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TRAILS: Tree reconstruction of ancestry using incomplete lineage sorting [1]

['Iker Rivas-González', 'Bioinformatics Research Center', 'Birc', 'Aarhus University', 'Aarhus', 'Mikkel H. Schierup', 'John Wakeley', 'Department Of Organismic', 'Evolutionary Biology', 'Harvard University']

Date: 2024-03

Genome-wide genealogies of multiple species carry detailed information about demographic and selection processes on individual branches of the phylogeny. Here, we introduce TRAILS, a hidden Markov model that accurately infers time-resolved population genetics parameters, such as ancestral effective population sizes and speciation times, for ancestral branches using a multi-species alignment of three species and an outgroup. TRAILS leverages the information contained in incomplete lineage sorting fragments by modelling genealogies along the genome as rooted three-leaved trees, each with a topology and two coalescent events happening in discretized time intervals within the phylogeny. Posterior decoding of the hidden Markov model can be used to infer the ancestral recombination graph for the alignment and details on demographic changes within a branch. Since TRAILS performs posterior decoding at the base-pair level, genome-wide scans based on the posterior probabilities can be devised to detect deviations from neutrality. Using TRAILS on a human-chimp-gorilla-orangutan alignment, we recover speciation parameters and extract information about the topology and coalescent times at high resolution.

DNA sequences can be compared to reconstruct the evolutionary history of different species. While the ancestral history is usually represented by a single phylogenetic tree, speciation is a more complex process, and, due to the effect of recombination, different parts of the genome might follow different genealogies. For example, even though humans are more closely related to chimps than to gorillas, around 15% of our genome is more similar to the gorilla genome than to the chimp one. Even for those parts of the genome that do follow the same human-chimp topology, we might encounter a last common ancestor at different time points in the past for different genomic fragments. Here, we present TRAILS, a new framework that utilizes the information contained in all these genealogies to reconstruct the speciation process. TRAILS infers unbiased estimates of the speciation times and the ancestral effective population sizes, improving the accuracy when compared to previous methods. TRAILS also reconstructs the genealogy at the highest resolution, inferring, for example, when common ancestry was found for different parts of the genome. This information can also be used to detect deviations from neutrality, effectively inferring natural selection that happened millions of years ago. We validate the method using extensive simulations, and we apply TRAILS to a human-chimp-gorilla multiple genome alignment, from where we recover speciation parameters that are in good agreement with previous estimates.

Introduction

Orthologous sites in two or more sequences share a unique genealogical history, with coalescent events happening at certain time points in the past. In the absence of recombination, all sites along the sequences follow the same genealogy. In reality, however, ancestral recombination events might have decoupled consecutive sites, generating an array of segments with different yet correlated genealogies, collectively known as the ancestral recombination graph (ARG) [1, 2]. In principle, if inferred accurately, the ARG contains all available information about the demography of the samples, and it can be used to estimate population parameters (such as the recombination rate and the ancestral effective population sizes), historical events (such as introgression and hybridization), and selective processes [3]. The ARG, however, is challenging to infer because the underlying genealogies along the genome alignment cannot be directly observed. Instead, inference of the genealogy along the genome relies on the site patterns of the accumulated mutations.

The ARG can also be formulated as a spatial process along the genomic alignment [4]. This process, however, contains a long-range correlation structure because if two recombination events happen flanking a genomic fragment, the fragment might be surrounded by the exact same genealogy. However, disregarding the fact that the process is non-Markovian in nature, the ARG can be approximated by a hidden Markov model (HMM), where the genealogy of a certain genomic position only depends on the genealogy of the previous position [5, 6]. It has been shown that this approach, commonly referred to as sequentially Markovian coalescent or SMC, is a good approximation of the true coalescent-with-recombination process [7]. Perhaps the simplest of such models is the pairwise sequentially Markovian coalescent (PSMC) [8], in which the ARG between two sequences (typically, the two copies of a diploid individual) is modelled. Here, the hidden states are coalescent events that happen in discretized time intervals, which correspond to two-leafed gene trees (Fig 1A). The transition probabilities between pairs of hidden states can be calculated using standard coalescent theory, parameterized by the recombination rate and the ancestral effective population sizes (N e ) in each time interval [8]. PSMC, and other SMCs, such as MSMC [9], MSMC2 [10], ASMC [11], and SMC++ [12], allow the use of standard HMM machinery to infer population parameters, and are thus also useful for inferring the most plausible coalescent times from the posterior decoding. However, SMC models are generally restricted to a single coalescent event between a pair of samples, which limits their usefulness. More recently, there have been new developments to model multiple samples explicitly. For example, ARGweaver [13], Relate [14], tsinfer+tsdate [15, 16] or ARG-Needle [17] use techniques such as resampling, threading and mathematical approximations to sequentially build the ARG [18].

