Site Frequency Spectrum Research Articles

Genomic Assessment of Cancer Susceptibility in the Threatened Catalina Island Fox (Urocyon littoralis catalinae).

Small effective population sizes raise the probability of extinction by increasing the frequency of potentially deleterious alleles and reducing fitness. However, the extent to which cancers play a role in the fitness reduction of genetically depauperate wildlife populations is unknown. Santa Catalina island foxes (Urocyon littoralis catalinae) sampled in 2007–2008 have a high prevalence of ceruminous gland tumors, which was not detected in the population prior to a recent bottleneck caused by a canine distemper epidemic. The disease appears to be associated with inflammation from chronic ear mite (Otodectes) infections and secondary elevated levels of Staphyloccus pseudointermedius bacterial infections. However, no other environmental factors to date have been found to be associated with elevated cancer risk in this population. Here, we used whole genome sequencing of the case and control individuals from two islands to identify candidate loci associated with cancer based on genetic divergence, nucleotide diversity, allele frequency spectrum, and runs of homozygosity. We identified several candidate loci based on genomic signatures and putative gene functions, suggesting that cancer susceptibility in this population may be polygenic. Due to the efforts of a recovery program and weak fitness effects of late-onset disease, the population size has increased, which may allow selection to be more effective in removing these presumably slightly deleterious alleles. Long-term monitoring of the disease alleles, as well as overall genetic diversity, will provide crucial information for the long-term persistence of this threatened population.

Contrasting Patterns in the Early Stage of SARS-CoV-2 Evolution between Humans and Minks.

One of the unique features of SARS-CoV-2 is its apparent neutral evolution during the early pandemic (before February 2020). This contrasts with the preceding SARS-CoV epidemics, where viruses evolved adaptively. SARS-CoV-2 may exhibit a unique or adaptive feature which deviates from other coronaviruses. Alternatively, the virus may have been cryptically circulating in humans for a sufficient time to have acquired adaptive changes before the onset of the current pandemic. To test the scenarios above, we analyzed the SARS-CoV-2 sequences from minks (Neovision vision) and parental humans. In the early phase of the mink epidemic (April to May 2020), nonsynonymous to synonymous mutation ratio per site in the spike protein is 2.93, indicating a selection process favoring adaptive amino acid changes. Mutations in the spike protein were concentrated within its receptor-binding domain and receptor-binding motif. An excess of high-frequency derived variants produced by genetic hitchhiking was found during the middle (June to July 2020) and late phase I (August to September 2020) of the mink epidemic. In contrast, the site frequency spectra of early SARS-CoV-2 in humans only show an excess of low-frequency mutations, consistent with the recent outbreak of the virus. Strong positive selection in the mink SARS-CoV-2 implies that the virus may not be preadapted to a wide range of hosts and illustrates how a virus evolves to establish a continuous infection in a new host. Therefore, the lack of positive selection signal during the early pandemic in humans deserves further investigation.

Genome-Environment Associations, an Innovative Tool for Studying Heritable Evolutionary Adaptation in Orphan Crops and Wild Relatives.

