Bayes Empirical Bayes Research Articles

Complete chloroplast genomes and comparative analysis of Ligustrum species

In this study, we assembled and annotated the chloroplast (cp) genomes of four Ligustrum species, L. sinense, L. obtusifolium, L. vicaryi, and L. ovalifolium ‘Aureum’. Including six other published Ligustrum species, we compared various characteristics such as gene structure, sequence alignment, codon preference, and nucleic acid diversity, and performed positive-selection genes screening and phylogenetic analysis. The results showed that the cp genome of Ligustrum was 162,185–166,800 bp in length, with a circular tetrad structure, including a large single-copy region (86,885–90,106 bp), a small single-copy region (11,446–11,499 bp), and a pair of IRa and IRb sequences with the same coding but in opposite directions (31,608–32,624 bp). This structure is similar to the cp genomes of most angiosperms. We found 132–137 genes in the cp genome of Ligustrum, including 89–90 protein-coding genes, 35–39 tRNAs, and 8 rRNAs. The GC content was 37.93–38.06% and varied among regions, with the IR region having the highest content. The single-nucleotide (A/T)n was dominant in simple-sequence repeats of the Ligustrum cp genome, with an obvious A/T preference. Six hotspot regions were identified from multiple sequence alignment of Ligustrum; the ycf1 gene region and the clpP1 exon region can be used as potential DNA barcodes for the identification and phylogeny of the genus Ligustrum. Branch-site model and Bayes empirical Bayes (BEB) analysis showed that four protein-coding genes (accD, clpP, ycf1, and ycf2) were positively selected, and BEB analysis showed that accD and rpl20 had positively selected sites. A phylogenetic tree of Oleaceae species was constructed based on the whole cp genomes, and the results were consistent with the traditional taxonomic results. The phylogenetic results showed that genus Ligustrum is most closely related to genus Syringa. Our study provides important genetic information to support further investigations of the phylogenetic development and adaptive evolution of Ligustrum species.

Smoothed Bootstrap Aggregation for Assessing Selection Pressure at Amino Acid Sites.

To detect positive selection at individual amino acid sites, most methods use an empirical Bayes approach. After parameters of a Markov process of codon evolution are estimated via maximum likelihood, they are passed to Bayes formula to compute the posterior probability that a site evolved under positive selection. A difficulty with this approach is that parameter estimates with large errors can negatively impact Bayesian classification. By assigning priors to some parameters, Bayes Empirical Bayes (BEB) mitigates this problem. However, as implemented, it imposes uniform priors, which causes it to be overly conservative in some cases. When standard regularity conditions are not met and parameter estimates are unstable, inference, even under BEB, can be negatively impacted. We present an alternative to BEB called smoothed bootstrap aggregation (SBA), which bootstraps site patterns from an alignment of protein coding DNA sequences to accommodate the uncertainty in the parameter estimates. We show that deriving the correction for parameter uncertainty from the data in hand, in combination with kernel smoothing techniques, improves site specific inference of positive selection. We compare BEB to SBA by simulation and real data analysis. Simulation results show that SBA balances accuracy and power at least as well as BEB, and when parameter estimates are unstable, the performance gap between BEB and SBA can widen in favor of SBA. SBA is applicable to a wide variety of other inference problems in molecular evolution.

Adaptive evolution in the S gene of hepatitis B virus from patients with occult HBV infection

Objective To detect the positively selected sites in the surface （ S） gene of hepatitis B viruses （ HBVs） from patients with occult HBV infection and to study the molecular mechanism of occult HBV infection.Methods The sequence of S gene from patients with occult HBV infection and reference strains of eight HBV genotypes （ A through H） were downloaded from GenBank and then alignment analysis were performed by using Clustal W software .Phylogenetic trees were constructed by using MEGA 5.05 soft-ware package.PAML4.7 was used to analyze positively selected sites .Results A total of 1286 HBV se-quences from patients with occult infection were searched in GenBank .One hundred and seventy-four com-plete gene sequences encoding surface S protein were screened after alignment analysis and confirmation , of which 13 sequences with nonsense mutation were removed .The likelihood ratio test showed that for both the 161 remained sequences and the 31 reference sequences , the selection models of M2, M3 and M8 were sig-nificantly better than the neutral models of M0, M1 and M7 （2△lnL〈55.12, P〈0.001）.By using Bayes Empirical Bayes （BEB） analysis, 14 positively selected sites （including codon 3, 8, 40, 45, 46, 47, 49, 68, 126, 127, 164, 184, 207 and 210） were detected in the surface gene of HBVs from patients with occult HBV infection, eight of which were located at the immune epitope of HBsAg .However, only 2 positively se-lected sites were identified in reference sequences .Conclusion The long-lasting persistence of HBV in pa-tients with occult HBV infection might be caused by the adaptive evolution of their surface gene in a form of escape mutant under immune suppressive condition . Key words: Hepatitis B virus; Occult infection; Adaptive evolution

