Biobank-scale inference of ancestral recombination graphs enables genealogical analysis of complex traits

Urofacial (Ochoa) syndrome with a founder pathogenic variant in the HPSE2 gene: a case report and mutation origin

Urofacial syndrome or Ochoa syndrome (UFS or UFOS) is a rare disease characterized by inverted facial expression and bladder dysfunction that was described for the first time in Colombia. It is an autosomal recessive pathology with mutations in the HPSE2 and LRIG2 genes. However, 16% of patients do not have any mutations associated with the syndrome. Despite the importance of neurobiology in its pathophysiology, there are no neurological, neuropsychological, or psychological studies in these patients. A 30-year-old male from Medellín, Colombia, with a significant perinatal history, was diagnosed with grade 4 hydronephrosis on his first ultrasound test. At 4 months of age, symptoms such as hypomimia, lagophthalmos, and recurrent urinary tract infections started to manifest. Imaging studies revealed urinary tract dilatation, vesicoureteral reflux, and a double collector system on his left side, which led to the diagnosis of UFS. Multiple procedures, including vesicostomy, ureterostomy, and enterocystoplasty, were performed. At 20 years of age, he achieved urinary sphincter control. Genetic analysis revealed a founder pathogenic variant, c.1516C > T (p.Arg506Ter), in the HPSE2 gene, which produces a truncated protein that lacks 86 amino acids. This variant is classified as pathogenic according to the ClinVar database for UFS. The mutation age is approximately 260-360 years, and the two alleles share a 7.2-7.4 Mb IBD segment. Moreover, we detected European local ancestry in the IBD segment, which is consistent with a Spanish introduction. Neurological examination, neuropsychological assessment, and psychological testing revealed no abnormalities, except for high stress levels. Clinical analysis of this patient revealed distorted facial expression and detrusor-sphincter dyssynergia, which are typical of patients with UFS. Genetic analysis revealed a pathogenic variant in the HPSE2 gene of European origin and a mutation age of 260-360 years. From a neurological, neuropsychological, and psychological (emotional and personality) perspective, the patient showed no signs or symptoms of clinical interest.

Promoting equity in polygenic risk assessment through global collaboration

The long delay before genomic technologies become available in low- and middle-income countries is a concern from both scientific and ethical standpoints. Polygenic risk scores (PRSs), a relatively recent advance in genomics, could have a substantial impact on promoting health by improving disease risk prediction and guiding preventive strategies. However, clinical use of PRSs in their current forms might widen global health disparities, as their portability to diverse groups is limited. This Perspective highlights the need for global collaboration to develop and implement PRSs that perform equitably across the world. Such collaboration requires capacity building and the generation of new data in low-resource settings, the sharing of harmonized genotype and phenotype data securely across borders, novel population genetics and statistical methods to improve PRS performance, and thoughtful clinical implementation in diverse settings. All this needs to occur while considering the ethical, legal and social implications, with support from regulatory and funding agencies and policymakers.

Fast and Accurate Estimation of Selection Coefficients and Allele Histories from Ancient and Modern DNA

We here present CLUES2, a full-likelihood method to infer natural selection from sequence data that is an extension of the method CLUES. We make several substantial improvements to the CLUES method that greatly increases both its applicability and its speed. We add the ability to use ancestral recombination graphs on ancient data as emissions to the underlying hidden Markov model, which enables CLUES2 to use both temporal and linkage information to make estimates of selection coefficients. We also fully implement the ability to estimate distinct selection coefficients in different epochs, which allows for the analysis of changes in selective pressures through time, as well as selection with dominance. In addition, we greatly increase the computational efficiency of CLUES2 over CLUES using several approximations to the forward-backward algorithms and develop a new way to reconstruct historic allele frequencies by integrating over the uncertainty in the estimation of the selection coefficients. We illustrate the accuracy of CLUES2 through extensive simulations and validate the importance sampling framework for integrating over the uncertainty in the inference of gene trees. We also show that CLUES2 is well-calibrated by showing that under the null hypothesis, the distribution of log-likelihood ratios follows a χ2 distribution with the appropriate degrees of freedom. We run CLUES2 on a set of recently published ancient human data from Western Eurasia and test for evidence of changing selection coefficients through time. We find significant evidence of changing selective pressures in several genes correlated with the introduction of agriculture to Europe and the ensuing dietary and demographic shifts of that time. In particular, our analysis supports previous hypotheses of strong selection on lactase persistence during periods of ancient famines and attenuated selection in more modern periods.

