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Timestamp: 2019-04-19 16:29:22+00:00

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FIGURE 1. A hierarchy of evolutionary processes contribute to sequence evolution. a) Individual species (circles) and their genomes evolve among a population of species, according to a diversiﬁcation process consisting of speciation (light gray, green online) and extinction (dark gray, red online) events. The variation in the number of species existing at any given time is indicated by the dashed contour. When attempting to infer the species tree typically only a fraction of existing species (gray and black circles on dashed line) are sampled (black circles). b) Inside each genome, each gene evolves according to gene duplication, loss, and transfer events. c) Individual sites evolve through point mutations. Processes at the gene and site level are played out at the population level, where changes ﬁx or are lost.
shown improved accuracy for inferring both gene trees and the species tree. In this review we present these methods, explain the assumptions they make, introduce how they work, and highlight some of the results obtained with them. We focus on probabilistic models, but discuss parsimony-based approaches in situations where probabilistic models have not been developed yet. We do not review methods that consider gene count or gene presence/absence information, as they altogether ignore sequence information once homology relationships have been deﬁned (some of these methods do account for several processes however, for example, gene duplication, transfer, and loss (Csuros et al. 2006)).
the generated tree topology. Models of gene family evolution, however, are constrained by the species tree, whereas species diversiﬁcation models are not. The species tree constitutes a set of constraints corresponding to speciation events and branch lengths that control the birth–death process generating the gene family tree. A gene family evolution model is in essence a series of birth–death models ﬁtted piecewise along the branches of a species tree (Fig. 2). The birth–death process generating the gene tree starts above the root of the species tree. Each time the birth–death process reaches a speciation node, two new processes are created in the children lineages. These processes can be identical, or can have different parameters. In general, for n branches in the species tree, counting the branch above the root, there are n independent birth–death processes. Of course, the parameters of these n independent processes do not need to be independent: one can imagine that the birth parameter for instance evolves according to for example a Brownian motion process running along the species tree. Such a model would penalize large jumps in the birth parameter between neighboring branches of the species tree, but to our knowledge such an idea has not yet been implemented. Another source of dependence between processes is lateral gene transfer: a birth in a lineage may originate in another. The above describes how a gene tree, complete with branch lengths in units of time, is generated along the clock-like branches of the species tree. In practice, to simplify the problem, we will see that several methods choose to consider only the topologies of gene trees, that is the branch length information is discarded. In this case, the mathematical machinery of the birth death model is not used to compute the probability of a speciﬁc dated scenario of observed birth and death events; instead it is used to compute the probability of a given succession of birth and death events (Degnan and Salter 2005; Wu 2011), or the probability of observing k genes at the beginning of a branch of the species tree, and l genes at the end of this same branch (Boussau et al. 2013). The choice of discarding branch length information in the gene tree in some cases simpliﬁes the problem, because fewer processes need to be modeled. Potentially useful information, however, is discarded in the process.
MODELING THE DEPENDENCE BETWEEN GENE TREE AND SPECIES TREE A gene family can contain genes from different species at the same locus, or genes in a same genome at different loci. The processes known to contribute to gene family evolution include speciation and lineage sorting (ILS if incomplete), gene duplication and loss (DL), and gene transfer (T). Lineage sorting concerns genes from different genomes at the same locus, whereas duplications give rise to homologous genes on the same genome at different loci. Transfers can insert a gene at a new locus, or replace a homologous gene at its locus. Hybridization can be seen as a special type of transfer, affecting a large portion of the genome, and resulting in a gene replacement in the receiving species. Allopolyploidization is a particular type of hybridization, in which the two genomes keep cohabiting in subsequent generations. For each individual process, there are published models accounting for its effect, and recently some tend to integrate several of them. So far, no model has been published that deals with all processes together in a coherent statistical framework.
