Inference of Super-exponential Human Population Growth via Efficient Computation of the Site Frequency Spectrum for Generalized Models

Estimation of demography and mutation rates from one million haploid genomes

As genetic sequencing costs have plummeted, datasets with sizes previously un-thinkable have begun to appear. Such datasets present new opportunities to learn about evolutionary history, particularly via rare alleles that record the very recent past. However, beyond the computational challenges inherent in the analysis of many large-scale datasets, large population-genetic datasets present theoretical problems. In particular, the majority of population-genetic tools require the assumption that each mutant allele in the sample is the result of a single mutation (the "infinite sites" assumption), which is violated in large samples. Here, we present DR EVIL, a method for estimating mutation rates and recent demographic history from very large samples. DR EVIL avoids the infinite-sites assumption by using a diffusion approximation to a branching-process model with recurrent mutation. The branching-process approach limits the method to rare alleles, but, along with recent results, renders tractable likelihoods with recurrent mutation. We show that DR EVIL performs well in simulations and apply it to rare-variant data from a million haploid samples, identifying a signal of mutation-rate heterogeneity within commonly analyzed classes and predicting that in modern sample sizes, most rare variants at sites with high mutation rates represent the descendants of multiple mutation events.

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.

Anthropogenic stressors and the marine environment: From sources and impacts to solutions and mitigation

Human-released contaminants are often poorly understood wholistically in marine ecosystems. This review examines the sources, pathways, impacts on marine animals, and mitigation strategies of five pollutants (plastics, per- and polyfluoroalkyl substances, bisphenol compounds, ethynylestradiol, and petroleum hydrocarbons). Both abiotic and biotic mechanisms contribute to all five contaminants' movement. These pollutants cause short- and long-term effects on many biological processes genetically, molecularly, neurologically, physiologically, reproductively, and developmentally. We explore the extension of adverse outcome pathways to ecosystem effects by considering known inter-generational and trophic relations resulting in large-scale direct and indirect impacts. In doing so, we develop an understanding of their roles as environmental stressors in marine environments for targeted mitigation and future work. Ecosystems are interconnected and so international collaboration, standards, measures preceding mass production, and citizen involvement are required to protect and conserve marine life.

Recurrent mutation in the ancestry of a rare variant

Recurrent mutation produces multiple copies of the same allele which may be co-segregating in a population. Yet, most analyses of allele-frequency or site-frequency spectra assume that all observed copies of an allele trace back to a single mutation. We develop a sampling theory for the number of latent mutations in the ancestry of a rare variant, specifically a variant observed in relatively small count in a large sample. Our results follow from the statistical independence of low-count mutations, which we show to hold for the standard neutral coalescent or diffusion model of population genetics as well as for more general coalescent trees. For populations of constant size, these counts are distributed like the number of alleles in the Ewens sampling formula. We develop a Poisson sampling model for populations of varying size and illustrate it using new results for site-frequency spectra in an exponentially growing population. We apply our model to a large data set of human SNPs and use it to explain dramatic differences in site-frequency spectra across the range of mutation rates in the human genome.

Human cooperation and evolutionary transitions in individuality

A major evolutionary transition in individuality involves the formation of a cooperative group and the transformation of that group into an evolutionary entity. Human cooperation shares principles with those of multicellular organisms that have undergone transitions in individuality: division of labour, communication, and fitness interdependence. After the split from the last common ancestor of hominoids, early hominins adapted to an increasingly terrestrial niche for several million years. We posit that new challenges in this niche set in motion a positive feedback loop in selection pressure for cooperation that ratcheted coevolutionary changes in sociality, communication, brains, cognition, kin relations and technology, eventually resulting in egalitarian societies with suppressed competition and rapid cumulative culture. The increasing pace of information innovation and transmission became a key aspect of the evolutionary niche that enabled humans to become formidable cooperators with explosive population growth, the ability to cooperate and compete in groups of millions, and emergent social norms, e.g. private property. Despite considerable fitness interdependence, the rise of private property, in concert with population explosion and socioeconomic inequality, subverts potential transition of human groups into evolutionary entities due to resurgence of latent competition and conflict. This article is part of the theme issue 'Human socio-cultural evolution in light of evolutionary transitions'.