A general and efficient representation of ancestral recombination graphs

As a result of recombination, adjacent nucleotides can have different paths of genetic inheritance and therefore the genealogical trees for a sample of DNA sequences vary along the genome. The structure capturing the details of these intricately interwoven paths of inheritance is referred to as an ancestral recombination graph (ARG). Classical formalisms have focused on mapping coalescence and recombination events to the nodes in an ARG. However, this approach is out of step with some modern developments, which do not represent genetic inheritance in terms of these events or explicitly infer them. We present a simple formalism that defines an ARG in terms of specific genomes and their intervals of genetic inheritance, and show how it generalizes these classical treatments and encompasses the outputs of recent methods. We discuss nuances arising from this more general structure, and argue that it forms an appropriate basis for a software standard in this rapidly growing field.

Biases in ARG-Based Inference of Historical Population Size in Populations Experiencing Selection

Inferring the demographic history of populations provides fundamental insights into species dynamics and is essential for developing a null model to accurately study selective processes. However, background selection and selective sweeps can produce genomic signatures at linked sites that mimic or mask signals associated with historical population size change. While the theoretical biases introduced by the linked effects of selection have been well established, it is unclear whether ancestral recombination graph (ARG)-based approaches to demographic inference in typical empirical analyses are susceptible to misinference due to these effects. To address this, we developed highly realistic forward simulations of human and Drosophila melanogaster populations, including empirically estimated variability of gene density, mutation rates, recombination rates, purifying, and positive selection, across different historical demographic scenarios, to broadly assess the impact of selection on demographic inference using a genealogy-based approach. Our results indicate that the linked effects of selection minimally impact demographic inference for human populations, although it could cause misinference in populations with similar genome architecture and population parameters experiencing more frequent recurrent sweeps. We found that accurate demographic inference of D. melanogaster populations by ARG-based methods is compromised by the presence of pervasive background selection alone, leading to spurious inferences of recent population expansion, which may be further worsened by recurrent sweeps, depending on the proportion and strength of beneficial mutations. Caution and additional testing with species-specific simulations are needed when inferring population history with non-human populations using ARG-based approaches to avoid misinference due to the linked effects of selection.

tstrait: a quantitative trait simulator for ancestral recombination graphs

SUMMARY

Ancestral recombination graphs (ARGs) encode the ensemble of correlated genealogical trees arising from recombination in a compact and efficient structure and are of fundamental importance in population and statistical genetics. Recent breakthroughs have made it possible to simulate and infer ARGs at biobank scale, and there is now intense interest in using ARG-based methods across a broad range of applications, particularly in genome-wide association studies (GWAS). Sophisticated methods exist to simulate ARGs using population genetics models, but there is currently no software to simulate quantitative traits directly from these ARGs. To apply existing quantitative trait simulators users must export genotype data, losing important information about ancestral processes and producing prohibitively large files when applied to the biobank-scale datasets currently of interest in GWAS. We present tstrait, an open-source Python library to simulate quantitative traits on ARGs, and show how this user-friendly software can quickly simulate phenotypes for biobank-scale datasets on a laptop computer.

AVAILABILITY AND IMPLEMENTATION

tstrait is available for download on the Python Package Index. Full documentation with examples and workflow templates is available on https://tskit.dev/tstrait/docs/, and the development version is maintained on GitHub (https://github.com/tskit-dev/tstrait).

Evaluating ARG-estimation methods in the context of estimating population-mean polygenic score histories

