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Relaxing the molecular clock using models of how substitution rates change across lineages has become essential for addressing evolutionary problems. The diversity of rate evolution models and their implementations are substantial, and studies have demonstrated their impact on divergence time estimates can be as significant as that of calibration information. In this review, we trace the development of rate evolution models from the proposal of the molecular clock concept to the development of sophisticated Bayesian and non-Bayesian methods that handle rate variation in phylogenies. We discuss the various approaches to modeling rate evolution, provide a comprehensive list of available software, and examine the challenges and advancements of the prevalent Bayesian framework, contrasting them to faster non-Bayesian methods. Lastly, we offer insights into potential advancements in the field in the era of big data., (© The Author(s) 2024. Published by Oxford University Press on behalf of Society for Molecular Biology and Evolution.)

Recent advancement in genome-wide association studies (GWAS) comes from not only increasingly larger sample sizes but also the shift in focus towards underrepresented populations. Multipopulation GWAS increase power to detect novel risk variants and improve fine-mapping resolution by leveraging evidence and differences in linkage disequilibrium (LD) from diverse populations. Here, we expand upon our previous approach for single-population fine-mapping through Joint Analysis of Marginal SNP Effects (JAM) to a multipopulation analysis (mJAM). Under the assumption that true causal variants are common across studies, we implement a hierarchical model framework that conditions on multiple SNPs while explicitly incorporating the different LD structures across populations. The mJAM framework can be used to first select index variants using the mJAM likelihood with different feature selection approaches. In addition, we present a novel approach leveraging the ideas of mediation to construct credible sets for these index variants. Construction of such credible sets can be performed given any existing index variants. We illustrate the implementation of the mJAM likelihood through two implementations: mJAM-SuSiE (a Bayesian approach) and mJAM-Forward selection. Through simulation studies based on realistic effect sizes and levels of LD, we demonstrated that mJAM performs well for constructing concise credible sets that include the underlying causal variants. In real data examples taken from the most recent multipopulation prostate cancer GWAS, we showed several practical advantages of mJAM over other existing multipopulation methods., (© 2024 The Authors. Genetic Epidemiology published by Wiley Periodicals LLC.)

Count traits are usually explored in livestock breeding programs, and they usually do not fit into normal distribution, requiring alternatives to adjust the phenotype to estimate accurate genetic parameters and breeding values. Alternatively, distribution such as Poisson can be used to evaluate count traits. This study aimed to compare and discuss the genetic evaluation for oocyte and embryo counts considering Gaussian (untransformed variable - LIN; transformed by logarithm - LOG; transformed by Anscombe - ANS) and Poisson (POI) distributions. The data comprised 11,343 total oocytes (TO), viable oocytes (VO), cleaved embryos (CE), and viable embryo (VE) records of ovum pick-up from 1740 Dairy Gir heifers and cows. The genetic parameters and breeding values were estimated by the MCMCglmm package of the R software. The posterior means of heritability varied from 0.40 (LIN) to 0.49 (POI) for TO, 0.39 (LIN) to 0.49 (POI) for VO, 0.30 (LOG) to 0.41 (POI) for cleaved embryos, and 0.19 (LIN) to 0.32 (POI) for viable embryos. The posterior means of repeatability varied from 0.56 (LIN) to 0.65 (POI) for TO, 0.53 (LOG) to 0.63 (POI) for VO, 0.44 (LOG) to 0.60 (POI) for CE, and 0.36 (LOG) to 0.56 (POI) for VE. Deviance information criterion and mean squared residuals indicated that POI model should be used for the genetic evaluation of embryo and oocyte count traits. Spearman's rank correlation between estimated breeding value (EBV) for embryo and oocyte count traits computed by POI, LOG, and ANS models was high (ranging from 0.77 to 0.99), indicating little reranking among the best animals. The POI model is the most adequate for genetic evaluation, resulting in more reliable EBV of oocyte and embryo count traits for Dairy Gir cattle., (© 2024. The Author(s), under exclusive licence to Institute of Plant Genetics Polish Academy of Sciences.)

Genome-wide association studies (GWAS) implicate broad genomic loci containing clusters of highly correlated genetic variants. Finemapping techniques can select and prioritize variants within each GWAS locus which are more likely to have a functional influence on the trait. Here, we present a novel method, Finemap-MiXeR, for finemapping causal variants from GWAS summary statistics, controlling for correlation among variants due to linkage disequilibrium. Our method is based on a variational Bayesian approach and direct optimization of the Evidence Lower Bound (ELBO) of the likelihood function derived from the MiXeR model. After obtaining the analytical expression for ELBO's gradient, we apply Adaptive Moment Estimation (ADAM) algorithm for optimization, allowing us to obtain the posterior causal probability of each variant. Using these posterior causal probabilities, we validated Finemap-MiXeR across a wide range of scenarios using both synthetic data, and real data on height from the UK Biobank. Comparison of Finemap-MiXeR with two existing methods, FINEMAP and SuSiE RSS, demonstrated similar or improved accuracy. Furthermore, our method is computationally efficient in several aspects. For example, unlike many other methods in the literature, its computational complexity does not increase with the number of true causal variants in a locus and it does not require any matrix inversion operation. The mathematical framework of Finemap-MiXeR is flexible and may also be applied to other problems including cross-trait and cross-ancestry finemapping., Competing Interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests: Dr. AMD is a Founder of and holds equity in CorTechs Labs, Inc, and serves on its Scientific Advisory Board. He is a member of the Scientific Advisory Board of Human Longevity, Inc. and receives funding through research agreements with General Electric Healthcare and Medtronic, Inc. The terms of these arrangements have been reviewed and approved by UCSD in accordance with its conflict-of-interest policies. Dr. OAA is a consultant for cortechs.ai, and received speaker’s honorarium from Janssen, Lundbeck and Sunovion unrelated to the topic of this study. The remaining authors have no competing interest., (Copyright: © 2024 Akdeniz et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Bayesian phylogenetic inference is powerful but computationally intensive. Researchers may find themselves with two phylogenetic posteriors on overlapping data sets and may wish to approximate a combined result without having to re-run potentially expensive Markov chains on the combined data set. This raises the question: given overlapping subsets of a set of taxa (e.g. species or virus samples), and given posterior distributions on phylogenetic tree topologies for each of these taxon sets, how can we optimize a probability distribution on phylogenetic tree topologies for the entire taxon set? In this paper we develop a variational approach to this problem and demonstrate its effectiveness. Specifically, we develop an algorithm to find a suitable support of the variational tree topology distribution on the entire taxon set, as well as a gradient-descent algorithm to minimize the divergence from the restrictions of the variational distribution to each of the given per-subset probability distributions, in an effort to approximate the posterior distribution on the entire taxon set., (© 2024. The Author(s).)

Genetic improvement of complex traits in animal and plant breeding depends on the efficient and accurate estimation of breeding values. Deep learning methods have been shown to be not superior over traditional genomic selection (GS) methods, partially due to the degradation problem (i.e. with the increase of the model depth, the performance of the deeper model deteriorates). Since the deep learning method residual network (ResNet) is designed to solve gradient degradation, we examined its performance and factors related to its prediction accuracy in GS. Here we compared the prediction accuracy of conventional genomic best linear unbiased prediction, Bayesian methods (BayesA, BayesB, BayesC, and Bayesian Lasso), and two deep learning methods, convolutional neural network and ResNet, on three datasets (wheat, simulated and real pig data). ResNet outperformed other methods in both Pearson's correlation coefficient (PCC) and mean squared error (MSE) on the wheat and simulated data. For the pig backfat depth trait, ResNet still had the lowest MSE, whereas Bayesian Lasso had the highest PCC. We further clustered the pig data into four groups and, on one separated group, ResNet had the highest prediction accuracy (both PCC and MSE). Transfer learning was adopted and capable of enhancing the performance of both convolutional neural network and ResNet. Taken together, our findings indicate that ResNet could improve GS prediction accuracy, affected potentially by factors such as the genetic architecture of complex traits, data volume, and heterogeneity., (© 2024 Stichting International Foundation for Animal Genetics.)

