HIERARCHICAL BAYESIAN METHODS TO MODEL HETEROGENEITY IN COW- AND HERD-LEVEL RELATIONSHIPS BETWEEN MILK PRODUCTION AND REPRODUCTION IN DAIRY COWS

Two of the most important broad classifications of phenotypes for successful dairy production are milk yield and fertility. The nature of the relationship between milk production and reproductive performance of dairy cows is uncertain due to conflicting results reported in many studies. A common deficiency in many such studies is an underappreciation of the dual dimension of the production-reproduction relationship, as defined by herd (random or u) level and cow (residual or e) level sources of (co)variation. Our overall hypothesis is that the e- and u- level relationships between milk production and reproduction in dairy cows are heterogeneous and depend upon various herd-related and management factors. Our objective is to develop hierarchical Bayesian extensions that capture heterogeneity in the relationships between traits by mixed effects modeling of u level and e level covariances between traits of interest. We specify a bivariate Bayesian model to jointly model two continuous traits and we apply a square-root free Cholesky decomposition to the variance-covariance matrices of the residuals (cow-level) and random effects (herd-level). As a result, the e- and u-level covariances among the traits are reparameterized into unconstrained and easily interpretable e- and u- regression parameters, respectively. These regression parameters specify the cow- and herd-level relationships, respectively, between the traits and can be easily modeled as functions of relevant fixed and random effects, thereby providing a mixed model extension of Pourahmadi’s method. We validate our method using a simulation study and apply it to data on 305-day milk yield and calving interval of Michigan dairy cows

Reassessing Design and Analysis of two-Colour Microarray Experiments Using Mixed Effects Models

Gene expression microarray studies have led to interesting experimental design and statistical analysis challenges. The comparison of expression profiles across populations is one of the most common objectives of microarray experiments. In this manuscript we review some issues regarding design and statistical analysis for two-colour microarray platforms using mixed linear models, with special attention directed towards the different hierarchical levels of replication and the consequent effect on the use of appropriate error terms for comparing experimental groups. We examine the traditional analysis of variance (ANOVA) models proposed for microarray data and their extensions to hierarchically replicated experiments. In addition, we discuss a mixed model methodology for power and efficiency calculations of different microarray experimental designs

Genomic Prediction Accounting for Residual Heteroskedasticity

Citation: Ou, Z. N., Tempelman, R. J., Steibel, J. P., Ernst, C. W., Bates, R. O., & Bello, N. M. (2016). Genomic Prediction Accounting for Residual Heteroskedasticity. G3-Genes Genomes Genetics, 6(1), 1-13. doi:10.1534/g3.115.022897Whole-genome prediction (WGP) models that use single-nucleotide polymorphism marker information to predict genetic merit of animals and plants typically assume homogeneous residual variance. However, variability is often heterogeneous across agricultural production systems and may subsequently bias WGP-based inferences. This study extends classical WGP models based on normality, heavy-tailed specifications and variable selection to explicitly account for environmentally-driven residual heteroske-dasticity under a hierarchical Bayesian mixed-models framework. WGP models assuming homogeneous or heterogeneous residual variances were fitted to training data generated under simulation scenarios reflecting a gradient of increasing heteroskedasticity. Model fit was based on pseudo-Bayes factors and also on prediction accuracy of genomic breeding values computed on a validation data subset one generation removed from the simulated training dataset. Homogeneous vs. heterogeneous residual variance WGP models were also fitted to two quantitative traits, namely 45-min postmortem carcass temperature and loin muscle pH, recorded in a swine resource population dataset prescreened for high and mild residual heteroskedasticity, respectively. Fit of competing WGP models was compared using pseudo-Bayes factors. Predictive ability, defined as the correlation between predicted and observed phenotypes in validation sets of a five-fold cross-validation was also computed. Heteroskedastic error WGP models showed improved model fit and enhanced prediction accuracy compared to homoskedastic error WGP models although the magnitude of the improvement was small (less than two percentage points net gain in prediction accuracy). Nevertheless, accounting for residual heteroskedasticity did improve accuracy of selection, especially on individuals of extreme genetic merit

Analysis of social interactions in group-housed animals using dyadic linear models

