An estimator of first coalescent time reveals selection on young variants and large heterogeneity in rare allele ages among human populations

Latent mutations in the ancestries of alleles under selection

We consider a single genetic locus with two alleles A1 and A2 in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming the allele frequencies follow a Wright-Fisher diffusion and have reached stationarity, we describe the asymptotic behaviors of the conditional gene genealogy and the latent mutations of a sample with known allele counts, when the count n1 of allele A1 is fixed, and when either or both the sample size n and the selection strength |α| tend to infinity. Our study extends previous work under neutrality to the case of non-neutral rare alleles, asserting that when selection is not too strong relative to the sample size, even if it is strongly positive or strongly negative in the usual sense (α→-∞ or α→+∞), the number of latent mutations of the n1 copies of allele A1 follows the same distribution as the number of alleles in the Ewens sampling formula. On the other hand, very strong positive selection relative to the sample size leads to neutral gene genealogies with a single ancient latent mutation. We also demonstrate robustness of our asymptotic results against changing population sizes, when one of |α| or n is large.

CINner: modeling and simulation of chromosomal instability in cancer at single-cell resolution

Cancer development is characterized by chromosomal instability, manifesting in frequent occurrences of different genomic alteration mechanisms ranging in extent and impact. Mathematical modeling can help evaluate the role of each mutational process during tumor progression, however existing frameworks can only capture certain aspects of chromosomal instability (CIN). We present CINner, a mathematical framework for modeling genomic diversity and selection during tumor evolution. The main advantage of CINner is its flexibility to incorporate many genomic events that directly impact cellular fitness, from driver gene mutations to copy number alterations (CNAs), including focal amplifications and deletions, missegregations and whole-genome duplication (WGD). We apply CINner to find chromosome-arm selection parameters that drive tumorigenesis in the absence of WGD in chromosomally stable cancer types. We found that the selection parameters predict WGD prevalence among different chromosomally unstable tumors, hinting that the selective advantage of WGD cells hinges on their tolerance for aneuploidy and escape from nullisomy. Direct application of CINner to model the WGD proportion and fraction of genome altered (FGA) further uncovers the increase in CNA probabilities associated with WGD in each cancer type. CINner can also be utilized to study chromosomally stable cancer types, by applying a selection model based on driver gene mutations and focal amplifications or deletions. Finally, we used CINner to analyze the impact of CNA probabilities, chromosome selection parameters, tumor growth dynamics and population size on cancer fitness and heterogeneity. We expect that CINner will provide a powerful modeling tool for the oncology community to quantify the impact of newly uncovered genomic alteration mechanisms on shaping tumor progression and adaptation.

Models for the retention of duplicate genes and their biological underpinnings

Gene content in genomes changes through several different processes, with gene duplication being an important contributor to such changes. Gene duplication occurs over a range of scales from individual genes to whole genomes, and the dynamics of this process can be context dependent. Still, there are rules by which genes are retained or lost from genomes after duplication, and probabilistic modeling has enabled characterization of these rules, including their context-dependence. Here, we describe the biology and corresponding mathematical models that are used to understand duplicate gene retention and its contribution to the set of biochemical functions encoded in a genome.

Allele age estimators designed for whole genome datasets show only a modest decrease in accuracy when applied to whole exome datasets

Personalized genomics in the healthcare system is becoming increasingly accessible as the costs of sequencing decreases. With the increase in number of genomes, larger numbers of rare variants are being discovered and much work is being done to identify their functional impacts in relation to disease phenotypes. One way to characterize these variants is to estimate the time the mutation entered the population. However, allele age estimators such as Relate, Genealogical Estimator of Variant Age, and time of coalescence, were developed based on the assumption that datasets include the entire genome. We examined the performance of each of these estimators on simulated exome data under a neutral constant population size model and found that each provides usable estimates of allele age from whole-exome datasets. To test the robustness of these methods, analyses were undertaken to simulate data under a population expansion model and background selection. Relate performs the best amongst all three estimators with Pearson coefficients of 0.64 and 0.68 (neutral constant and expansion population model) with a 17 percent and 15 percent drop in accuracy between whole genome and whole exome estimations. Of the three estimators, Relate is best able to parallelize to yield quick results with little resources, however even Relate is only able to scale to thousands of samples making it unable to match the hundreds of thousands of samples being currently released. While more work is needed to expand the capabilities of current methods of estimating allele age, these methods estimate the age of mutations with a modest decrease in performance.