The estimation of haplotype structure and frequencies provides crucial information about the composition of genomes. Techniques, such as single-individual haplotyping, aim to reconstruct individual haplotypes from diploid genome sequencing data. However, our focus is distinct. We address the challenge of reconstructing haplotype structure and frequencies from pooled sequencing samples where multiple individuals are sequenced simultaneously. A frequentist method to address this issue has recently been proposed. In contrast to this and other methods that compute point estimates, our proposed Bayesian hierarchical model delivers a posterior that permits us to also quantify uncertainty. Since matching permutations in both haplotype structure and corresponding frequency matrix lead to the same reconstruction of their product, we introduce an order-preserving shrinkage prior that ensures identifiability with respect to permutations. For inference, we introduce a blocked Gibbs sampler that enforces the required constraints. In a simulation study, we assessed the performance of our method. Furthermore, by using our approach on two distinct sets of real data, we demonstrate that our Bayesian approach can reconstruct the dominant haplotypes in a challenging, high-dimensional set-up.

Swallows (Hirundinidae) are a globally distributed family of passerine birds that exhibit remarkable similarity in body shape but tremendous variation in plumage, sociality, nesting behavior, and migratory strategies. As a result, swallow species have become models for empirical behavioral ecology and evolutionary studies, and variation across the Hirundinidae presents an excellent opportunity for comparative analyses of trait evolution. Exploiting this potential requires a comprehensive and well-resolved phylogenetic tree of the family. To address this need, we estimated swallow phylogeny using genetic data from thousands of ultraconserved element (UCE) loci sampled from nearly all recognized swallow species. Maximum likelihood, coalescent-based, and Bayesian approaches yielded a well-resolved phylogenetic tree to the generic level, with minor disagreement among inferences at the species level, which likely reflect ongoing population genetic processes. The UCE data were particularly useful in helping to resolve deep nodes, which previously confounded phylogenetic reconstruction efforts. Divergence time estimates from the improved swallow tree support a Miocene origin of the family, roughly 13 million years ago, with subsequent diversification of major groups in the late Miocene and Pliocene. Our estimates of historical biogeography support the hypothesis that swallows originated in the Afrotropics and have subsequently expanded across the globe, with major in situ diversification in Africa and a secondary major radiation following colonization of the Neotropics. Initial examination of nesting and sociality indicates that the origin of mud nesting - a relatively rare nest construction phenotype in birds - was a major innovation coincident with the origin of a clade giving rise to over 40% of extant swallow diversity. In contrast, transitions between social and solitary nesting appear less important for explaining patterns of diversification among swallows., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Measures of selective constraint on genes have been used for many applications, including clinical interpretation of rare coding variants, disease gene discovery and studies of genome evolution. However, widely used metrics are severely underpowered at detecting constraints for the shortest ~25% of genes, potentially causing important pathogenic mutations to be overlooked. Here we developed a framework combining a population genetics model with machine learning on gene features to enable accurate inference of an interpretable constraint metric, s het . Our estimates outperform existing metrics for prioritizing genes important for cell essentiality, human disease and other phenotypes, especially for short genes. Our estimates of selective constraint should have wide utility for characterizing genes relevant to human disease. Finally, our inference framework, GeneBayes, provides a flexible platform that can improve the estimation of many gene-level properties, such as rare variant burden or gene expression differences., (© 2024. The Author(s), under exclusive licence to Springer Nature America, Inc.)

A robust and stable phylogenetic framework is a fundamental goal of evolutionary biology. As the third largest insect order in the world following Coleoptera and Diptera, Lepidoptera (butterflies and moths) play a central role in almost every terrestrial ecosystem as indicators of environmental change and serve as important models for biologists exploring questions related to ecology and evolutionary biology. However, for such a charismatic insect group, the higher-level phylogenetic relationships among its superfamilies are still poorly resolved. Compared to earlier phylogenomic studies, we increased taxon sampling among Lepidoptera (37 superfamilies and 68 families containing 263 taxa) and acquired a series of large amino-acid datasets from 69,680 to 400,330 for phylogenomic reconstructions. Using these datasets, we explored the effect of different taxon sampling with significant increases in the number of included genes on tree topology by considering a series of systematic errors using maximum-likelihood (ML) and Bayesian inference (BI) methods. Moreover, we also tested the effectiveness in topology robustness among the three ML-based models. The results showed that taxon sampling is an important determinant in tree robustness of accurate lepidopteran phylogenetic estimation. Long-branch attraction (LBA) caused by site-wise heterogeneity is a significant source of bias giving rise to unstable positions of ditrysian groups in phylogenomic reconstruction. Phylogenetic inference showed the most comprehensive framework to reveal the relationships among lepidopteran superfamilies, and presented some newly relationships with strong supports (Papilionoidea was sister to Gelechioidea and Immoidea was sister to Galacticoidea, respectively), but limited by taxon sampling, the relationships within the species-rich and relatively rapid radiation Ditrysia and especially Apoditrysia remain poorly resolved, which need to increase taxon sampling for further phylogenomic reconstruction. The present study demonstrates that taxon sampling is an important determinant for an accurate lepidopteran tree of life and provides some essential insights for future lepidopteran phylogenomic studies., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Inc. All rights reserved.)

This study presents a novel approach for the optimization of genomic parental selection in breeding programs involving categorical and continuous-categorical multi-trait mixtures (CMs and CCMMs). Utilizing the Bayesian decision theory (BDT) and latent trait models within a multivariate normal distribution framework, we address the complexities of selecting new parental lines across ordinal and continuous traits for breeding. Our methodology enhances precision and flexibility in genetic selection, validated through extensive simulations. This unified approach presents significant potential for the advancement of genetic improvements in diverse breeding contexts, underscoring the importance of integrating both categorical and continuous traits in genomic selection frameworks.

