Genomic prediction of cotton fibre quality and yield traits using Bayesian regression methods

Genomic selection or genomic prediction (GP) has increasingly become an important molecular breeding technology for crop improvement. GP aims to utilise genome-wide marker data to predict genomic breeding value for traits of economic importance. Though GP studies have been widely conducted in various crop species such as wheat and maize, its application in cotton, an essential renewable textile fibre crop, is still significantly underdeveloped. We aim to develop a new GP-based breeding system that can improve the efficiency of our cotton breeding program. This article presents a GP study on cotton fibre quality and yield traits using 1385 breeding lines from the Commonwealth Scientific and Industrial Research Organisation (CSIRO, Australia) cotton breeding program which were genotyped using a high-density SNP chip that generated 12,296 informative SNPs. The aim of this study was twofold: (1) to identify the models and data sources (i.e. genomic and pedigree) that produce the highest prediction accuracies; and (2) to assess the effectiveness of GP as a selection tool in the CSIRO cotton breeding program. The prediction analyses were conducted under various scenarios using different Bayesian predictive models. Results highlighted that the model combining genomic and pedigree information resulted in the best cross validated prediction accuracies: 0.76 for fibre length, 0.65 for fibre strength, and 0.64 for lint yield. Overall, this work represents the largest scale genomic selection studies based on cotton breeding trial data. Prediction accuracies reported in our study indicate the potential of GP as a breeding tool for cotton. The study highlighted the importance of incorporating pedigree and environmental factors in GP models to optimise the prediction performance.Subject terms: Plant breeding, Genome     

Genomic prediction of reproduction traits for Merino sheep

Economically important reproduction traits in sheep, such as number of lambs weaned and litter size, are expressed only in females and later in life after most selection decisions are made, which makes them ideal candidates for genomic selection. Accurate genomic predictions would lead to greater genetic gain for these traits by enabling accurate selection of young rams with high genetic merit. The aim of this study was to design and evaluate the accuracy of a genomic prediction method for female reproduction in sheep using daughter trait deviations (DTD) for sires and ewe phenotypes (when individual ewes were genotyped) for three reproduction traits: number of lambs born (NLB), litter size (LSIZE) and number of lambs weaned. Genomic best linear unbiased prediction (GBLUP), BayesR and pedigree BLUP analyses of the three reproduction traits measured on 5340 sheep (4503 ewes and 837 sires) with real and imputed genotypes for 510 174 SNPs were performed. The prediction of breeding values using both sire and ewe trait records was validated in Merino sheep. Prediction accuracy was evaluated by across sire family and random cross‐validations. Accuracies of genomic estimated breeding values (GEBVs) were assessed as the mean Pearson correlation adjusted by the accuracy of the input phenotypes. The addition of sire DTD into the prediction analysis resulted in higher accuracies compared with using only ewe records in genomic predictions or pedigree BLUP. Using GBLUP, the average accuracy based on the combined records (ewes and sire DTD) was 0.43 across traits, but the accuracies varied by trait and type of cross‐validations. The accuracies of GEBVs from random cross‐validations (range 0.17–0.61) were higher than were those from sire family cross‐validations (range 0.00–0.51). The GEBV accuracies of 0.41–0.54 for NLB and LSIZE based on the combined records were amongst the highest in the study. Although BayesR was not significantly different from GBLUP in prediction accuracy, it identified several candidate genes which are known to be associated with NLB and LSIZE. The approach provides a way to make use of all data available in genomic prediction for traits that have limited recording.     

Regressive logistic models for familial disease and other binary traits

The simple Markovian structures of dependence, defined previously for continuous traits, are extended here to familial disease and other binary traits through the use of the logistic function. The regressive models so formulated can incorporate explanatory variables and major gene effects for segregation and linkage analyses. Thus, the goals of epidemiology and genetics in the analysis of familial disease can be accomplished in the same computational scheme.     