SEQUENTIAL IMPORTANCE SAMPLING FOR MULTIRESOLUTION KINGMAN-TAJIMA COALESCENT COUNTING

Statistical inference of evolutionary parameters from molecular sequence data relies on coalescent models to account for the shared genealogical ancestry of the samples. However, inferential algorithms do not scale to available data sets. A strategy to improve computational efficiency is to rely on simpler coalescent and mutation models, resulting in smaller hidden state spaces. An estimate of the cardinality of the state-space of genealogical trees at different resolutions is essential to decide the best modeling strategy for a given dataset. To our knowledge, there is neither an exact nor approximate method to determine these cardinalities. We propose a sequential importance sampling algorithm to estimate the cardinality of the sample space of genealogical trees under different coalescent resolutions. Our sampling scheme proceeds sequentially across the set of combinatorial constraints imposed by the data, which in this work are completely linked sequences of DNA at a non recombining segment. We analyze the cardinality of different genealogical tree spaces on simulations to study the settings that favor coarser resolutions. We apply our method to estimate the cardinality of genealogical tree spaces from mtDNA data from the 1000 genomes and a sample from a Melanesian population at the β-globin locus.

Genetic profiles of 103,106 individuals in the Taiwan Biobank provide insights into the health and history of Han Chinese

Personalized medical care focuses on prediction of disease risk and response to medications. To build the risk models, access to both large-scale genomic resources and human genetic studies is required. The Taiwan Biobank (TWB) has generated high-coverage, whole-genome sequencing data from 1492 individuals and genome-wide SNP data from 103,106 individuals of Han Chinese ancestry using custom SNP arrays. Principal components analysis of the genotyping data showed that the full range of Han Chinese genetic variation was found in the cohort. The arrays also include thousands of known functional variants, allowing for simultaneous ascertainment of Mendelian disease-causing mutations and variants that affect drug metabolism. We found that 21.2% of the population are mutation carriers of autosomal recessive diseases, 3.1% have mutations in cancer-predisposing genes, and 87.3% carry variants that affect drug response. We highlight how TWB data provide insight into both population history and disease burden, while showing how widespread genetic testing can be used to improve clinical care.

Sequencing of 53,831 diverse genomes from the NHLBI TOPMed Program

The Trans-Omics for Precision Medicine (TOPMed) programme seeks to elucidate the genetic architecture and biology of heart, lung, blood and sleep disorders, with the ultimate goal of improving diagnosis, treatment and prevention of these diseases. The initial phases of the programme focused on whole-genome sequencing of individuals with rich phenotypic data and diverse backgrounds. Here we describe the TOPMed goals and design as well as the available resources and early insights obtained from the sequence data. The resources include a variant browser, a genotype imputation server, and genomic and phenotypic data that are available through dbGaP (Database of Genotypes and Phenotypes)1. In the first 53,831 TOPMed samples, we detected more than 400 million single-nucleotide and insertion or deletion variants after alignment with the reference genome. Additional previously undescribed variants were detected through assembly of unmapped reads and customized analysis in highly variable loci. Among the more than 400 million detected variants, 97% have frequencies of less than 1% and 46% are singletons that are present in only one individual (53% among unrelated individuals). These rare variants provide insights into mutational processes and recent human evolutionary history. The extensive catalogue of genetic variation in TOPMed studies provides unique opportunities for exploring the contributions of rare and noncoding sequence variants to phenotypic variation. Furthermore, combining TOPMed haplotypes with modern imputation methods improves the power and reach of genome-wide association studies to include variants down to a frequency of approximately 0.01%.

A Computational Approach for Modeling the Allele Frequency Spectrum of Populations with Arbitrarily Varying Size

The allele frequency spectrum (AFS), or site frequency spectrum, is commonly used to summarize the genomic polymorphism pattern of a sample, which is informative for inferring population history and detecting natural selection. In 2013, Chen and Chen developed a method for analytically deriving the AFS for populations with temporally varying size through the coalescence time-scaling function. However, their approach is only applicable to population history scenarios in which the analytical form of the time-scaling function is tractable. In this paper, we propose a computational approach to extend the method to populations with arbitrary complex varying size by numerically approximating the time-scaling function. We demonstrate the performance of the approach by constructing the AFS for two population history scenarios: the logistic growth model and the Gompertz growth model, for which the AFS are unavailable with existing approaches. Software for implementing the algorithm can be downloaded at http://chenlab.big.ac.cn/software/.

Methods for Estimating Demography and Detecting Between-Locus Differences in the Effective Population Size and Mutation Rate

It is known that the effective population size (N_e) and the mutation rate (u) vary across the genome. Here, we show that ignoring this heterogeneity may lead to biased estimates of past demography. To solve the problem, we develop new methods for jointly inferring past changes in population size and detecting variation in N_e and u between loci. These methods rely on either polymorphism data alone or both polymorphism and divergence data. In addition to inferring demography, we can use the methods to study a variety of questions: 1) comparing sex chromosomes with autosomes (for finding evidence for male-driven evolution, an unequal sex ratio, or sex-biased demographic changes) and 2) analyzing multilocus data from within autosomes or sex chromosomes (for studying determinants of variability in N_e and u). Simulations suggest that the methods can provide accurate parameter estimates and have substantial statistical power for detecting difference in N_e and u. As an example, we use the methods to analyze a polymorphism data set from Drosophila simulans. We find clear evidence for rapid population expansion. The results also indicate that the autosomes have a higher mutation rate than the X chromosome and that the sex ratio is probably female-biased. The new methods have been implemented in a user-friendly package.

