Different models of genetic variation and their effect on genomic evaluation

<p>Abstract</p> <p>Background</p> <p>The theory of genomic selection is based on the prediction of the effects of quantitative trait loci (QTL) in linkage disequilibrium (LD) with markers. However, there is increasing evidence that genomic selection also relies on "relationships" between individuals to accurately predict genetic values. Therefore, a better understanding of what genomic selection actually predicts is relevant so that appropriate methods of analysis are used in genomic evaluations.</p> <p>Methods</p> <p>Simulation was used to compare the performance of estimates of breeding values based on pedigree relationships (Best Linear Unbiased Prediction, BLUP), genomic relationships (gBLUP), and based on a Bayesian variable selection model (Bayes B) to estimate breeding values under a range of different underlying models of genetic variation. The effects of different marker densities and varying animal relationships were also examined.</p> <p>Results</p> <p>This study shows that genomic selection methods can predict a proportion of the additive genetic value when genetic variation is controlled by common quantitative trait loci (QTL model), rare loci (rare variant model), all loci (infinitesimal model) and a random association (a polygenic model). The Bayes B method was able to estimate breeding values more accurately than gBLUP under the QTL and rare variant models, for the alternative marker densities and reference populations. The Bayes B and gBLUP methods had similar accuracies under the infinitesimal model.</p> <p>Conclusions</p> <p>Our results suggest that Bayes B is superior to gBLUP to estimate breeding values from genomic data. The underlying model of genetic variation greatly affects the predictive ability of genomic selection methods, and the superiority of Bayes B over gBLUP is highly dependent on the presence of large QTL effects. The use of SNP sequence data will outperform the less dense marker panels. However, the size and distribution of QTL effects and the size of reference populations still greatly influence the effectiveness of using sequence data for genomic prediction.</p

Estimation of prediction error variances via Monte Carlo sampling methods using different formulations of the prediction error variance

Calculation of the exact prediction error variance covariance matrix is often computationally too demanding, which limits its application in REML algorithms, the calculation of accuracies of estimated breeding values and the control of variance of response to selection. Alternatively Monte Carlo sampling can be used to calculate approximations of the prediction error variance, which converge to the true values if enough samples are used. However, in practical situations the number of samples, which are computationally feasible, is limited. The objective of this study was to compare the convergence rate of different formulations of the prediction error variance calculated using Monte Carlo sampling. Four of these formulations were published, four were corresponding alternative versions, and two were derived as part of this study. The different formulations had different convergence rates and these were shown to depend on the number of samples and on the level of prediction error variance. Four formulations were competitive and these made use of information on either the variance of the estimated breeding value and on the variance of the true breeding value minus the estimated breeding value or on the covariance between the true and estimated breeding values

The importance of information on relatives for the prediction of genomic breeding values and the implications for the makeup of reference data sets in livestock breeding schemes.

<p>Abstract</p> <p>Background</p> <p>The theory of genomic selection is based on the prediction of the effects of genetic markers in linkage disequilibrium with quantitative trait loci. However, genomic selection also relies on relationships between individuals to accurately predict genetic value. This study aimed to examine the importance of information on relatives versus that of unrelated or more distantly related individuals on the estimation of genomic breeding values.</p> <p>Methods</p> <p>Simulated and real data were used to examine the effects of various degrees of relationship on the accuracy of genomic selection. Genomic Best Linear Unbiased Prediction (gBLUP) was compared to two pedigree based BLUP methods, one with a shallow one generation pedigree and the other with a deep ten generation pedigree. The accuracy of estimated breeding values for different groups of selection candidates that had varying degrees of relationships to a reference data set of 1750 animals was investigated.</p> <p>Results</p> <p>The gBLUP method predicted breeding values more accurately than BLUP. The most accurate breeding values were estimated using gBLUP for closely related animals. Similarly, the pedigree based BLUP methods were also accurate for closely related animals, however when the pedigree based BLUP methods were used to predict unrelated animals, the accuracy was close to zero. In contrast, gBLUP breeding values, for animals that had no pedigree relationship with animals in the reference data set, allowed substantial accuracy.</p> <p>Conclusions</p> <p>An animal's relationship to the reference data set is an important factor for the accuracy of genomic predictions. Animals that share a close relationship to the reference data set had the highest accuracy from genomic predictions. However a baseline accuracy that is driven by the reference data set size and the overall population effective population size enables gBLUP to estimate a breeding value for unrelated animals within a population (breed), using information previously ignored by pedigree based BLUP methods.</p

