Incomplete lineage sorting and phenotypic evolution in marsupials

This article reviews the various models that have been used to describe the relationships between gene trees and species trees. Molecular phylogeny has focused mainly on improving models for the reconstruction of gene trees based on sequence alignments. Yet, most phylogeneticists seek to reveal the history of species. Although the histories of genes and species are tightly linked, they are seldom identical, because genes duplicate, are lost or horizontally transferred, and because alleles can coexist in populations for periods that may span several speciation events. Building models describing the relationship between gene and species trees can thus improve the reconstruction of gene trees when a species tree is known, and vice versa. Several approaches have been proposed to solve the problem in one direction or the other, but in general neither gene trees nor species trees are known. Only a few studies have attempted to jointly infer gene trees and species trees. These models account for gene duplication and loss, transfer or incomplete lineage sorting. Some of them consider several types of events together, but none exists currently that considers the full repertoire of processes that generate gene trees along the species tree. Simulations as well as empirical studies on genomic data show that combining gene tree–species tree models with models of sequence evolution improves gene tree reconstruction. In turn, these better gene trees provide a more reliable basis for studying genome evolution or reconstructing ancestral chromosomes and ancestral gene sequences. We predict that gene tree–species tree methods that can deal with genomic data sets will be instrumental to advancing our understanding of genomic evolution.

BackgroundSpecies phylogenies are not estimated directly, but rather through phylogenetic analyses of different gene datasets. However, true gene trees can differ from the true species tree (and hence from one another) due to biological processes such as horizontal gene transfer, incomplete lineage sorting, and gene duplication and loss, so that no single gene tree is a reliable estimate of the species tree. Several methods have been developed to estimate species trees from estimated gene trees, differing according to the specific algorithmic technique used and the biological model used to explain differences between species and gene trees. Relatively little is known about the relative performance of these methods.ResultsWe report on a study evaluating several different methods for estimating species trees from sequence datasets, simulating sequence evolution under a complex model including indels (insertions and deletions), substitutions, and incomplete lineage sorting. The most important finding of our study is that some fast and simple methods are nearly as accurate as the most accurate methods, which employ sophisticated statistical methods and are computationally quite intensive. We also observe that methods that explicitly consider errors in the estimated gene trees produce more accurate trees than methods that assume the estimated gene trees are correct.ConclusionsOur study shows that highly accurate estimations of species trees are achievable, even when gene trees differ from each other and from the species tree, and that these estimations can be obtained using fairly simple and computationally tractable methods.

The concept of homology lies at the root of evolutionary biology. Since the seminal work of Fitch (1970), three main categories of homology relationships have been defined at the molecular level: orthology, paralogy, and xenology. In brief, if two gene copies arose by duplication they are paralogs, whereas if they arose through speciation they are orthologs. If one of them was transferred from a contemporaneous species, we call them xenologs (Supplementary Fig. S1 in Supplementary Material online, available at http://dx.doi.org/10.5061/dryad.87k57; see Gray and Fitch (1983); Fitch (2000)). Indeed, these terms were coined under a phylogenetic framework in which species were represented by single individuals, and as such they have remained very much intact during the last four decades—although particular cases within these categories have received specific names (Mindell and Meyer 2001). However, advances in sequencing technology have changed the field, and it is now very common to collect data sets containing multiple gene loci and/or multiple individuals per species. In general, such genome-wide data sets not only have unveiled extensive phylogenomic incongruence (Jeffroy et al. 2006; Salichos and Rokas 2013) but have brought back to the spotlight the consideration of how ancestral polymorphisms sort within populations (Edwards 2009). Altogether, phylogenomic data make imperative the explicit distinction between organismal and gene histories. Let us consider phylogenetic relationships at three different levels: species, loci, and gene copies (Fig. 1). The distinction between species/population trees and gene trees has been known for decades (Goodman et al. 1979; Pamilo and Nei 1988; Takahata 1989), whereas the introduction of locus trees into these models is very recent (Rasmussen and Kellis 2012). In brief, a species tree depicts the evolutionary history of the sampled organisms. In this case, the nodes represent speciation events, connected by branches that reflect the population history along these periods, and where their widths represent effective population size (Ne) and their lengths represent time (usually in years or number of generations). Apart from speciations, only evolutionary processes that affect species as a whole are represented at this level, like hybridization. Note that species trees are equivalent to population trees when the organismal units of interest are conspecific populations. In this case, the nodes of the population trees represent isolation events. In general, we will refer to “species” as any diverging, interbreeding group of individuals regardless of its taxonomic rank. On the other hand, a locus tree represents the evolutionary history of the sampled loci for a given gene family (see Rasmussen and Kellis 2012). Since the loci exist inside individuals evolving as part of a population, the locus tree is embedded within the species tree. In a locus tree, the nodes depict either genetic divergence due to speciation in the embedding species tree or locus-level events such as duplication, losses, or horizontal gene transfers, whereas the branch lengths and widths represent time and Ne, respectively. Here, we assume that the locuslevel events get immediately fixed in the population, so these Ne are equivalent to those in the species tree and are the same for every locus. Finally, a gene tree represents the evolutionary history of the sampled gene copies that evolve inside the locus tree. Gene tree nodes indicate coalescent events, which looking forward in time correspond to the process of DNA replication and divergence, and that can occur around the speciation time, well before (deep coalescence) or afterwards (migration in population trees). The branches of the gene tree usually represent amount of substitutions per site, and can also represent number of generations or other measures of time. Importantly, these three historical layers do not necessarily coincide. True species/population trees can differ from true locus trees due to gene duplications, losses, and/or horizontal gene transfers, whereas true gene trees can differ from their embedding locus and species trees if there is incomplete lineage sorting (ILS) (Maddison 1997; Page and Charleston 1997) (and migration in the case of population trees). In this regard,