Diffusion kernel-based logistic regression models for protein function prediction

Assigning functions to unknown proteins is one of the most important problems in proteomics. Several approaches have used protein-protein interaction data to predict protein functions. We previously developed a Markov random field (MRF) based method to infer a protein's functions using protein-protein interaction data and the functional annotations of its protein interaction partners. In the original model, only direct interactions were considered and each function was considered separately. In this study, we develop a new model which extends direct interactions to all neighboring proteins, and one function to multiple functions. The goal is to understand a protein's function based on information on all the neighboring proteins in the interaction network. We first developed a novel kernel logistic regression (KLR) method based on diffusion kernels for protein interaction networks. The diffusion kernels provide means to incorporate all neighbors of proteins in the network. Second, we identified a set of functions that are highly correlated with the function of interest, referred to as the correlated functions, using the chi-square test. Third, the correlated functions were incorporated into our new KLR model. Fourth, we extended our model by incorporating multiple biological data sources such as protein domains, protein complexes, and gene expressions by converting them into networks. We showed that the KLR approach of incorporating all protein neighbors significantly improved the accuracy of protein function predictions over the MRF model. The incorporation of multiple data sets also improved prediction accuracy. The prediction accuracy is comparable to another protein function classifier based on the support vector machine (SVM), using a diffusion kernel. The advantages of the KLR model include its simplicity as well as its ability to explore the contribution of neighbors to the functions of proteins of interest.     

Bayesian prediction of breeding values for multivariate binary and continuous traits in simulated horse populations using threshold-linear models with Gibbs sampling

Simulated data were used to determine the properties of multivariate prediction of breeding values for categorical and continuous traits using phenotypic, molecular genetic and pedigree information by mixed linear-threshold animal models via Gibbs sampling. Simulation parameters were chosen such that the data resembled situations encountered in Warmblood horse populations. Genetic evaluation was performed in the context of the radiographic findings in the equine limbs. The simulated pedigree comprised seven generations and 40 000 animals per generation. The simulated data included additive genetic values, residuals and fixed effects for one continuous trait and liabilities of four binary traits. For one of the binary traits, quantitative trait locus (QTL) effects and genetic markers were simulated, with three different scenarios with respect to recombination rate (r) between genetic markers and QTL and polymorphism information content (PIC) of genetic markers being studied: r = 0.00 and PIC = 0.90 (r0p9), r = 0.01 and PIC = 0.90 (r1p9), and r = 0.00 and PIC = 0.70 (r0p7). For each scenario, 10 replicates were sampled from the simulated horse population, and six different data sets were generated per replicate. Data sets differed in number and distribution of animals with trait records and the availability of genetic marker information. Breeding values were predicted via Gibbs sampling using a Bayesian mixed linear-threshold animal model with residual covariances fixed to zero and a proper prior for the genetic covariance matrix. Relative breeding values were used to investigate expected response to multi- and single-trait selection. In the sires with 10 or more offspring with trait information, correlations between true and predicted breeding values ranged between 0.89 and 0.94 for the continuous traits and between 0.39 and 0.77 for the binary traits. Proportions of successful identification of sires of average, favourable and unfavourable genetic value were 81% to 86% for the continuous trait and 57% to 74% for the binary traits in these sires. Expected decrease of prevalence of the QTL trait was 3% to 12% after multi-trait selection for all binary traits and 9% to 17% after single-trait selection for the QTL trait. The combined use of phenotype and genotype data was superior to the use of phenotype data alone. It was concluded that information on phenotypes and highly informative genetic markers should be used for prediction of breeding values in mixed linear-threshold animal models via Gibbs sampling to achieve maximum reduction in prevalences of binary traits.     

Bayesian multivariate logistic regression

Bayesian analyses of multivariate binary or categorical outcomes typically rely on probit or mixed effects logistic regression models that do not have a marginal logistic structure for the individual outcomes. In addition, difficulties arise when simple noninformative priors are chosen for the covariance parameters. Motivated by these problems, we propose a new type of multivariate logistic distribution that can be used to construct a likelihood for multivariate logistic regression analysis of binary and categorical data. The model for individual outcomes has a marginal logistic structure, simplifying interpretation. We follow a Bayesian approach to estimation and inference, developing an efficient data augmentation algorithm for posterior computation. The method is illustrated with application to a neurotoxicology study.     