Leveraging innovative tools to speed up prebreeding and discovery of genotypic sources of adaptation from landraces, crop wild relatives, and orphan crops is a key prerequisite to accelerate genetic gain of abiotic stress tolerance in annual crops such as legumes and cereals, many of which are still orphan species despite advances in major row crops. Here, we review a novel, interdisciplinary approach to combine ecological climate data with evolutionary genomics under the paradigm of a new field of study: genome–environment associations (GEAs). We first exemplify how GEA utilizes in situ georeferencing from genotypically characterized, gene bank accessions to pinpoint genomic signatures of natural selection. We later discuss the necessity to update the current GEA models to predict both regional- and local- or micro-habitat–based adaptation with mechanistic ecophysiological climate indices and cutting-edge GWAS-type genetic association models. Furthermore, to account for polygenic evolutionary adaptation, we encourage the community to start gathering genomic estimated adaptive values (GEAVs) for genomic prediction (GP) and multi-dimensional machine learning (ML) models. The latter two should ideally be weighted by de novo GWAS-based GEA estimates and optimized for a scalable marker subset. We end the review by envisioning avenues to make adaptation inferences more robust through the merging of high-resolution data sources, such as environmental remote sensing and summary statistics of the genomic site frequency spectrum, with the epigenetic molecular functionality responsible for plastic inheritance in the wild. Ultimately, we believe that coupling evolutionary adaptive predictions with innovations in ecological genomics such as GEA will help capture hidden genetic adaptations to abiotic stresses based on crop germplasm resources to assist responses to climate change.“I shall endeavor to find out how nature’s forces act upon one another, and in what manner the geographic environment exerts its influence on animals and plants. In short, I must find out about the harmony in nature” Alexander von Humboldt—Letter to Karl Freiesleben, June 1799.

Neural networks for self-adjusting mutation rate estimation when the recombination rate is unknown.

Estimating the mutation rate, or equivalently effective population size, is a common task in population genetics. If recombination is low or high, optimal linear estimation methods are known and well understood. For intermediate recombination rates, the calculation of optimal estimators is more challenging. As an alternative to model-based estimation, neural networks and other machine learning tools could help to develop good estimators in these involved scenarios. However, if no benchmark is available it is difficult to assess how well suited these tools are for different applications in population genetics. Here we investigate feedforward neural networks for the estimation of the mutation rate based on the site frequency spectrum and compare their performance with model-based estimators. For this we use the model-based estimators introduced by Fu, Futschik et al., and Watterson that minimize the variance or mean squared error for no and free recombination. We find that neural networks reproduce these estimators if provided with the appropriate features and training sets. Remarkably, using the model-based estimators to adjust the weights of the training data, only one hidden layer is necessary to obtain a single estimator that performs almost as well as model-based estimators for low and high recombination rates, and at the same time provides a superior estimation method for intermediate recombination rates. We apply the method to simulated data based on the human chromosome 2 recombination map, highlighting its robustness in a realistic setting where local recombination rates vary and/or are unknown.

Bias and inconsistency in the estimation of tumour mutation burden

BackgroundTumour mutation burden (TMB), defined as the number of somatic mutations per megabase within the sequenced region in the tumour sample, has been used as a biomarker for predicting response to immune therapy. Several studies have been conducted to assess the utility of TMB for various cancer types; however, methods to measure TMB have not been adequately evaluated. In this study, we identified two sources of bias in current methods to calculate TMB.MethodsWe used simulated data to quantify the two sources of bias and their effect on TMB calculation, we down-sampled sequencing reads from exome sequencing datasets from TCGA to evaluate the consistency in TMB estimation across different sequencing depths. We analyzed data from ten cancer cohorts to investigate the relationship between inferred TMB and sequencing depth.ResultsWe found that TMB, estimated by counting the number of somatic mutations above a threshold frequency (typically 0.05), is not robust to sequencing depth. Furthermore, we show that, because only mutations with an observed frequency greater than the threshold are considered, the observed mutant allele frequency provides a biased estimate of the true frequency. This can result in substantial over-estimation of the TMB, when the cancer sample includes a large number of somatic mutations at low frequencies, and exacerbates the lack of robustness of TMB to variation in sequencing depth and tumour purity.ConclusionOur results demonstrate that care needs to be taken in the estimation of TMB to ensure that results are unbiased and consistent across studies and we suggest that accurate and robust estimation of TMB could be achieved using statistical models that estimate the full mutant allele frequency spectrum.

Modes of Selection in Tumors as Reflected by Two Mathematical Models and Site Frequency Spectra.

