number of taxa in the case that there is one gene sampled per species. Applications for gene tree distributions include determining exact probabilities of topological equivalence between gene trees and species trees and inferring species trees from multiple datasets. In addition, we examine the shapes of gene tree distributions and their sensitivity to changes in branch lengths, species tree shape, and tree size. The method for computing gene tree distributions is implemented in the computer program COAL. [ABSTRACT FROM AUTHOR]