A general approach to mixed effects modeling of residual variances in generalized linear mixed models

We propose a general Bayesian approach to heteroskedastic error modeling for generalized linear mixed models (GLMM) in which linked functions of conditional means and residual variances are specified as separate linear combinations of fixed and random effects. We focus on the linear mixed model (LMM) analysis of birth weight (BW) and the cumulative probit mixed model (CPMM) analysis of calving ease (CE). The deviance information criterion (DIC) was demonstrated to be useful in correctly choosing between homoskedastic and heteroskedastic error GLMM for both traits when data was generated according to a mixed model specification for both location parameters and residual variances. Heteroskedastic error LMM and CPMM were fitted, respectively, to BW and CE data on 8847 Italian Piemontese first parity dams in which residual variances were modeled as functions of fixed calf sex and random herd effects. The posterior mean residual variance for male calves was over 40% greater than that for female calves for both traits. Also, the posterior means of the standard deviation of the herd-specific variance ratios (relative to a unitary baseline) were estimated to be 0.60 ± 0.09 for BW and 0.74 ± 0.14 for CE. For both traits, the heteroskedastic error LMM and CPMM were chosen over their homoskedastic error counterparts based on DIC values

High-Density SNP Genotypes for Predicting Genetic Merit of Beef Cattle

Current selection strategies result in annual rates of genetic improvement less than one-quarter of the progress that is theoretically possible if merit could be accurately predicted by breeding age. Tens of thousands of single gene markers (called SNPs), spread throughout the genome, enable the ancestral inheritance of small chromosome fragments to be tracked. Genetic merit of new, perhaps unrelated cattle can be predicted by summing up the values of all the fragments they have inherited. Such predictions at young ages will facilitate faster rates of genetic gain, especially for traits that are difficult to measure

Cumulative t-link threshold models for the genetic analysis of calving ease scores

In this study, a hierarchical threshold mixed model based on a cumulative t-link specification for the analysis of ordinal data or more, specifically, calving ease scores, was developed. The validation of this model and the Markov chain Monte Carlo (MCMC) algorithm was carried out on simulated data from normally and t4 (i.e. a t-distribution with four degrees of freedom) distributed populations using the deviance information criterion (DIC) and a pseudo Bayes factor (PBF) measure to validate recently proposed model choice criteria. The simulation study indicated that although inference on the degrees of freedom parameter is possible, MCMC mixing was problematic. Nevertheless, the DIC and PBF were validated to be satisfactory measures of model fit to data. A sire and maternal grandsire cumulative t-link model was applied to a calving ease dataset from 8847 Italian Piemontese first parity dams. The cumulative t-link model was shown to lead to posterior means of direct and maternal heritabilities (0.40 ± 0.06, 0.11 ± 0.04) and a direct maternal genetic correlation (-0.58 ± 0.15) that were not different from the corresponding posterior means of the heritabilities (0.42 ± 0.07, 0.14 ± 0.04) and the genetic correlation (-0.55 ± 0.14) inferred under the conventional cumulative probit link threshold model. Furthermore, the correlation (> 0.99) between posterior means of sire progeny merit from the two models suggested no meaningful rerankings. Nevertheless, the cumulative t-link model was decisively chosen as the better fitting model for this calving ease data using DIC and PBF

Whole genome analysis of infectious bovine keratoconjunctivitis in Angus cattle using Bayesian threshold models

Infectious bovine keratoconjunctivitis (IBK), also known as pinkeye, is characterized by damage to the cornea and is an economically important, lowly heritable, categorical disease trait in beef cattle. Scores of eye damage were collected at weaning on 858 Angus cattle. SNP genotypes for each animal were obtained from BovineSNP50 Infinium-beadchips. Simultaneous associations of all SNP with IBK phenotype were determined using Bayes-C that treats SNP effects as random with equal variance for an assumed fraction (π=0.999) of SNP having no effect on IBK scores. Bayes-C threshold models were used to estimate SNP effects by classifying IBK into two, three or nine ordered categories. Magnitudes of genetic variances estimated in localized regions across the genome indicated that SNP within the most informative regions accounted for much of the genetic variance of IBK and pointed out some degree of association to IBK. There are many candidate genes in these regions which could include a gene or group of genes associated with bacterial disease in cattle