FIGURE 2. Birth–death processes for generating species trees and gene trees. Death events (species extinctions and gene loss) are in dark gray (red online), birth events (speciation, duplication and transfer events) are light gray (green online). a) Birth–death processes modeling speciation and extinction. b) Birth–death process modeling gene family evolution inside a species tree.
expected number of species, but also through a guide tree, whose other purpose is to improve the efﬁciency of the MCMC algorithm used for inference. Under this model, they can analyze about 10 species for 100 sequences, with a ﬁnite number of loci. They apply this method to well studied data sets of asexual rotifers and fence lizards, and recover the species found by other means.
Models of Gene Duplication and Loss Models of gene duplication and loss usually ignore population-level processes (but see Rasmussen and Kellis (2012), discussed below) that drive the ﬁxation or disappearance of an allele, and only consider events of gene duplication and loss that have ﬁxed in the species. In this setting, birth events correspond to ﬁxed gene duplications, and death events to ﬁxed gene losses. Probabilistic models for gene duplication and loss were ﬁrst proposed by Arvestad (2003), and further developed in subsequent papers by the same group (Arvestad et al. 2004; Akerborg et al. 2009; Sjöstrand et al. 2012) and by a few others (Dubb 2005; Rasmussen and Kellis 2007, 2010). The focus of these works was to infer gene trees given a ﬁxed species tree, with clock-like branch lengths in units of time, and with ﬁxed rates of gene duplication and gene loss over the entire tree. Combined with the birth– death model of gene evolution is a hierarchical model of the rate of sequence evolution, wherein the species tree provides dates, and each gene family is associated with one or several rates. Alternatively, Górecki et al. (2011); Górecki and Eulenstein (2013) developed another model for gene duplication, not based on a birth–death process, but based on a Poisson process for computing the probability of a parsimonious reconciliation of a gene tree topology against a species tree. The gene tree does not need to have branch lengths, but the species tree does. For this reason, and because it does not include a loss parameter, this model misses some of the realism of the birth death processes described above, but gains in speed. More recently, we modiﬁed birth–death models to allow different duplication/loss parameters for each branch of a nondated species tree (Boussau et al. 2013). To speed-up computations, we took an approach similar to Górecki et al. (2011), and did not account for the branch lengths of gene trees in their reconciliation with the species tree. Instead we only reconciled topologies. However, because our hierarchical model includes a model of sequence evolution for joint inference of gene trees and species tree, we still needed to estimate branch lengths in the gene trees. To simplify the problem, we chose not to have a hierarchical model of rates of sequence evolution: rates for each gene family were considered to be entirely independent. This decreased the number of global parameters to estimate, but increased drastically the number of gene family-speciﬁc parameters to estimate.
are time-consistent: in principle a gene can only be transferred to contemporaneous species, present in the sample analyzed or not, and certainly not to more ancient species. In Suchard (2005)’s approach, because the species tree topology is not anchored in time, time-consistent transfers and “back-to-the-future” type transfers are not distinguished. Bloomquist and Suchard (2010) chose another road to modeling gene replacement, by drawing on models of population genetics. They considered the Ancestral Recombination Graph (ARG). An ARG is a type of rooted network that combines both vertical and transfer edges. Once an ARG is built, it can be used to generate dated gene trees, which correspond to tree-like paths obtained by selecting edges of the ARG. They aimed at reconstructing an ARG that represents all of the evolutionary histories of a set of distinct loci, some of which evolved along the species tree, and some of which underwent replacement events. They used MCMC to propose ARGs, adding or subtracting transfer edges through reversible jumps. Given an ARG, a gene tree is drawn for each locus under study; these gene trees can be totally independent of each other, or can incorporate spatial information, so that two neighboring genes on the genome are more likely to be transferred together than distant genes. This allows modeling different situations, such as single-gene conversion or homologous recombination. In addition, the sequences of different genes can evolve at different rates. In the end, the method builds dated gene trees, and a dated ARG in which vertices are annotated as vertical or transfer nodes, and in which edges involved in a transfer event can be annotated with the genes that are inferred to have been transferred.