Proper variance partitioning and estimation of genetic parameters at appropriate time interval is crucial for understanding the dynamics of trait variance and genetic correlations and for deciding the future breeding strategy of the population. This study was conducted on the same premise to estimate genetic parameters of major economic traits in a White Leghorn strain IWH using Bayesian approach and to identify the role of maternal effects in the regulation of trait variance. Three different models incorporating the direct additive effect (Model 1), direct additive and maternal genetic effect (Model 2) and direct additive, maternal genetic and maternal permanent environmental effects (Model 3) were tried to estimate the genetic parameters for body weight traits (birth weight, body weight at 16, 20, 40 and 52 weeks), Age at sexual maturity (ASM), egg production traits (egg production up to 24, 28, 40, 52, 64 and 72 weeks) and egg weight traits (egg weight at 28, 40 and 52 weeks). Model 2 and Model 3 with maternal effects were found to be the best having the highest accuracy for almost all the traits. The direct additive genetic heritability was moderate for ASM, moderate to high for body weight traits and egg weight traits and low to moderate for egg production traits. Though the maternal heritability (h2mat) and permanent environmental effect (c2mpe) was low (<0.1) for most of the traits, they formed an important component of trait variance. Traits like egg weight at 28 weeks (0.14±0.06) and egg production at 72 weeks (0.13±0.07) reported comparatively higher values for c2mpe and h2mat respectively. Additive genetic correlation was high and positive between body weight traits, between egg weight traits, between consecutive egg production traits and between body weight and egg weight traits. However, a negative genetic correlation existed between egg production and egg weight traits, egg production and body weight traits, ASM and early egg production traits. Overall, a moderate positive genetic correlation was estimated between ASM and body weight traits and ASM and egg weight traits. Based on our findings, we can deduce that maternal effects constitute an important source of variation for all the major economic traits in White Leghorn and should be necessarily considered in genetic evaluation programs., Competing Interests: The authors do not have any competing interests, (Copyright: © 2024 Kour et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Classification of gene trees is an important task both in the analysis of multi-locus phylogenetic data, and assessment of the convergence of Markov Chain Monte Carlo (MCMC) analyses used in Bayesian phylogenetic tree reconstruction. The logistic regression model is one of the most popular classification models in statistical learning, thanks to its computational speed and interpretability. However, it is not appropriate to directly apply the standard logistic regression model to a set of phylogenetic trees, as the space of phylogenetic trees is non-Euclidean and thus contradicts the standard assumptions on covariates. It is well-known in tropical geometry and phylogenetics that the space of phylogenetic trees is a tropical linear space in terms of the max-plus algebra. Therefore, in this paper, we propose an analogue approach of the logistic regression model in the setting of tropical geometry. Our proposed method outperforms classical logistic regression in terms of Area under the ROC Curve in numerical examples, including with data generated by the multi-species coalescent model. Theoretical properties such as statistical consistency have been proved and generalization error rates have been derived. Finally, our classification algorithm is proposed as an MCMC convergence criterion for Mr Bayes. Unlike the convergence metric used by Mr Bayes which is only dependent on tree topologies, our method is sensitive to branch lengths and therefore provides a more robust metric for convergence. In a test case, it is illustrated that the tropical logistic regression can differentiate between two independently run MCMC chains, even when the standard metric cannot., (© 2024. The Author(s).)

Key Message: A Bayesian linkage disequilibrium-based multiple-locus mixed model identified QTLs for fibre, seed and oil traits and predicted breeding worthiness of test lines, enabling their simultaneous improvement in cotton. Improving cotton seed and oil yields has become increasingly important while continuing to breed for higher lint yield. In this study, a novel Bayesian linkage disequilibrium-based multiple-locus mixed model was developed for QTL identification and genomic prediction (GP). A multi-parent population consisting of 256 recombinant inbred lines, derived from four elite cultivars with distinct combinations of traits, was used in the analysis of QTLs for lint percentage, seed index, lint index and seed oil content and their interrelations. All four traits were moderately heritable and correlated but with no large influence of genotype × environment interactions across multiple seasons. Seven to ten major QTLs were identified for each trait with many being adjacent or overlapping for different trait pairs. A fivefold cross-validation of the model indicated prediction accuracies of 0.46-0.62. GP results based on any two-season phenotypes were strongly correlated with phenotypic means of a pooled analysis of three-season experiments (r = 0.83-0.92). When used for selection of improvement in lint, seed and oil yields, GP captured 40-100% of individuals with comparable lint yields of those selected based on the three-season phenotypic results. Thus, this quantitative genomics-enabled approach can not only decipher the genomic variation underlying lint, seed and seed oil traits and their interrelations, but can provide predictions for their simultaneous improvement. We discuss future breeding strategies in cotton that will enhance the entire value of the crop, not just its fibre., (© 2024. Crown.)

We unify evolutionary dynamics on graphs in strategic uncertainty through a decaying Bayesian update. Our analysis focuses on the Price theorem of selection, which governs replicator(-mutator) dynamics, based on a stratified interaction mechanism and a composite strategy update rule. Our findings suggest that the replication of a certain mutation in a strategy, leading to a shift from competition to cooperation in a well-mixed population, is equivalent to the replication of a strategy in a Bayesian-structured population without any mutation. Likewise, the replication of a strategy in a Bayesian-structured population with a certain mutation, resulting in a move from competition to cooperation, is equivalent to the replication of a strategy in a well-mixed population without any mutation. This equivalence holds when the transition rate from competition to cooperation is equal to the relative strength of selection acting on either competition or cooperation in relation to the selection differential between cooperators and competitors. Our research allows us to identify situations where cooperation is more likely, irrespective of the specific payoff levels. This approach provides new perspectives into the intended purpose of Price's equation, which was initially not designed for this type of analysis., (© 2024. The Author(s), under exclusive licence to the Society for Mathematical Biology.)

Bayesian coalescent skyline plot models are widely used to infer demographic histories. The first (non-Bayesian) coalescent skyline plot model assumed a known genealogy as data, while subsequent models and implementations jointly inferred the genealogy and demographic history from sequence data, including heterochronous samples. Overall, there exist multiple different Bayesian coalescent skyline plot models which mainly differ in two key aspects: (i) how changes in population size are modeled through independent or autocorrelated prior distributions, and (ii) how many change-points in the demographic history are used, where they occur and if the number is pre-specified or inferred. The specific impact of each of these choices on the inferred demographic history is not known because of two reasons: first, not all models are implemented in the same software, and second, each model implementation makes specific choices that the biologist cannot influence. To facilitate a detailed evaluation of Bayesian coalescent skyline plot models, we implemented all currently described models in a flexible design into the software RevBayes. Furthermore, we evaluated models and choices on an empirical dataset of horses supplemented by a small simulation study. We find that estimated demographic histories can be grouped broadly into two groups depending on how change-points in the demographic history are specified (either independent of or at coalescent events). Our simulations suggest that models using change-points at coalescent events produce spurious variation near the present, while most models using independent change-points tend to over-smooth the inferred demographic history., (© The Author(s) 2024. Published by Oxford University Press on behalf of Society for Molecular Biology and Evolution.)

ABSTRACT An alternative transcription start site (ATSS) is a major driving force for increasing the complexity of transcripts in human tissues. As a transcriptional regulatory mechanism, ATSS has biological significance. Many studies have confirmed that ATSS plays an important role in diseases and cell development and differentiation. However, exploration of its dynamic mechanisms remains insufficient. Identifying ATSS change points during cell differentiation is critical for elucidating potential dynamic mechanisms. For relative ATSS usage as percentage data, the existing methods lack sensitivity to detect the change point for ATSS longitudinal data. In addition, some methods have strict requirements for data distribution and cannot be applied to deal with this problem. In this study, the Bayesian change point detection model was first constructed using reparameterization techniques for two parameters of a beta distribution for the percentage data type, and the posterior distributions of parameters and change points were obtained using Markov Chain Monte Carlo (MCMC) sampling. With comprehensive simulation studies, the performance of the Bayesian change point detection model is found to be consistently powerful and robust across most scenarios with different sample sizes and beta distributions. Second, differential ATSS events in the real data, whose change points were identified using our method, were clustered according to their change points. Last, for each change point, pathway and transcription factor motif analyses were performed on its differential ATSS events. The results of our analyses demonstrated the effectiveness of the Bayesian change point detection model and provided biological insights into cell differentiation .

Adaptation can occur at remarkably short timescales in natural populations, leading to drastic changes in phenotypes and genotype frequencies over a few generations only. The inference of demographic parameters can allow understanding how evolutionary forces interact and shape the genetic trajectories of populations during rapid adaptation. Here we propose a new Approximate Bayesian Computation (ABC) framework that couples a forward and individual-based model with temporal genetic data to disentangle genetic changes and demographic variations in a case of rapid adaptation. We test the accuracy of our inferential framework and evaluate the benefit of considering a dense versus sparse sampling. Theoretical investigations demonstrate high accuracy in both model and parameter estimations, even if a strong thinning is applied to time series data. Then, we apply our ABC inferential framework to empirical data describing the population genetic changes of the poplar rust pathogen following a major event of resistance overcoming. We successfully estimate key demographic and genetic parameters, including the proportion of resistant hosts deployed in the landscape and the level of standing genetic variation from which selection occurred. Inferred values are in accordance with our empirical knowledge of this biological system. This new inferential framework, which contrasts with coalescent-based ABC analyses, is promising for a better understanding of evolutionary trajectories of populations subjected to rapid adaptation., (© 2023 John Wiley & Sons Ltd.)

