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

... As a Dynamic Result of Gesture

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Stability and response of polygenic traits to stabilizing selection and mutation

When polygenic traits are under stabilizing selection, many different combinations of alleles allow close adaptation to the optimum. If alleles have equal effects, all combinations that result in the same deviation from the optimum are equivalent. Furthermore, the genetic variance that is maintained by mutation-selection balance is $2 \mu/S$ per locus, where $\mu$ is the mutation rate and $S$ the strength of stabilizing selection. In reality, alleles vary in their effects, making the fitness landscape asymmetric, and complicating analysis of the equilibria. We show that that the resulting genetic variance depends on the fraction of alleles near fixation, which contribute by $2 \mu/S$, and on the total mutational effects of alleles that are at intermediate frequency. The interplay between stabilizing selection and mutation leads to a sharp transition: alleles with effects smaller than a threshold value of $2\sqrt{\mu / S}$ remain polymorphic, whereas those with larger effects are fixed. The genetic load in equilibrium is less than for traits of equal effects, and the fitness equilibria are more similar. We find that if the optimum is displaced, alleles with effects close to the threshold value sweep first, and their rate of increase is bounded by $\sqrt{\mu S}$. Long term response leads in general to well-adapted traits, unlike the case of equal effects that often end up at a sub-optimal fitness peak. However, the particular peaks to which the populations converge are extremely sensitive to the initial states, and to the speed of the shift of the optimum trait value.Comment: Accepted in Genetic

The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population

We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the biological process. We focus on the growth of fixation times with the number of subpopulations, and variation of fixation probabilities and times with initial distributions of mutants. A general formula for the fixation probability for arbitrary initial condition is derived by extending a duality relation between forwards- and backwards-time properties of the model from a panmictic to a subdivided population. From this we obtain new formulae, formally exact in the limit of extremely weak migration, for the mean fixation time from an arbitrary initial condition for Wright's island model, presenting two cases as examples. For more general models of population subdivision, formulae are introduced for an arbitrary number of mutants that are randomly located, and a single mutant whose position is known. These formulae contain parameters that typically have to be obtained numerically, a procedure we follow for two contrasting clustered models. These data suggest that variation of fixation time with the initial condition is slight, but depends strongly on the nature of subdivision. In particular, we demonstrate conditions under which the fixation time remains finite even in the limit of an infinite number of demes. In many cases - except this last where fixation in a finite time is seen - the time to fixation is shown to be in precise agreement with predictions from formulae for the asymptotic effective population size.Comment: 17 pages, 8 figures, requires elsart5p.cls; substantially revised and improved version; accepted for publication in Theoretical Population Biolog