Estimating phylogenetic relationships among closely related species can be extremely difficult when there is incongruence among gene trees and between the gene trees and the species tree. Here we show that incorporating a model of the stochastic loss of gene lineages by genetic drift into the phylogenetic estimation procedure can provide a robust estimate of species relationships, despite widespread incomplete sorting of ancestral polymorphism. This approach is applied to a group of montane Melanoplus grasshoppers for which genealogical discordance among loci and incomplete lineage sorting obscures any obvious phylogenetic relationships among species. Unlike traditional treatments where gene trees estimated using standard phylogenetic methods are implicitly equated with the species tree, with the coalescent-based approach the species tree is modeled probabilistically from the estimated gene trees. The estimated species phylogeny (the ESP) is calculated for the grasshoppers from multiple gene trees reconstructed for nuclear loci and a mitochondrial gene. This empirical application is coupled with a simulation study to explore the performance of the coalescent-based approach. Specifically, we test the accuracy of the ESP given the data based on analyses of simulated data matching the multilocus data collected in Melanoplus (i.e., data were simulated for each locus with the same number of base pairs and locus-specific mutational models). The results of the study show that ESPs can be computed using the coalescent-based approach long before reciprocal monophyly has been achieved, and that these statistical estimates are accurate. This contrasts with analyses of the empirical data collected in Melanoplus and simulated data based on concatenation of multiple loci, for which the incomplete lineage sorting of recently diverged species posed significant problems. The strengths and potential challenges associated with incorporating an explicit model of gene-lineage coalescence into the phylogenetic procedure to obtain an ESP, as illustrated by application to Melanoplus, versus concatenation and consensus approaches are discussed. This study represents a fundamental shift in how species relationships are estimated - the relationship between the gene trees and the species phylogeny is modeled probabilistically rather than equating gene trees with a species tree.

Species tree estimation faces many significant hurdles. Chief among them is that the trees describing the ancestral lineages of each individual gene-the gene trees-often differ from the species tree. The multispecies coalescent is commonly used to model this gene tree discordance, at least when it is believed to arise from incomplete lineage sorting, a population-genetic effect. Another significant challenge in this area is that molecular sequences associated to each gene typically provide limited information about the gene trees themselves. While the modeling of sequence evolution by single-site substitutions is well-studied, few species tree reconstruction methods with theoretical guarantees actually address this latter issue. Instead, a standard-but unsatisfactory-assumption is that gene trees are perfectly reconstructed before being fed into a so-called summary method. Hence much remains to be done in the development of inference methodologies that rigorously account for gene tree estimation error-or completely avoid gene tree estimation in the first place. In previous work, a data requirement trade-off was derived between the number of loci m needed for an accurate reconstruction and the length of the locus sequences k. It was shown that to reconstruct an internal branch of length f, one needs m to be of the order of [Formula: see text]. That previous result was obtained under the restrictive assumption that mutation rates as well as population sizes are constant across the species phylogeny. Here we further generalize this result beyond this assumption. Our main contribution is a novel reduction to the molecular clock case under the multispecies coalescent, which we refer to as a stochastic Farris transform. As a corollary, we also obtain a new identifiability result of independent interest: for any species tree with [Formula: see text] species, the rooted topology of the species tree can be identified from the distribution of its unrooted weighted gene trees even in the absence of a molecular clock.