Genomic prediction ability for feed efficiency traits using different models and pseudo-phenotypes under several validation strategies in Nelore cattle

There is a growing interest to improve feed efficiency (FE) traits in cattle. The genomic selection was proposed to improve these traits since they are difficult and expensive to measure. Up to date, there are scarce studies about the implementation of genomic selection for FE traits in indicine cattle under different scenarios of pseudo-phenotypes, models, and validation strategies on a commercial large scale. Thus, the aim was to evaluate the feasibility of genomic selection implementation for FE traits in Nelore cattle applying different models and pseudo-phenotypes under validation strategies. Phenotypic and genotypic information from 4 329 and 3 467 animals were used, respectively, which were tested for residual feed intake, DM intake, feed efficiency, feed conversion ratio, residual BW gain, and residual intake and BW gain. Six prediction methods were used: single-step genomic best linear unbiased prediction, Bayes A, Bayes B, Bayes Cπ, Bayesian least absolute shrinkage and selection operator (BLASSO), and Bayes R. Phenotypes adjusted for fixed effects (Y*), estimated breeding value (EBV), and EBV deregressed (DEBV) were used as pseudo-phenotypes. The validation approaches used were: (1) random: the data was randomly divided into ten subsets and the validation was done in each subset at a time; (2) age: the partition into training and testing sets was based on year of birth and testing animals were born after 2016; and (3) EBV accuracy: the data was split into two groups, being animals with accuracy above 0.45 the training set; and below 0.45 the validation set. In the analyses that used the Y* as pseudo-phenotype, prediction ability (PA) was obtained by dividing the correlation between pseudo-phenotype and genomic EBV (GEBV) by the square root of the heritability of the trait. When EBV and DEBV were used as the pseudo-phenotype, the simple correlation of this quantity with the GEBV was considered as PA. The prediction methods show similar results for PA and bias. The random cross-validation presented higher PA (0.17) than EBV accuracy (0.14) and age (0.13). The PA was higher for Y* than for EBV and DEBV (30.0 and 34.3%, respectively). Random validation presented the highest PA, being indicated for use in populations composed mainly of young animals and traits with few generations of data recording. For high heritability traits, the validation can be done by age, enabling the prediction of the next-generation genetic merit. These results would support breeders to identify genomic approaches that are more viable for genomic prediction for FE-related traits.     

Genomic prediction ability for yield-related traits in German winter barley elite material

Key message

Genomic prediction was evaluated in German winter barley breeding lines. In this material, prediction ability is strongly influenced by population structure and main determinant of prediction ability is the close genetic relatedness of the breeding material.

Abstract

To ensure breeding progress under changing environmental conditions the implementation and evaluation of new breeding methods is of crucial importance. Modern breeding approaches like genomic selection may significantly accelerate breeding progress. We assessed the potential of genomic prediction in a training population of 750 genotypes, consisting of multiple six-rowed winter barley (Hordeum vulgare L.) elite material families and old cultivars, which reflect the breeding history of barley in Germany. Crosses of parents selected from the training set were used to create a set of double-haploid families consisting of 750 genotypes. Those were used to confirm prediction ability estimates based on a cross-validation with the training set material using 11 different genomic prediction models. Population structure was inferred with dimensionality reduction methods like discriminant analysis of principle components and the influence of population structure on prediction ability was investigated. In addition to the size of the training set, marker density is of crucial importance for genomic prediction. We used genome-wide linkage disequilibrium and persistence of linkage phase as indicators to estimate that 11,203 evenly spaced markers are required to capture all QTL effects. Although a 9k SNP array does not contain a sufficient number of polymorphic markers for long-term genomic selection, we obtained fairly high prediction accuracies ranging from 0.31 to 0.71 for the traits earing, hectoliter weight, spikes per square meter, thousand kernel weight and yield and show that they result from the close genetic relatedness of the material. Our work contributes to designing long-term genetic prediction programs for barley breeding.