FIGURE 3. Duplication and loss events within a multispecies coalescent with the locus tree in gray (blue online) and the gene tree in black. a) A duplication occurs in one chromosome and creates a new locus, locus 2 in the genome. At locus 2, the Wright–Fisher model dictates how the frequency p of the daughter duplicate (black dots) competes with the null allele (white dots) until it eventually ﬁxes (p = 1). A gene tree is therefore a traceback in this combined process. b) A new duplicate can undergo hemiplasy, and ﬁxes in some lineages and goes extinct in others. c) Similar to duplication, a gene loss (deletion) starts in one chromosome and drifts until it ﬁxes or goes extinct. Reproduced from Figure 1 in Rasmussen M.D., and Kellis M., Genome Res. 2012;22:755–765.
posterior distributions of phylogenetic trees have been built from these families, Bucky attempts to cluster the families by similarity of their evolutionary history. This clustering is done in a nonparametric Bayesian framework, which means that both the clustering and the number of clusters are estimated from the data. The end result may provide insight into the sources of the heterogeneity among gene histories, for instance in cases where neighboring genes are found to share the same history. Additionally, Bucky has also often been used to provide a candidate species tree, by gathering clade frequencies from all gene histories. One strength of Bucky is the fact that, provided orthology between genes has been well deﬁned, it does not depend on a particular model of gene family evolution, and will work equally well in the presence of transfers or incomplete lineage sorting for instance. The corresponding drawback is that it does not return direct estimates of the species tree, or of rates of events such as duplications or transfers that might be of interest to students of molecular evolution.
reads into contigs and scaffolds, gene annotation, gene family clustering, alignment, and tree reconstruction. Most of these steps are done sequentially, so that later steps in the pipeline entirely disregard any estimate of uncertainty from the previous steps, and do not provide any feedback to these. Gene tree–species tree models take a step toward a more principled approach, by allowing communication between two steps of this pipeline, the construction of gene trees, and the construction of a species tree. Figure 5 places the above discussed models and associated phylogenetic software in the context of the complete phylogenetic inference pipeline. Gray nodes are considered known, and white nodes are inferred. This ﬁgure shows that a large diversity of inferential problems have been addressed, considering gene alignments, gene trees, species trees, or several of these as data. In this section, we review some of the methods and algorithms that have been used to address these inferential problems. We do not discuss methods aiming at reconstructing an alignment, and instead focus on gene tree–species tree methods. As a consequence, in the following we use “probability of an alignment” loosely to describe the probability coming from events of substitutions or jointly from events of substitutions and insertion–deletions. We present how data can be simulated, how the likelihood of a gene tree or of a species tree can be computed efﬁciently, and how good gene trees and species trees can be searched for.
FIGURE 4. Left: the hierarchy of sequence evolutionary processes plotted along two dimensions: sequence length, from single nucleotides through genes to whole genomes; and time, from single generations through the neutral ﬁxation time to large numbers of generations. Events occurring in single individuals, such as point mutations, insertions/deletions etc. are ﬁltered by the population-level process of selection and drift with only a minority reaching eventual ﬁxation. Speciation and extinction events affect entire genomes and require many generations. Incomplete lineage sorting (blue online) occurs when ﬁxation time overlaps with speciation time. Transfer events can cross large phylogenetic distances and almost always involve evolution along extinct or unrepresented species and hence are affected by speciation dynamics. Right: distribution of models discussed in the text based on the time and length scales of the evolutionary process they model. Classic molecular phylogeny methods model only substitutions. DL models handle ﬁxed duplication and loss events along with substitutions. The multispecies coalescent and related methods model explicitly the ﬁxation of point mutations (blue online). DLCoal models the ﬁxation of both point mutations and of gene-scale insertion/deletion events that lead to ﬁxed duplication and loss events. DTL models (red online; ODT, DTLSR) extend DL models to ﬁxed transfer events, but ignore speciation dynamics. The ex-ODT model combines speciation dynamics with DTL events to provide a more realistic model of transfer paths. A potential “ex-DTLCoal” model, as discussed in the main text would cover the area of all these models.