Consistency and inconsistency of consensus methods for inferring species trees from gene trees in the presence of ancestral population structure

It is well known that species with elevated substitution rates can give rise to disproportionately long branches in the species tree. This combination of long and short branches can contribute to long-branch artifacts (LBA). Despite efforts to remedy LBA via increased taxon sampling and methodological improvements in gene tree estimation, it remains unclear how long and short branches affect species tree estimation in the presence of incomplete lineage sorting (ILS). Here, we examine the combined influence of long external and short internal branches on concatenation and coalescent methods using both simulated and empirical data. Our results demonstrate that the presence of long and short branches alone does not obviously confound the consistency of concatenation and coalescent methods. However, when long external and short internal branches occur simultaneously with high ILS, concatenation methods can be misled, especially when two of these long branches are sister lineages. In contrast, coalescent methods are more robust under these circumstances. This is particularly relevant because this topological pattern also characterizes numerous ancient rapid radiations across the tree of life. Because short internal branches can increase the potential for ILS and gene tree discordance, our results collectively suggest that coalescent methods are more likely to infer the correct species tree in cases of ancient rapid radiations where long external and short internal branches are in close phylogenetic proximity.

Incomplete lineage sorting can cause incongruence between the phylogenetic history of genes (the gene tree) and that of the species (the species tree), which can complicate the inference of phylogenies. In this article, I present a new coalescent-based algorithm for species tree inference with maximum likelihood. I first describe an improved method for computing the probability of a gene tree topology given a species tree, which is much faster than an existing algorithm by Degnan and Salter (2005). Based on this method, I develop a practical algorithm that takes a set of gene tree topologies and infers species trees with maximum likelihood. This algorithm searches for the best species tree by starting from initial species trees and performing heuristic search to obtain better trees with higher likelihood. This algorithm, called STELLS (which stands for Species Tree InfErence with Likelihood for Lineage Sorting), has been implemented in a program that is downloadable from the author's web page. The simulation results show that the STELLS algorithm is more accurate than an existing maximum likelihood method for many datasets, especially when there is noise in gene trees. I also show that the STELLS algorithm is efficient and can be applied to real biological datasets.

A transcriptome-based study on the phylogeny and evolution of the taxonomically controversial subfamily Apioideae (Apiaceae).

The traditional Tree of Life (ToL) model is increasingly challenged by the Web of Life (WoL) paradigm, which offers a more accurate depiction of organismal phylogeny, particularly in light of the incongruences often observed between gene and species trees. However, the absence of a standardised method for resolving evolutionary mechanisms - such as Incomplete Lineage Sorting (ILS), hybridisation, introgression, polyploidisation, and whole-genome duplication - remains a significant obstacle in defining the WoL. Characterised by extensive hybridisation events, the pear genus Pyrus provides an ideal model for exploring these complexities. In this study, we present a Step-by-Step Exclusion (SSE) approach for investigating the evolutionary pathways of Pyrus, based on Whole Genome Sequencing (WGS) and Deep Genome Skimming (DGS) data, and our results demonstrate that: (1) ILS, rather than polyploidisation, plays a dominant role in the origination of Pyrus; (2) the two subgenera of Pyrus followed independent evolutionary paths, influenced by geographical barriers formed through the uplift of the Tibetan Plateau and increased aridity in Central Asia; (3) both ILS and hybridisation have driven the diversification of subg. Pashia, while hybridisation alone has shaped the reticulate evolution of subg. Pyrus; (4) the establishment of the Silk Road during the Han Dynasty facilitated genetic exchange between subg. Pyrus and subg. Pashia. The SSE approach offers a versatile framework for studying the evolutionary mechanisms underlying the WoL paradigm.