Scalable methods for estimating marginal coalescent trees across the genome present new opportunities for studying evolution and have generated considerable excitement, with new methods extending scalability to thousands of samples. Benchmarking of the available methods has revealed general tradeoffs between accuracy and scalability, but performance in downstream applications has not always been easily predictable from general performance measures, suggesting that specific features of the ARG may be important for specific downstream applications of estimated ARGs. To exemplify this point, we benchmark ARG estimation methods with respect to a specific set of methods for estimating the historical time course of a population-mean polygenic score (PGS) using the marginal coalescent trees encoded by the ancestral recombination graph (ARG). Here we examine the performance in simulation of six ARG estimation methods: ARGweaver, RENT+, Relate, tsinfer+tsdate, ARG-Needle/ASMC-clust , and SINGER , using their estimated coalescent trees and examining bias, mean squared error (MSE), confidence interval coverage, and Type I and II error rates of the downstream methods. Although it does not scale to the sample sizes attainable by other new methods, SINGER produced the most accurate estimated PGS histories in many instances, even when Relate, tsinfer+tsdate , and ARG-Needle/ASMC-clust used samples ten times as large as those used by SINGER. In general, the best choice of method depends on the number of samples available and the historical time period of interest. In particular, the unprecedented sample sizes allowed by Relate, tsinfer+tsdate , and ARG-Needle/ASMC-clust are of greatest importance when the recent past is of interest-further back in time, most of the tree has coalesced, and differences in contemporary sample size are less salient.

Bursts of coalescence within population pedigrees whenever big families occur

We consider a simple diploid population-genetic model with potentially high variability of offspring numbers among individuals. Specifically, against a backdrop of Wright-Fisher reproduction and no selection, there is an additional probability that a big family occurs, meaning that a pair of individuals has a number of offspring on the order of the population size. We study how the pedigree of the population generated under this model affects the ancestral genetic process of a sample of size two at a single autosomal locus without recombination. Our population model is of the type for which multiple-merger coalescent processes have been described. We prove that the conditional distribution of the pairwise coalescence time given the random pedigree converges to a limit law as the population size tends to infinity. This limit law may or may not be the usual exponential distribution of the Kingman coalescent, depending on the frequency of big families. But because it includes the number and times of big families, it differs from the usual multiple-merger coalescent models. The usual multiple-merger coalescent models are seen as describing the ancestral process marginal to, or averaging over, the pedigree. In the limiting ancestral process conditional on the pedigree, the intervals between big families can be modeled using the Kingman coalescent but each big family causes a discrete jump in the probability of coalescence. Analogous results should hold for larger samples and other population models. We illustrate these results with simulations and additional analysis, highlighting their implications for inference and understanding of multilocus data.

Genotype Representation Graphs: Enabling Efficient Analysis of Biobank-Scale Data

Computational analysis of a large number of genomes requires a data structure that can represent the dataset compactly while also enabling efficient operations on variants and samples. Current practice is to store large-scale genetic polymorphism data using tabular data structures and file formats, where rows and columns represent samples and genetic variants. However, encoding genetic data in such formats has become unsustainable. For example, the UK Biobank polymorphism data of 200,000 phased whole genomes has exceeded 350 terabytes (TB) in Variant Call Format (VCF), too large to fit into hard drives in uncompressed form. To mitigate the computational burden, we introduce the Genotype Representation Graph (GRG), an extremely compact data structure to losslessly present phased whole-genome polymorphisms. A GRG is a fully connected hierarchical graph that exploits variant-sharing across samples, leveraging on ideas inspired by Ancestral Recombination Graphs. Capturing variant-sharing in a graph format compresses biobank-scale data to the point where it can fit in a typical server's RAM (5-26GB per chromosome), and enables graph-traversal algorithms to trivially reuse computed values, both of which can significantly reduce computation time. We have developed a command-line tool and a library usable via both C++ and Python for constructing and processing GRG files which scales to a million whole genomes. It takes 160GB disk space to encode the information in 200,000 UK Biobank phased whole genomes as a GRG, more than 2000 times smaller than the size of VCF. Moreover, the size of GRG increases sublinearly with the number of samples stored, making it a sustainable solution to the increasing number of samples in large datasets. We show that summaries of genetic variants can be computed on GRG via graph traversal that runs 230 times faster than on VCF. We anticipate that GRG-based algorithms will improve the scalability of various types of computation and generally lower the cost of analyzing large genomic datasets.