Genetic parameters for EUROP carcass traits within different groups of cattle in Ireland

The first objective of this study was to test the ability of systems of weighing and classifying bovine carcasses used in commercial abattoirs in Ireland to provide information that can be used for the purposes of genetic evaluation of carcass weight, carcass fatness class, and carcass conformation class. Secondly, the study aimed to test whether genetic and phenotypic variances differed by breed of sire. Variance components for carcass traits were estimated for crosses between dairy cows and 8 breeds of sire commonly found in the Irish cattle population. These 8 breeds were Aberdeen Angus, Belgian Blue, Charolais, Friesian, Hereford, Holstein, Limousin, and Simmental. A multivariate animal model was used to estimate genetic parameters within the Holstein sire breed group. Univariate analyses were used to estimate variance components for the remaining 7 sire breed groups. Multivariate sire models were used to formally test differences in genetic variances in sire breed groups. Field data on 64,443 animals, which were slaughtered in commercial abattoirs between the ages of 300 and 875 d, were analyzed in 8 analyses. Carcass fat class and carcass conformation class were measured using the European Union beef carcass classification system (EUROP) scale. For all 3 traits, the sire breed group with the greatest genetic variance had a value of more than 8 times the sire breed group with least genetic variance. Heritabilities ranged from zero to moderate for carcass fatness class (0.00 to 0.40), from low to moderate for carcass conformation class (0.04 to 0.36), and from low to high for carcass weight (0.06 to 0.65). Carcass weight was the most heritable (0.26) of the 3 traits. Carcass conformation class and carcass fatness class were equally heritable (0.17). Genetic and phenotypic correlations were all positive in the Holstein sire breed group. The genetic correlations varied from 0.11 for the relationship between carcass weight and carcass fatness class to 0.44 for the relationship between carcass conformation class and carcass fatness class. Carcass weight and classification data collected in Irish abattoirs are useful for the purposes of genetic evaluation for beef traits of Irish cattle. There were significantly different variance components across the sire breed groups

Optical analysis of Lithium Carbonate: Towards the development of a Portable Lithium Blood Level analyzer for Bipolar Disorder Patients

Lithium medication is the gold standard of treatment in Bipolar Disorder patients, preventing and reducing mood swings and suicidality. However, despite its effectiveness, it is a potentially hazardous drug requiring regular monitoring of blood levels to ensure toxic levels are not reached. This paper describes the first steps towards developing a new portable device that can be used by Bipolar Disorder patients to facilitate the analysis of lithium blood levels at home. Solutions of lithium carbonate have been optically fingerprinted using a high-end spectrophotometer. Preliminary measurements indicate that while the visible to near infrared region of the absorption spectra fall heavily within the water band, measurements in the Ultraviolet region show a strong distinction between different lithium concentrations. The optical spectra of Lithium in the 220 nm to 230 nm region demonstrated the ability to differentiate between concentrations representing those found in patients

Pb, Sr, and Nd isotopic characteristics of a variety of lithologies from the Guerrero composite terrane, west-central Mexico: constraints on their origin

Lead, Sr, and Nd isotope analyses of Mesozoic and Cenozoic rocks from the southern part of Guerrero terrane in Mexico provide a better understanding of their origin. Metamorphic rocks collected south of Arteaga (Zihuatanejo terrane) have similar Pb isotope values to basement rocks from Nevado de Toluca, indicating a possible connection of the basement in these areas. Lead isotope ratios of rocks from the Mesozoic Guerrero and Paleozoic Mixteca terranes are similar to those of north Peruvian Mesozoic Olmos and Paleozoic Marañón complexes, but more radiogenic than Grenville-age basement of southeast Mexico (Guichicovi complex) and north Colombia (Garzón massif and Santa Marta massif). Present-day Pb, Sr, and Nd isotope ratios of Mesozoic sedimentary rocks from Zihuatanejo and Teloloapan terranes define two clusters: rock from the Huetamo region (Zihuatanejo terrane), with less evolved isotopic signatures, and rocks from the Coastal belt (Colima and Purificación areas in Zihuatanejo terrane) and from the Teloloapan area (Teloloapan terrane) with higher isotopic ratios. Pb, Sr, and Nd isotopic ratios suggest the involvement of a more evolved component, possibly the basement rocks, in the generation of the sedimentary rocks from the Coastal belt and south of Teloloapan area compared to the sedimentary rocks from the Huetamo area. Cenozoic plutonic rocks from La Verde have more radiogenic isotopic ratios than samples from Inguarán, El Malacate, and La Esmeralda. These differences could result from assimilation of different rocks (Arteaga complex or sedimentary rocks) or different extents of contamination. Initial Sr and Nd isotopic values of the Cretaceous granitoids from Manzanillo and Jilotlán plot very close to the igneous samples from Inguarán, El Malacate, and La Esmeralda; this similarity may indicate that they had a common source. Isotopic compositions of Cenozoic plutonic rocks are consistent with subduction-related magmatism and suggest involvement of crustal material by assimilation during the rise of the magma, or by incorporation of subducted sediments, or both