Species tree reconstruction from genomic data is increasingly performed using methods that account for sources of gene tree discordance such as incomplete lineage sorting. One popular method for reconstructing species trees from unrooted gene tree topologies is ASTRAL. In this paper, we derive theoretical sample complexity results for the number of genes required by ASTRAL to guarantee reconstruction of the correct species tree with high probability. We also validate those theoretical bounds in a simulation study. Our results indicate that ASTRAL requires gene trees to reconstruct the species tree correctly with high probability where is the number of species and is the length of the shortest branch in the species tree. Our simulations, some under the anomaly zone, show trends consistent with the theoretical bounds and also provide some practical insights on the conditions where ASTRAL works well.

The coalescent and multispecies coalescent model rooted genealogies backward through time. Often, the direction of time is unknown in trees estimated from molecular sequences due to reversible mutation models, absence of an appropriate outgroup, and the absence of the molecular clock. In this article, probabilities of unrooted gene-tree topologies under the multispecies coalescent are considered. The main result is that for any species-tree topology with seven or more taxa, there exist branch lengths such that there are unrooted gene-tree topologies that are more likely than the one that has the same unrooted topology as the species tree. Species trees with such anomalous unrooted gene trees (AUGTs) are characterized for trees with five and six taxa, and patterns of branch lengths leading to AUGTs and rooted anomalous gene trees are explored. The results could be useful for understanding gene tree discordance and designing simulations studies for inferring challenging species trees.

Incomplete lineage sorting (ILS) is a common source of gene tree incongruence in multilocus analyses. Numerous approaches have been developed to infer species trees in the presence of ILS. Here we provide a mathematical analysis of several coalescent-based methods. The analysis is performed on a three-taxon species tree and assumes that the gene trees are correctly reconstructed along with their branch lengths. It suggests that maximum likelihood (and some equivalents) can be significantly more accurate in this setting than other methods, especially as ILS gets more pronounced.

Accurate gene tree-species tree reconciliation is fundamental to inferring the evolutionary history of a gene family. However, although it has long been appreciated that population-related effects such as incomplete lineage sorting (ILS) can dramatically affect the gene tree, many of the most popular reconciliation methods consider discordance only due to gene duplication and loss (and sometimes horizontal gene transfer). Methods that do model ILS are either highly parameterized or consider a restricted set of histories, thus limiting their applicability and accuracy. To address these challenges, we present a novel algorithm DLCpar for inferring a most parsimonious (MP) history of a gene family in the presence of duplications, losses, and ILS. Our algorithm relies on a new reconciliation structure, the labeled coalescent tree (LCT), that simultaneously describes coalescent and duplication-loss history. We show that the LCT representation enables an exhaustive and efficient search over the space of reconciliations, and, for most gene families, the least common ancestor (LCA) mapping is an optimal solution for the species mapping between the gene tree and species tree in an MP LCT. Applying our algorithm to a variety of clades, including flies, fungi, and primates, as well as to simulated phylogenies, we achieve high accuracy, comparable to sophisticated probabilistic reconciliation methods, at reduced run time and with far fewer parameters. These properties enable inferences of the complex evolution of gene families across a broad range of species and large data sets.

Species tree estimation from multi-locus data is complicated as biological processes can result in different loci having different evolutionary histories. Incomplete lineage sorting (ILS), modeled by the multi-species coalescent (MSC), is considered to be a dominant cause for gene tree incongruence. Various optimization criteria (e.g., quartet score, pseudo-likelihood, etc.) are statistically consistent under the MSC model, meaning that they return the true species tree with high probability given sufficiently large numbers of accurate gene trees. However, the number of genes is limited and estimating highly accurate gene trees is difficult. Therefore, even popular methods, optimizing a particular criterion, may fail to reconstruct highly accurate trees under practical model conditions with limited numbers of genes and in the presence of gene tree estimation error. In this study, we advocate multi-objective optimization to tackle this challenge. Particularly, we present a multi-objective metaheuristic (i.e., SNOGA), a modified version of the popular NSGAII, which combines various optimization criteria to find a suitable search space containing highly accurate species trees.