A general and efficient representation of ancestral recombination graphs

As a result of recombination, adjacent nucleotides can have different paths of genetic inheritance and therefore the genealogical trees for a sample of DNA sequences vary along the genome. The structure capturing the details of these intricately interwoven paths of inheritance is referred to as an ancestral recombination graph (ARG). Classical formalisms have focused on mapping coalescence and recombination events to the nodes in an ARG. This approach is out of step with modern developments, which do not represent genetic inheritance in terms of these events or explicitly infer them. We present a simple formalism that defines an ARG in terms of specific genomes and their intervals of genetic inheritance, and show how it generalises these classical treatments and encompasses the outputs of recent methods. We discuss nuances arising from this more general structure, and argue that it forms an appropriate basis for a software standard in this rapidly growing field.

tstrait: a quantitative trait simulator for ancestral recombination graphs

Summary

Ancestral recombination graphs (ARGs) encode the ensemble of correlated genealogical trees arising from recombination in a compact and efficient structure, and are of fundamental importance in population and statistical genetics. Recent breakthroughs have made it possible to simulate and infer ARGs at biobank scale, and there is now intense interest in using ARG-based methods across a broad range of applications, particularly in genome-wide association studies (GWAS). Sophisticated methods exist to simulate ARGs using population genetics models, but there is currently no software to simulate quantitative traits directly from these ARGs. To apply existing quantitative trait simulators users must export genotype data, losing important information about ancestral processes and producing prohibitively large files when applied to the biobank-scale datasets currently of interest in GWAS. We present tstrait, an open-source Python library to simulate quantitative traits on ARGs, and show how this user-friendly software can quickly simulate phenotypes for biobank-scale datasets on a laptop computer.

Availability and Implementation

tstrait is available for download on the Python Package Index. Full documentation with examples and workflow templates is available on https://tskit.dev/tstrait/docs/, and the development version is maintained on GitHub (https://github.com/tskit-dev/tstrait).

Contact

daiki.tagami@hertford.ox.ac.uk.

Estimating evolutionary and demographic parameters via ARG-derived IBD

Inference of demographic and evolutionary parameters from a sample of genome sequences often proceeds by first inferring identical-by-descent (IBD) genome segments. By exploiting efficient data encoding based on the ancestral recombination graph (ARG), we obtain three major advantages over current approaches: (i) no need to impose a length threshold on IBD segments, (ii) IBD can be defined without the hard-to-verify requirement of no recombination, and (iii) computation time can be reduced with little loss of statistical efficiency using only the IBD segments from a set of sequence pairs that scales linearly with sample size. We first demonstrate powerful inferences when true IBD information is available from simulated data. For IBD inferred from real data, we propose an approximate Bayesian computation inference algorithm and use it to show that poorly-inferred short IBD segments can improve estimation precision. We show estimation precision similar to a previously-published estimator despite a 4 000-fold reduction in data used for inference. Computational cost limits model complexity in our approach, but we are able to incorporate unknown nuisance parameters and model misspecification, still finding improved parameter inference.

Unifying approaches from statistical genetics and phylogenetics for mapping phenotypes in structured populations

In both statistical genetics and phylogenetics, a major goal is to identify correlations between genetic loci or other aspects of the phenotype or environment and a focal trait. In these two fields, there are sophisticated but disparate statistical traditions aimed at these tasks. The disconnect between their respective approaches is becoming untenable as questions in medicine, conservation biology, and evolutionary biology increasingly rely on integrating data from within and among species, and once-clear conceptual divisions are becoming increasingly blurred. To help bridge this divide, we derive a general model describing the covariance between the genetic contributions to the quantitative phenotypes of different individuals. Taking this approach shows that standard models in both statistical genetics (e.g., Genome-Wide Association Studies; GWAS) and phylogenetic comparative biology (e.g., phylogenetic regression) can be interpreted as special cases of this more general quantitative-genetic model. The fact that these models share the same core architecture means that we can build a unified understanding of the strengths and limitations of different methods for controlling for genetic structure when testing for associations. We develop intuition for why and when spurious correlations may occur using analytical theory and conduct population-genetic and phylogenetic simulations of quantitative traits. The structural similarity of problems in statistical genetics and phylogenetics enables us to take methodological advances from one field and apply them in the other. We demonstrate this by showing how a standard GWAS technique-including both the genetic relatedness matrix (GRM) as well as its leading eigenvectors, corresponding to the principal components of the genotype matrix, in a regression model-can mitigate spurious correlations in phylogenetic analyses. As a case study of this, we re-examine an analysis testing for co-evolution of expression levels between genes across a fungal phylogeny, and show that including covariance matrix eigenvectors as covariates decreases the false positive rate while simultaneously increasing the true positive rate. More generally, this work provides a foundation for more integrative approaches for understanding the genetic architecture of phenotypes and how evolutionary processes shape it.

