Using Ancient Samples in Projection Analysis.

Projection analysis is a tool that extracts information from the joint allele frequency spectrum to better understand the relationship between two populations. In projection analysis, a test genome is compared to a set of genomes from a reference population. The projection's shape depends on the historical relationship of the test genome's population to the reference population. Here, we explore in greater depth the effects on the projection when ancient samples are included in the analysis. First, we conduct a series of simulations in which the ancient sample is directly ancestral to a present-day population (one-population model), or the ancient sample is ancestral to a sister population that diverged before the time of sampling (two-population model). We find that there are characteristic differences between the projections for the one-population and two-population models, which indicate that the projection can be used to determine whether a test genome is directly ancestral to a present-day population or not. Second, we compute projections for several published ancient genomes. We compare two Neanderthals and three ancient human genomes to European, Han Chinese and Yoruba reference panels. We use a previously constructed demographic model and insert these five ancient genomes to assess how well the observed projections are recovered

Non-equilibrium theory of the allele frequency spectrum

A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection and varying population size, the boundary condition is $\lim_{x \downarrow 0} x f(x,t)=\theta \rho(t)$, where $f(\cdot,t)$ is the frequency spectrum of derived alleles at independent loci at time $t$ and $\rho(t)$ is the relative population size at time $t$. When population size and selection intensity are independent of time, the forward equation is equivalent to the backwards diffusion usually used to derive the frequency spectrum, but the forward equation allows computation of the time dependence of the spectrum both before an equilibrium is attained and when population size and selection intensity vary with time. From the diffusion equation, we derive a set of ordinary differential equations for the moments of $f(\cdot,t)$ and express the expected spectrum of a finite sample in terms of those moments. We illustrate the use of the forward equation by considering neutral and selected alleles in a highly simplified model of human history. For example, we show that approximately 30% of the expected heterozygosity of neutral loci is attributable to mutations that arose since the onset of population growth in roughly the last $150,000$ years.Comment: 24 pages, 7 figures, updated to accomodate referees' suggestions, to appear in Theoretical Population Biolog

Bayesian inference of natural selection from allele frequency time series

The advent of accessible ancient DNA technology now allows the direct ascertainment of allele frequencies in ancestral populations, thereby enabling the use of allele frequency time series to detect and estimate natural selection. Such direct observations of allele frequency dynamics are expected to be more powerful than inferences made using patterns of linked neutral variation obtained from modern individuals. We develop a Bayesian method to make use of allele frequency time series data and infer the parameters of general diploid selection, along with allele age, in non-equilibrium populations. We introduce a novel path augmentation approach, in which we use Markov chain Monte Carlo to integrate over the space of allele frequency trajectories consistent with the observed data. Using simulations, we show that this approach has good power to estimate selection coefficients and allele age. Moreover, when applying our approach to data on horse coat color, we find that ignoring a relevant demographic history can significantly bias the results of inference. Our approach is made available in a C++ software package.Comment: 27 page

The influence of relatives on the efficiency and error rate of familial searching

We investigate the consequences of adopting the criteria used by the state of California, as described by Myers et al. (2011), for conducting familial searches. We carried out a simulation study of randomly generated profiles of related and unrelated individuals with 13-locus CODIS genotypes and YFiler Y-chromosome haplotypes, on which the Myers protocol for relative identification was carried out. For Y-chromosome sharing first degree relatives, the Myers protocol has a high probability (80 - 99%) of identifying their relationship. For unrelated individuals, there is a low probability that an unrelated person in the database will be identified as a first-degree relative. For more distant Y-haplotype sharing relatives (half-siblings, first cousins, half-first cousins or second cousins) there is a substantial probability that the more distant relative will be incorrectly identified as a first-degree relative. For example, there is a 3 - 18% probability that a first cousin will be identified as a full sibling, with the probability depending on the population background. Although the California familial search policy is likely to identify a first degree relative if his profile is in the database, and it poses little risk of falsely identifying an unrelated individual in a database as a first-degree relative, there is a substantial risk of falsely identifying a more distant Y-haplotype sharing relative in the database as a first-degree relative, with the consequence that their immediate family may become the target for further investigation. This risk falls disproportionately on those ethnic groups that are currently overrepresented in state and federal databases.Comment: main text: 19 pages, 4 tables, 2 figures supplemental text: 2 pages, 5 tables all together as single fil