     

Joint prediction of multiple quantitative traits using a Bayesian multivariate antedependence model

Predicting organismal phenotypes from genotype data is important for preventive and personalized medicine as well as plant and animal breeding. Although genome-wide association studies (GWAS) for complex traits have discovered a large number of trait- and disease-associated variants, phenotype prediction based on associated variants is usually in low accuracy even for a high-heritability trait because these variants can typically account for a limited fraction of total genetic variance. In comparison with GWAS, the whole-genome prediction (WGP) methods can increase prediction accuracy by making use of a huge number of variants simultaneously. Among various statistical methods for WGP, multiple-trait model and antedependence model show their respective advantages. To take advantage of both strategies within a unified framework, we proposed a novel multivariate antedependence-based method for joint prediction of multiple quantitative traits using a Bayesian algorithm via modeling a linear relationship of effect vector between each pair of adjacent markers. Through both simulation and real-data analyses, our studies demonstrated that the proposed antedependence-based multiple-trait WGP method is more accurate and robust than corresponding traditional counterparts (Bayes A and multi-trait Bayes A) under various scenarios. Our method can be readily extended to deal with missing phenotypes and resequence data with rare variants, offering a feasible way to jointly predict phenotypes for multiple complex traits in human genetic epidemiology as well as plant and livestock breeding.     

Bayesian variable selection logistic regression with paired proteomic measurements

We explore the problem of variable selection in a case‐control setting with mass spectrometry proteomic data consisting of paired measurements. Each pair corresponds to a distinct isotope cluster and each component within pair represents a summary of isotopic expression based on either the intensity or the shape of the cluster. Our objective is to identify a collection of isotope clusters associated with the disease outcome and at the same time assess the predictive added‐value of shape beyond intensity while maintaining predictive performance. We propose a Bayesian model that exploits the paired structure of our data and utilizes prior information on the relative predictive power of each source by introducing multiple layers of selection. This allows us to make simultaneous inference on which are the most informative pairs and for which—and to what extent—shape has a complementary value in separating the two groups. We evaluate the Bayesian model on pancreatic cancer data. Results from the fitted model show that most predictive potential is achieved with a subset of just six (out of 1289) pairs while the contribution of the intensity components is much higher than the shape components. To demonstrate how the method behaves under a controlled setting we consider a simulation study. Results from this study indicate that the proposed approach can successfully select the truly predictive pairs and accurately estimate the effects of both components although, in some cases, the model tends to overestimate the inclusion probability of the second component.     

Bayesian analysis of binary prediction tree models for retrospectively sampled outcomes

Classification tree models are flexible analysis tools which have the ability to evaluate interactions among predictors as well as generate predictions for responses of interest. We describe Bayesian analysis of a specific class of tree models in which binary response data arise from a retrospective case-control design. We are also particularly interested in problems with potentially very many candidate predictors. This scenario is common in studies concerning gene expression data, which is a key motivating example context. Innovations here include the introduction of tree models that explicitly address and incorporate the retrospective design, and the use of nonparametric Bayesian models involving Dirichlet process priors on the distributions of predictor variables. The model specification influences the generation of trees through Bayes' factor based tests of association that determine significant binary partitions of nodes during a process of forward generation of trees. We describe this constructive process and discuss questions of generating and combining multiple trees via Bayesian model averaging for prediction. Additional discussion of parameter selection and sensitivity is given in the context of an example which concerns prediction of breast tumour status utilizing high-dimensional gene expression data; the example demonstrates the exploratory/explanatory uses of such models as well as their primary utility in prediction. Shortcomings of the approach and comparison with alternative tree modelling algorithms are also discussed, as are issues of modelling and computational extensions.     

Bayesian prediction of spatial count data using generalized linear mixed models

Spatial weed count data are modeled and predicted using a generalized linear mixed model combined with a Bayesian approach and Markov chain Monte Carlo. Informative priors for a data set with sparse sampling are elicited using a previously collected data set with extensive sampling. Furthermore, we demonstrate that so-called Langevin-Hastings updates are useful for efficient simulation of the posterior distributions, and we discuss computational issues concerning prediction.     