FIGURE 5. Gene tree–species tree models in the context of the phylogenomics inference pipeline. Left: the inference pipeline (some steps are not represented, such as sequencing error correction). Right: graphical representation of the inferential problem for a selection of the models and associated phylogenetic software discussed in the main text. The sequence of steps in the graphical model representations correspond to the hierarchical sequence of evolutionary process generating genomic sequences (cf. Fig. 1). The likelihood that must be computed is also shown. Graphical model conventions are observed: stochastic nodes, nodes corresponding to data considered as known are gray, and nodes whose states are inferred are in white. The models have been simpliﬁed, and parameters others than the gene tree and the species tree have not been represented.
given subtree, according to the process considered in the branches. At the root, dynamic programming algorithms yield a probability for the entire tree. The rough description above outlines the algorithm developed by Felsenstein (1981) to compute the probability of a multiple alignment of gene sequences given a gene tree and a model of sequence evolution. In this case, the differential equations corresponding to the Markovian process of sequence evolution can be solved analytically to obtain substitution probabilities along a branch of a given length. Computing the probability of a gene tree given a species tree is a bit more complicated, as it involves mapping the gene tree onto the species tree to compute the probability of presence of a gene tree node or branch at each node or branch of the species tree. This mapping is natural at the leaves: a gene from species A is mapped onto leaf A of the species tree. For internal nodes, the mapping can be helped by the consideration of node ages in models that consider that both the gene trees and the species tree are dated. This is typically the case with multispecies coalescent models (e.g., Rannala and Yang 2003). Such a method yields a single mapping between the nodes of a given gene tree and a given species tree, for given rates of sequence evolution. In a duplication and loss context, Akerborg et al. (2009) improved upon this approach by analytically integrating over the possible mappings as well as over rates of sequence evolution, again through dynamic programming. Their approach requires “slicing” the species tree by dropping extra nodes along the branches of the tree. These two methods yielding either a single mapping or integrating over all mappings in the context of dated trees have counterparts in the context of nondated trees. On one hand, Boussau et al. (2013) assumed the most parsimonious mapping between the nodes of the gene tree and the nodes of the species tree. This most parsimonious mapping is obtained with a single tree traversal (Zmasek and Eddy 2001). On the other hand, Szöll˝osi et al. (2012) took a similar approach to Akerborg et al. (2009) by integrating over all the possible mappings between the nodes of the gene tree and the nodes of the species tree, again through dynamic programming, but without considering dated gene trees. This allowed them to avoid using a model of rate evolution. However, it was necessary to order the nodes of the species tree, which has the effect of slicing it and adding new nodes, for correctly computing the probability of a gene tree given a species tree. As this inference includes transfer in addition to duplication and loss, numerical integration is necessary to solve the differential equations describing the birth and death process because gene lineages mapping to different branches of the species tree are dependent and no analytical solutions are available. Usually such algorithms can achieve linear complexity in the number of genes for coalescent or DL models, but modeling transfers raises the complexity to the product between the number of nodes in the gene tree and the number of nodes in the species tree. Methods that require slicing the species tree (Akerborg et al.
model (ALE standing for Amalgamated Likelihood Estimation) to produce simulated alignments based on a species tree and real alignments from 36 cyanobacteria. The approach consisted of ﬁrst reconstructing the most probable gene trees according to the joint likelihood associated with duplication, transfer and loss rates given a ﬁxed species tree and the gene family alignments. Second, the inferred gene trees were then used to simulate alignments. Third, these alignments were fed back into ALE+ex-ODT to assess its reconstruction accuracy, comparing both the reconstructed gene trees and the associated duplication, transfer and loss events to those used in the simulation. This approach has the advantage of circumventing potentially complex simulations while at the same time retaining otherwise hard to reproduce properties of biological datasets, such as the distribution of gene family sizes and the variation of evolutionary rates within and among gene families Szöll˝osi and Daubin (2012).