The tug-of-war model was developed in a series of papers of McFarland and co-authors to account for existence of mutually counteracting rare advantageous driver mutations and more frequent slightly deleterious passenger mutations in cancer. In its original version, it was a state-dependent branching process. Because of its formulation, the tug-of-war model is of importance for tackling the problem as to whether evolution of cancerous tumors is "Darwinian" or "non-Darwinian." We define two Time-Continuous Markov Chain versions of the model, including identical mutation processes but adopting different drift and selection components. In Model A, drift and selection process preserves expected fitness whereas in Model B it leads to non-decreasing expected fitness. We investigate these properties using mathematical analysis and extensive simulations, which detect the effect of the so-called drift barrier in Model B but not in Model A. These effects are reflected in different structure of clone genealogies in the two models. Our work is related to the past theoretical work in the field of evolutionary genetics, concerning the interplay among mutation, drift and selection, in absence of recombination (asexual reproduction), where epistasis plays a major role. Finally, we use the statistics of mutation frequencies known as the Site Frequency Spectra (SFS), to compare the variant frequencies in DNA of sequenced HER2+ breast cancers, to those based on Model A and B simulations. The tumor-based SFS are better reproduced by Model A, pointing out a possible selection pattern of HER2+ tumor evolution. To put our models in context, we carried out an exploratory study of how publicly accessible data from breast, prostate, skin and ovarian cancers fit a range of models found in the literature.

Insights From a Large-Scale Whole-Genome Sequencing Study of Systolic Blood Pressure, Diastolic Blood Pressure, and Hypertension.

The availability of whole-genome sequencing data in large studies has enabled the assessment of coding and noncoding variants across the allele frequency spectrum for their associations with blood pressure. We conducted a multiancestry whole-genome sequencing analysis of blood pressure among 51 456 Trans-Omics for Precision Medicine and Centers for Common Disease Genomics program participants (stage-1). Stage-2 analyses leveraged array data from UK Biobank (N=383 145), Million Veteran Program (N=318 891), and Reasons for Geographic and Racial Differences in Stroke (N=10 643) participants, along with whole-exome sequencing data from UK Biobank (N=199 631) participants. Two blood pressure signals achieved genome-wide significance in meta-analyses of stage-1 and stage-2 single variant findings (P<5×10-8). Among them, a rare intergenic variant at novel locus, LOC100506274, was associated with lower systolic blood pressure in stage-1 (beta [SE]=-32.6 [6.0]; P=4.99×10-8) but not stage-2 analysis (P=0.11). Furthermore, a novel common variant at the known INSR locus was suggestively associated with diastolic blood pressure in stage-1 (beta [SE]=-0.36 [0.07]; P=4.18×10-7) and attained genome-wide significance in stage-2 (beta [SE]=-0.29 [0.03]; P=7.28×10-23). Nineteen additional signals suggestively associated with blood pressure in meta-analysis of single and aggregate rare variant findings (P<1×10-6 and P<1×10-4, respectively). We report one promising but unconfirmed rare variant for blood pressure and, more importantly, contribute insights for future blood pressure sequencing studies. Our findings suggest promise of aggregate analyses to complement single variant analysis strategies and the need for larger, diverse samples, and family studies to enable robust rare variant identification.

Revisiting the number of self-incompatibility alleles in finite populations: From old models to new results.

Under gametophytic self-incompatibility (GSI), plants are heterozygous at the self-incompatibility locus (S-locus) and can only be fertilized by pollen with a different allele at that locus. The last century has seen a heated debate about the correct way of modelling the allele diversity in a GSI population that was never formally resolved. Starting from an individual-based model, we derive the deterministic dynamics as proposed by Fisher (The genetical theory of natural selection - A complete, Variorum edition, Oxford University Press, 1958) and compute the stationary S-allele frequency distribution. We find that the stationary distribution proposed by Wright (Evolution, 18, 609, 1964) is close to our theoretical prediction, in line with earlier numerical confirmation. Additionally, we approximate the invasion probability of a new S-allele, which scales inversely with the number of resident S-alleles. Lastly, we use the stationary allele frequency distribution to estimate the population size of a plant population from an empirically obtained allele frequency spectrum, which complements the existing estimator of the number of S-alleles. Our expression of the stationary distribution resolves the long-standing debate about the correct approximation of the number of S-alleles and paves the way for new statistical developments for the estimation of the plant population size based on S-allele frequencies.

