Four estimators of the directed information rate between a pair of jointly stationary ergodic finite-alphabet processes are proposed, based on universal probability assignments. The first one is a Shannon--McMillan--Breiman type estimator, similar to those used by Verd\'u (2005) and Cai, Kulkarni, and Verd\'u (2006) for estimation of other information measures. We show the almost sure and $L_1$ convergence properties of the estimator for any underlying universal probability assignment. The other three estimators map universal probability assignments to different functionals, each exhibiting relative merits such as smoothness, nonnegativity, and boundedness. We establish the consistency of these estimators in almost sure and $L_1$ senses, and derive near-optimal rates of convergence in the minimax sense under mild conditions. These estimators carry over directly to estimating other information measures of stationary ergodic finite-alphabet processes, such as entropy rate and mutual information rate, with near-optimal performance and provide alternatives to classical approaches in the existing literature. Guided by these theoretical results, the proposed estimators are implemented using the context-tree weighting algorithm as the universal probability assignment. Experiments on synthetic and real data are presented, demonstrating the potential of the proposed schemes in practice and the utility of directed information estimation in detecting and measuring causal influence and delay.Comment: 23 pages, 10 figures, to appear in IEEE Transactions on Information Theor
We used whole-genome resequencing data from a population of Drosophila melanogaster to investigate the causes of the negative correlation between the within-population synonymous nucleotide site diversity (π S ) of a gene and its degree of divergence from related species at nonsynonymous nucleotide sites (K A ). By using the estimated distributions of mutational effects on fitness at nonsynonymous and UTR sites, we predicted the effects of background selection at sites within a gene on π S and found that these could account for only part of the observed correlation between π S and K A . We developed a model of the effects of selective sweeps that included gene conversion as well as crossing over. We used this model to estimate the average strength of selection on positively selected mutations in coding sequences and in UTRs, as well as the proportions of new mutations that are selectively advantageous. Genes with high levels of selective constraint on nonsynonymous sites were found to have lower strengths of positive selection and lower proportions of advantageous mutations than genes with low levels of constraint. Overall, background selection and selective sweeps within a typical gene reduce its synonymous diversity to ∼75% of its value in the absence of selection, with larger reductions for genes with high K A . Gene conversion has a major effect on the estimates of the parameters of positive selection, such that the estimated strength of selection on favorable mutations is greatly reduced if it is ignored. background selection | selective sweeps | sequence diversity | gene conversion | Drosophila melanogaster
The transitions from foraging to farming and later to pastoralism in Stone Age Eurasia (c. 11-3 thousand years before present, BP) represent some of the most dramatic lifestyle changes in human evolution. We sequenced 317 genomes of primarily Mesolithic and Neolithic individuals from across Eurasia combined with radiocarbon dates, stable isotope data, and pollen records. Genome imputation and co-analysis with previously published shotgun sequencing data resulted in >1600 complete ancient genome sequences offering fine-grained resolution into the Stone Age populations. We observe that: 1) Hunter-gatherer groups were more genetically diverse than previously known, and deeply divergent between western and eastern Eurasia. 2) We identify hitherto genetically undescribed hunter-gatherers from the Middle Don region that contributed ancestry to the later Yamnaya steppe pastoralists; 3) The genetic impact of the Neolithic transition was highly distinct, east and west of a boundary zone extending from the Black Sea to the Baltic. Large-scale shifts in genetic ancestry occurred to the west of this "Great Divide", including an almost complete replacement of hunter-gatherers in Denmark, while no substantial ancestry shifts took place during the same period to the east. This difference is also reflected in genetic relatedness within the populations, decreasing substantially in the west but not in the east where it remained high until c. 4,000 BP; 4) The second major genetic transformation around 5,000 BP happened at a much faster pace with Steppe-related ancestry reaching most parts