Genetic and molecular architecture of complex traits

Human genetics has emerged as one of the most dynamic areas of biology, with a broadening societal impact. In this review, we discuss recent achievements, ongoing efforts, and future challenges in the field. Advances in technology, statistical methods, and the growing scale of research efforts have all provided many insights into the processes that have given rise to the current patterns of genetic variation. Vast maps of genetic associations with human traits and diseases have allowed characterization of their genetic architecture. Finally, studies of molecular and cellular effects of genetic variants have provided insights into biological processes underlying disease. Many outstanding questions remain, but the field is well poised for groundbreaking discoveries as it increases the use of genetic data to understand both the history of our species and its applications to improve human health.

The Promise of Inferring the Past Using the Ancestral Recombination Graph

The ancestral recombination graph (ARG) is a structure that represents the history of coalescent and recombination events connecting a set of sequences (Hudson RR. In: Futuyma D, Antonovics J, editors. Gene genealogies and the coalescent process. In: Oxford Surveys in Evolutionary Biology; 1991. p. 1 to 44.). The full ARG can be represented as a set of genealogical trees at every locus in the genome, annotated with recombination events that change the topology of the trees between adjacent loci and the mutations that occurred along the branches of those trees (Griffiths RC, Marjoram P. An ancestral recombination graph. In: Donnelly P, Tavare S, editors. Progress in population genetics and human evolution. Springer; 1997. p. 257 to 270.). Valuable insights can be gained into past evolutionary processes, such as demographic events or the influence of natural selection, by studying the ARG. It is regarded as the "holy grail" of population genetics (Hubisz M, Siepel A. Inference of ancestral recombination graphs using ARGweaver. In: Dutheil JY, editors. Statistical population genomics. New York, NY: Springer US; 2020. p. 231-266.) since it encodes the processes that generate all patterns of allelic and haplotypic variation from which all commonly used summary statistics in population genetic research (e.g. heterozygosity and linkage disequilibrium) can be derived. Many previous evolutionary inferences relied on summary statistics extracted from the genotype matrix. Evolutionary inferences using the ARG represent a significant advancement as the ARG is a representation of the evolutionary history of a sample that shows the past history of recombination, coalescence, and mutation events across a particular sequence. This representation in theory contains as much information, if not more, than the combination of all independent summary statistics that could be derived from the genotype matrix. Consistent with this idea, some of the first ARG-based analyses have proven to be more powerful than summary statistic-based analyses (Speidel L, Forest M, Shi S, Myers SR. A method for genome-wide genealogy estimation for thousands of samples. Nat Genet. 2019:51(9):1321 to 1329.; Stern AJ, Wilton PR, Nielsen R. An approximate full-likelihood method for inferring selection and allele frequency trajectories from DNA sequence data. PLoS Genet. 2019:15(9):e1008384.; Hubisz MJ, Williams AL, Siepel A. Mapping gene flow between ancient hominins through demography-aware inference of the ancestral recombination graph. PLoS Genet. 2020:16(8):e1008895.; Fan C, Mancuso N, Chiang CWK. A genealogical estimate of genetic relationships. Am J Hum Genet. 2022:109(5):812-824.; Fan C, Cahoon JL, Dinh BL, Ortega-Del Vecchyo D, Huber C, Edge MD, Mancuso N, Chiang CWK. A likelihood-based framework for demographic inference from genealogical trees. bioRxiv. 2023.10.10.561787. 2023.; Hejase HA, Mo Z, Campagna L, Siepel A. A deep-learning approach for inference of selective sweeps from the ancestral recombination graph. Mol Biol Evol. 2022:39(1):msab332.; Link V, Schraiber JG, Fan C, Dinh B, Mancuso N, Chiang CWK, Edge MD. Tree-based QTL mapping with expected local genetic relatedness matrices. bioRxiv. 2023.04.07.536093. 2023.; Zhang BC, Biddanda A, Gunnarsson ÁF, Cooper F, Palamara PF. Biobank-scale inference of ancestral recombination graphs enables genealogical analysis of complex traits. Nat Genet. 2023:55(5):768-776.). As such, there has been significant interest in the field to investigate 2 main problems related to the ARG: (i) How can we estimate the ARG based on genomic data, and (ii) how can we extract information of past evolutionary processes from the ARG? In this perspective, we highlight 3 topics that pertain to these main issues: The development of computational innovations that enable the estimation of the ARG; remaining challenges in estimating the ARG; and methodological advances for deducing evolutionary forces and mechanisms using the ARG. This perspective serves to introduce the readers to the types of questions that can be explored using the ARG and to highlight some of the most pressing issues that must be addressed in order to make ARG-based inference an indispensable tool for evolutionary research.