Joint effect of changing selection and demography on the site frequency spectrum

The site frequency spectrum (SFS) is an important statistic that summarizes the molecular variation in a population, and is used to estimate population-genetic parameters and detect natural selection. Here, we study the SFS in a randomly mating, diploid population in which both the population size and selection coefficient vary periodically with time using a diffusion theory approach, and derive simple analytical expressions for the time-averaged SFS in slowly and rapidly changing environments. We show that for strong selection and in slowly changing environments where the population experiences both positive and negative cycles of the selection coefficient, the time-averaged SFS differs significantly from the equilibrium SFS in a constant environment. The deviation is found to depend on the time spent by the population in the deleterious part of the selection cycle and the phase difference between the selection coefficient and population size, and can be captured by an effective population size.

Assessing the contribution of rare genetic variants to phenotypes of chronic obstructive pulmonary disease using whole-genome sequence data.

Genetic variation has a substantial contribution to chronic obstructive pulmonary disease (COPD) and lung function measurements. Heritability estimates using genome-wide genotyping data can be biased if analyses do not appropriately account for the nonuniform distribution of genetic effects across the allele frequency and linkage disequilibrium (LD) spectrum. In addition, the contribution of rare variants has been unclear. We sought to assess the heritability of COPD and lung function using whole-genome sequence data from the Trans-Omics for Precision Medicine program. Using the genome-based restricted maximum likelihood method, we partitioned the genome into bins based on minor allele frequency and LD scores and estimated heritability of COPD, FEV1% predicted and FEV1/FVC ratio in 11 051 European ancestry and 5853 African-American participants. In European ancestry participants, the estimated heritability of COPD, FEV1% predicted and FEV1/FVC ratio were 35.5%, 55.6% and 32.5%, of which 18.8%, 19.7%, 17.8% were from common variants, and 16.6%, 35.8%, and 14.6% were from rare variants. These estimates had wide confidence intervals, with common variants and some sets of rare variants showing a statistically significant contribution (P-value < 0.05). In African-Americans, common variant heritability was similar to European ancestry participants, but lower sample size precluded calculation of rare variant heritability. Our study provides updated and unbiased estimates of heritability for COPD and lung function, and suggests an important contribution of rare variants. Larger studies of more diverse ancestry will improve accuracy of these estimates.

Ultra-rare and common genetic variant analysis converge to implicate negative selection and neuronal processes in the aetiology of schizophrenia

Both common and rare genetic variants (minor allele frequency >1% and <0.1% respectively) have been implicated in the aetiology of schizophrenia. In this study, we integrate single-cell gene expression data with publicly available Genome-Wide Association Study (GWAS) and exome sequenced data in order to investigate in parallel, the enrichment of common and (ultra-)rare variants related to schizophrenia in several functionally relevant gene-sets. Four types of gene-sets were constructed 1) protein-truncating variant (PTV)-intolerant (PI) genes 2) genes expressed in brain cell types and neurons ascertained from mouse and human brain tissue 3) genes defined by synaptic function and location and 4) intersection genes, i.e., PI genes that are expressed in the human and mouse brain cell gene-sets. We show that common as well as ultra-rare schizophrenia-associated variants are overrepresented in PI genes, in excitatory neurons from the prefrontal cortex and hippocampus, medium spiny neurons, and genes enriched for synaptic processes. We also observed stronger enrichment in the intersection genes. Our findings suggest that across the allele frequency spectrum, genes and genetic variants likely to be under stringent selection, and those expressed in particular brain cell types, are involved in the same biological pathways influencing the risk for schizophrenia.

Fast and accurate estimation of multidimensional site frequency spectra from low-coverage high-throughput sequencing data.

