Coalescent Hidden Markov Model Research Articles

Robust inference of population size histories from genomic sequencing data.

Unraveling the complex demographic histories of natural populations is a central problem in population genetics. Understanding past demographic events is of general anthropological interest, but is also an important step in establishing accurate null models when identifying adaptive or disease-associated genetic variation. An important class of tools for inferring past population size changes from genomic sequence data are Coalescent Hidden Markov Models (CHMMs). These models make efficient use of the linkage information in population genomic datasets by using the local genealogies relating sampled individuals as latent states that evolve along the chromosome in an HMM framework. Extending these models to large sample sizes is challenging, since the number of possible latent states increases rapidly.Here, we present our method CHIMP (CHMM History-Inference Maximum-Likelihood Procedure), a novel CHMM method for inferring the size history of a population. It can be applied to large samples (hundreds of haplotypes) and only requires unphased genomes as input. The two implementations of CHIMP that we present here use either the height of the genealogical tree (TMRCA) or the total branch length, respectively, as the latent variable at each position in the genome. The requisite transition and emission probabilities are obtained by numerically solving certain systems of differential equations derived from the ancestral process with recombination. The parameters of the population size history are subsequently inferred using an Expectation-Maximization algorithm. In addition, we implement a composite likelihood scheme to allow the method to scale to large sample sizes.We demonstrate the efficiency and accuracy of our method in a variety of benchmark tests using simulated data and present comparisons to other state-of-the-art methods. Specifically, our implementation using TMRCA as the latent variable shows comparable performance and provides accurate estimates of effective population sizes in intermediate and ancient times. Our method is agnostic to the phasing of the data, which makes it a promising alternative in scenarios where high quality data is not available, and has potential applications for pseudo-haploid data.

Variational inference using approximate likelihood under the coalescent with recombination.

Coalescent methods are proven and powerful tools for population genetics, phylogenetics, epidemiology, and other fields. A promising avenue for the analysis of large genomic alignments, which are increasingly common, is coalescent hidden Markov model (coalHMM) methods, but these methods have lacked general usability and flexibility. We introduce a novel method for automatically learning a coalHMM and inferring the posterior distributions of evolutionary parameters using black-box variational inference, with the transition rates between local genealogies derived empirically by simulation. This derivation enables our method to work directly with three or four taxa and through a divide-and-conquer approach with more taxa. Using a simulated data set resembling a human–chimp–gorilla scenario, we show that our method has comparable or better accuracy to previous coalHMM methods. Both species divergence times and population sizes were accurately inferred. The method also infers local genealogies, and we report on their accuracy. Furthermore, we discuss a potential direction for scaling the method to larger data sets through a divide-and-conquer approach. This accuracy means our method is useful now, and by deriving transition rates by simulation, it is flexible enough to enable future implementations of various population models.

Ancestral Population Genomics with Jocx, a Coalescent Hidden Markov Model.

Coalescence theory lets us probe the past demographics of present-day genetic samples and much information about the past can be gleaned from variation in rates of coalescence event as we trace genetic lineages back in time. Fewer and fewer lineages will remain, however, so there is a limit to how far back we can explore. Without recombination, we would not be able to explore ancient speciation events because of this-any meaningful species concept would require that individuals of one species are closer related than they are to individuals of another species, once speciation is complete. Recombination, however, opens a window to the deeper past. By scanning along a genomic alignment, we get a sequential variant of the coalescence process as it looked at the time of the speciation. This pattern of coalescence times is fixed at speciation time and does not erode with time; although accumulated mutations and genomic rearrangements will eventually hide the signal, it enables us to glance at events in the past that would not be observable without recombination. So-called coalescence hidden Markov models allow us to exploit this, and in this chapter, we present the tool Jocx that uses a framework of these models to infer demographic parameters in ancient speciation events.