Accurate inference of population history in the presence of background selection

All published methods for learning about demographic history make the simplifying assumption that the genome evolves neutrally, and do not seek to account for the effects of natural selection on patterns of variation. This is a major concern, as ample work has demonstrated the pervasive effects of natural selection and in particular background selection (BGS) on patterns of genetic variation in diverse species. Simulations and theoretical work have shown that methods to infer changes in effective population size over time (Ne(t)) become increasingly inaccurate as the strength of linked selection increases. Here, we introduce an extension to the Pairwise Sequentially Markovian Coalescent (PSMC) algorithm, PSMC+, which explicitly co-models demographic history and natural selection. We benchmark our method using forward-in-time simulations with BGS and find that our approach improves the accuracy of effective population size inference. Leveraging a high resolution map of BGS in humans, we infer considerable changes in the magnitude of inferred effective population size relative to previous reports. Finally, we separately infer Ne(t) on the X chromosome and on the autosomes in diverse great apes without making a correction for selection, and find that the inferred ratio fluctuates substantially through time in a way that differs across species, showing that uncorrected selection may be an important driver of signals of genetic difference on the X chromosome and autosomes.

The era of the ARG: An introduction to ancestral recombination graphs and their significance in empirical evolutionary genomics

In the presence of recombination, the evolutionary relationships between a set of sampled genomes cannot be described by a single genealogical tree. Instead, the genomes are related by a complex, interwoven collection of genealogies formalized in a structure called an ancestral recombination graph (ARG). An ARG extensively encodes the ancestry of the genome(s) and thus is replete with valuable information for addressing diverse questions in evolutionary biology. Despite its potential utility, technological and methodological limitations, along with a lack of approachable literature, have severely restricted awareness and application of ARGs in evolution research. Excitingly, recent progress in ARG reconstruction and simulation have made ARG-based approaches feasible for many questions and systems. In this review, we provide an accessible introduction and exploration of ARGs, survey recent methodological breakthroughs, and describe the potential for ARGs to further existing goals and open avenues of inquiry that were previously inaccessible in evolutionary genomics. Through this discussion, we aim to more widely disseminate the promise of ARGs in evolutionary genomics and encourage the broader development and adoption of ARG-based inference.

Tree-based QTL mapping with expected local genetic relatedness matrices

Understanding the genetic basis of complex phenotypes is a central pursuit of genetics. Genome-wide association studies (GWASs) are a powerful way to find genetic loci associated with phenotypes. GWASs are widely and successfully used, but they face challenges related to the fact that variants are tested for association with a phenotype independently, whereas in reality variants at different sites are correlated because of their shared evolutionary history. One way to model this shared history is through the ancestral recombination graph (ARG), which encodes a series of local coalescent trees. Recent computational and methodological breakthroughs have made it feasible to estimate approximate ARGs from large-scale samples. Here, we explore the potential of an ARG-based approach to quantitative-trait locus (QTL) mapping, echoing existing variance-components approaches. We propose a framework that relies on the conditional expectation of a local genetic relatedness matrix (local eGRM) given the ARG. Simulations show that our method is especially beneficial for finding QTLs in the presence of allelic heterogeneity. By framing QTL mapping in terms of the estimated ARG, we can also facilitate the detection of QTLs in understudied populations. We use local eGRM to analyze two chromosomes containing known body size loci in a sample of Native Hawaiians. Our investigations can provide intuition about the benefits of using estimated ARGs in population- and statistical-genetic methods in general.