BackgroundThe site frequency spectrum summarizes the distribution of allele frequencies throughout the genome, and it is widely used as a summary statistic to infer demographic parameters and to detect signals of natural selection. The use of high-throughput low-coverage DNA sequencing data can lead to biased estimates of the site frequency spectrum due to high levels of uncertainty in genotyping.ResultsHere we design and implement a method to efficiently and accurately estimate the multidimensional joint site frequency spectrum for large numbers of haploid or diploid individuals across an arbitrary number of populations, using low-coverage sequencing data. The method maximizes a likelihood function that represents the probability of the sequencing data observed given a multidimensional site frequency spectrum using genotype likelihoods. Notably, it uses an advanced binning heuristic paired with an accelerated expectation-maximization algorithm for a fast and memory-efficient computation, and can generate both unfolded and folded spectra and bootstrapped replicates for haploid and diploid genomes. On the basis of extensive simulations, we show that the new method requires remarkably less storage and is faster than previous implementations whilst retaining the same accuracy. When applied to low-coverage sequencing data from the fungal pathogen Neonectria neomacrospora, results recapitulate the patterns of population differentiation generated using the original high-coverage data.ConclusionThe new implementation allows for accurate estimation of population genetic parameters from arbitrarily large, low-coverage datasets, thus facilitating cost-effective sequencing experiments in model and non-model organisms.

Genetic Admixture History and Forensic Characteristics of Guizhou Sui People Inferred From Autosomal Insertion/Deletion and Genome-Wide Single-Nucleotide Polymorphisms

Insertion-deletion (Indel) serves as one of the important markers in forensic personal identification and parentage testing, especially for cases with degraded samples. However, the genetic diversity and forensic features in ethnolinguistically diverse southwestern Chinese populations remain to be explored. Sui, one Tai-Kadai-speaking population residing in Guizhou, has a complex genetic history based on linguistic, historic, and anthropological evidence. In this study, we genotyped 30 Indels from 511 Guizhou Sui individuals and obtained approximately 700,000 genome-wide single-nucleotide polymorphisms (SNPs) in 15 representative Sui individuals to comprehensively characterize the genetic diversity, forensic characteristics, and genomic landscape of Guizhou Sui people. The estimated forensic statistically allele frequency spectrum and parameters demonstrated that this Indels panel was polymorphic and informative in Tai-Kadai populations in southern China. Results of principal component analysis (PCA), STRUCTURE, and phylogenetic trees showed that Guizhou Sui had a close genetic relationship with geographically close Tai-Kadai and Hmong-Mien people. Furthermore, genomic analysis based on the Fst and f4-statistics further suggested the genetic affinity within southern Chinese Tai-Kadai-speaking populations and a close relationship with geographically adjoining Guizhou populations. Admixture models based on the ADMIXTURE, f4, three-way qpAdm, and ALDER results demonstrated the interaction between the common ancestor for Tai-Kadai/Austronesian, Hmong-Mien, and Austroasiatic speaking populations played a significant role in the formation of modern Tai-Kadai people. We observed a sex-biased influence in Sui people by finding that the dominant Y chromosomal type was a Hmong-Mien specific lineage O2a2a1a2a1a2-N5 but the mtDNA lineages were commonly found in Tai-Kadai populations. The additional southward expansion of millet farmers in the Yellow River Basin has impacted the gene pool of southern populations including Tai-Kadai. The whole-genome sequencing in the future will shed more light on the finer genetic profile of Guizhou populations.

A Nearly Neutral Model of Molecular Signatures of Natural Selection after Change in Population Size.