Understanding factors affecting social interactions among animals is important for applied animal behavior research. Thus, there is a need to elicit statistical models to analyze data collected from pairwise behavioral interactions. In this study, we propose treating social interaction data as dyadic observations and propose a statistical model for their analysis. We performed posterior predictive checks of the model through different validation strategies: stratified 5-fold random cross-validation, block-by-social-group cross-validation, and block-by-focal-animals validation. The proposed model was applied to a pig behavior dataset collected from 797 growing pigs freshly remixed into 59 social groups that resulted in 10,032 records of directional dyadic interactions. The response variable was the duration in seconds that each animal spent delivering attacks on another group mate. Generalized linear mixed models were fitted. Fixed effects included sex, individual weight, prior nursery mate experience, and prior littermate experience of the two pigs in the dyad. Random effects included aggression giver, aggression receiver, dyad, and social group. A Bayesian framework was utilized for parameter estimation and posterior predictive model checking. Prior nursery mate experience was the only significant fixed effect. In addition, a weak but significant correlation between the random giver effect and the random receiver effect was obtained when analyzing the attacking duration. The predictive performance of the model varied depending on the validation strategy, with substantially lower performance from the block-by-social-group strategy than other validation strategies. Collectively, this paper demonstrates a statistical model to analyze interactive animal behaviors, particularly dyadic interactions

Linkage disequilibrium, persistence of phase and effective population size estimates in Hereford and Braford cattle.

The objective of this study was to estimate LD levels, persistence of phase and effective population size in Hereford and Braford cattle populations sampled in Brazil.Article 32

Estimation of linkage disequilibrium, persistence of phase and effective population size of Brazilian Hereford and Braford breeds.

A set of 41,241 SNP genotypes from 2,435 Hereford (HH) and Braford (BO) bovines were analyzed to estimate linkage disequilibrium (LD) levels, persistence of phase and effective population size of these populations. LD levels were estimated using the squared correlation of alleles at two loci (r2) at varying distances. Average r2 between adjacent SNP was 0.21 for HH and 0.16 for BO. Average inter-marker distance was 61 kb in both breeds. Useful LD values (r2>0.2) were observed at 0-60 kb bins in HH and 0-20 kb bins in BO. Breeds demonstrated moderate to strong persistence of phase at all distances (range=0.53-0.97). The greatest phase correlations (r>0.9) were found in 0-50 kb bins. LD estimates decreased rapidly with increasing distances between SNPs, however, useful LD was observed in genomic regions spanning up to ~50 kb

Estimation of linkage disequilibrium, persistence of phase and effective population size of Brazilian Hereford and Braford breeds.

A set of 41,241 SNP genotypes from 2,435 Hereford (HH) and Braford (BO) bovines were analyzed to estimate linkage disequilibrium (LD) levels, persistence of phase and effective population size of these populations. LD levels were estimated using the squared correlation of alleles at two loci (r2) at varying distances. Average r2 between adjacent SNP was 0.21 for HH and 0.16 for BO. Average inter-marker distance was 61 kb in both breeds. Useful LD values (r2>0.2) were observed at 0-60 kb bins in HH and 0-20 kb bins in BO. Breeds demonstrated moderate to strong persistence of phase at all distances (range=0.53- 0.97). The greatest phase correlations (r>0.9) were found in 0-50 kb bins. LD estimates decreased rapidly with increasing distances between SNPs, however, useful LD was observed in genomic regions spanning up to ~50 kb

Probing genetic control of swine responses to PRRSV infection: current progress of the PRRS host genetics consortium

<p>Abstract</p> <p>Background</p> <p>Understanding the role of host genetics in resistance to porcine reproductive and respiratory syndrome virus (PRRSV) infection, and the effects of PRRS on pig health and related growth, are goals of the PRRS Host Genetics Consortium (PHGC).</p> <p>Methods</p> <p>The project uses a nursery pig model to assess pig resistance/susceptibility to primary PRRSV infection. To date, 6 groups of 200 crossbred pigs from high health farms were donated by commercial sources. After acclimation, the pigs were infected with PRRSV in a biosecure facility and followed for 42 days post infection (dpi). Blood samples were collected at 0, 4, 7, 10, 14, 21, 28, 35 and 42 dpi for serum and whole blood RNA gene expression analyses; weekly weights were recorded for growth traits. All data have been entered into the PHGC relational database. Genomic DNAs from all PHGC1-6 pigs were prepared and genotyped with the Porcine SNP60 SNPchip.</p> <p>Results</p> <p>Results have affirmed that all challenged pigs become PRRSV infected with peak viremia being observed between 4-21 dpi. Multivariate statistical analyses of viral load and weight data have identified PHGC pigs in different virus/weight categories. Sera are now being compared for factors involved in recovery from infection, including speed of response and levels of immune cytokines. Genome-wide association studies (GWAS) are underway to identify genes and chromosomal locations that identify PRRS resistant/susceptible pigs and pigs able to maintain growth while infected with PRRSV.</p> <p>Conclusions</p> <p>Overall, the PHGC project will enable researchers to discover and verify important genotypes and phenotypes that predict resistance/susceptibility to PRRSV infection. The availability of PHGC samples provides a unique opportunity to continue to develop deeper phenotypes on every PRRSV infected pig.</p