Bacteria are nonsexual organisms but are capable of exchanging DNA at diverse degrees through homologous recombination. Intriguingly, the rates of recombination vary immensely across lineages where some species have been described as purely clonal and others as "quasi-sexual." However, estimating recombination rates has proven a difficult endeavor and estimates often vary substantially across studies. It is unclear whether these variations reflect natural variations across populations or are due to differences in methodologies. Consequently, the impact of recombination on bacterial evolution has not been extensively evaluated and the evolution of recombination rate-as a trait-remains to be accurately described. Here, we developed an approach based on Approximate Bayesian Computation that integrates multiple signals of recombination to estimate recombination rates. We inferred the rate of recombination of 162 bacterial species and one archaeon and tested the robustness of our approach. Our results confirm that recombination rates vary drastically across bacteria; however, we found that recombination rate-as a trait-is conserved in several lineages but evolves rapidly in others. Although some traits are thought to be associated with recombination rate (e.g., GC-content), we found no clear association between genomic or phenotypic traits and recombination rate. Overall, our results provide an overview of recombination rate, its evolution, and its impact on bacterial evolution., Competing Interests: Competing interests statement:The authors declare no competing interest.

Genomic prediction was conducted using 2494 Japanese Black cattle from Hiroshima Prefecture and both single-nucleotide polymorphism information and phenotype data on monounsaturated fatty acid (MUFA) and oleic acid (C18:1) analyzed with gas chromatography. We compared the prediction accuracy for four models (A, additive genetic effects; AD, as for A with dominance genetic effects; ADR, as for AD with the runs of homozygosity (ROH) effects calculated by ROH-based relationship matrix; and ADF, as for AD with the ROH-based inbreeding coefficient of the linear regression). Bayesian methods were used to estimate variance components. The narrow-sense heritability estimates for MUFA and C18:1 were 0.52-0.53 and 0.57, respectively; the corresponding proportions of dominance genetic variance were 0.04-0.07 and 0.04-0.05, and the proportion of ROH variance was 0.02. The deviance information criterion values showed slight differences among the models, and the models provided similar prediction accuracy., (© 2024 Japanese Society of Animal Science.)

Molecular evolutionary rate variation is a key aspect of the evolution of many organisms that can be modeled using molecular clock models. For example, fixed local clocks revealed the role of episodic evolution in the emergence of SARS-CoV-2 variants of concern. Like all statistical models, however, the reliability of such inferences is contingent on an assessment of statistical evidence. We present a novel Bayesian phylogenetic approach for detecting episodic evolution. It consists of computing Bayes factors, as the ratio of posterior and prior odds of evolutionary rate increases, effectively quantifying support for the effect size. We conducted an extensive simulation study to illustrate the power of this method and benchmarked it to formal model comparison of a range of molecular clock models using (log) marginal likelihood estimation, and to inference under a random local clock model. Quantifying support for the effect size has higher sensitivity than formal model testing and is straight-forward to compute, because it only needs samples from the posterior and prior distribution. However, formal model testing has the advantage of accommodating a wide range molecular clock models. We also assessed the ability of an automated approach, known as the random local clock, where branches under episodic evolution may be detected without their a priori definition. In an empirical analysis of a data set of SARS-CoV-2 genomes, we find "very strong" evidence for episodic evolution. Our results provide guidelines and practical methods for Bayesian detection of episodic evolution, as well as avenues for further research into this phenomenon., (© The Author(s) 2023. Published by Oxford University Press on behalf of Society for Molecular Biology and Evolution.)

Signalling transduction pathways (STPs) are commonly hijacked by many cancers for their growth and malignancy, but demystifying their underlying mechanisms is difficult. Here, we developed methodologies with a fully Bayesian approach in discovering novel driver bio-markers in aberrant STPs given high-throughput gene expression (GE) data. This project, namely 'PathTurbEr' (Pathway Perturbation Driver) uses the GE dataset derived from the lapatinib (an EGFR/HER dual inhibitor) sensitive and resistant samples from breast cancer cell lines (SKBR3). Differential expression analysis revealed 512 differentially expressed genes (DEGs) and their pathway enrichment revealed 13 highly perturbed singalling pathways in lapatinib resistance, including PI3K-AKT, Chemokine, Hippo and TGF-$\beta $ singalling pathways. Next, the aberration in TGF-$\beta $ STP was modelled as a causal Bayesian network (BN) using three MCMC sampling methods, i.e. Neighbourhood sampler (NS) and Hit-and-Run (HAR) sampler that potentially yield robust inference with lower chances of getting stuck at local optima and faster convergence compared to other state-of-art methods. Next, we examined the structural features of the optimal BN as a statistical process that generates the global structure using $p&#95;1$-model, a special class of Exponential Random Graph Models (ERGMs), and MCMC methods for their hyper-parameter sampling. This step enabled key drivers identification that drive the aberration within the perturbed BN structure of STP, and yielded 34, 34 and 23 perturbation driver genes out of 80 constituent genes of three perturbed STP models of TGF-$\beta $ signalling inferred by NS, HAR and MH sampling methods, respectively. Functional-relevance and disease-relevance analyses suggested their significant associations with breast cancer progression/resistance., (© The Author(s) 2021. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

High-throughput data make it possible to study expression levels of thousands of genes simultaneously under a particular condition. However, only few of the genes are discriminatively expressed. How to identify these biomarkers precisely is significant for disease diagnosis, prognosis, and therapy. Many studies utilized pathway information to identify the biomarkers. However, most of these studies only incorporate the group information while the pathway structural information is ignored. In this paper, we proposed a Bayesian gene selection with a network-constrained regularization method, which can incorporate the pathway structural information as priors to perform gene selection. All the priors are conjugated; thus, the parameters can be estimated effectively through Gibbs sampling. We present the application of our method on 6 microarray datasets, comparing with Bayesian Lasso, Bayesian Elastic Net, and Bayesian Fused Lasso. The results show that our method performs better than other Bayesian methods and pathway structural information can improve the result., Competing Interests: The authors declare that there is no conflict of interest regarding the publication of this paper., (Copyright © 2021 Ming Cao et al.)

Almost all haplotype-based variant callers were designed specifically for detecting common germline variation in diploid populations, and give suboptimal results in other scenarios. Here we present Octopus, a variant caller that uses a polymorphic Bayesian genotyping model capable of modeling sequencing data from a range of experimental designs within a unified haplotype-aware framework. Octopus combines sequencing reads and prior information to phase-called genotypes of arbitrary ploidy, including those with somatic mutations. We show that Octopus accurately calls germline variants in individuals, including single nucleotide variants, indels and small complex replacements such as microinversions. Using a synthetic tumor data set derived from clean sequencing data from a sample with known germline haplotypes and observed mutations in a large cohort of tumor samples, we show that Octopus is more sensitive to low-frequency somatic variation, yet calls considerably fewer false positives than other methods. Octopus also outputs realigned evidence BAM files to aid validation and interpretation., (© 2021. The Author(s), under exclusive licence to Springer Nature America, Inc.)