The nearly neutral theory is a common framework to describe natural selection at the molecular level. This theory emphasizes the importance of slightly deleterious mutations by recognizing their ability to segregate and eventually get fixed due to genetic drift in spite of the presence of purifying selection. As genetic drift is stronger in smaller than in larger populations, a correlation between population size and molecular measures of natural selection is expected within the nearly neutral theory. However, this hypothesis was originally formulated under equilibrium conditions. As most natural populations are not in equilibrium, testing the relationship empirically may lead to confounded outcomes. Demographic nonequilibria, for instance following a change in population size, are common scenarios that are expected to push the selection–drift relationship off equilibrium. By explicitly modeling the effects of a change in population size on allele frequency trajectories in the Poisson random field framework, we obtain analytical solutions of the nonstationary allele frequency spectrum. This enables us to derive exact results of measures of natural selection and effective population size in a demographic nonequilibrium. The study of their time-dependent relationship reveals a substantial deviation from the equilibrium selection–drift balance after a change in population size. Moreover, we show that the deviation is sensitive to the combination of different measures. These results therefore constitute relevant tools for empirical studies to choose suitable measures for investigating the selection–drift relationship in natural populations. Additionally, our new modeling approach extends existing population genetics theory and can serve as foundation for methodological developments.

A dynamic ancestral graph model and GPU-based simulation of a community based on metagenomic sampling.

In this paper, we present an ancestral graph model of the evolution of a guild in an ecological community. The model is based on a metagenomic sampling design in that a random sample is taken at the community, as opposed the taxon, level and species are discovered by genetic sequencing. The specific implementation of the model envisions an ecological guild that was founded by colonization at some point in the past that then potentially undergoes diversification by natural selection. Within the graph, species emerge and evolve through the diversification process and their densities in the graph are dynamic and governed by both ecological drift and random genetic drift, as well as differential viability. We employ the 3% sequence divergence rule at a marker locus to identify operational taxonomic units. We then explore approaches to see whether there are indirect signals of the diversification process, including population genetic and ecological approaches. In terms of population genetics, we study the joint site frequency spectrum of OTUs, as well its associated statistics. In terms of ecology, we study the species (or OTU) abundance distribution. For both, we observe deviations from neutrality, which indicates that there may be signals of diversifying selection in metagenomic studies under certain conditions. The model is available as a GPU-based computer program in C/C++ and using OpenCL, with the long-term goal of adding functionality iteratively to model large-scale eco-evolutionary processes for metagenomic data.

Population genetics of polymorphism and divergence in rapidly evolving populations.

In rapidly evolving populations, numerous beneficial and deleterious mutations can arise and segregate within a population at the same time. In this regime, evolutionary dynamics cannot be analyzed using traditional population genetic approaches that assume that sites evolve independently. Instead, the dynamics of many loci must be analyzed simultaneously. Recent work has made progress by first analyzing the fitness variation within a population, and then studying how individual lineages interact with this traveling fitness wave. However, these "traveling wave" models have previously been restricted to extreme cases where selection on individual mutations is either much faster or much slower than the typical coalescent timescale Tc. In this work, we show how the traveling wave framework can be extended to intermediate regimes in which the scaled fitness effects of mutations (Tcs) are neither large nor small compared to one. This enables us to describe the dynamics of populations subject to a wide range of fitness effects, and in particular, in cases where it is not immediately clear which mutations are most important in shaping the dynamics and statistics of genetic diversity. We use this approach to derive new expressions for the fixation probabilities and site frequency spectra of mutations as a function of their scaled fitness effects, along with related results for the coalescent timescale Tc and the rate of adaptation or Muller's ratchet. We find that competition between linked mutations can have a dramatic impact on the proportions of neutral and selected polymorphisms, which is not simply summarized by the scaled selection coefficient Tcs. We conclude by discussing the implications of these results for population genetic inferences.