FIGURE 6. Based on gene trees sampled according to their posterior probability, conditional clade probabilities (CCP) can used to estimate the posterior probability of any tree that can be amalgamated (Höhna and Drummond 2012) from clades present in the sample. Conditional clade frequencies can be used to approximate CCPs and are computed as the fraction of times a particular split of a clade, for example (abc,de) is observed among all trees in which the containing clade, for example (abcde) is found. Estimates based on the sample of trees on the left are shown as fractions for two different gene trees that can be amalgamated. The estimate for a gene tree is given by the product of the frequencies. Amalgamated likelihood estimation (ALE (Szöll˝osi et al. 2013a)) is a probabilistic approach to exhaustively explore all reconciled gene trees that can be amalgamated as a combination of clades observed in a sample of gene trees. Based on the sample on the left, the tree with the highest posterior probability is the third tree (blue online). Reconciling it with the species tree requires 1 transfer and 1 loss event. It is, however, possible to combine clades present in the second (green online) and third (blue online) trees to produce a gene tree that is not present in the original sample but is identical to the species tree, that is it requires 0 events to draw it into the species tree. Depending on the relative probabilities of P(0 events) and P(1 transfer and 1 loss), the joint conditional probability may prefer the scenario without transfer.
IMPACT ON SYSTEMATICS AND GENOME EVOLUTION The methods we described in the previous sections have shown repeatedly that they improve on methods that do not model gene family evolution for problems as diverse as species tree estimation, gene tree estimation, and the study of genomic evolution. In this section, we present some of their most salient results.
heuristics perform SPRs in a speciﬁc order, so that only a small portion of the mapping between gene trees and species trees needs to be recomputed, hence resulting in signiﬁcant savings in computing time. Alternatives to local searches are the search for exact solutions (Chang et al. 2011), or, inspired by coalescent models, supertree methods resembling the amalgamation of gene trees mentioned in the previous section, which seem to quickly provide good approximations of parsimonious species trees (Bayzid et al. 2013). Considering transfers in a probabilistic framework, Szöll˝osi et al. (2012) explored time-ordered species trees, that is, species trees in which internal nodes are totally ordered. Topology search was performed by a directed local search guided by apparent highways of transfers: rearrangements are proposed in parts of the species tree that show the highest numbers of transfers in the hope of proposing rearrangements that reduce phylogenetic discord. All of the above methods take as their input ﬁxed gene trees. However, as we have several times recalled, good gene trees computed with the help of the (correct) species tree are substantially more accurate. Joint estimation has been achieved by Heled and Drummond (2010); Boussau et al. (2013), but with a very high computational cost. Improvements in the algorithms used would be very welcome.