Genomic selection prediction models comparing sequence capture and SNP array genotyping methods

The successful application of genomic selection (GS) approaches is dependent on genetic makers derived from high-throughput and low-cost genotyping methods. Recent GS studies in trees have predominantly relied on SNP arrays as the source of genotyping, though this technology has a high entry cost. The recent development of alternative genotyping platforms, tailored to specific species and with low entry cost, has become possible due to advances in next-generation sequencing and genome complexity reduction methods such as sequence capture. However, the performance of these new platforms in GS models has not yet been evaluated, or compared to models developed from SNP arrays. Here, we evaluate the impact of these genotyping technologies on the development of GS prediction models for a Eucalyptus breeding population composed of 739 trees phenotyped for 13 wood quality and growth traits. Genotyping data obtained with both methods were compared for linkage disequilibrium, minor allele frequency, and missing data. Phenotypic prediction methods RR-BLUP and BayesB were employed, while predictive ability using cross validation was used to evaluate the performance of GS models derived from the different genotyping platforms. Differences in linkage disequilibrium patterns, minor allele frequency, missing data, and marker distribution were detected between sequence capture and SNP arrays. However, RR-BLUP and BayesB GS models resulted in similar predictive abilities. These results demonstrate that both genotyping methods are equivalent for genomic prediction of the traits evaluated. Sequence capture offers an alternative for species where SNP arrays are not available, or for when the initial development cost is too high.     

Genomic prediction of hybrid performance in maize with models incorporating dominance and population specific marker effects

Identifying high performing hybrids is an essential part of every maize breeding program. Genomic prediction of maize hybrid performance allows to identify promising hybrids, when they themselves or other hybrids produced from their parents were not tested in field trials. Using simulations, we investigated the effects of marker density (10, 1, 0.3 marker per mega base pair, Mbp(-1)), convergent or divergent parental populations, number of parents tested in other combinations (2, 1, 0), genetic model (including population-specific and/or dominance marker effects or not), and estimation method (GBLUP or BayesB) on the prediction accuracy. We based our simulations on marker genotypes of Central European flint and dent inbred lines from an ongoing maize breeding program. To simulate convergent or divergent parent populations, we generated phenotypes by assigning QTL to markers with similar or very different allele frequencies in both pools, respectively. Prediction accuracies increased with marker density and number of parents tested and were higher under divergent compared with convergent parental populations. Modeling marker effects as population-specific slightly improved prediction accuracy under lower marker densities (1 and 0.3?Mbp(-1)). This indicated that modeling marker effects as population-specific will be most beneficial under low linkage disequilibrium. Incorporating dominance effects improved prediction accuracies considerably for convergent parent populations, where dominance results in major contributions of SCA effects to the genetic variance among inter-population hybrids. While the general trends regarding the effects of the aforementioned influence factors on prediction accuracy were similar for GBLUP and BayesB, the latter method produced significantly higher accuracies for models incorporating dominance.     

Analysis of logistic growth models

A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most predictive models are shown to be based on variations of the classical Verhulst logistic growth equation. We review and compare several such models and analyse properties of interest for these. We also identify and detail several associated limitations and restrictions.A generalized form of the logistic growth curve is introduced which incorporates these models as special cases. Several properties of the generalized growth are also presented. We furthermore prove that the new growth form incorporates additional growth models which are markedly different from the logistic growth and its variants, at least in their mathematical representation. Finally, we give a brief outline of how the new curve could be used for curve-fitting.     

Bayesian logistic regression using a perfect phylogeny

Haplotype data capture the genetic variation among individuals in a population and among populations. An understanding of this variation and the ancestral history of haplotypes is important in genetic association studies of complex disease. We introduce a method for detecting associations between disease and haplotypes in a candidate gene region or candidate block with little or no recombination. A perfect phylogeny demonstrates the evolutionary relationship between single-nucleotide polymorphisms (SNPs) in the haplotype blocks. Our approach extends the logic regression technique of Ruczinski and others (2003) to a Bayesian framework, and constrains the model space to that of a perfect phylogeny. Environmental factors, as well as their interactions with SNPs, may be incorporated into the regression framework. We demonstrate our method on simulated data from a coalescent model, as well as data from a candidate gene study of sarcoidosis.