Variances and covariances of linear summary statistics of segregating sites

Each mutation in a population sample of DNA sequences can be classified by the number of sequences that inherit the mutant nucleotide, the resulting frequencies are known as mutations of different sizes or site frequency spectrum. Many summary statistics can be defined as a linear function of these frequencies. A flexible class of such linear summary statistics is explored analytically in this paper which include several well-known quantities, such as the number of segregating sizes and the mean number of nucleotide differences between two sequences. Some asymptotic variances and covariances are obtained while the analytical formulas for the variances and covariances of nine such linear summary statistics are derived, most of which are unknown to date. This study not only provides some theoretical foundations for exploring linear summary statistics, but also provides some newlinear summary statistics that may be utilized for analyzing sample polymorphism. Furthermore it is showed that a newly developed linear summary statistics has a smaller variance almost uniformly than Watterson’s estimator, and that a class of linear summary statistics given too heavy weights on mutations of smaller sizes result in asymptotically non-zero variance.

Exploratory analysis of multi-trait coadaptations in light of population history.

During the process of range expansion, populations encounter a variety of environments. They respond to the local environments by modifying their mutually interacting traits. Common approaches of landscape analysis include first focusing on the genes that undergo diversifying selection or directional selection in response to environmental variation. To understand the whole history of populations, it is ideal to capture the history of their range expansion with reference to the series of surrounding environments and to infer the multitrait coadaptation. To this end, we propose a complementary approach; it is an exploratory analysis using up‐to‐date methods that integrate population genetic features and features of selection on multiple traits. First, we conduct correspondence analysis of site frequency spectra, traits, and environments with auxiliary information of population‐specific fixation index (F ST). This visualizes the structure and the ages of populations and helps infer the history of range expansion, encountered environmental changes, and selection on multiple traits. Next, we further investigate the inferred history using an admixture graph that describes the population split and admixture. Finally, principal component analysis of the selection on edge‐by‐trait (SET) matrix identifies multitrait coadaptation and the associated edges of the admixture graph. We introduce a newly defined factor loadings of environmental variables in order to identify the environmental factors that caused the coadaptation. A numerical simulation of one‐dimensional stepping‐stone population expansion showed that the exploratory analysis reconstructed the pattern of the environmental selection that was missed by analysis of individual traits. Analysis of a public dataset of natural populations of black cottonwood in northwestern America identified the first principal component (PC) coadaptation of photosynthesis‐ vs growth‐related traits responding to the geographical clines of temperature and day length. The second PC coadaptation of volume‐related traits suggested that soil condition was a limiting factor for aboveground environmental selection.

Genetic associations of protein-coding variants in human disease

Genome-wide association studies (GWAS) have identified thousands of genetic variants linked to the risk of human disease. However, GWAS have so far remained largely underpowered in relation to identifying associations in the rare and low-frequency allelic spectrum and have lacked the resolution to trace causal mechanisms to underlying genes1. Here we combined whole-exome sequencing in 392,814 UK Biobank participants with imputed genotypes from 260,405 FinnGen participants (653,219 total individuals) to conduct association meta-analyses for 744 disease endpoints across the protein-coding allelic frequency spectrum, bridging the gap between common and rare variant studies. We identified 975 associations, with more than one-third being previously unreported. We demonstrate population-level relevance for mutations previously ascribed to causing single-gene disorders, map GWAS associations to likely causal genes, explain disease mechanisms, and systematically relate disease associations to levels of 117 biomarkers and clinical-stage drug targets. Combining sequencing and genotyping in two population biobanks enabled us to benefit from increased power to detect and explain disease associations, validate findings through replication and propose medical actionability for rare genetic variants. Our study provides a compendium of protein-coding variant associations for future insights into disease biology and drug discovery.

Sparse Moments of Univariate Step Functions and Allele Frequency Spectra

We study the univariate moment problem of piecewise-constant density functions on the interval [0,1] and its consequences for an inference problem in population genetics. We show that, up to closure, any collection of n moments is achieved by a step function with at most n − 1 breakpoints and that this bound is tight. We use this to show that any point in the n th coalescence manifold in population genetics can be attained by a piecewise constant population history with at most n − 2 changes. Both the moment cones and the coalescence manifold are projected spectrahedra and we describe the problem of finding a nearest point on them as a semidefinite program.