recombination to increase effective population size: because, at each meiosis, each chromosome undergoes at least one recombination event, there are more recombination events per base on small chromosomes, which then increases the effective population sizes on small chromosomes. The use of a species tree in addition to a gene alignment yields better gene trees than methods that only consider the gene alignment. Akerborg et al. (2009) studied a dataset of about 180 gene families in 17 yeast genomes with two methods, their own method that uses the sequence alignment and a species tree, and mrBayes, that only uses the alignment (Ronquist et al. 2012). Several of these yeast species descend from a species whose genome has been duplicated. As a consequence, all gene trees in the data set must show a duplication event in the branch containing this species. They found that their method detects a branch corresponding to a whole genome duplication in 66% of the gene families, when mrBayes only detects this branch in 35% of the cases. Rasmussen and Kellis (2010) obtained a similar result by comparing the inferred orthologs from gene trees obtained using 11 methods to orthologs inferred from synteny information, on a data set of 16 fungi. The seven methods that use the information provided by the species tree were found to outperform the four methods that only use the sequence alignments, agreeing with synteny in about 90% of the cases versus 60%, respectively. Other tests based on a measure of tree balance after a duplication, or based on simulated data all concurred that the information provided by the species tree and interpreted by DL models greatly improves phylogenetic reconstruction. More recently Mahmudi et al. (2013) sample gene trees and reconciliations in an MCMC framework under a DL model and infer duplication and loss rates on a vertebrate tree. Their conclusion is not only that sequence-based trees are often wrong, but also that most parsimonious reconciliations of good gene trees are often improbable. Reconciled gene trees have also been used to detect paralogs that originate from whole genome duplications in teleosts (Ouangraoua et al. 2011; Howe et al. 2013) or at the base of vertebrates (Makino and McLysaght 2010; Affeldt et al. 2013) and understand the causes of their maintenance or detect the current traces of these duplications and reconstruct ancestral genomes. They have also been used to study the evolution of metabolism in fungi (Eastwood et al. 2011; Floudas et al. 2012). These authors study fungi that digest wood: brown-rot fungi, which digest only cellulose, and white-rot fungi, which digest both cellulose and lignin, the most resistant component in wood. Focusing on a subset of enzymes, and reconciling their gene trees with the species tree, they ﬁnd that brown-rot fungi are derived white-rot fungi that have lost several important genes. They also infer that white-rot fungi appeared concomitantly with the disappearance of coal deposits, and suggest that lignin decay pathways in white-rot fungi may have caused this disappearance.
of the tree. In addition, we ﬁnd that support for our unusual root comes from more than 200 transfer events. Overall, the information gained thanks to the use of a model of gene family evolution provides a new light into the order of speciation events in Cyanobacteria. It also provides a unique insight into genomic evolution in this clade, by providing an accurate reconstruction of ancestral gene contents. Because the ODT model infers events of gene transfers, duplications and losses, the number of genes present in ancestral genomes in each gene family is a natural outcome. Future analyses of ancestral gene contents based on models like ODT should provide windows into ancient metabolisms and phenotypes. Another important process shaping species relationships is hybridization. Models that aim at inferring hybridization in the presence of incomplete lineage sorting have been used in several systems and have often found cases of hybrid speciations. Meng and Kubatko (2009) studied four genes in four species of cicadas from New Zealand to support an hypothesized hybrid origin for one species. Yu et al. (2012) and Bloomquist and Suchard (2010), using a Maximum Likelihood and a Bayesian approach, investigated 106 genes from yeast species (6 in Bloomquist and Suchard (2010), 5 in Yu et al. (2012)) and agreed about their inference of hybridization ancestral to two species. In addition, Bloomquist and Suchard (2010) studied 9 gene regions in spirochaete Bacteria, and conﬁrmed previous results that one horizontal gene transfer happened in the history of these genes. Thanks to their integrative Bayesian method, they were able to date this event. Finally, Yu et al. (2012) studied more than 9000 genes in three Drosophila genomes and also detected hybridization ancestral to one of the three species, this time in disagreement with Pollard et al. (2006), whose analysis concluded that incomplete lineage sorting was enough to explain the pattern of incongruence in these genomes. Overall, these results show that network-based methods are powerful and can detect past hybridization events. Only Bloomquist and Suchard (2010)’s method can infer the network topology, but the other methods can be run on a set of topologies to compare their likelihoods.
