Estimation of covariance components between one continuous and one binary trait

International audienc

Approximate restricted maximum likelihood and approximate prediction error variance of the Mendelian sampling effect

In an Expectation-Maximization type Restricted Maximum Likelihood (REML) procedure, the estimation of a genetic (co-)variance component involves the trace of the product of the inverse of the coefficient matrix by the inverse of the relationship matrix. Computation of this trace is usually the limiting factor of this procedure. In this paper, a method is presented to approximate this trace in the case of an animal model, by using an equivalent model based on the Mendelian sampling effect and by simplifying its coefficient matrix and its inversion. This approximation appeared very accurate for low heritabilities but was downwards biased when the heritability was high. Implemented in a REML procedure, this approximation reduced dramatically the amount of computation, but provided downwards biased estimates of genetic variances. Several examples are presented to illustrate the method.Dans certaines procédures de Maximum de Vraisemblance Restreint (REML), l’estimation des composantes de (co)variance génétique implique le calcul de la trace du produit de l’inverse de la matrice des coefficients par l’inverse de la matrice de parentés, calcul qui constitue généralement le facteur limitant de ce type de procédure. Nous présentons dans cet article une méthode visant à obtenir une valeur approchée de cette trace dans le cadre d’un modèle animal, en utilisant un modèle équivalent basé sur l’aléa de méiose, en simplifiant sa matrice des coefficients et en en calculant une inverse approchée. Cette approximation est très précise lorsque l’héritabilité du caractère est faible mais elle tend à sous-estimer la trace vraie lorsque l’héritabilité est élevée. Intégrée dans une procédure de REML, cette méthode en réduit considérablement le coût mais fournit en général des valeurs sous-estimées de variance génétique. Divers exemples sont présentés à titre d'illustratio

Estimation of heritability in the base population when only records from later generations are available

International audienc

Impacts of both reference population size and inclusion of a residual polygenic effect on the accuracy of genomic prediction

<p>Abstract</p> <p>Background</p> <p>The purpose of this work was to study the impact of both the size of genomic reference populations and the inclusion of a residual polygenic effect on dairy cattle genetic evaluations enhanced with genomic information.</p> <p>Methods</p> <p>Direct genomic values were estimated for German Holstein cattle with a genomic BLUP model including a residual polygenic effect. A total of 17,429 genotyped Holstein bulls were evaluated using the phenotypes of 44 traits. The Interbull genomic validation test was implemented to investigate how the inclusion of a residual polygenic effect impacted genomic estimated breeding values.</p> <p>Results</p> <p>As the number of reference bulls increased, both the variance of the estimates of single nucleotide polymorphism effects and the reliability of the direct genomic values of selection candidates increased. Fitting a residual polygenic effect in the model resulted in less biased genome-enhanced breeding values and decreased the correlation between direct genomic values and estimated breeding values of sires in the reference population.</p> <p>Conclusions</p> <p>Genetic evaluation of dairy cattle enhanced with genomic information is highly effective in increasing reliability, as well as using large genomic reference populations. We found that fitting a residual polygenic effect reduced the bias in genome-enhanced breeding values, decreased the correlation between direct genomic values and sire's estimated breeding values and made genome-enhanced breeding values more consistent in mean and variance as is the case for pedigree-based estimated breeding values.</p

Statistical modelling of growth using a mixed model with orthogonal polynomials

In statistical modelling, the effects of single-nucleotide polymorphisms (SNPs) are often regarded as time-independent. However, for traits recorded repeatedly, it is very interesting to investigate the behaviour of gene effects over time. In the analysis, simulated data from the 13th QTL-MAS Workshop (Wageningen, The Netherlands, April 2009) was used and the major goal was the modelling of genetic effects as time-dependent. For this purpose, a mixed model which describes each effect using the third-order Legendre orthogonal polynomials, in order to account for the correlation between consecutive measurements, is fitted. In this model, SNPs are modelled as fixed, while the environment is modelled as random effects. The maximum likelihood estimates of model parameters are obtained by the expectation–maximisation (EM) algorithm and the significance of the additive SNP effects is based on the likelihood ratio test, with p-values corrected for multiple testing. For each significant SNP, the percentage of the total variance contributed by this SNP is calculated. Moreover, by using a model which simultaneously incorporates effects of all of the SNPs, the prediction of future yields is conducted. As a result, 179 from the total of 453 SNPs covering 16 out of 18 true quantitative trait loci (QTL) were selected. The correlation between predicted and true breeding values was 0.73 for the data set with all SNPs and 0.84 for the data set with selected SNPs. In conclusion, we showed that a longitudinal approach allows for estimating changes of the variance contributed by each SNP over time and demonstrated that, for prediction, the pre-selection of SNPs plays an important role