Computing the joint distribution of the total tree length across loci in populations with variable size

In recent years, a number of methods have been developed to infer complex demographic histories, especially historical population size changes, from genomic sequence data. Coalescent Hidden Markov Models have proven to be particularly useful for this type of inference. Due to the Markovian structure of these models, an essential building block is the joint distribution of local genealogical trees, or statistics of these genealogies, at two neighboring loci in populations of variable size. Here, we present a novel method to compute the marginal and the joint distribution of the total length of the genealogical trees at two loci separated by at most one recombination event for samples of arbitrary size. To our knowledge, no method to compute these distributions has been presented in the literature to date. We show that they can be obtained from the solution of certain hyperbolic systems of partial differential equations. We present a numerical algorithm, based on the method of characteristics, that can be used to efficiently and accurately solve these systems and compute the marginal and the joint distributions. We demonstrate its utility to study the properties of the joint distribution. Our flexible method can be straightforwardly extended to handle an arbitrary fixed number of recombination events, to include the distributions of other statistics of the genealogies as well, and can also be applied in structured populations.

Inferring Local Genealogies on Closely Related Genomes.

The relationship between the evolution of a set of genomes and of individual loci therein could be very complex. For example, in eukaryotic species, meiotic recombination combined with effects of random genetic drift result in loci whose genealogies differ from each other as well as from the phylogeny of the species or populations-a phenomenon known as incomplete lineage sorting, or ILS. The most common practice for inferring local genealogies of individual loci is to slide a fixed-width window across an alignment of the genomes, and infer a phylogenetic tree from the sequence alignment of each window. However, at the evolutionary scale where ILS is extensive, it is often the case that the phylogenetic signal within each window is too low to infer an accurate local genealogy. In this paper, we propose a hidden Markov model (HMM) based method for inferring local genealogies conditional on a known species tree. The method borrows ideas from the work on coalescent HMMs, yet approximates the model parameterization to focus on computationally efficient inference of local genealogies, rather than on obtaining detailed model parameters. We also show how the method is extended to cases that involve hybridization in addition to recombination and ILS. We demonstrate the performance of our method on synthetic data and one empirical data set, and compare it to the sliding-window approach that is, arguably, the most commonly used technique for inferring local genealogies.

Unraveling recombination rate evolution using ancestral recombination maps.

Recombination maps of ancestral species can be constructed from comparative analyses of genomes from closely related species, exemplified by a recently published map of the human-chimpanzee ancestor. Such maps resolve differences in recombination rate between species into changes along individual branches in the speciation tree, and allow identification of associated changes in the genomic sequences. We describe how coalescent hidden Markov models are able to call individual recombination events in ancestral species through inference of incomplete lineage sorting along a genomic alignment. In the great apes, speciation events are sufficiently close in time that a map can be inferred for the ancestral species at each internal branch - allowing evolution of recombination rate to be tracked over evolutionary time scales from speciation event to speciation event. We see this approach as a way of characterizing the evolution of recombination rate and the genomic properties that influence it.

Genomic Relationships and Speciation Times of Human, Chimpanzee, and Gorilla Inferred from a Coalescent Hidden Markov Model

The genealogical relationship of human, chimpanzee, and gorilla varies along the genome. We develop a hidden Markov model (HMM) that incorporates this variation and relate the model parameters to population genetics quantities such as speciation times and ancestral population sizes. Our HMM is an analytically tractable approximation to the coalescent process with recombination, and in simulations we see no apparent bias in the HMM estimates. We apply the HMM to four autosomal contiguous human–chimp–gorilla–orangutan alignments comprising a total of 1.9 million base pairs. We find a very recent speciation time of human–chimp (4.1 ± 0.4 million years), and fairly large ancestral effective population sizes (65,000 ± 30,000 for the human–chimp ancestor and 45,000 ± 10,000 for the human–chimp–gorilla ancestor). Furthermore, around 50% of the human genome coalesces with chimpanzee after speciation with gorilla. We also consider 250,000 base pairs of X-chromosome alignments and find an effective population size much smaller than 75% of the autosomal effective population sizes. Finally, we find that the rate of transitions between different genealogies correlates well with the region-wide present-day human recombination rate, but does not correlate with the fine-scale recombination rates and recombination hot spots, suggesting that the latter are evolutionarily transient.

Genomic relationships and speciation times of human, chimpanzee and gorilla inferred from a coalescent Hidden Markov Model

Genomic relationships and speciation times of human, chimpanzee and gorilla inferred from a coalescent Hidden Markov Model