Bayesian Methods for Examining Hardy–Weinberg Equilibrium

Summary .  Testing for Hardy–Weinberg equilibrium is ubiquitous and has traditionally been carried out via frequentist approaches. However, the discreteness of the sample space means that uniformity of  p -values under the null cannot be assumed, with enumeration of all possible counts, conditional on the minor allele count, offering a computationally expensive way of  p -value calibration. In addition, the interpretation of the subsequent  p -values, and choice of significance threshold depends critically on sample size, because equilibrium will always be rejected at conventional levels with large sample sizes. We argue for a Bayesian approach using both Bayes factors, and the examination of posterior distributions. We describe simple conjugate approaches, and methods based on importance sampling Monte Carlo. The former are convenient because they yield closed-form expressions for Bayes factors, which allow their application to a large number of single nucleotide polymorphisms (SNPs), in particular in genome-wide contexts. We also describe straightforward direct sampling methods for examining posterior distributions of parameters of interest. For large numbers of alleles at a locus we resort to Markov chain Monte Carlo. We discuss a number of possibilities for prior specification, and apply the suggested methods to a number of real datasets.     

基于卫星遥感数据的黄淮海地区植被覆盖时空变化特征

利用1982—2003年GIMMS NDVI遥感数据,在进行合成、重采样和时间序列滤波处理的基础上,采用线性趋势分析、经验正交函数分解等方法,对中国黄淮海地区植被覆盖的时空特征进行了研究。结果表明:22年来黄淮海地区植被覆盖总体上呈略微增加的趋势,且该区域生长季有提前和延长的趋势;黄淮海大部分地区植被活动在增强的同时,局部地区出现了植被退化现象;从季节变化上看,春季上升和夏季下降趋势明显;林地为主的自然植被、草甸类自然植被和所有农业植被未变化类别占主导地位,而草原植被则以增加趋势为主。主要生长季的NDVI距平EOF分析表明,第1模态的主要特征是区域中间、北部和南端为正,四周为负变化;第2模态的主要特征是从东南向西北由正到负变化且正值区明显偏多;第3模态从东南向西北呈现"正-负-正"的空间分布,其中负值区大部分为以林地为主的自然植被区和一年一熟农业植被,正值区大部分为农耕区和草原牧区,该模态大致反映了农牧区和林区的NDVI分布型。     

Bayesian Estimation of the Number of Species using Noninformative Priors

Consider a sample of animal abundances collected from one sampling occasion. Our focus is in estimating the number of species in a closed population. In order to conduct a noninformative Bayesian inference when modeling this data, we derive Jeffreys and reference priors from the full likelihood. We assume that the species' abundances are randomly distributed according to a distribution indexed by a finite‐dimensional parameter. We consider two specific cases which assume that the mean abundances are constant or exponentially distributed. The Jeffreys and reference priors are functions of the Fisher information for the model parameters; the information is calculated in part using the linear difference score for integer parameter models (Lindsay & Roeder 1987). The Jeffreys and reference priors perform similarly in a data example we consider. The posteriors based on the Jeffreys and reference priors are proper. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phylogenetic Analyses Under Secondary Structure-Specific Substitution Models Outperform Traditional Approaches: Case Studies with Diploblast LSU

Many rDNA molecular phylogenetic studies result in trees that are incongruent to either alternative gene tree reconstructions and/or morphological assumptions. One reason for this outcome might be the application of suboptimal phylogenetic substitution models. While the most commonly implemented models describe the evolution of independently evolving characters fairly well, they do not account for character dependencies such as rRNA strands that form a helix in the ribosome. Such nonindependent sites require the use of models that take into account the coevolution of the complete nucleotide pair (doublet). We analyzed 28S rDNA (LSU) demosponge phylogenies using a “doublet” model for pairing sites (rRNA-helices) and compared our findings with the results of “standard” approaches using Bayes factors. We demonstrate that paired and unpaired sites of the same gene result in different reconstructions and that usage of a doublet model leads to more reliable demosponge trees. We show the influence of more sophisticated models on phylogenetic reconstructions of early-branching metazoans and the phylogenetic relationships of demosponge orders. [Reviewing Editor: Dr. Rasmus Nielsen]     

Bayes factor for testing between different structures of random genetic groups: A case study using weaning weight in Bruna dels Pirineus beef cattle

The implementation of genetic groups in BLUP evaluations accounts for different expectations of breeding values in base animals. Notwithstanding, many feasible structures of genetic groups exist and there are no analytical tools described to compare them easily. In this sense, the recent development of a simple and stable procedure to calculate the Bayes factor between nested competing models allowed us to develop a new approach of that method focused on compared models with different structures of random genetic groups. The procedure is based on a reparameterization of the model in terms of intraclass correlation of genetic groups. The Bayes factor can be easily calculated from the output of a Markov chain Monte Carlo sampling by averaging conditional densities at the null intraclass correlation. It compares two nested models, a model with a given structure of genetic groups against a model without genetic groups. The calculation of the Bayes factor between different structures of genetic groups can be quickly and easily obtained from the Bayes factor between the nested models. We applied this approach to a weaning weight data set of the Bruna dels Pirineus beef cattle, comparing several structures of genetic groups, and the final results showed that the preferable structure was an only group for unknown dams and different groups for unknown sires for each year of calving.     