Accuracy of estimated genomic breeding values for wool and meat traits in a multi-breed sheep population

Estimated breeding values for the selection of more profitable sheep for the sheep meat and wool industries are currently based on pedigree and phenotypic records. With the advent of a medium-density DNA marker array, which genotypes ∼50000 ovine single nucleotide polymorphisms, a third source of information has become available. The aim of this paper was to determine whether this genomic information can be used to predict estimated breeding values for wool and meat traits. The effects of all single nucleotide polymorphism markers in a multi-breed sheep reference population of 7180 individuals with phenotypic records were estimated to derive prediction equations for genomic estimated breeding values (GEBV) for greasy fleece weight, fibre diameter, staple strength, breech wrinkle score, weight at ultrasound scanning, scanned eye muscle depth and scanned fat depth. Five hundred and forty industry sires with very accurate Australian sheep breeding values were used as a validation population and the accuracies of GEBV were assessed according to correlations between GEBV and Australian sheep breeding values . The accuracies of GEBV ranged from 0.15 to 0.79 for wool traits in Merino sheep and from 0.07 to 0.57 for meat traits in all breeds studied. Merino industry sires tended to have more accurate GEBV than terminal and maternal breeds because the reference population consisted mainly of Merino haplotypes. The lower accuracy for terminal and maternal breeds suggests that the density of genetic markers used was not high enough for accurate across-breed prediction of marker effects. Our results indicate that an increase in the size of the reference population will increase the accuracy of GEBV

Estimation of accuracy and bias in genetic evaluations with genetic groups using sampling

Accuracy and bias of estimated breeding values are important measures of the quality of genetic evaluations. A sampling method that accounts for the uncertainty in the estimation of genetic group effects was used to calculate accuracy and bias of estimated effects. The method works by repeatedly simulating phenotypes for multiple traits for a defined data and pedigree structure. These simulated values are analysed using BLUP with genetic groups in the relationship matrix. Accuracies and biases are then calculated as correlations among and differences between true and estimated values across all replicates, respectively. The method was applied to the Irish beef production data set for 15 traits and with 15 genetic groups to account for differences in breed means. Accuracy and bias of estimated genetic groups effects, estimated comparisons between genetic groups effects, estimated breeding values within genetic group, and estimated breeding values across genetic group were calculated. Small biases were detected for most estimated genetic group effects and most estimated comparisons between genetic group effects. Most of these were not of importance relative to the phenotypic standard deviation of the traits involved. For example, a bias of 0.78% of the phenotypic standard deviation was detected for carcass conformation in Aberdeen Angus. However, one trait, calf quality, which has very few performance records in the data set, displayed larger bias ranging from -10.31% to 5.85% of the phenotypic standard deviation across the different estimated genetic group effects. Large differences were observed in the accuracies of genetic group effects, ranging from 0.02 for feed intake in Holstein, which had no data recorded, to >0.97 for carcass conformation, a trait with large amounts of data recorded in the different genetic groups. Large differences were also observed in the accuracies of the comparisons among genetic group effects. The accuracies of the estimated breeding values within genetic group and estimated breeding values across genetic group were sometimes different; for example, carcass conformation in Belgian Blue had an average accuracy within genetic group of 0.69 compared to an average accuracy across genetic group of 0.89. This suggests that the accuracy of genetic groups should be taken into account when publishing estimated breeding values across genetic groups

A characterization of the multivariate excess wealth ordering

In this paper, some new properties of the upper-corrected orthant of a random vector are proved. The univariate right-spread or excess wealth function, introduced by Fernández-Ponce et al. (1996), is extended to multivariate random vectors, and some properties of this multivariate function are studied. Later, this function was used to define the excess wealth ordering by Shaked and Shanthikumar (1998) and Fernández-Ponce et al. (1998). The multivariate excess wealth function enable us to define a new stochastic comparison which is weaker than the multivariate dispersion orderings. Also, some properties relating the multivariate excess wealth order with stochastic dependence are describe