These models are typically used to analyze samples from the same species to get within-species information about the ancestral process. Analyzing inter-species coalescent events adds another layer of complexity, since the coalescent events need to be contained within the underlying phylogeny or speciation tree [22–24]. Moreover, the models described above typically use the presence or absence of a certain mutation to construct haplotypes, but ignore or filter out instances where more than two alleles are observed. This infinite sites model poses a problem for inter-species analysis, because recurrent mutation is more likely to happen, generating instances of sites that have experienced more than a single mutation [25, 26].

Some other models have tried to extend these concepts for the analyses of multiple species. For example, the coalescent-with-isolation model [19] is conceptually similar to PSMC, but, backwards in time, the two analyzed samples are kept isolated until the speciation event, after which they can coalesce (Fig 1B). This model can be used to estimate the speciation time between the two samples and the N e of the ancestral species, and an extension of it can be used to model isolation-with-migration [27]. These models, similar to SMCs, can output a posterior decoding of the coalescent times.

Beyond two samples, CoalHMM models the coalescent with recombination of three species [20, 21], where the hidden states are the four possible genealogies that might arise within the underlying species tree (Fig 1C). Two of the four genealogies differ from the species tree, which generate incongruencies that might pose a problem for standard phylogenetic reconstruction. Nevertheless, this phenomenon, commonly referred to as incomplete lineage sorting or ILS, is very informative about the demographic parameters of the underlying species tree, and CoalHMM can thus be used to estimate ancestral N e and two speciation times. Moreover, CoalHMM uses a substitution model for mutations, so recurrent mutations are allowed. However, unlike SMCs, CoalHMM does not model coalescent events at discretized time intervals and, instead, coalescent times are modelled as single time points within an individual branch. Because of this, some of the parameter estimates of CoalHMM are biased [21], and, although obtaining accurate estimates is still possible [28], the debiasing procedure involves costly coalescent simulations. Moreover, posterior decoding can only be performed on the topology of the gene trees, and not on the coalescent times.

Here we present TRAILS, an HMM that combines modelling the information-rich ILS signal in the style of CoalHMM and the time discretization of SMC-like models to infer unbiased estimates of the demographic parameters (ancestral N e and speciation times), and to enable the posterior decoding of both topology and coalescent times. In TRAILS, the hidden states are three-leaved gene trees, each with a specified topology and two coalescent events that happen at discretized time intervals on an underlying speciation tree (Fig 1D and Fig K in S1 Text). The genealogies are rooted by a fourth sample from an outgroup species. The transition probabilities between the hidden states of TRAILS are calculated using coalescent-with-recombination theory for one, two and three lineages that segregate within the branches of the phylogeny. We provide formulas in matrix notation to calculate these transition probabilities for a varying number of discretized time intervals (see Methods for a short explanation, and S1 Text for an in-depth description of the theory). The emitted states are sites in a four-way multiple genome alignment, containing the sequences of the three species and the outgroup. The transition and emission probabilities are parameterized by two ancestral N e , speciation times, and the recombination rate. Keeping the mutation rate at a fixed value, TRAILS allows for the estimation of the other parameters by optimizing the HMM likelihood given the alignment. After fitting the HMM, TRAILS can perform posterior decoding of the hidden states, inferring a posterior probability of coalescent events through time within the speciation tree.

Here we derive the transition and emission probabilities, implement the model and demonstrate its use on simulated and real data. After optimizing the population parameters using TRAILS on a simulated dataset, we show that increasing the number of discrete coalescence intervals reduces the bias in the parameter estimation. We also show how the posterior decoding can accurately reconstruct the true ARG, by inferring the topology of gene trees and the time in which coalescent events occurred. We perform additional simulations to show that the posterior decoding of TRAILS can be used to detect selective sweeps that happened on ancestral branches of the phylogeny. Finally, we analyze a human-chimp-gorilla-orangutan alignment, inferring the demographic parameters of the underlying species tree and performing genome-wide posterior decoding at the base-pair level.

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[1] Url: https://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1010836

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