Positive selection of Kranz and non-Kranz C4 phosphoenolpyruvate carboxylase amino acids in Suaedoideae (Chenopodiaceae).

In subfamily Suaedoideae, four independent gains of C4 photosynthesis are proposed, which includes two parallel origins of Kranz anatomy (sections Salsina and Schoberia) and two independent origins of single-cell C4 anatomy (Bienertia and Suaeda aralocaspica). Additional phylogenetic support for this hypothesis was generated from sequence data of the C-terminal portion of the phosphoenolpyruvate carboxylase (PEPC) gene used in C4 photosynthesis (ppc-1) in combination with previous sequence data. ppc-1 sequence was generated for 20 species in Suaedoideae and two outgroup Salsola species that included all types of C4 anatomies as well as two types of C3 anatomies. A branch-site test for positively selected codons was performed using the software package PAML. From labelling of the four branches where C4 is hypothesized to have developed (foreground branches), residue 733 (maize numbering) was identified to be under positive selection with a posterior probability >0.99 and residue 868 at the >0.95 interval using Bayes empirical Bayes (BEB). When labelling all the branches within C4 clades, the branch-site test identified 13 codons to be under selection with a posterior probability >0.95 by BEB; this is discussed considering current information on functional residues. The signature C4 substitution of an alanine for a serine at position 780 in the C-terminal end (which is considered a major determinant of affinity for PEP) was only found in four of the C4 species sampled, while eight of the C4 species and all the C3 species have an alanine residue; indicating that this substitution is not a requirement for C4 function.

Evolutionary genetic analyses of MEF2C gene: Implications for learning and memory in Homo sapiens

MEF2C facilitates context-dependent fear conditioning (CFC) which is a salient aspect of hippocampus-dependent learning and memory. CFC might have played a crucial role in human evolution because of its advantageous influence on survival of species. In this study, we analyzed 23 orthologous mammalian gene sequences of MEF2C gene to examine the evidence for positive selection on this gene in Homo sapiens using Phylogenetic Analysis by Maximum Likelihood (PAML) and HyPhy software. Both PAML Bayes Empirical Bayes (BEB) and HyPhy Fixed Effects Likelihood (FEL) analyses supported significant positive selection on 4 codon sites in H. sapiens. Also, haplotter analysis revealed significant ongoing positive selection on this gene in Central European population. The study findings suggest that adaptive selective pressure on this gene might have influenced human evolution. Further research on this gene might unravel the potential role of this gene in learning and memory as well as its pathogenetic effect in certain hippocampal disorders with evolutionary basis like schizophrenia.

Evolution of mitochondrial-encoded cytochrome oxidase subunits in endothermic fish: The importance of taxon-sampling in codon-based models

While endothermy is ubiquitous in birds and mammals, it is not exclusive to these most recently arisen vertebrate classes. The ability to warm specific organs and/or tissues above ambient temperature (regional endothermy) has evolved at least three times in phylogentically discrete fish lineages: lamnid sharks (Lamnidae), tunas (Scombridae) and billfishes (Istiophoridae and Xiphidae). Given the links between endothermy and metabolic rate, we looked for evidence of convergent molecular evolution in mtDNA-encoded cytochrome c oxidase (COX) subunits in each of these discrete lineages. We found no evidence that the endothermic phenotype in fishes is driven or accompanied by molecular convergence. Though we found little evidence for positively-selected sites in any of the lineages in any subunit, the conclusions were sensitive to the choice of maximum-likelihood model. Several sites identified by Naïve Empirical Bayes (NEB) were not found when Bayes Empirical Bayes (BEB) was employed. As well, conclusions were profoundly influenced by taxon-sampling. Several of the putative sites of positive selection in COX II were no longer apparent as we augmented taxon sampling. The lack of convergent molecular evolution in these remarkable taxa, combined with the profound influence of model choice and taxon sampling provide a cautionary note on the use of rates of non-synonymous to synonymous mutations (dN/dS) to explore questions of the evolution of physiological function.