Genome-wide association study of infectious bovine keratoconjunctivitis in Angus cattle

Background Infectious Bovine Keratoconjunctivitis (IBK) in beef cattle, commonly known as pinkeye, is a bacterial disease caused by Moraxella bovis. IBK is characterized by excessive tearing and ulceration of the cornea. Perforation of the cornea may also occur in severe cases. IBK is considered the most important ocular disease in cattle production, due to the decreased growth performance of infected individuals and its subsequent economic effects. IBK is an economically important, lowly heritable categorical disease trait. Mass selection of unaffected animals has not been successful at reducing disease incidence. Genome-wide studies can determine chromosomal regions associated with IBK susceptibility. The objective of the study was to detect single-nucleotide polymorphism (SNP) markers in linkage disequilibrium (LD) with genetic variants associated with IBK in American Angus cattle. ResultsThe proportion of phenotypic variance explained by markers was 0.06 in the whole genome analysis of IBK incidence classified as two, three or nine categories. Whole-genome analysis using any categorisation of (two, three or nine) IBK scores showed that locations on chromosomes 2, 12, 13 and 21 were associated with IBK disease. The genomic locations on chromosomes 13 and 21 overlap with QTLs associated with Bovine spongiform encephalopathy, clinical mastitis or somatic cell count. ConclusionsResults of these genome-wide analyses indicated that if the underlying genetic factors confer not only IBK susceptibility but also IBK severity, treating IBK phenotypes as a two-categorical trait can cause information loss in the genome-wide analysis. These results help our overall understanding of the genetics of IBK and have the potential to provide information for future use in breeding schemes

Whole Genome Association Analysis of Idiopathic Eosinophilic Enteritis in Brown Egg Layers

Idiopathic Eosinophilic Enteritis (IEE) is an intestine disease that affects absorption of nutrients and performance. Hens of a commercial breeding layer line and its two reciprocal crosses with another line were recorded for IEE related traits and genotyped for over 40,000 genetic markers across the genome. Whole genome association analysis was performed on 288 daughters from high and low incidence sire families. Single marker association analyses of IEE incidence in separate lines showed consistent significant regions on chromosomes 4 and 5 (p\u3c0.001). Simultaneous analyses of all SNPs in all 3 lines using Bayesian whole genome selection methods indicated evidence of associations on chromosomes 1, 2 and 4 for additive effects and on chromosome 5 for dominance effects. Line specific regions also appeared on chromosome Z. With further investigation, these results can be used to develop genetic markers to select against this disease and to understand its genetic basis

Managing soil carbon and nitrogen for productivity and environmental quality

Includes bibliographical references (pages 774-775).In this study, we investigated the impact of cropping system management on C and N pools, crop yield, and N leaching in a long-term agronomic experiment in Southwest Michigan. Four management types, conventional (CO), integrated fertilizer (IF), integrated compost (IC), and transitional organic (TO) were applied to two crop sequences, a corn (Zea mays L.)–corn–soybean [Glycine max (L.) Merr.]–wheat (Triticum aestivum L.) rotation and continuous corn, which were grown with and without cover crops in the IF, IC, and TO managements. Using compost as a fertility source and reducing the use of herbicides and other chemicals resulted in long-term changes in soil organic matter pools such TO ≥ IC > IF ≥ CO for total C and N and for the labile C and N measured through aerobic incubations at 70 and 150 d. Mineralizable N varied within the rotation, tending to increase after soybean and decrease after corn production in all systems. Corn yield was closely associated with 70-d N mineralization potential, being greatest for first-year corn with cover and least for continuous corn without cover under all management types. Although the TO and IC systems produced the lowest yield for second-year or continuous corn, the combination of soybean and wheat plus red clover (Trifolium pratense L.) always supported high yield for first-year corn. Fall nitrate level and nitrate leaching were higher for commercially fertilized corn than for any other crop or for compost-amended corn

