A Bayesian framework for comparative quantitative genetics

Bayesian approaches have been extensively used in animal breeding sciences, but similar approaches in the context of evolutionary quantitative genetics have been rare. We compared the performance of Bayesian and frequentist approaches in estimation of quantitative genetic parameters (viz. matrices of additive and dominance variances) in datasets typical of evolutionary studies and traits differing in their genetic architecture. Our results illustrate that it is difficult to disentangle the relative roles of different genetic components from small datasets, and that ignoring, e.g. dominance is likely to lead to biased estimates of additive variance. We suggest that a natural summary statistic for G-matrix comparisons can be obtained by examining how different the underlying multinormal probability distributions are, and illustrate our approach with data on the common frog (Rana temporaria). Furthermore, we derive a simple Monte Carlo method for computation of fraternity coefficients needed for the estimation of dominance variance, and use the pedigree of a natural Siberian jay (Perisoreus infaustus) population to illustrate that the commonly used approximate values can be substantially biased.     

Bayesian species delimitation combining multiple genes and traits in a unified framework

Delimitation of species based exclusively on genetic data has been advocated despite a critical knowledge gap: how might such approaches fail because they rely on genetic data alone, and would their accuracy be improved by using multiple data types. We provide here the requisite framework for addressing these key questions. Because both phenotypic and molecular data can be analyzed in a common Bayesian framework with our program iBPP, we can compare the accuracy of delimited taxa based on genetic data alone versus when integrated with phenotypic data. We can also evaluate how the integration of phenotypic data might improve species delimitation when divergence occurs with gene flow and/or is selectively driven. These two realities of the speciation process are ignored by currently available genetic approaches. Our model accommodates phenotypic characters that exhibit different degrees of divergence, allowing for both neutral traits and traits under selection. We found a greater accuracy of estimated species boundaries with the integration of phenotypic and genetic data, with a strong beneficial influence of phenotypic data from traits under selection when the speciation process involves gene flow. Our results highlight the benefits of multiple data types, but also draws into question the rationale of species delimitation based exclusively on genetic data.     

A Bayesian framework for the analysis of cospeciation

Abstract.— Information on the history of cospeciation and host switching for a group of host and parasite species is contained in the DNA sequences sampled from each. Here, we develop a Bayesian framework for the analysis of cospeciation. We suggest a simple model of host switching by a parasite on a host phylogeny in which host switching events are assumed to occur at a constant rate over the entire evolutionary history of associated hosts and parasites. The posterior probability density of the parameters of the model of host switching are evaluated numerically using Markov chain Monte Carlo. In particular, the method generates the probability density of the number of host switches and of the host switching rate. Moreover, the method provides information on the probability that an event of host switching is associated with a particular pair of branches. A Bayesian approach has several advantages over other methods for the analysis of cospeciation. In particular, it does not assume that the host or parasite phylogenies are known without error; many alternative phylogenies are sampled in proportion to their probability of being correct.     

A statistical framework for combining and interpreting proteomic datasets

MOTIVATION: To identify accurately protein function on a proteome-wide scale requires integrating data within and between high-throughput experiments. High-throughput proteomic datasets often have high rates of errors and thus yield incomplete and contradictory information. In this study, we develop a simple statistical framework using Bayes' law to interpret such data and combine information from different high-throughput experiments. In order to illustrate our approach we apply it to two protein complex purification datasets. RESULTS: Our approach shows how to use high-throughput data to calculate accurately the probability that two proteins are part of the same complex. Importantly, our approach does not need a reference set of verified protein interactions to determine false positive and false negative error rates of protein association. We also demonstrate how to combine information from two separate protein purification datasets into a combined dataset that has greater coverage and accuracy than either dataset alone. In addition, we also provide a technique for estimating the total number of proteins which can be detected using a particular experimental technique. AVAILABILITY: A suite of simple programs to accomplish some of the above tasks is available at www.unm.edu/~compbio/software/DatasetAssess     

A Bayesian hierarchical approach for combining case-control and prospective studies

Motivated by the absolute risk predictions required in medical decision making and patient counseling, we propose an approach for the combined analysis of case-control and prospective studies of disease risk factors. The approach is hierarchical to account for parameter heterogeneity among studies and among sampling units of the same study. It is based on modeling the retrospective distribution of the covariates given the disease outcome, a strategy that greatly simplifies both the combination of prospective and retrospective studies and the computation of Bayesian predictions in the hierarchical case-control context. Retrospective modeling differentiates our approach from most current strategies for inference on risk factors, which are based on the assumption of a specific prospective model. To ensure modeling flexibility, we propose using a mixture model for the retrospective distributions of the covariates. This leads to a general nonlinear regression family for the implied prospective likelihood. After introducing and motivating our proposal, we present simple results that highlight its relationship with existing approaches, develop Markov chain Monte Carlo methods for inference and prediction, and present an illustration using ovarian cancer data.     