and rates of duplication, transfer, and loss, which can be given or all be inferred provided enough information is given to the program. Simulations and measures based on reconstructed ancestral genomes show that these gene trees are more accurate, but the biological relevance of how improved these trees are is perhaps best shown by ancestral sequence reconstruction. Groussin et al. (submitted) reconstructed sequences based on trees inferred through the Szöll˝osi et al. (2013a) approach, which uses the species tree and a distribution of gene trees, or through PhyML (Guindon et al. 2010), an accurate method that does not take the species tree into account. On simulations, this comparison showed that the ancestral sequences were much more accurate when based on the trees obtained with the help of the species tree. More strikingly, the in vitro resurrection of a protein belonging to the ancestor of Firmicutes, an ancient group of Bacteria, showed that the protein reconstructed based on the method using the species tree was thermodynamically more stable than the protein reconstructed from the alignmentonly tree, and exhibited better enzymatic capabilities. As ancestral sequence resurrection is a popular and powerful approach (Gaucher et al. 2003; Thomson et al. 2005; Gaucher et al. 2008; Bridgham et al. 2009; PerezJimenez et al. 2011; Finnigan et al. 2012; Harms and Thornton 2013), methods using a model of gene family evolution could make an important contribution toward a better understanding of molecular evolution.
FIGURE 7. Left: species tree inferred by PHYLDOG, with ancestral genome contents reconstructed by different methods on selected nodes. Ancestral genomes reconstructed by PHYLDOG, in blue, have a size similar to that of extant genomes. Right: reconstruction of ancestral gene neighborhoods. Two genes are considered neighbors if there is no other gene between them in the dataset, so in a linear chromosome every gene (except two) should have two neighboring genes. So we expect from a method to recover exactly two neighbors for most ancestral genes. PHYLDOG is in blue. Figure reprinted with permission from Boussau et al. (2013).
coalescent gene tree-species tree models is still an open question.
More Integrative Models The integrative program of Goodman et al. (1979) is being progressively implemented. The probabilistic framework makes it possible to integrate sequence mutations with gene duplications and losses through the coalescent (Rasmussen and Kellis 2012), or to integrate duplications, losses, and transfers with substitutions (Szöll˝osi et al. 2012; Boussau et al. 2013; Szöll˝osi et al. 2013a,b). Rearrangements can be handled using parsimony if ILS is ignored (Bérard et al. 2012; Patterson et al. 2013). A model and method to handle a union of all of these processes is currently missing. However, there are very good reasons for the integration of different levels of data analysis to continue. For instance, below the gene tree / species tree problem, is the inference of gene alignments. Only recently has the problem of joint inference of alignments and gene trees been considered seriously, with attempts to model the process of insertion/deletion in the evolution of sequences. Such approaches show dramatic improvements over phylogenetically unaware alignment methods (Redelings and Suchard 2005; Satija et al. 2009; Warnow 2013). However, they obviously need all the information necessary to have the best possible gene tree, for example a link to the species tree. Hence, it is probable that the integration of gene tree–species tree models and alignment methods should beneﬁt the inference of alignments, gene trees and perhaps species trees. Although a global model seems difﬁcult to imagine presently, the entire pipeline of sequence data analysis, from sequencing error corrections to gene annotation and genome assembly is likely to beneﬁt from probabilistic evolutionary models. The recognition of homologous sequences, the prediction of gene functions based on information from other organisms, and the proximity of genes on chromosomes all depend ultimately on the structure of the species tree and the possible events of substitution, duplication, loss, and lateral transfer that may have occurred in the history of genomes. There is currently no proposition of an integration of these processes on all levels of the pipeline described in Figure 5, but phylogenetically aware methods have proved very promising at many different steps of the process (Boussau and Daubin 2010) including on genome assembly (Husemann and Stoye 2010; Rajaraman et al. 2013).
potential of already available methods can be exploited on an increasingly large scale.
estimation of parameters, and exploration of dated or ordered species trees combine intractable problems. In practice, optimizing a gene tree can necessitate up to a few hours for very large families. As there can be thousands of gene families in a typical dataset, the computations even for a ﬁxed species tree can take a long time. However, models of gene family evolution as well as sequence-based models all make the assumption that genes evolve independently from each other. This assumption can be questioned (see below) and is also broken by evolutionary parameters shared among gene families. But it allows a trivial parallelization by the data. All genes trees can be computed independently, given a common species tree. Hence, a species tree exploration is mainly constrained by the largest multigene families. A simple way to increase computational efﬁciency is to ignore these large families in a ﬁrst step of species tree exploration. Large multigene families can be considered later, when a good species tree is found based on smaller gene families, or, in a sampling context, using importance sampling. However, such tricks can only help as long as the number of genomes under study is relatively small. For studying larger datasets, we will need to devise more efﬁcient algorithms.