of Europe within 1,000-years. Local Neolithic farmers admixed with incoming pastoralists in eastern, western, and southern Europe whereas Scandinavia experienced another near-complete population replacement. Similar dramatic turnover-patterns are evident in western Siberia; 5) Extensive regional differences in the ancestry components involved in these early events remain visible to this day, even within countries. Neolithic farmer ancestry is highest in southern and eastern England while Steppe-related ancestry is highest in the Celtic populations of Scotland, Wales, and Cornwall (this research has been conducted using the UK Biobank resource); 6) Shifts in diet, lifestyle and environment introduced new selection pressures involving at least 21 genomic regions. Most such variants were not universally selected across populations but were only advantageous in particular ancestral backgrounds. Contrary to previous claims, we find that selection on the FADS regions, associated with fatty acid metabolism, began before the Neolithisation of Europe. Similarly, the lactase persistence allele started increasing in frequency before the expansion of Steppe-related groups into Europe and has continued to increase up to the present. Along the genetic cline separating Mesolithic hunter-gatherers from Neolithic farmers, we find significant correlations with trait associations related to skin disorders, diet and lifestyle and mental health status, suggesting marked phenotypic differences between these groups with very different lifestyles. This work provides new insights into major transformations in recent human evolution, elucidating the complex interplay between selection and admixture that shaped patterns of genetic variation in modern populations.
In small populations, genetic linkage between a polymorphic neutral locus and loci subject to selection, either against partially recessive mutations or in favor of heterozygotes, may result in an apparent selective advantage to heterozygotes at the neutral locus (associative overdominance) and a retardation of the rate of loss of variability by genetic drift at this locus. In large populations, selection against deleterious mutations has previously been shown to reduce variability at linked neutral loci (background selection). We describe analytical, numerical, and simulation studies that shed light on the conditions under which retardation vs. acceleration of loss of variability occurs at a neutral locus linked to a locus under selection. We consider a finite, randomly mating population initiated from an infinite population in equilibrium at a locus under selection. With mutation and selection, retardation occurs only when S, the product of twice the effective population size and the selection coefficient, is of order 1. With S .. 1, background selection always causes an acceleration of loss of variability. Apparent heterozygote advantage at the neutral locus is, however, always observed when mutations are partially recessive, even if there is an accelerated rate of loss of variability. With heterozygote advantage at the selected locus, loss of variability is nearly always retarded. The results shed light on experiments on the loss of variability at marker loci in laboratory populations and on the results of computer simulations of the effects of multiple selected loci on neutral variability.KEYWORDS associative overdominance; background selection; deleterious mutations; heterozygote advantage; neutral variability T HERE has recently been much interest in the effects of selection at one locus on patterns of evolution and variation at linked neutral or nearly neutral loci, with mounting evidence for such effects from surveys of genome-wide patterns of molecular variability and evolution (Cutter and Payseur 2013;Neher 2013;Charlesworth and Campos 2014). Attention has especially been directed at the possibility of enhanced neutral variability at nucleotide sites that are closely linked to sites under long-term balancing selection (Charlesworth 2006;Gao et al. 2015) and at the reduction in variability caused by the hitchhiking effects of directional selection, involving either positive selection (selective sweeps) (Maynard Smith and Haigh 1974) or negative selection (background selection) (Charlesworth et al. 1993). There seems little doubt that such linkage effects play an important role in shaping patterns of variability across the genome (Cutter and Payseur 2013;Charlesworth and Campos 2014).Recent studies have, however, made little or no reference to classical work on associative overdominance (AOD), dating back to .40 years ago. Following a proposal by Frydenberg (1963), who coined the term, it was shown by Sved (1968, 1971, 1972) and by Ohta and Kimura (1970;Ohta , 1973) that linkage disequilibriu...