A Bayesian framework for parameter estimation in dynamical models

Mathematical models in biology are powerful tools for the study and exploration of complex dynamics. Nevertheless, bringing theoretical results to an agreement with experimental observations involves acknowledging a great deal of uncertainty intrinsic to our theoretical representation of a real system. Proper handling of such uncertainties is key to the successful usage of models to predict experimental or field observations. This problem has been addressed over the years by many tools for model calibration and parameter estimation. In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used. We apply the framework to fit an SIR-like influenza transmission model to 7 years of incidence data in three European countries: Belgium, the Netherlands and Portugal.     

A mechanistic framework for a priori pharmacokinetic predictions of orally inhaled drugs

The fate of orally inhaled drugs is determined by pulmonary pharmacokinetic processes such as particle deposition, pulmonary drug dissolution, and mucociliary clearance. Even though each single process has been systematically investigated, a quantitative understanding on the interaction of processes remains limited and therefore identifying optimal drug and formulation characteristics for orally inhaled drugs is still challenging. To investigate this complex interplay, the pulmonary processes can be integrated into mathematical models. However, existing modeling attempts considerably simplify these processes or are not systematically evaluated against (clinical) data. In this work, we developed a mathematical framework based on physiologically-structured population equations to integrate all relevant pulmonary processes mechanistically. A tailored numerical resolution strategy was chosen and the mechanistic model was evaluated systematically against data from different clinical studies. Without adapting the mechanistic model or estimating kinetic parameters based on individual study data, the developed model was able to predict simultaneously (i) lung retention profiles of inhaled insoluble particles, (ii) particle size-dependent pharmacokinetics of inhaled monodisperse particles, (iii) pharmacokinetic differences between inhaled fluticasone propionate and budesonide, as well as (iv) pharmacokinetic differences between healthy volunteers and asthmatic patients. Finally, to identify the most impactful optimization criteria for orally inhaled drugs, the developed mechanistic model was applied to investigate the impact of input parameters on both the pulmonary and systemic exposure. Interestingly, the solubility of the inhaled drug did not have any relevant impact on the local and systemic pharmacokinetics. Instead, the pulmonary dissolution rate, the particle size, the tissue affinity, and the systemic clearance were the most impactful potential optimization parameters. In the future, the developed prediction framework should be considered a powerful tool for identifying optimal drug and formulation characteristics.     

A Bayesian calibration model for combining different pre-processing methods in Affymetrix chips

Background  

In gene expression studies a key role is played by the so called "pre-processing", a series of steps designed to extract the signal and account for the sources of variability due to the technology used rather than to biological differences between the RNA samples. At the moment there is no commonly agreed gold standard pre-processing method and each researcher has the responsibility to choose one method, incurring the risk of false positive and false negative features arising from the particular method chosen.     

A Bayesian framework for inference of the genotype-phenotype map for segregating populations

Complex genetic interactions lie at the foundation of many diseases. Understanding the nature of these interactions is critical to developing rational intervention strategies. In mammalian systems hypothesis testing in vivo is expensive, time consuming, and often restricted to a few physiological endpoints. Thus, computational methods that generate causal hypotheses can help to prioritize targets for experimental intervention. We propose a Bayesian statistical method to infer networks of causal relationships among genotypes and phenotypes using expression quantitative trait loci (eQTL) data from genetically randomized populations. Causal relationships between network variables are described with hierarchical regression models. Prior distributions on the network structure enforce graph sparsity and have the potential to encode prior biological knowledge about the network. An efficient Monte Carlo method is used to search across the model space and sample highly probable networks. The result is an ensemble of networks that provide a measure of confidence in the estimated network topology. These networks can be used to make predictions of system-wide response to perturbations. We applied our method to kidney gene expression data from an MRL/MpJ × SM/J intercross population and predicted a previously uncharacterized feedback loop in the local renin-angiotensin system.     