Detecting range expansions from genetic data

We propose a method that uses genetic data to test for the occurrence of a recent range expansion and to infer the location of the origin of the expansion. We introduce a statistic for pairs of populations $\psi$ (the directionality index) that detects asymmetries in the two-dimensional allele frequency spectrum caused by the series of founder events that happen during an expansion. Such asymmetry arises because low frequency alleles tend to be lost during founder events, thus creating clines in the frequencies of surviving low-frequency alleles. Using simulations, we further show that $\psi$ is more powerful for detecting range expansions than both $F_{ST}$ and clines in heterozygosity. We illustrate the utility of $\psi$ by applying it to a data set from modern humans and show how we can include more complicated scenarios such as multiple expansion origins or barriers to migration in the model

Inference of Microbial Recombination Rates from Metagenomic Data

Metagenomic sequencing projects from environments dominated by a small number of species produce genome-wide population samples. We present a two-site composite likelihood estimator of the scaled recombination rate, ρ = 2Nec, that operates on metagenomic assemblies in which each sequenced fragment derives from a different individual. This new estimator properly accounts for sequencing error, as quantified by per-base quality scores, and missing data, as inferred from the placement of reads in a metagenomic assembly. We apply our estimator to data from a sludge metagenome project to demonstrate how this method will elucidate the rates of exchange of genetic material in natural microbial populations. Surprisingly, for a fixed amount of sequencing, this estimator has lower variance than similar methods that operate on more traditional population genetic samples of comparable size. In addition, we can infer variation in recombination rate across the genome because metagenomic projects sample genetic diversity genome-wide, not just at particular loci. The method itself makes no assumption specific to microbial populations, opening the door for application to any mixed population sample where the number of individuals sampled is much greater than the number of fragments sequenced

The Geographic Spread of the CCR5 Δ32 HIV-Resistance Allele

The Δ32 mutation at the CCR5 locus is a well-studied example of natural selection acting in humans. The mutation is found principally in Europe and western Asia, with higher frequencies generally in the north. Homozygous carriers of the Δ32 mutation are resistant to HIV-1 infection because the mutation prevents functional expression of the CCR5 chemokine receptor normally used by HIV-1 to enter CD4+ T cells. HIV has emerged only recently, but population genetic data strongly suggest Δ32 has been under intense selection for much of its evolutionary history. To understand how selection and dispersal have interacted during the history of the Δ32 allele, we implemented a spatially explicit model of the spread of Δ32. The model includes the effects of sampling, which we show can give rise to local peaks in observed allele frequencies. In addition, we show that with modest gradients in selection intensity, the origin of the Δ32 allele may be relatively far from the current areas of highest allele frequency. The geographic distribution of the Δ32 allele is consistent with previous reports of a strong selective advantage (>10%) for Δ32 carriers and of dispersal over relatively long distances (>100 km/generation). When selection is assumed to be uniform across Europe and western Asia, we find support for a northern European origin and long-range dispersal consistent with the Viking-mediated dispersal of Δ32 proposed by G. Lucotte and G. Mercier. However, when we allow for gradients in selection intensity, we estimate the origin to be outside of northern Europe and selection intensities to be strongest in the northwest. Our results describe the evolutionary history of the Δ32 allele and establish a general methodology for studying the geographic distribution of selected alleles

Testing for ancient admixture between closely related populations.

Abstract One enduring question in evolutionary biology is the extent of archaic admixture in the genomes of present-day populations. In this paper, we present a test for ancient admixture that exploits the asymmetry in the frequencies of the two nonconcordant gene trees in a three-population tree. This test was first applied to detect interbreeding between Neandertals and modern humans. We derive the analytic expectation of a test statistic, called the D statistic, which is sensitive to asymmetry under alternative demographic scenarios. We show that the D statistic is insensitive to some demographic assumptions such as ancestral population sizes and requires only the assumption that the ancestral populations were randomly mating. An important aspect of D statistics is that they can be used to detect archaic admixture even when no archaic sample is available. We explore the effect of sequencing error on the false-positive rate of the test for admixture, and we show how to estimate the proportion of archaic ancestry in the genomes of present-day populations. We also investigate a model of subdivision in ancestral populations that can result in D statistics that indicate recent admixture