Genomic inference using diffusion models and the allele frequency spectrum

Evolutionary, biological, and demographic processes together shape observed variation in populations. Understanding how these processes influence variation allows us to infer past demography and the nature of selection in populations. Forward in time models such as the diffusion approximation provide a powerful tool for performing inference based on the distribution of allele frequencies. Here, we discuss recent computational developments and their application to reconstructing human demographic history. Using whole-genome sequence data for 797 French Canadian individuals, we assess the neutrality of synonymous variants and show that selection can bias inferred demography, mutation rates, and distributions of fitness effects. We argue that the simple evolutionary models investigated by Kimura and Ohta still provide important insight into modern genetic research.

Non-parametric estimation of population size changes from the site frequency spectrum

Changes in population size is a useful quantity for understanding the evolutionary history of a species. Genetic variation within a species can be summarized by the site frequency spectrum (SFS). For a sample of size n, the SFS is a vector of length n - 1 where entry i is the number of sites where the mutant base appears i times and the ancestral base appears n - i times. We present a new method, CubSFS, for estimating the changes in population size of a panmictic population from an observed SFS. First, we provide a straightforward proof for the expression of the expected site frequency spectrum depending only on the population size. Our derivation is based on an eigenvalue decomposition of the instantaneous coalescent rate matrix. Second, we solve the inverse problem of determining the changes in population size from an observed SFS. Our solution is based on a cubic spline for the population size. The cubic spline is determined by minimizing the weighted average of two terms, namely (i) the goodness of fit to the observed SFS, and (ii) a penalty term based on the smoothness of the changes. The weight is determined by cross-validation. The new method is validated on simulated demographic histories and applied on unfolded and folded SFS from 26 different human populations from the 1000 Genomes Project.

Population genomic analysis of elongated skulls reveals extensive female-biased immigration in Early Medieval Bavaria

Many modern European states trace their roots back to a period known as the Migration Period that spans from Late Antiquity to the early Middle Ages. We have conducted the first population-level analysis of people from this era, generating genomic data from 41 graves from archaeological sites in present-day Bavaria in southern Germany mostly dating to around 500 AD. While they are predominantly of northern/central European ancestry, we also find significant evidence for a nonlocal genetic provenance that is highly enriched among resident Early Medieval women, demonstrating artificial skull deformation. We infer that the most likely origin of the majority of these women was southeastern Europe, resolving a debate that has lasted for more than half a century.

Modern European genetic structure demonstrates strong correlations with geography, while genetic analysis of prehistoric humans has indicated at least two major waves of immigration from outside the continent during periods of cultural change. However, population-level genome data that could shed light on the demographic processes occurring during the intervening periods have been absent. Therefore, we generated genomic data from 41 individuals dating mostly to the late 5th/early 6th century AD from present-day Bavaria in southern Germany, including 11 whole genomes (mean depth 5.56×). In addition we developed a capture array to sequence neutral regions spanning a total of 5 Mb and 486 functional polymorphic sites to high depth (mean 72×) in all individuals. Our data indicate that while men generally had ancestry that closely resembles modern northern and central Europeans, women exhibit a very high genetic heterogeneity; this includes signals of genetic ancestry ranging from western Europe to East Asia. Particularly striking are women with artificial skull deformations; the analysis of their collective genetic ancestry suggests an origin in southeastern Europe. In addition, functional variants indicate that they also differed in visible characteristics. This example of female-biased migration indicates that complex demographic processes during the Early Medieval period may have contributed in an unexpected way to shape the modern European genetic landscape. Examination of the panel of functional loci also revealed that many alleles associated with recent positive selection were already at modern-like frequencies in European populations ∼1,500 years ago.

Forward and backward evolutionary processes and allele frequency spectrum in a cancer cell population

A cancer grows from a single cell, thereby constituting a large cell population. In this work, we are interested in how mutations accumulate in a cancer cell population. We provide a theoretical framework of the stochastic process in a cancer cell population and obtain near exact expressions of allele frequency spectrum or AFS (only continuous approximation is involved) from both forward and backward treatments under a simple setting; all cells undergo cell divisions and die at constant rates, b and d, respectively, such that the entire population grows exponentially. This setting means that once a parental cancer cell is established, in the following growth phase, all mutations are assumed to have no effect on b or d (i.e., neutral or passengers). Our theoretical results show that the difference from organismal population genetics is mainly in the coalescent time scale, and the mutation rate is defined per cell division, not per time unit (e.g., generation). Except for these two factors, the basic logic is very similar between organismal and cancer population genetics, indicating that a number of well established theories of organismal population genetics could be translated to cancer population genetics with simple modifications.