Towards unbiased parentage assignment: combining genetic, behavioural and spatial data in a Bayesian framework

Inferring the parentage of a sample of individuals is often a prerequisite for many types of analysis in molecular ecology, evolutionary biology and quantitative genetics. In all but a few cases, the method of parentage assignment is divorced from the methods used to estimate the parameters of primary interest, such as mate choice or heritability. Here we present a Bayesian approach that simultaneously estimates the parentage of a sample of individuals and a wide range of population-level parameters in which we are interested. We show that joint estimation of parentage and population-level parameters increases the power of parentage assignment, reduces bias in parameter estimation, and accurately evaluates uncertainty in both. We illustrate the method by analysing a number of simulated test data sets, and through a re-analysis of parentage in the Seychelles warbler, Acrocephalus sechellensis. A combination of behavioural, spatial and genetic data are used in the analyses and, importantly, the method does not require strong prior information about the relationship between nongenetic data and parentage.     

Conflicting phylogenies of balsaminoid families and the polytomy in Ericales: combining data in a Bayesian framework

The balsaminoid Ericales, namely Balsaminaceae, Marcgraviaceae, Tetrameristaceae, and Pellicieraceae have been confidently placed at the base of Ericales, but the relations among these families have been resolved differently in recent analyses. Sister to this basal group is a large polytomy comprising all other families of Ericales, which is associated with short internodes. Because there are more than 13 kb of sequences for a large sampling of representatives, a thorough examination of the available data with novel methods seemed in place. Because of its computational speed, Bayesian phylogenetics allows for the use of parameter-rich models that can accommodate differences in the evolutionary process between partitions in a simultaneous analysis. In addition, there are recently proposed Bayesian strategies of assessing incongruence between partitions. We have applied these methods to the current problems in Ericales phylogeny, taking into account reported pitfalls in Bayesian analysis such as model selection uncertainty. Based on our results we infer several, previously unresolved relationships in the order Ericales. In balsaminoid families, we find that the closest relatives of Balsaminaceae are Marcgraviaceae. In the Ericales polytomy, we find strong support for Pentaphylacaceae sensu APG II as the sister group of Maesaceae. In addition, Symplocaceae receive a position as sister to Theaceae and these families form a monophyletic group together with Styracaceae-Diapensiaceae. At the base of this clade are Actinidiaceae and Clethraceae. The positions of Ebenaceae and Lecythidaceae remain uncertain.     

Fine mapping of complex trait genes combining pedigree and linkage disequilibrium information: a Bayesian unified framework

We present a Bayesian method that combines linkage and linkage disequilibrium (LDL) information for quantitative trait locus (QTL) mapping. This method uses jointly all marker information (haplotypes) and all available pedigree information; i.e., it is not restricted to any specific experimental design and it is not required that phases are known. Infinitesimal genetic effects or environmental noise ("fixed") effects can equally be fitted. A diallelic QTL is assumed and both additive and dominant effects can be estimated. We have implemented a combined Gibbs/Metropolis-Hastings sampling to obtain the marginal posterior distributions of the parameters of interest. We have also implemented a Bayesian variant of usual disequilibrium measures like D' and r(2) between QTL and markers. We illustrate the method with simulated data in "simple" (two-generation full-sib families) and "complex" (four-generation) pedigrees. We compared the estimates with and without using linkage disequilibrium information. In general, using LDL resulted in estimates of QTL position that were much better than linkage-only estimates when there was complete disequilibrium between the mutant QTL allele and the marker. This advantage, however, decreased when the association was only partial. In all cases, additive and dominant effects were estimated accurately either with or without disequilibrium information.     

A variational Bayesian mixture modelling framework for cluster analysis of gene-expression data

MOTIVATION: Accurate subcategorization of tumour types through gene-expression profiling requires analytical techniques that estimate the number of categories or clusters rigorously and reliably. Parametric mixture modelling provides a natural setting to address this problem. RESULTS: We compare a criterion for model selection that is derived from a variational Bayesian framework with a popular alternative based on the Bayesian information criterion. Using simulated data, we show that the variational Bayesian method is more accurate in finding the true number of clusters in situations that are relevant to current and future microarray studies. We also compare the two criteria using freely available tumour microarray datasets and show that the variational Bayesian method is more sensitive to capturing biologically relevant structure.