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Register a new userBayesian inference of natural selection from allele frequency time series
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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.
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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.
Here we introduce a general class of multiple calibration birth-death tree priors for use in Bayesian phylogenetic inference. All tree priors in this class separate ancestral node heights into a set of calibrated nodes and uncalibrated nodes such that the marginal distribution of the calibrated nodes is user-specified whereas the density ratio of the birth-death prior is retained for trees with equal values for the calibrated nodes. We describe two formulations, one in which the calibration information informs the prior on ranked tree topologies, through the (conditional) prior, and the other which factorizes the prior on divergence times and ranked topologies, thus allowing uniform, or any arbitrary prior distribution on ranked topologies. While the first of these formulations has some attractive properties the algorithm we present for computing its prior density is computationally intensive. On the other hand, the second formulation is always computationally efficient. We demonstrate the utility of the new class of multiple-calibration tree priors using both small simulations and a real-world analysis and compare the results to existing schemes. The two new calibrated tree priors described in this paper offer greater flexibility and control of prior specification in calibrated time-tree inference and divergence time dating, and will remove the need for indirect approaches to the assessment of the combined effect of calibration densities and tree process priors in Bayesian phylogenetic inference.
Suppose we have $n$ different types of self-replicating entity, with the population $P_i$ of the $i$th type changing at a rate equal to $P_i$ times the fitness $f_i$ of that type. Suppose the fitness $f_i$ is any continuous function of all the populations $P_1, dots, P_n$. Let $p_i$ be the fraction of replicators that are of the $i$th type. Then $p = (p_1, dots, p_n)$ is a time-dependent probability distribution, and we prove that its speed as measured by the Fisher information metric equals the variance in fitness. In rough terms, this says that the speed at which information is updated through natural selection equals the variance in fitness. This result can be seen as a modified version of Fishers fundamental theorem of natural selection. We compare it to Fishers original result as interpreted by Price, Ewens and Edwards.
In this article, we propose new Bayesian methods for selecting and estimating a sparse coefficient vector for skewed heteroscedastic response. Our novel Bayesian procedures effectively estimate the median and other quantile functions, accommodate non-local prior for regression effects without compromising ease of implementation via sampling based tools, and asymptotically select the true set of predictors even when the number of covariates increases in the same order of the sample size. We also extend our method to deal with some observations with very large errors. Via simulation studies and a re-analysis of a medical cost study with large number of potential predictors, we illustrate the ease of implementation and other practical advantages of our approach compared to existing methods for such studies.
We present a Bayesian reconstruction algorithm to generate unbiased samples of the underlying dark matter field from halo catalogues. Our new contribution consists of implementing a non-Poisson likelihood including a deterministic non-linear and scale-dependent bias. In particular we present the Hamiltonian equations of motions for the negative binomial (NB) probability distribution function. This permits us to efficiently sample the posterior distribution function of density fields given a sample of galaxies using the Hamiltonian Monte Carlo technique implemented in the Argo code. We have tested our algorithm with the Bolshoi $N$-body simulation at redshift $z = 0$, inferring the underlying dark matter density field from sub-samples of the halo catalogue with biases smaller and larger than one. Our method shows that we can draw closely unbiased samples (compatible within 1-$sigma$) from the posterior distribution up to scales of about $k$~1 h/Mpc in terms of power-spectra and cell-to-cell correlations. We find that a Poisson likelihood yields reconstructions with power spectra deviating more than 10% at $k$=0.2 h/Mpc. Our reconstruction algorithm is especially suited for emission line galaxy data for which a complex non-linear stochastic biasing treatment beyond Poissonity becomes indispensable.
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