Inferring Recent Demography from Isolation by Distance of Long Shared Sequence Blocks

Recently it has become feasible to detect long blocks of nearly identical sequence shared between pairs of genomes. These identity-by-descent (IBD) blocks are direct traces of recent coalescence events and, as such, contain ample signal to infer recent demography. Here, we examine sharing of such blocks in two-dimensional populations with local migration. Using a diffusion approximation to trace genetic ancestry, we derive analytical formulas for patterns of isolation by distance of IBD blocks, which can also incorporate recent population density changes. We introduce an inference scheme that uses a composite-likelihood approach to fit these formulas. We then extensively evaluate our theory and inference method on a range of scenarios using simulated data. We first validate the diffusion approximation by showing that the theoretical results closely match the simulated block-sharing patterns. We then demonstrate that our inference scheme can accurately and robustly infer dispersal rate and effective density, as well as bounds on recent dynamics of population density. To demonstrate an application, we use our estimation scheme to explore the fit of a diffusion model to Eastern European samples in the Population Reference Sample data set. We show that ancestry diffusing with a rate of [Formula: see text] during the last centuries, combined with accelerating population growth, can explain the observed exponential decay of block sharing with increasing pairwise sample distance.

Explosive genetic evidence for explosive human population growth

The advent of next-generation sequencing technology has allowed the collection of vast amounts of genetic variation data. A recurring discovery from studying larger and larger samples of individuals had been the extreme, previously unexpected, excess of very rare genetic variants, which has been shown to be mostly due to the recent explosive growth of human populations. Here, we review recent literature that inferred recent changes in population size in different human populations and with different methodologies, with many pointing to recent explosive growth, especially in European populations for which more data has been available. We also review the state-of-the-art methods and software for the inference of historical population size changes that lead to these discoveries. Finally, we discuss the implications of recent population growth on personalized genomics, on purifying selection in the non-equilibrium state it entails and, as a consequence, on the genetic architecture underlying complex disease and the performance of mapping methods in discovering rare variants that contribute to complex disease risk.

Effects of Linked Selective Sweeps on Demographic Inference and Model Selection

The availability of large-scale population genomic sequence data has resulted in an explosion in efforts to infer the demographic histories of natural populations across a broad range of organisms. As demographic events alter coalescent genealogies, they leave detectable signatures in patterns of genetic variation within and between populations. Accordingly, a variety of approaches have been designed to leverage population genetic data to uncover the footprints of demographic change in the genome. The vast majority of these methods make the simplifying assumption that the measures of genetic variation used as their input are unaffected by natural selection. However, natural selection can dramatically skew patterns of variation not only at selected sites, but at linked, neutral loci as well. Here we assess the impact of recent positive selection on demographic inference by characterizing the performance of three popular methods through extensive simulation of data sets with varying numbers of linked selective sweeps. In particular, we examined three different demographic models relevant to a number of species, finding that positive selection can bias parameter estimates of each of these models-often severely. We find that selection can lead to incorrect inferences of population size changes when none have occurred. Moreover, we show that linked selection can lead to incorrect demographic model selection, when multiple demographic scenarios are compared. We argue that natural populations may experience the amount of recent positive selection required to skew inferences. These results suggest that demographic studies conducted in many species to date may have exaggerated the extent and frequency of population size changes.

The Site Frequency Spectrum for General Coalescents

General genealogical processes such as Λ- and Ξ-coalescents, which respectively model multiple and simultaneous mergers, have important applications in studying marine species, strong positive selection, recurrent selective sweeps, strong bottlenecks, large sample sizes, and so on. Recently, there has been significant progress in developing useful inference tools for such general models. In particular, inference methods based on the site frequency spectrum (SFS) have received noticeable attention. Here, we derive a new formula for the expected SFS for general Λ- and Ξ-coalescents, which leads to an efficient algorithm. For time-homogeneous coalescents, the runtime of our algorithm for computing the expected SFS is O(n2) where n is the sample size. This is a factor of[Formula: see text]faster than the state-of-the-art method. Furthermore, in contrast to existing methods, our method generalizes to time-inhomogeneous Λ- and Ξ-coalescents with measures that factorize as[Formula: see text] and [Formula: see text]respectively, where ζ denotes a strictly positive function of time. The runtime of our algorithm in this setting is[Formula: see text]We also obtain general theoretical results for the identifiability of the Λ measure when ζ is a constant function, as well as for the identifiability of the function ζ under a fixed Ξ measure.