Analyses of allele age and fitness impact reveal human beneficial alleles to be older than neutral controls

A classic population genetic prediction is that alleles experiencing directional selection should swiftly traverse allele frequency space, leaving detectable reductions in genetic variation in linked regions. However, despite this expectation, identifying clear footprints of beneficial allele passage has proven to be surprisingly challenging. We addressed the basic premise underlying this expectation by estimating the ages of large numbers of beneficial and deleterious alleles in a human population genomic data set. Deleterious alleles were found to be young, on average, given their allele frequency. However, beneficial alleles were older on average than non-coding, non-regulatory alleles of the same frequency. This finding is not consistent with directional selection and instead indicates some type of balancing selection. Among derived beneficial alleles, those fixed in the population show higher local recombination rates than those still segregating, consistent with a model in which new beneficial alleles experience an initial period of balancing selection due to linkage disequilibrium with deleterious recessive alleles. Alleles that ultimately fix following a period of balancing selection will leave a modest 'soft' sweep impact on the local variation, consistent with the overall paucity of species-wide 'hard' sweeps in human genomes.

Accurate rare variant phasing of whole-genome and whole-exome sequencing data in the UK Biobank

Phasing involves distinguishing the two parentally inherited copies of each chromosome into haplotypes. Here, we introduce SHAPEIT5, a new phasing method that quickly and accurately processes large sequencing datasets and applied it to UK Biobank (UKB) whole-genome and whole-exome sequencing data. We demonstrate that SHAPEIT5 phases rare variants with low switch error rates of below 5% for variants present in just 1 sample out of 100,000. Furthermore, we outline a method for phasing singletons, which, although less precise, constitutes an important step towards future developments. We then demonstrate that the use of UKB as a reference panel improves the accuracy of genotype imputation, which is even more pronounced when phased with SHAPEIT5 compared with other methods. Finally, we screen the UKB data for loss-of-function compound heterozygous events and identify 549 genes where both gene copies are knocked out. These genes complement current knowledge of gene essentiality in the human genome.

Genetic architecture and evolution of color variation in American black bears

Color variation is a frequent evolutionary substrate for camouflage in small mammals, but the underlying genetics and evolutionary forces that drive color variation in natural populations of large mammals are mostly unexplained. The American black bear, Ursus americanus (U. americanus), exhibits a range of colors including the cinnamon morph, which has a similar color to the brown bear, U. arctos, and is found at high frequency in the American southwest. Reflectance and chemical melanin measurements showed little distinction between U. arctos and cinnamon U. americanus individuals. We used a genome-wide association for hair color as a quantitative trait in 151 U. americanus individuals and identified a single major locus (p < 10-13). Additional genomic and functional studies identified a missense alteration (R153C) in Tyrosinase-related protein 1 (TYRP1) that likely affects binding of the zinc cofactor, impairs protein localization, and results in decreased pigment production. Population genetic analyses and demographic modeling indicated that the R153C variant arose 9.36 kya in a southwestern population where it likely provided a selective advantage, spreading both northwards and eastwards by gene flow. A different TYRP1 allele, R114C, contributes to the characteristic brown color of U. arctos but is not fixed across the range.