Bayes Empirical Bayes Classification of Components Using Masked Data

For classification and pattern recognition, it is known that the Bayes decision rule is the best decision rule, which gives the minimum probability of misclassification. The Bayes classifier cannot be immediately applied, since it contains unknown parameters (means, variances, and percentages of k classes). In this study, a set of masked life data is used to establish a Bayes empirical Bayes (BEB) classifier to identify a component in a closed multi-component system whose lifetime is the masked lifetime, such that: (1) it only contains the observations of unclassified masked life data; (2) no other classifier is strictly better than our BEB classifier; and (3) when the number of masked samples increases, the recognition rate of our classifier converges to the rate of the Bayes decision rule. Furthermore, in this article, the BEB estimation leads to a good estimation of each component mean life in the masked system.

Bayes Empirical Bayes Inference of Amino Acid Sites Under Positive Selection

Codon-based substitution models have been widely used to identify amino acid sites under positive selection in comparative analysis of protein-coding DNA sequences. The nonsynonymous-synonymous substitution rate ratio (d(N)/d(S), denoted omega) is used as a measure of selective pressure at the protein level, with omega > 1 indicating positive selection. Statistical distributions are used to model the variation in omega among sites, allowing a subset of sites to have omega > 1 while the rest of the sequence may be under purifying selection with omega < 1. An empirical Bayes (EB) approach is then used to calculate posterior probabilities that a site comes from the site class with omega > 1. Current implementations, however, use the naive EB (NEB) approach and fail to account for sampling errors in maximum likelihood estimates of model parameters, such as the proportions and omega ratios for the site classes. In small data sets lacking information, this approach may lead to unreliable posterior probability calculations. In this paper, we develop a Bayes empirical Bayes (BEB) approach to the problem, which assigns a prior to the model parameters and integrates over their uncertainties. We compare the new and old methods on real and simulated data sets. The results suggest that in small data sets the new BEB method does not generate false positives as did the old NEB approach, while in large data sets it retains the good power of the NEB approach for inferring positively selected sites.

BAYES EMPIRICAL BAYES APPROACH TO ESTIMATION OF THE FAILURE RATE IN EXPONENTIAL DISTRIBUTION

ABSTRACT In the empirical Bayes (EB) decision problem consisting of squared error estimation of the failure rate in exponential distribution, a prior Λ is placed on the gamma family of prior distributions to produce Bayes EB estimators which are admissible. A subclass of such estimators is shown to be asymptotically optimal (a.o.). The results of a Monte Carlo study are presented to demonstrate the a.o. property of the Bayes EB estimators.

How to be a Better Bayesian

Abstract Consider an experiment yielding an observable random quantity X whose distribution is indexed by a real parameter o. Suppose that a statistician is prepared to execute a Bayes procedure in estimating o and has quantified available prior information about o in his chosen prior distribution G. Suppose that before this estimation process is completed, the statistician becomes aware of the outcome Y of a “similar” experiment. In this article we investigate the questions of whether, and when, this additional information can be exploited so as to provide a better estimate of o in the “current” experiment. We show that in the traditional empirical Bayes framework and in situations involving exponential families, conjugate priors, and squared error loss, the answer is “essentially always.” An explicit Bayes empirical Bayes (BEB) estimator of o is given that is superior to the original Bayes estimator, showing that the statistician has, in these problems, the opportunity to be a “better Bayesian” by combi...

A Unifying Perspective on Statistical Modeling

This paper presents a streamlined perspective on the various approaches to statistical modeling. This perspective can bethought of as a way to unify the Bayes, empirical-Bayes, Bayes–empirical-Bayes, parametric, nonparametric, and semiparametric models used to describe uncertainty. It is emphasized here that this paper concentrates on modeling, not on the approaches to inference that can also be categorized under the above labels, but that are quite different in their philosophical orientation.