Approaches in topical ocular drug delivery and developments in the use of contact lenses as drug-delivery devices

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Drug-delivery approaches have diversified over the last two decades with the emergence of nanotechnologies, smart polymeric systems and multimodal functionalities. The intended target for specific treatment of disease is the key defining developing parameter. One such area which has undergone significant advancements relates to ocular delivery. This has been expedited by the development of material advancement, mechanistic concepts and through the deployment of advanced process technologies. This review will focus on the developments within lens-based drug delivery while touching on conventional and current methods of topical ocular drug delivery. A summary table will provide quick reference to note the key findings in this area. In addition, the review also elucidates current theranostic and diagnostic approaches based on ocular lenses

Studies on changes of estimated breeding values of U.S. Holstein bulls for final score from the first to second crop of daughters

The purpose of this study was to find ways of reducing changes of sire predicted transmitting ability for type’s final scores (PTATs) from the first to second crop of daughters. The PTATs were estimated from two datasets: D01 (scores recorded up to 2001) and D05 (scores recorded up to 2005). The PTAT changes were calculated as the difference between the evaluations based on D01 and D05. The PTATs were adjusted to a common genetic base of all evaluated cows born in 1995. The single-trait (ST) animal model included the fixed effects of the herd–year–season–classifier, age by year group at classification, stage of lactation at classification, registry status of animals, and additive genetic and permanent environment random effects. Unknown parent groups (UPGs) were defined based on every other birth year starting from 1972. Modifications to the ST model included the usage of a single record per cow, separate UPGs for first and second crop daughters, separate UPGs for sires and dams, and deepened pedigrees for dams with missing phenotypic records. Also, the multiple-trait (MT) model treated records of registered and grade cows as correlated traits. The mean PTAT change, for all of the sires, was close to zero in all of the models analyzed. The estimated mean PTAT change for 145 sires with 40 to 100 first crop and ≥200 second crop daughters was −0.33, −0.20, −0.13, −0.28, and −0.12 with ST, only first records, only last records, updated pedigrees, and allowing separate parent groups (PGs) for sires and dams after updating the pedigrees, respectively. The percentages of sires showing PTAT decline were reduced from 74.5 (with ST) to 57.3 by using only the last records of cows, and to 56.4 by allowing separate UPGs for sires and dams after updating the pedigrees. Though updating of the pedigrees alone was not effective, separate UPGs for sires together with additional pedigree was helpful in reducing the bias

Mapping quantitative trait loci in line cross with repeat records

<p>Abstract</p> <p>Background</p> <p>Phenotypes with repeat records from one individual or multiple individuals were often encountered in practices of mapping QTL in linecross. The current genetic mapping method for a trait with repeat records is adopted by simply replacing the phenotype by the average value of the repeat records. This simple treatment has not sufficiently utilized the information from the replication and ignored the impacts of the permanent environmental effects on the accuracy of the estimated QTL.</p> <p>Results</p> <p>We propose to map QTL by using the repeatability model to directly analyze the repeat records rather than simply analyze the mean phenotype, improving the efficiency of QTL detecting because of adequately utilizing the information from data and allowing for the permanent environmental effects. A maximum likelihood method implemented via the expectation-maximization (EM) algorithm is applied to perform the parameter estimation of the repeatability model. The superiority of the mapping method based on the repeatability model over simple analysis using the mean phenotype was demonstrated by a series of simulations.</p> <p>Conclusion</p> <p>Our results suggest that the proposed method can serve as a powerful alternative to existing methods. By mean of the repeatability model, utilizing the repeat records on individual may improve the efficiency of QTL detecting in line cross.</p