Modeling the spatiotemporal spread of beneficial alleles using ancient genomes

Ancient genome sequencing technologies now provide the opportunity to study natural selection in unprecedented detail. Rather than making inferences from indirect footprints left by selection in present-day genomes, we can directly observe whether a given allele was present or absent in a particular region of the world at almost any period of human history within the last 10,000 years. Methods for studying selection using ancient genomes often rely on partitioning individuals into discrete time periods or regions of the world. However, a complete understanding of natural selection requires more nuanced statistical methods which can explicitly model allele frequency changes in a continuum across space and time. Here we introduce a method for inferring the spread of a beneficial allele across a landscape using two-dimensional partial differential equations. Unlike previous approaches, our framework can handle time-stamped ancient samples, as well as genotype likelihoods and pseudohaploid sequences from low-coverage genomes. We apply the method to a panel of published ancient West Eurasian genomes to produce dynamic maps showcasing the inferred spread of candidate beneficial alleles over time and space. We also provide estimates for the strength of selection and diffusion rate for each of these alleles. Finally, we highlight possible avenues of improvement for accurately tracing the spread of beneficial alleles in more complex scenarios.

Identifying rare variants inconsistent with identity-by-descent in population-scale whole-genome sequencing data

Analyses of genetic variation typically assume that rare variants within a population are inherited from a single common ancestral event identity-by-descent (IBD). However, there are genetic and technical processes through which rare variants in population genetic data may deviate from this simple evolutionary model, including recurrent mutations, gene conversions and genotyping error. All these processes can decrease the expected length of shared background haplotype surrounding a rare variant if that variant was inherited from a single event descending from a common ancestor. No method exists to computationally infer rare variants inconsistent with this simple model-denoted here as 'IBD-inconsistent'-using unphased population sequencing data.We hypothesized that the difference in shared haplotype background length can distinguish variants consistent and inconsistent with this simple IBD transmission population sequencing data without pedigree information. We implemented a Bayesian hierarchical model and used Gibbs sampling to estimate the posterior probability of IBD state for rare variants, using simulated recurrent mutations to demonstrate that our approach accurately distinguishes rare variants consistent and inconsistent with a simple IBD inheritance model.Applying our method to whole-genome sequencing data from 3,621 human individuals in the UK10K consortium, we found that IBD-inconsistent variants correlated with higher local mutation rates and genomic features like replication timing. Using a heuristic to categorize IBD-inconsistent variants as gene conversions, we found that potential gene conversions had expected properties such as enriched local GC content.By identifying IBD-inconsistent variants, we can better understand the spectrum of recent mutations in human populations, a source of genetic variation driving evolution and a key factor in understanding recent demographic history.

Haplotype-based inference of the distribution of fitness effects

Recent genome sequencing studies with large sample sizes in humans have discovered a vast quantity of low-frequency variants, providing an important source of information to analyze how selection is acting on human genetic variation. In order to estimate the strength of natural selection acting on low-frequency variants, we have developed a likelihood-based method that uses the lengths of pairwise identity-by-state between haplotypes carrying low-frequency variants. We show that in some non-equilibrium populations (such as those that have had recent population expansions) it is possible to distinguish between positive or negative selection acting on a set of variants. With our new framework, one can infer a fixed selection intensity acting on a set of variants at a particular frequency, or a distribution of selection coefficients for standing variants and new mutations. We show an application of our method to the UK10K phased haplotype dataset of individuals.

Characterizing Amino Acid Substitution with Complete Linkage of Sites on a Lineage

Amino acid substitution models are commonly used for phylogenetic inference, for ancestral sequence reconstruction, and for the inference of positive selection. All commonly used models explicitly assume that each site evolves independently, an assumption that is violated by both linkage and protein structural and functional constraints. We introduce two new models for amino acid substitution which incorporate linkage between sites, each based on the (population-genetic) Moran model. The first model is a generalized population process tracking arbitrarily many sites which undergo mutation, with individuals replaced according to their fitnesses. This model provides a reasonably complete framework for simulations but is numerically and analytically intractable. We also introduce a second model which includes several simplifying assumptions but for which some theoretical results can be derived. We analyze the simplified model to determine conditions where linkage is likely to have meaningful effects on sitewise substitution probabilities, as well as conditions under which the effects are likely to be negligible. These findings are an important step in the generation of tractable phylogenetic models that parameterize selective coefficients for amino acid substitution while accounting for linkage of sites leading to both hitchhiking and background selection.