The era of the ARG: an empiricist's guide to ancestral recombination graphs

In the presence of recombination, the evolutionary relationships between a set of sampled genomes cannot be described by a single genealogical tree. Instead, the genomes are related by a complex, interwoven collection of genealogies formalized in a structure called an ancestral recombination graph (ARG). An ARG extensively encodes the ancestry of the genome(s) and thus is replete with valuable information for addressing diverse questions in evolutionary biology. Despite its potential utility, technological and methodological limitations, along with a lack of approachable literature, have severely restricted awareness and application of ARGs in empirical evolution research. Excitingly, recent progress in ARG reconstruction and simulation have made ARG-based approaches feasible for many questions and systems. In this review, we provide an accessible introduction and exploration of ARGs, survey recent methodological breakthroughs, and describe the potential for ARGs to further existing goals and open avenues of inquiry that were previously inaccessible in evolutionary genomics. Through this discussion, we aim to more widely disseminate the promise of ARGs in evolutionary genomics and encourage the broader development and adoption of ARG-based inference.

Inference of Coalescence Times and Variant Ages Using Convolutional Neural Networks

Accurate inference of the time to the most recent common ancestor (TMRCA) between pairs of individuals and of the age of genomic variants is key in several population genetic analyses. We developed a likelihood-free approach, called CoalNN, which uses a convolutional neural network to predict pairwise TMRCAs and allele ages from sequencing or SNP array data. CoalNN is trained through simulation and can be adapted to varying parameters, such as demographic history, using transfer learning. Across several simulated scenarios, CoalNN matched or outperformed the accuracy of model-based approaches for pairwise TMRCA and allele age prediction. We applied CoalNN to settings for which model-based approaches are under-developed and performed analyses to gain insights into the set of features it uses to perform TMRCA prediction. We next used CoalNN to analyze 2,504 samples from 26 populations in the 1,000 Genome Project data set, inferring the age of ∼80 million variants. We observed substantial variation across populations and for variants predicted to be pathogenic, reflecting heterogeneous demographic histories and the action of negative selection. We used CoalNN's predicted allele ages to construct genome-wide annotations capturing the signature of past negative selection. We performed LD-score regression analysis of heritability using summary association statistics from 63 independent complex traits and diseases (average N=314k), observing increased annotation-specific effects on heritability compared to a previous allele age annotation. These results highlight the effectiveness of using likelihood-free, simulation-trained models to infer properties of gene genealogies in large genomic data sets.

Extremely sparse models of linkage disequilibrium in ancestrally diverse association studies

Linkage disequilibrium (LD) is the correlation among nearby genetic variants. In genetic association studies, LD is often modeled using large correlation matrices, but this approach is inefficient, especially in ancestrally diverse studies. In the present study, we introduce LD graphical models (LDGMs), which are an extremely sparse and efficient representation of LD. LDGMs are derived from genome-wide genealogies; statistical relationships among alleles in the LDGM correspond to genealogical relationships among haplotypes. We published LDGMs and ancestry-specific LDGM precision matrices for 18 million common variants (minor allele frequency >1%) in five ancestry groups, validated their accuracy and demonstrated order-of-magnitude improvements in runtime for commonly used LD matrix computations. We implemented an extremely fast multiancestry polygenic prediction method, BLUPx-ldgm, which performs better than a similar method based on the reference LD correlation matrix. LDGMs will enable sophisticated methods that scale to ancestrally diverse genetic association data across millions of variants and individuals.

Ultrafast genome-wide inference of pairwise coalescence times

The pairwise sequentially Markovian coalescent (PSMC) algorithm and its extensions infer the coalescence time of two homologous chromosomes at each genomic position. This inference is used in reconstructing demographic histories, detecting selection signatures, studying genome-wide associations, constructing ancestral recombination graphs, and more. Inference of coalescence times between each pair of haplotypes in a large data set is of great interest, as they may provide rich information about the population structure and history of the sample. Here, we introduce a new method, Gamma-SMC, which is more than 10 times faster than current methods. To obtain this speed-up, we represent the posterior coalescence time distributions succinctly as a gamma distribution with just two parameters; in contrast, PSMC and its extensions hold these in a vector over discrete intervals of time. Thus, Gamma-SMC has constant time-complexity per site, without dependence on the number of discrete time states. Additionally, because of this continuous representation, our method is able to infer times spanning many orders of magnitude and, as such, is robust to parameter misspecification. We describe how this approach works, show its performance on simulated and real data, and illustrate its use in studying recent positive selection in the 1000 Genomes Project data set.

Using enormous genealogies to map causal variants in space and time

A new method infers huge gene trees and tests the tree branches for phenotypic associations. This improves power to map the effects of rare variants that are missing from genotype arrays and imputation panels.