A general comparison of relaxed molecular clock models

Several models have been proposed to relax the molecular clock in order to estimate divergence times. However, it is unclear which model has the best fit to real data and should therefore be used to perform molecular dating. In particular, we do not know whether rate autocorrelation should be considered or which prior on divergence times should be used. In this work, we propose a general bench mark of alternative relaxed clock models. We have reimplemented most of the already existing models, including the popular lognormal model, as well as various prior choices for divergence times (birth-death, Dirichlet, uniform), in a common Bayesian statistical framework. We also propose a new autocorrelated model, called the "CIR" process, with well-defined stationary properties. We assess the relative fitness of these models and priors, when applied to 3 different protein data sets from eukaryotes, vertebrates, and mammals, by computing Bayes factors using a numerical method called thermodynamic integration. We find that the 2 autocorrelated models, CIR and lognormal, have a similar fit and clearly outperform uncorrelated models on all 3 data sets. In contrast, the optimal choice for the divergence time prior is more dependent on the data investigated. Altogether, our results provide useful guidelines for model choice in the field of molecular dating while opening the way to more extensive model comparisons.     

Learning Proteome Domain Folding Using LSTMs in an Empirical Kernel Space

The recognition of protein structural folds is the starting point for protein function inference and for many structural prediction tools. We previously introduced the idea of using empirical comparisons to create a data-augmented feature space called PESS (Protein Empirical Structure Space)¹ as a novel approach for protein structure prediction. Here, we extend the previous approach by generating the PESS feature space over fixed-length subsequences of query peptides, and applying a sequential neural network model, with one long short-term memory cell layer followed by a fully connected layer. Using this approach, we show that only a small group of domains as a training set is needed to achieve near state-of-the-art accuracy on fold recognition. Our method improves on the previous approach by reducing the training set required and improving the model’s ability to generalize across species, which will help fold prediction for newly discovered proteins.     

Inferring the microscopic surface energy of protein–protein interfaces from mutation data

Mutations at protein–protein recognition sites alter binding strength by altering the chemical nature of the interacting surfaces. We present a simple surface energy model, parameterized with empirical values, yielding mean energies of ?48 cal mol^?1 Å^?2 for interactions between hydrophobic surfaces, ?51 to ?80 cal mol^?1 Å^?2 for surfaces of complementary charge, and 66–83 cal mol^?1 Å^?2 for electrostatically repelling surfaces, relative to the aqueous phase. This places the mean energy of hydrophobic surface burial at ?24 cal mol^?1 Å^?2. Despite neglecting configurational entropy and intramolecular changes, the model correlates with empirical binding free energies of a functionally diverse set of rigid‐body interactions (r = 0.66). When used to rerank docking poses, it can place near‐native solutions in the top 10 for 37% of the complexes evaluated, and 82% in the top 100. The method shows that hydrophobic burial is the driving force for protein association, accounting for 50–95% of the cohesive energy. The model is available open‐source from http://life.bsc.es/pid/web/surface_energy/ and via the CCharpPPI web server http://life.bsc.es/pid/ccharppi/ . Proteins 2015; 83:640–650. © 2015 Wiley Periodicals, Inc.     

Heterozygote advantage at MHC DRB may influence response to infectious disease epizootics

The effect of MHC polymorphism on individual fitness variation in the wild remains equivocal; however, much evidence suggests that heterozygote advantage is a major determinant. To understand the contribution of MHC polymorphism to individual disease resistance or susceptibility in natural populations, we investigated two MHC class II B loci, DQB and DRB, in the New Zealand sea lion (NZSL, Phocarctos hookeri). The NZSL is a threatened species which is unusually susceptible to death by bacterial infection at an early age; it has suffered three bacterial induced epizootics resulting in high mortality levels of young pups since 1997. The MHC DQB and DRB haplotypes of dead NZSL pups with known cause of death (bacteria, enteritis or trauma) were sequenced and reconstructed, compared to pups that survived beyond 2 months of age, and distinct MHC DRB allele frequency and genotype differences were identified. Two findings were striking: (i) one DRB allele was present only in dead pups, and (ii) one heterozygous DRB genotype, common in live pups, was absent from dead pups. These results are consistent with some functional relationship with these variants and suggest heterozygote advantage is operating at DRB. We found no association between heterozygosity and fitness at 17 microsatellite loci, indicating that general heterozygosity is not responsible for the effect on fitness detected here. This result may be a consequence of recurrent selection by multiple pathogen assault over recent years and highlights the importance of heterozygote advantage at MHC as a potential mechanism for fitness differences in wild populations.     

热消散法(TDP)在5种竹子蒸腾耗水测定中的适用性评价

为评价热消散法在竹子蒸腾耗水测定中的适用性,利用室内离体竹段注水变压法结合野外整株容器称重法对Granier 公式进行了验证和系数校正,同时观察了5 种竹子(毛竹Phyllostachys edulis、粉单竹Bambusa chungii、青皮竹B. textilis、茶秆竹Arundinaria amabilis、龙头竹B. vulgaris)的茎秆维管束结构。结果表明,茎秆维管束分布不均,维管束发育程度从竹壁外向内逐渐成熟,输水能力也逐渐增强。液流密度(F_d)和液流指数(K)呈幂函数关系,相关系数R²>0.83,说明热消散探针方法能较好地估算竹类的液流密度。用整株容器称重法对推导出的液流密度公式进行校正,校正后的液流密度公式与原始Granier 公式中各系数均不同,尤其是α 值。分别采用校正前后公式计算的竹子日蒸腾量差异显著,尤其是一天中液流高峰时段(午间)的差异最大。因此,只要对热消散探针方法准确验证、校正Granier 原始公式系数,TDP 技术是估计竹类植物水分利用的一种适宜方法。