Detecting Selection on Segregating Gene Duplicates in a Population

Gene duplication is a fundamental process that has the potential to drive phenotypic differences between populations and species. While evolutionarily neutral changes have the potential to affect phenotypes, detecting selection acting on gene duplicates can uncover cases of adaptive diversification. Existing methods to detect selection on duplicates work mostly inter-specifically and are based upon selection on coding sequence changes, here we present a method to detect selection directly on a copy number variant segregating in a population. The method relies upon expected relationships between allele (new duplication) age and frequency in the population dependent upon the effective population size. Using both a haploid and a diploid population with a Moran Model under several population sizes, the neutral baseline for copy number variants is established. The ability of the method to reject neutrality for duplicates with known age (measured in pairwise dS value) and frequency in the population is established through mathematical analysis and through simulations. Power is particularly good in the diploid case and with larger effective population sizes, as expected. With extension of this method to larger population sizes, this is a tool to analyze selection on copy number variants in any natural or experimentally evolving population. We have made an R package available at https://github.com/peterbchi/CNVSelectR/ which implements the method introduced here.

Characterizing the demographic history and prion protein variation to infer susceptibility to chronic wasting disease in a naïve population of white-tailed deer (Odocoileus virginianus)

Assessments of the adaptive potential in natural populations are essential for understanding and predicting responses to environmental stressors like climate change and infectious disease. Species face a range of stressors in human-dominated landscapes, often with contrasting effects. White-tailed deer (Odocoileus virginianus; deer) are expanding in the northern part of their range following decreasing winter severity and increasing forage availability. Chronic wasting disease (CWD), a prion disease affecting deer, is likewise expanding and represents a major threat to deer and other cervids. We obtained tissue samples from free-ranging deer across their native range in Ontario, Canada, which has yet to detect CWD in wild populations. We used high-throughput sequencing to assess neutral genomic variation and variation in the prion protein gene (PRNP) that is partly responsible for the protein misfolding when deer contract CWD. Neutral variation revealed a high number of rare alleles and no population structure, and demographic models suggested a rapid historical population expansion. Allele frequencies of PRNP variants associated with CWD susceptibility and disease progression were evenly distributed across the landscape and consistent with deer populations not infected with CWD. We estimated the selection coefficient of CWD, with simulations showing an observable and rapid shift in PRNP allele frequencies that coincides with the start of a novel CWD outbreak. Sustained surveillance of genomic and PRNP variation can be a useful tool for guiding management practices, which is especially important for CWD-free regions where deer are managed for ecological and economic benefits.

A variant-centric perspective on geographic patterns of human allele frequency variation

A key challenge in human genetics is to understand the geographic distribution of human genetic variation. Often genetic variation is described by showing relationships among populations or individuals, drawing inferences over many variants. Here, we introduce an alternative representation of genetic variation that reveals the relative abundance of different allele frequency patterns. This approach allows viewers to easily see several features of human genetic structure: (1) most variants are rare and geographically localized, (2) variants that are common in a single geographic region are more likely to be shared across the globe than to be private to that region, and (3) where two individuals differ, it is most often due to variants that are found globally, regardless of whether the individuals are from the same region or different regions. Our variant-centric visualization clarifies the geographic patterns of human variation and can help address misconceptions about genetic differentiation among populations.

Dating genomic variants and shared ancestry in population-scale sequencing data

The origin and fate of new mutations within species is the fundamental process underlying evolution. However, while much attention has been focused on characterizing the presence, frequency, and phenotypic impact of genetic variation, the evolutionary histories of most variants are largely unexplored. We have developed a nonparametric approach for estimating the date of origin of genetic variants in large-scale sequencing data sets. The accuracy and robustness of the approach is demonstrated through simulation. Using data from two publicly available human genomic diversity resources, we estimated the age of more than 45 million single-nucleotide polymorphisms (SNPs) in the human genome and release the Atlas of Variant Age as a public online database. We characterize the relationship between variant age and frequency in different geographical regions and demonstrate the value of age information in interpreting variants of functional and selective importance. Finally, we use allele age estimates to power a rapid approach for inferring the ancestry shared between individual genomes and to quantify genealogical relationships at different points in the past, as well as to describe and explore the evolutionary history of modern human populations.