Key Message: A new R-software procedure for fixed/random Diallel models was developed. We eased the diallel schemes approach by considering them as specific cases with different parameterisations of a general linear model. Diallel experiments are based on a set of possible crosses between some homozygous (inbred) lines. For these experiments, six main diallel models are available in literature, to quantify genetic effects, such as general combining ability (GCA), specific combining ability (SCA), reciprocal (maternal) effects and heterosis. Those models tend to be presented as separate entities, to be fitted by using specialised software. In this manuscript, we reinforce the idea that diallel models should be better regarded as specific cases (different parameterisations) of a general linear model and might be fitted with general purpose software facilities, as used for all other types of linear models. We start from the estimation of fixed genetical effects within the R environment and try to bridge the gap between diallel models, linear models and ordinary least squares estimation (OLS). First, we review the main diallel models in literature. Second, we build a set of tools to enable geneticists, plant/animal breeders and students to fit diallel models by using the most widely known R functions for OLS fitting, i.e. the 'lm()' function and related methods. Here, we give three examples to show how diallel models can be built by using the typical process of GLMs and fitted, inspected and processed as all other types of linear models in R. Finally, we give a fourth example to show how our tools can be also used to fit random/mixed effect diallel models in the Bayesian framework.

The prediction of appearance traits by use of solely genetic information has become an established approach and a number of statistical prediction models have already been developed for this purpose. However, given limited knowledge on appearance genetics, currently available models are incomplete and do not include all causal genetic variants as predictors. Therefore such prediction models may benefit from the inclusion of additional information that acts as a proxy for this unknown genetic background. Use of priors, possibly informed by trait category prevalence values in biogeographic ancestry groups, in a Bayesian framework may thus improve the prediction accuracy of previously predicted externally visible characteristics, but has not been investigated as of yet. In this study, we assessed the impact of using trait prevalence-informed priors on the prediction performance in Bayesian models for eye, hair and skin color as well as hair structure and freckles in comparison to the respective prior-free models. Those prior-free models were either similarly defined either very close to the already established ones by using a reduced predictive marker set. However, these differences in the number of the predictive markers should not affect significantly our main outcomes. We observed that such priors often had a strong effect on the prediction performance, but to varying degrees between different traits and also different trait categories, with some categories barely showing an effect. While we found potential for improving the prediction accuracy of many of the appearance trait categories tested by using priors, our analyses also showed that misspecification of those prior values often severely diminished the accuracy compared to the respective prior-free approach. This emphasizes the importance of accurate specification of prevalence-informed priors in Bayesian prediction modeling of appearance traits. However, the existing literature knowledge on spatial prevalence is sparse for most appearance traits, including those investigated here. Due to the limitations in appearance trait prevalence knowledge, our results render the use of trait prevalence-informed priors in DNA-based appearance trait prediction currently infeasible., (Copyright © 2020 The Author(s). Published by Elsevier B.V. All rights reserved.)

Phylogenetic methods can use the sampling times of molecular sequence data to calibrate the molecular clock, enabling the estimation of evolutionary rates and timescales for rapidly evolving pathogens and data sets containing ancient DNA samples. A key aspect of such calibrations is whether a sufficient amount of molecular evolution has occurred over the sampling time window, that is, whether the data can be treated as having come from a measurably evolving population. Here, we investigate the performance of a fully Bayesian evaluation of temporal signal (BETS) in sequence data. The method involves comparing the fit to the data of two models: a model in which the data are accompanied by the actual (heterochronous) sampling times, and a model in which the samples are constrained to be contemporaneous (isochronous). We conducted simulations under a wide range of conditions to demonstrate that BETS accurately classifies data sets according to whether they contain temporal signal or not, even when there is substantial among-lineage rate variation. We explore the behavior of this classification in analyses of five empirical data sets: modern samples of A/H1N1 influenza virus, the bacterium Bordetella pertussis, coronaviruses from mammalian hosts, ancient DNA from Hepatitis B virus, and mitochondrial genomes of dog species. Our results indicate that BETS is an effective alternative to other tests of temporal signal. In particular, this method has the key advantage of allowing a coherent assessment of the entire model, including the molecular clock and tree prior which are essential aspects of Bayesian phylodynamic analyses., (© The Author(s) 2020. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Next-generation sequencing of pathogen quasispecies within a host yields data sets of tens to hundreds of unique sequences. However, the full data set often contains thousands of sequences, because many of those unique sequences have multiple identical copies. Data sets of this size represent a computational challenge for currently available Bayesian phylogenetic and phylodynamic methods. Through simulations, we explore how large data sets with duplicate sequences affect the speed and accuracy of phylogenetic and phylodynamic analysis within BEAST 2. We show that using unique sequences only leads to biases, and using a random subset of sequences yields imprecise parameter estimates. To overcome these shortcomings, we introduce PIQMEE, a BEAST 2 add-on that produces reliable parameter estimates from full data sets with increased computational efficiency as compared with the currently available methods within BEAST 2. The principle behind PIQMEE is to resolve the tree structure of the unique sequences only, while simultaneously estimating the branching times of the duplicate sequences. Distinguishing between unique and duplicate sequences allows our method to perform well even for very large data sets. Although the classic method converges poorly for data sets of 6,000 sequences when allowed to run for 7 days, our method converges in slightly more than 1 day. In fact, PIQMEE can handle data sets of around 21,000 sequences with 20 unique sequences in 14 days. Finally, we apply the method to a real, within-host HIV sequencing data set with several thousand sequences per patient., (© The Author(s) 2020. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.)

Transcription elongation can be modelled as a three step process, involving polymerase translocation, NTP binding, and nucleotide incorporation into the nascent mRNA. This cycle of events can be simulated at the single-molecule level as a continuous-time Markov process using parameters derived from single-molecule experiments. Previously developed models differ in the way they are parameterised, and in their incorporation of partial equilibrium approximations. We have formulated a hierarchical network comprised of 12 sequence-dependent transcription elongation models. The simplest model has two parameters and assumes that both translocation and NTP binding can be modelled as equilibrium processes. The most complex model has six parameters makes no partial equilibrium assumptions. We systematically compared the ability of these models to explain published force-velocity data, using approximate Bayesian computation. This analysis was performed using data for the RNA polymerase complexes of E. coli, S. cerevisiae and Bacteriophage T7. Our analysis indicates that the polymerases differ significantly in their translocation rates, with the rates in T7 pol being fast compared to E. coli RNAP and S. cerevisiae pol II. Different models are applicable in different cases. We also show that all three RNA polymerases have an energetic preference for the posttranslocated state over the pretranslocated state. A Bayesian inference and model selection framework, like the one presented in this publication, should be routinely applicable to the interrogation of single-molecule datasets., Competing Interests: The authors have declared that no competing interests exist.

The ability to connect genetic information between traits over time allow Bayesian networks to offer a powerful probabilistic framework to construct genomic prediction models. In this study, we phenotyped a diversity panel of 869 biomass sorghum ( Sorghum bicolor (L.) Moench) lines, which had been genotyped with 100,435 SNP markers, for plant height (PH) with biweekly measurements from 30 to 120 days after planting (DAP) and for end-of-season dry biomass yield (DBY) in four environments. We evaluated five genomic prediction models: Bayesian network (BN), Pleiotropic Bayesian network (PBN), Dynamic Bayesian network (DBN), multi-trait GBLUP (MTr-GBLUP), and multi-time GBLUP (MTi-GBLUP) models. In fivefold cross-validation, prediction accuracies ranged from 0.46 (PBN) to 0.49 (MTr-GBLUP) for DBY and from 0.47 (DBN, DAP120) to 0.75 (MTi-GBLUP, DAP60) for PH. Forward-chaining cross-validation further improved prediction accuracies of the DBN, MTi-GBLUP and MTr-GBLUP models for PH (training slice: 30-45 DAP) by 36.4-52.4% relative to the BN and PBN models. Coincidence indices (target: biomass, secondary: PH) and a coincidence index based on lines (PH time series) showed that the ranking of lines by PH changed minimally after 45 DAP. These results suggest a two-level indirect selection method for PH at harvest (first-level target trait) and DBY (second-level target trait) could be conducted earlier in the season based on ranking of lines by PH at 45 DAP (secondary trait). With the advance of high-throughput phenotyping technologies, our proposed two-level indirect selection framework could be valuable for enhancing genetic gain per unit of time when selecting on developmental traits., (Copyright © 2020 dos Santos et al.)