Viruses exist within hosts at large population sizes and are subject to high rates of mutation. As such, viral populations exhibit considerable sequence diversity. A variety of summary statistics have been developed which describe, in a single number, the extent of diversity in a viral population; such measurements allow the diversities of different populations to be compared, and the effect of evolutionary forces on a population to be assessed. Here we highlight statistical artefacts underlying some common measures of sequence diversity, whereby variation in the depth of genome sequencing may substantially affect the extent of diversity measured in a viral population, making comparisons of population diversity invalid. Specifically, naive estimation of sequence entropy provides a systematically biased metric, a lower read depth being expected to produce a lower estimate of diversity. The number of polymorphic loci per kilobase of genome is more unpredictably affected by read depth, giving potentially flawed results at lower sequencing depths. We show that the nucleotide diversity statistic π provides an unbiased estimate of diversity in the sense that the expected value of the statistic is equal to the correct value of the property being measured. Our results are of importance for studies interpreting genome sequence data; we describe how diversity may be assessed in viral populations in a fair and unbiased manner.
A combination of favipiravir and zanamivir successfully cleared influenza B infection in a child who had undergone bone marrow transplant for X-linked severe combined immunodeficiency, with no recovery of T lymphocytes. Deep sequencing of viral samples illuminated the within-host dynamics of infection, demonstrating the effectiveness of favipiravir in this case.
Electronically-conducting polymers are a remarkable class of materials that can be used as electrode, interconnect and active layers in organic electronics, [1] such as thin-film transistors (OTFTs), light-emitting diodes (OLEDs), electrochromic devices, [2,3] super-capacitors, [4] actuators [5] and biosensors. [6] A particularly important member is p-type poly(3,4-ethylenedioxythiophene) (PEDT) doped in poly(styrenesulfonic acid) (PSSH), which has unprecedented thermal and electrochemical stability. [1,3,[7][8][9] We provide direct evidence here, however, that it undergoes injection de-doping by an electric current when stress-biased beyond a few tens of kV cm -1 between gold and other electrodes. Charge modulation spectroscopy shows that the oxidation state of PEDT decreases as holes are extracted marginally faster than they are injected. The decrease becomes locked-in when coupled to a compensating electrochemical oxidation of the counter-ion. In PEDT:PSSH this leads to a sharp fall in the doping level across the electrode gap, particularly at the negative contact, as evidenced by micro-Raman spectroscopy. Impedance spectroscopy gives the de-doped insulating width as of the order of tens of nm, which appears to be self-limited. This mechanism is the origin of the deep conductor-to-insulator transformation in PEDT:PSSH [10] and perhaps also other conducting polymers.[11] By substituting the acidic H + in the counter polyelectrolyte with the neutral and larger tetramethylammonium (TMA) ion, it is possible to shut down the electrochemistry and raise the electric field threshold for permanent de-doping by one order of magnitude.PEDT:PSSH has proven to be a particularly versatile conducting polymer with a DC conductivity (r DC ) tune-able over several orders of magnitude (10 1 to 10 -6 S cm -1 ) by matrix dilution and/or solvent treatment [12] to suit particular applications. It is obtained by persulfate oxidation of 3,4-ethylenedioxythiophene in the presence of PSSH, [1] to give a PSSH-rich inter-polyelectrolyte complex that is water-soluble and solution-processable.[13] PEDT:PSSH is strongly acidic on account of the excess PSSH, and often contaminated with ions leftover from the oxidation reaction. This excess PSSH may be undesirable in some circumstances. H + can be replaced readily, however, by other M + with a change in workfunction, but not processibility, the PEDT doping level, or its electronic conductivity. [14] Therefore it is appropriate to denote this material PEDT:PSSM, wherein PEDT is "doped" into the PSSM matrix. Figure 1a shows the chemical structure of materials (M = H, TMA) used in this work. We rigorously purified them by dialysis to remove low molecular-weight oligomers and ionic impurities (see Experimental) to be sure that the effects observed are intrinsic and not impurity-related. A further notation: We used "PEDT" here to refer to the material in general, PEDT + to refer to its p-doped positively-charged state, and PEDT 0 to refer to the undoped uncharged state.The PEDT doping level is typ...
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