Use of linear mixed models for genetic evaluation of gestation length and birth weight allowing for heavy-tailed residual effects

<p>Abstract</p> <p>Background</p> <p>The distribution of residual effects in linear mixed models in animal breeding applications is typically assumed normal, which makes inferences vulnerable to outlier observations. In order to mute the impact of outliers, one option is to fit models with residuals having a heavy-tailed distribution. Here, a Student's-<it>t </it>model was considered for the distribution of the residuals with the degrees of freedom treated as unknown. Bayesian inference was used to investigate a bivariate Student's-<it>t </it>(BS<it>t</it>) model using Markov chain Monte Carlo methods in a simulation study and analysing field data for gestation length and birth weight permitted to study the practical implications of fitting heavy-tailed distributions for residuals in linear mixed models.</p> <p>Methods</p> <p>In the simulation study, bivariate residuals were generated using Student's-<it>t </it>distribution with 4 or 12 degrees of freedom, or a normal distribution. Sire models with bivariate Student's-<it>t </it>or normal residuals were fitted to each simulated dataset using a hierarchical Bayesian approach. For the field data, consisting of gestation length and birth weight records on 7,883 Italian Piemontese cattle, a sire-maternal grandsire model including fixed effects of sex-age of dam and uncorrelated random herd-year-season effects were fitted using a hierarchical Bayesian approach. Residuals were defined to follow bivariate normal or Student's-<it>t </it>distributions with unknown degrees of freedom.</p> <p>Results</p> <p>Posterior mean estimates of degrees of freedom parameters seemed to be accurate and unbiased in the simulation study. Estimates of sire and herd variances were similar, if not identical, across fitted models. In the field data, there was strong support based on predictive log-likelihood values for the Student's-<it>t </it>error model. Most of the posterior density for degrees of freedom was below 4. Posterior means of direct and maternal heritabilities for birth weight were smaller in the Student's-<it>t </it>model than those in the normal model. Re-rankings of sires were observed between heavy-tailed and normal models.</p> <p>Conclusions</p> <p>Reliable estimates of degrees of freedom were obtained in all simulated heavy-tailed and normal datasets. The predictive log-likelihood was able to distinguish the correct model among the models fitted to heavy-tailed datasets. There was no disadvantage of fitting a heavy-tailed model when the true model was normal. Predictive log-likelihood values indicated that heavy-tailed models with low degrees of freedom values fitted gestation length and birth weight data better than a model with normally distributed residuals.</p> <p>Heavy-tailed and normal models resulted in different estimates of direct and maternal heritabilities, and different sire rankings. Heavy-tailed models may be more appropriate for reliable estimation of genetic parameters from field data.</p

Extension of the bayesian alphabet for genomic selection

<p>Abstract</p> <p>Background</p> <p>Two Bayesian methods, BayesC<it>π </it>and BayesD<it>π</it>, were developed for genomic prediction to address the drawback of BayesA and BayesB regarding the impact of prior hyperparameters and treat the prior probability <it>π </it>that a SNP has zero effect as unknown. The methods were compared in terms of inference of the number of QTL and accuracy of genomic estimated breeding values (GEBVs), using simulated scenarios and real data from North American Holstein bulls.</p> <p>Results</p> <p>Estimates of <it>π </it>from BayesC<it>π</it>, in contrast to BayesD<it>π</it>, were sensitive to the number of simulated QTL and training data size, and provide information about genetic architecture. Milk yield and fat yield have QTL with larger effects than protein yield and somatic cell score. The drawback of BayesA and BayesB did not impair the accuracy of GEBVs. Accuracies of alternative Bayesian methods were similar. BayesA was a good choice for GEBV with the real data. Computing time was shorter for BayesC<it>π </it>than for BayesD<it>π</it>, and longest for our implementation of BayesA.</p> <p>Conclusions</p> <p>Collectively, accounting for computing effort, uncertainty as to the number of QTL (which affects the GEBV accuracy of alternative methods), and fundamental interest in the number of QTL underlying quantitative traits, we believe that BayesC<it>π </it>has merit for routine applications.</p