Optimized breeding goals and management practices for the improvement of target traits requires knowledge regarding any potential functional relationships between them. Fitting a structural equation model (SEM) allows for inferences about the magnitude of causal effects between traits to be made. In recent years, an adaptation of SEM was proposed in the context of quantitative genetics and mixed models. Several studies have since applied the SEM in the context of animal breeding. However, fitting the SEM requires choosing a causal structure with prior biological or temporal knowledge. The inductive causation (IC) algorithm can be used to recover an underlying causal structure from observed associations between traits. The results of the papers, which are introduced in this review, showed that using the IC algorithm to infer a causal structure is a helpful tool for detecting a causal structure without proper prior knowledge or with uncertain relationships between traits. The reports also presented that fitting the SEM could infer the effects of interventions, which are not given by correlations. Hence, information from the SEM provides more insights into and suggestions on breeding strategy than that from a multiple-trait model, which is the conventional model used for multitrait analysis., (© 2020 The Authors. Animal Science Journal published by John Wiley & Sons Australia, Ltd on behalf of Japanese Society of Animal Science.)

In this paper we propose a Bayesian multi-output regressor stacking (BMORS) model that is a generalization of the multi-trait regressor stacking method. The proposed BMORS model consists of two stages: in the first stage, a univariate genomic best linear unbiased prediction (GBLUP including genotype × environment interaction GE) model is implemented for each of the L traits under study; then the predictions of all traits are included as covariates in the second stage, by implementing a Ridge regression model. The main objectives of this research were to study alternative models to the existing multi-trait multi-environment (BMTME) model with respect to (1) genomic-enabled prediction accuracy, and (2) potential advantages in terms of computing resources and implementation. We compared the predictions of the BMORS model to those of the univariate GBLUP model using 7 maize and wheat datasets. We found that the proposed BMORS produced similar predictions to the univariate GBLUP model and to the BMTME model in terms of prediction accuracy; however, the best predictions were obtained under the BMTME model. In terms of computing resources, we found that the BMORS is at least 9 times faster than the BMTME method. Based on our empirical findings, the proposed BMORS model is an alternative for predicting multi-trait and multi-environment data, which are very common in genomic-enabled prediction in plant and animal breeding programs., (Copyright © 2019 Montesinos-Lopez et al.)

Expression quantitative trait loci (eQTL) analyses detect genetic variants (SNPs) associated with RNA expression levels of genes. The conventional eQTL analysis is to perform individual tests for each gene-SNP pair using simple linear regression and to perform the test on each tissue separately ignoring the extensive information known about RNA expression in other tissue(s). Although Bayesian models have been recently developed to improve eQTL prediction on multiple tissues, they are often based on uninformative priors or treat all tissues equally. In this study, we develop a novel tissue augmented Bayesian model for eQTL analysis (TA-eQTL), which takes prior eQTL information from a different tissue into account to better predict eQTL for another tissue. We demonstrate that our modified Bayesian model has comparable performance to several existing methods in terms of sensitivity and specificity using allele-specific expression (ASE) as the gold standard. Furthermore, the tissue augmented Bayesian model improves the power and accuracy for local-eQTL prediction especially when the sample size is small. In summary, TA-eQTL's performance is comparable to existing methods but has additional flexibility to evaluate data from different platforms, can focus prediction on one tissue using only summary statistics from the secondary tissue(s), and provides a closed form solution for estimation.

Trace DNA and the manner in which it is transferred from item to item is a common topic arising in forensic science, both in case evaluations, and in Court testimony. In order to assign the probability of obtaining DNA findings, given competing propositions that specify transfer mechanisms, consideration must be given to a number of factors. Previous work by the authors developed a simple Object-Oriented Bayesian Network (OOBN) that pooled numerous published studies in order to attempt evaluation of trace DNA results given such propositions. In this work, we expand on the previously published OOBN and formalise a number of class networks that can be used together in a logical way to consider DNA movement through complex chains of transfer events. Specifically, we develop an OOBN that considers the two-way transfer of DNA that occurs when two items contact, and allows for the sampling of intermediary items involved in the chain of transfers. The aim is to show that adopting an approach involving basic building blocks, we offer the possibility to tackle complex and various cases for which the OOBN will be obtained by combining their elementary blocks. We conclude with a demonstration of applying the OOBN being applied to a chain of transfers in a case scenario., (Copyright © 2019 Elsevier B.V. All rights reserved.)

Background: Single-cell gene expression measurements offer opportunities in deriving mechanistic understanding of complex diseases, including cancer. However, due to the complex regulatory machinery of the cell, gene regulatory network (GRN) model inference based on such data still manifests significant uncertainty., Results: The goal of this paper is to develop optimal classification of single-cell trajectories accounting for potential model uncertainty. Partially-observed Boolean dynamical systems (POBDS) are used for modeling gene regulatory networks observed through noisy gene-expression data. We derive the exact optimal Bayesian classifier (OBC) for binary classification of single-cell trajectories. The application of the OBC becomes impractical for large GRNs, due to computational and memory requirements. To address this, we introduce a particle-based single-cell classification method that is highly scalable for large GRNs with much lower complexity than the optimal solution., Conclusion: The performance of the proposed particle-based method is demonstrated through numerical experiments using a POBDS model of the well-known T-cell large granular lymphocyte (T-LGL) leukemia network with noisy time-series gene-expression data.

Elaboration of Bayesian phylogenetic inference methods has continued at pace in recent years with major new advances in nearly all aspects of the joint modelling of evolutionary data. It is increasingly appreciated that some evolutionary questions can only be adequately answered by combining evidence from multiple independent sources of data, including genome sequences, sampling dates, phenotypic data, radiocarbon dates, fossil occurrences, and biogeographic range information among others. Including all relevant data into a single joint model is very challenging both conceptually and computationally. Advanced computational software packages that allow robust development of compatible (sub-)models which can be composed into a full model hierarchy have played a key role in these developments. Developing such software frameworks is increasingly a major scientific activity in its own right, and comes with specific challenges, from practical software design, development and engineering challenges to statistical and conceptual modelling challenges. BEAST 2 is one such computational software platform, and was first announced over 4 years ago. Here we describe a series of major new developments in the BEAST 2 core platform and model hierarchy that have occurred since the first release of the software, culminating in the recent 2.5 release., Competing Interests: The authors have declared that no competing interests exist.

An approach to the coalescent, the fractional coalescent (f-coalescent), is introduced. The derivation is based on the discrete-time Cannings population model in which the variance of the number of offspring depends on the parameter α. This additional parameter α affects the variability of the patterns of the waiting times; values of [Formula: see text] lead to an increase of short time intervals, but occasionally allow for very long time intervals. When [Formula: see text], the f-coalescent and the Kingman's n-coalescent are equivalent. The distribution of the time to the most recent common ancestor and the probability that n genes descend from m ancestral genes in a time interval of length T for the f-coalescent are derived. The f-coalescent has been implemented in the population genetic model inference software Migrate Simulation studies suggest that it is possible to accurately estimate α values from data that were generated with known α values and that the f-coalescent can detect potential environmental heterogeneity within a population. Bayes factor comparisons of simulated data with [Formula: see text] and real data (H1N1 influenza and malaria parasites) showed an improved model fit of the f-coalescent over the n-coalescent. The development of the f-coalescent and its inclusion into the inference program Migrate facilitates testing for deviations from the n-coalescent., Competing Interests: The authors declare no conflict of interest., (Copyright © 2019 the Author(s). Published by PNAS.)