wrong when he evoked the image of a tree of life, because he failed to foresee the role of lateral gene transfer in microbial evolution (Doolittle 1999). The models and methods described above actually show that the plurality of gene histories can not only be overcome but more importantly provides additional information on the processes and patterns of species evolution. The phylogenies for a diversity of clades have been reconstructed with coalescent, DL or DTL models. In each case, the degree of conﬂict among gene trees can be interpreted in biological terms, such as divergence time and ancestral population size with the coalescent, or relative timing of speciation with LGT. There is a great hope that the development and use of these models will help resolve many issues that were left pending by traditional methods.
FIGURE 8. Evolutionary units below or above genes. Individual units (red and blue online) can be inside genes or genes that are neighbors along a chromosome or genes involved in a protein complex. Adjacencies are binary relations between genes, and evolve along a species phylogeny. Adjacencies can be gained or lost regardless of the birth and death of the units. When two units together undergo speciation, duplication, or transfer, adjacencies undergo the same events.
Keeping Up with the Pace of Data Acquisition Currently, genome sequencing is no longer a limiting step for comparative genomics. Instead, assembling gene families, gene alignments, gene trees, and a species tree are becoming increasingly problematic. In this context, methods using models of gene family evolution may offer an advantage because they effectively reduce the space of possible solutions to explore: given a species tree, the space of possible gene trees is limited compared with species tree unaware methods, and consequently, so is the space of possible alignments.
together (Bansal et al. 2013; Patterson et al. 2013). Hence, the deﬁnition of evolutionary units is difﬁcult, and ﬂuctuates in time (Fig. 8). As we have shown, almost all existing models describe the reconciliation of one gene tree with one species tree, supposing its evolution is coherent and independent from other genes. Some genomic studies, however, allow genome-wide parameters like the rates of duplications and losses to vary across branches of the species tree (Boussau et al. 2013). This can be seen as a trick to model large-scale events like genome duplications without doing away with the independence of genes, which is computationally advantageous. But it fails to model more local rearrangements such as duplications of parts of a chromosome. These events could be informative for phylogeny, but models of genome rearrangements are often combinatorially so complex (Fertin et al. 2009) that they do not scale up well with the size and number of genomes (York et al. 2002; Darling et al. 2008; Miklós and Tannier 2010). Until now, their complexity has precluded a coupling with other models such as gene tree–species tree reconciliation. However, assuming neighborhoods between genes are independent, meaning that for any 3 genes A, B, C the neighborhood between genes A and B is independent of whether genes A and C are neighbors or not, it is possible to integrate rearrangements into DL (Bérard et al. 2012) or DTL (Patterson et al. 2013) models. Such approaches describe the evolution of neighborhoods (or any other relationship between genes, including functional ones) along pairs of reconciled gene trees, allowing one to reconstruct adjacencies in ancestral genomes and evolutionary events of duplication, loss, and transfer that have affected genomic fragments comprising several genes. Because such multiple events are frequent, it is likely that the parameters of duplication, transfer, and loss that are estimated in DL and DTL models are biased and it seems necessary to integrate models of neighborhood evolution with phylogenetic reconstruction into the reconstruction of genome histories. There are also models for detecting breakpoints inside gene sequences using HMMs for instance (McGuire et al. 2000; Suchard et al. 2002; Martins et al. 2008; Boussau et al. 2009), or detecting breakpoints of phylogenetic discordance at a whole genome scale (Ané 2011), but so far these models have not been included in models of gene family evolution.
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