Measurements of single-cell methylation are revolutionizing our understanding of epigenetic control of gene expression, yet the intrinsic data sparsity limits the scope for quantitative analysis of such data. Here, we introduce Melissa (MEthyLation Inference for Single cell Analysis), a Bayesian hierarchical method to cluster cells based on local methylation patterns, discovering patterns of epigenetic variability between cells. The clustering also acts as an effective regularization for data imputation on unassayed CpG sites, enabling transfer of information between individual cells. We show both on simulated and real data sets that Melissa provides accurate and biologically meaningful clusterings and state-of-the-art imputation performance.

Climatic changes have played major roles in plants' evolutionary history. Glacial oscillations have been particularly important, but some of their effects on plants' populations are poorly understood, including the numbers and locations of refugia in Asian warm temperate zones. In the present study, we investigated the demographic history of the broadleaved evergreen tree species Castanopsis sieboldii (Fagaceae) during the last glacial period in Japan. We used approximate Bayesian computation (ABC) for model comparison and parameter estimation for the demographic modeling using 27 EST-associated microsatellites. We also performed the species distribution modeling (SDM). The results strongly support a demographic scenario that the Ryukyu Islands and the western parts in the main islands (Kyushu and western Shikoku) were derived from separate refugia and the eastern parts in the main islands and the Japan Sea groups were diverged from the western parts prior to the coldest stage of the Last Glacial Maximum (LGM). Our data indicate that multiple refugia survived at least one in the Ryukyu Islands, and the other three regions of the western and eastern parts and around the Japan Sea of the main islands of Japan during the LGM. The SDM analysis also suggests the potential habitats under LGM climate conditions were mainly located along the Pacific Ocean side of the coastal region. Our ABC-based study helps efforts resolve the demographic history of a dominant species in warm temperate broadleaved forests during and after the last glacial period, which provides a basic model for future phylogeographical studies using this approach.

Motivation: Identifying variants, both discrete and continuous, that are associated with quantitative traits, or QTs, is the primary focus of quantitative genetics. Most current methods are limited to identifying mean effects, or associations between genotype or covariates and the mean value of a quantitative trait. It is possible, however, that a variant may affect the variance of the quantitative trait in lieu of, or in addition to, affecting the trait mean. Here, we develop a general methodology to identify covariates with variance effects on a quantitative trait using a Bayesian heteroskedastic linear regression model (BTH). We compare BTH with existing methods to detect variance effects across a large range of simulations drawn from scenarios common to the analysis of quantitative traits., Results: We find that BTH and a double generalized linear model (dglm) outperform classical tests used for detecting variance effects in recent genomic studies. We show BTH and dglm are less likely to generate spurious discoveries through simulations and application to identifying methylation variance QTs and expression variance QTs. We identify four variance effects of sex in the Cardiovascular and Pharmacogenetics study. Our work is the first to offer a comprehensive view of variance identifying methodology. We identify shortcomings in previously used methodology and provide a more conservative and robust alternative. We extend variance effect analysis to a wide array of covariates that enables a new statistical dimension in the study of sex and age specific quantitative trait effects., Availability and Implementation: https://github.com/b2du/bth., Supplementary Information: Supplementary data are available at Bioinformatics online.

Bayesian methods for molecular clock dating of species divergences have been greatly developed during the past decade. Advantages of the methods include the use of relaxed-clock models to describe evolutionary rate variation in the branches of a phylogenetic tree and the use of flexible fossil calibration densities to describe the uncertainty in node ages. The advent of next-generation sequencing technologies has led to a flood of genome-scale datasets for organisms belonging to all domains in the tree of life. Thus, a new era has begun where dating the tree of life using genome-scale data is now within reach. In this protocol, we explain how to use the computer program MCMCTree to perform Bayesian inference of divergence times using genome-scale datasets. We use a ten-species primate phylogeny, with a molecular alignment of over three million base pairs, as an exemplar on how to carry out the analysis. We pay particular attention to how to set up the analysis and the priors and how to diagnose the MCMC algorithm used to obtain the posterior estimates of divergence times and evolutionary rates.

Genetic variants in genome-wide association studies (GWAS) are tested for disease association mostly using simple regression, one variant at a time. Standard approaches to improve power in detecting disease-associated SNPs use multiple regression with Bayesian variable selection in which a sparsity-enforcing prior on effect sizes is used to avoid overtraining and all effect sizes are integrated out for posterior inference. For binary traits, the logistic model has not yielded clear improvements over the linear model. For multi-SNP analysis, the logistic model required costly and technically challenging MCMC sampling to perform the integration. Here, we introduce the quasi-Laplace approximation to solve the integral and avoid MCMC sampling. We expect the logistic model to perform much better than multiple linear regression except when predicted disease risks are spread closely around 0.5, because only close to its inflection point can the logistic function be well approximated by a linear function. Indeed, in extensive benchmarks with simulated phenotypes and real genotypes, our Bayesian multiple LOgistic REgression method (B-LORE) showed considerable improvements (1) when regressing on many variants in multiple loci at heritabilities ≥ 0.4 and (2) for unbalanced case-control ratios. B-LORE also enables meta-analysis by approximating the likelihood functions of individual studies by multivariate normal distributions, using their means and covariance matrices as summary statistics. Our work should make sparse multiple logistic regression attractive also for other applications with binary target variables. B-LORE is freely available from: https://github.com/soedinglab/b-lore., Competing Interests: The authors have declared that no competing interests exist.

The sequencing and comparative analysis of a collection of bacterial genomes from a single species or lineage of interest can lead to key insights into its evolution, ecology or epidemiology. The tool of choice for such a study is often to build a phylogenetic tree, and more specifically when possible a dated phylogeny, in which the dates of all common ancestors are estimated. Here, we propose a new Bayesian methodology to construct dated phylogenies which is specifically designed for bacterial genomics. Unlike previous Bayesian methods aimed at building dated phylogenies, we consider that the phylogenetic relationships between the genomes have been previously evaluated using a standard phylogenetic method, which makes our methodology much faster and scalable. This two-step approach also allows us to directly exploit existing phylogenetic methods that detect bacterial recombination, and therefore to account for the effect of recombination in the construction of a dated phylogeny. We analysed many simulated datasets in order to benchmark the performance of our approach in a wide range of situations. Furthermore, we present applications to three different real datasets from recent bacterial genomic studies. Our methodology is implemented in a R package called BactDating which is freely available for download at https://github.com/xavierdidelot/BactDating.

Background: Until recently, determining penetrance required large observational cohort studies. Data from the Exome Aggregate Consortium (ExAC) allows a Bayesian approach to calculate penetrance, in that population frequencies of pathogenic germline variants should be inversely proportional to their penetrance for disease. We tested this hypothesis using data from two cohorts for succinate dehydrogenase subunits A, B and C ( SDHA-C ) genetic variants associated with hereditary pheochromocytoma/paraganglioma (PC/PGL)., Methods: Two cohorts were 575 unrelated Australian subjects and 1240 unrelated UK subjects, respectively, with PC/PGL in whom genetic testing had been performed. Penetrance of pathogenic SDHA-C variants was calculated by comparing allelic frequencies in cases versus controls from ExAC (removing those variants contributed by The Cancer Genome Atlas)., Results: Pathogenic SDHA-C variants were identified in 106 subjects (18.4%) in cohort 1 and 317 subjects (25.6%) in cohort 2. Of 94 different pathogenic variants from both cohorts (seven in SDHA , 75 in SDHB and 12 in SDHC ), 13 are reported in ExAC (two in SDHA , nine in SDHB and two in SDHC ) accounting for 21% of subjects with SDHA-C variants. Combining data from both cohorts, estimated lifetime disease penetrance was 22.0% (95% CI 15.2% to 30.9%) for SDHB variants, 8.3% (95% CI 3.5% to 18.5%) for SDHC variants and 1.7% (95% CI 0.8% to 3.8%) for SDHA variants., Conclusion: Pathogenic variants in SDHB are more penetrant than those in SDHC and SDHA . Our findings have important implications for counselling and surveillance of subjects carrying these pathogenic variants., Competing Interests: Competing interests: None declared., (© Author(s) (or their employer(s)) 2018. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.)

Background and ObjectiveBayesian State Space models are recent advancement in stochastic modeling which capture the randomness of a hidden background process by scrutinizing the prior knowledge and likelihood of observed data. This article elucidate the scope of Bayesian state space modeling on predicting the future expression values of a longitudinal micro array data. MethodsThe study conveniently makes use of longitudinally collected clinical trial data (GSE30531) from NCBI Gene Expression Omnibus (GEO) data repository. Multiple testing methodology using t-test is used for selecting differentially expressed genes between groups for fitting the model. The parameter values of the predictive model and future expression levels are estimated by drawing samples from the posterior joint distribution using a stochastic Markov Chain Monte Carlo (MCMC) algorithm which relies on Gibbs Sampling. The study also made an attempt to get estimates and its 95% Credible Interval through assumptions of different covariance structures like Variance Components, First order Auto Regressive and Unstructured variance-covariance structure to showcase the flexibility of the algorithm. Results72 Distinct genes with significantly different expression levels where selected for model fitting. Parameter estimates showed almost similar trends under different covariance structure assumption. Cross tabulation of gene frequencies having minimum credible interval under each covariance structure and study group showed a significant P value of 0.02. ConclusionsPresent study reveals that Bayesian state space models can be effectively used to explain and predict a complex data like gene expression data., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Bayesian inference of phylogeny using Markov chain Monte Carlo (MCMC) plays a central role in understanding evolutionary history from molecular sequence data. Visualizing and analyzing the MCMC-generated samples from the posterior distribution is a key step in any non-trivial Bayesian inference. We present the software package Tracer (version 1.7) for visualizing and analyzing the MCMC trace files generated through Bayesian phylogenetic inference. Tracer provides kernel density estimation, multivariate visualization, demographic trajectory reconstruction, conditional posterior distribution summary, and more. Tracer is open-source and available at http://beast.community/tracer.

Bayesian models for genomic prediction and association mapping are being increasingly used in genetics analysis of quantitative traits. Given a point estimate of variance components, the popular methods SNP-BLUP and GBLUP result in joint estimates of the effect of all markers on the analyzed trait; single and multiple marker frequentist tests (EMMAX) can be constructed from these estimates. Indeed, BLUP methods can be seen simultaneously as Bayesian or frequentist methods. So far there is no formal method to produce Bayesian statistics from GBLUP. Here we show that the Bayes Factor, a commonly admitted statistical procedure, can be computed as the ratio of two normal densities: the first, of the estimate of the marker effect over its posterior standard deviation; the second of the null hypothesis (a value of 0 over the prior standard deviation). We extend the BF to pool evidence from several markers and of several traits. A real data set that we analyze, with ours and existing methods, analyzes 630 horses genotyped for 41711 polymorphic SNPs for the trait "outcome of the qualification test" (which addresses gait, or ambling, of horses) for which a known major gene exists. In the horse data, single marker EMMAX shows a significant effect at the right place at Bonferroni level. The BF points to the same location although with low numerical values. The strength of evidence combining information from several consecutive markers increases using the BF and decreases using EMMAX, which comes from a fundamental difference in the Bayesian and frequentist schools of hypothesis testing. We conclude that our BF method complements frequentist EMMAX analyses because it provides a better pooling of evidence across markers, although its use for primary detection is unclear due to the lack of defined rejection thresholds., (Copyright © 2018 Legarra et al.)

Using a nonparametric Bayesian approach Palacios and Minin (2013) dramatically improved the accuracy, precision of Bayesian inference of population size trajectories from gene genealogies. These authors proposed an extension of a Gaussian Process (GP) nonparametric inferential method for the intensity function of non-homogeneous Poisson processes. They found that not only the statistical properties of the estimators were improved with their method, but also, that key aspects of the demographic histories were recovered. The authors' work represents the first Bayesian nonparametric solution to this inferential problem because they specify a convenient prior belief without a particular functional form on the population trajectory. Their approach works so well and provides such a profound understanding of the biological process, that the question arises as to how truly "biology-free" their approach really is. Using well-known concepts of stochastic population dynamics, here I demonstrate that in fact, Palacios and Minin's GP model can be cast as a parametric population growth model with density dependence and environmental stochasticity. Making this link between population genetics and stochastic population dynamics modeling provides novel insights into eliciting biologically meaningful priors for the trajectory of the effective population size. The results presented here also bring novel understanding of GP as models for the evolution of a trait. Thus, the ecological principles foundation of Palacios and Minin (2013)'s prior adds to the conceptual and scientific value of these authors' inferential approach. I conclude this note by listing a series of insights brought about by this connection with Ecology., (Copyright © 2017 The Author. Published by Elsevier Inc. All rights reserved.)

The increasing availability of population-level allele frequency data across one or more related populations necessitates the development of methods that can efficiently estimate population genetics parameters, such as the strength of selection acting on the population(s), from such data. Existing methods for this problem in the setting of the Wright-Fisher diffusion model are primarily likelihood-based, and rely on numerical approximation for likelihood computation and on bootstrapping for assessment of variability in the resulting estimates, requiring extensive computation. Recent work has provided a method for obtaining exact samples from general Wright-Fisher diffusion processes, enabling the development of methods for Bayesian estimation in this setting. We develop and implement a Bayesian method for estimating the strength of selection based on the Wright-Fisher diffusion for data sampled at a single time point. The method utilizes the latest algorithms for exact sampling to devise a Markov chain Monte Carlo procedure to draw samples from the joint posterior distribution of the selection coefficient and the allele frequencies. We demonstrate that when assumptions about the initial allele frequencies are accurate the method performs well for both simulated data and for an empirical data set on hypoxia in flies, where we find evidence for strong positive selection in a region of chromosome 2L previously identified. We discuss possible extensions of our method to the more general settings commonly encountered in practice, highlighting the advantages of Bayesian approaches to inference in this setting.

Bayesian multiple-regression methods incorporating different mixture priors for marker effects are used widely in genomic prediction. Improvement in prediction accuracies from using those methods, such as BayesB, BayesC, and BayesC π , have been shown in single-trait analyses with both simulated and real data. These methods have been extended to multi-trait analyses, but only under the restrictive assumption that a locus simultaneously affects all the traits or none of them. This assumption is not biologically meaningful, especially in multi-trait analyses involving many traits. In this paper, we develop and implement a more general multi-trait BayesC[Formula: see text] and BayesB methods allowing a broader range of mixture priors. Our methods allow a locus to affect any combination of traits, e.g. , in a 5-trait analysis, the "restrictive" model only allows two situations, whereas ours allow all 32 situations. Further, we compare our methods to single-trait methods and the "restrictive" multi-trait formulation using real and simulated data. In the real data analysis, higher prediction accuracies were observed from both our new broad-based multi-trait methods and the "restrictive" formulation. The broad-based and restrictive multi-trait methods showed similar prediction accuracies. In the simulated data analysis, higher prediction accuracies to the "restrictive" method were observed from our general multi-trait methods for intermediate training population size. The software tool JWAS offers open-source routines to perform these analyses., (Copyright © 2018 by the Genetics Society of America.)