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ABSTRACT Genetic trends are a valuable tool for analysing the efficiency of breeding programs. They are calculated by averaging the predicted breeding values for all individuals born within a specific time period. Moreover, partitioned genetic trends allow dissecting the contributions of several selection paths to overall genetic progress. These trends are based on the linear relationship between breeding values and the Mendelian sampling terms of ancestors, enabling genetic trends to be split into contributions from different categories of individuals. However, (1) the use of predicted breeding values in calculating partitioned genetic trends depends on the variance components used and (2) a multiple trait analysis allows accounting for selection on correlated traits. These points are often not considered. To overcome these limitations, we present a software called “TM_TRENDS.” This software performs a Bayesian analysis of partitioned genetic trends in a multiple trait model, accounting for uncertainty in the variance components. To illustrate the capabilities of this tool, we analysed the partitioned genetic trends for five traits (Birth Weight, Weight at 210 days, Cold Carcass Weight, Carcass Conformation, and Fatness Conformation) in two Spanish beef cattle breeds, Pirenaica and Rubia Gallega. The global genetic trends showed an increase in Carcass Conformation and a decrease in Birth Weight, Weight at 210 days, Cold Carcass Weight, and Fatness Conformation. These trends were partitioned into six categories: non‐reproductive individuals, dams of females and non‐reproductive individuals, dams of sires, sires with fewer than 20 progeny, sires between 20 and 50 progeny, and sires with more than 50 progeny. The results showed that the main source of genetic progress comes from sires with more than 50 progenies, followed by dams of males. Additionally, two additional features of the Bayesian analysis are presented: the calculation of the posterior probability of the global and partitioned genetic response between two time points, and the calculation of the posterior probability of positive (or negative) genetic progress. [ABSTRACT FROM AUTHOR]

Abstract Breeding sheep populations for scrapie resistance could result in a loss of genetic variability. In this study, the effect on genetic variability of selection for increasing the ARR allele frequency was estimated in the Latxa breed. Two sources of information were used, pedigree and genetic polymorphisms (fifteen microsatellites). The results based on the genealogical information were conditioned by a low pedigree completeness level that revealed the interest of also using the information provided by the molecular markers. The overall results suggest that no great negative effect on genetic variability can be expected in the short time in the population analysed by selection of only ARR/ARR males. The estimated average relationship of ARR/ARR males with reproductive females was similar to that of all available males whatever its genotype: 0.010 vs. 0.012 for a genealogical relationship and 0.257 vs. 0.296 for molecular coancestry, respectively. However, selection of only ARR/ARR males implied important losses in founder animals (87 percent) and low frequency alleles (30 percent) in the ram population. The evaluation of mild selection strategies against scrapie susceptibility based on the use of some ARR heterozygous males was difficult because the genetic relationships estimated among animals differed when pedigree or molecular information was used, and the use of more molecular markers should be evaluated.

Single‐step genomic BLUP (ssGBLUP) relies on the combination of the genomic (G$$ \mathbf{G} $$) and pedigree relationship matrices for all (A$$ \mathbf{A} $$) and genotyped (A22$$ {\mathbf{A}}_{22} $$) animals. The procedure ensures G$$ \mathbf{G} $$ and A22$$ {\mathbf{A}}_{22} $$ are compatible so that both matrices refer to the same genetic base ('tuning'). Then G$$ \mathbf{G} $$ is combined with a proportion of A22$$ {\mathbf{A}}_{22} $$ ('blending') to avoid singularity problems and to account for the polygenic component not accounted for by markers. This computational procedure has been implemented in the reverse order (blending before tuning) following the sequential research developments. However, blending before tuning may result in less optimal tuning because the blended matrix already contains a proportion of A22$$ {\mathbf{A}}_{22} $$. In this study, the impact of 'tuning before blending' was compared with 'blending before tuning' on genomic estimated breeding values (GEBV), single nucleotide polymorphism (SNP) effects and indirect predictions (IP) from ssGBLUP using American Angus Association and Holstein Association USA, Inc. data. Two slightly different tuning methods were used; one that adjusts the mean diagonals and off‐diagonals of G$$ \mathbf{G} $$ to be similar to those in A22$$ {\mathbf{A}}_{22} $$ and another one that adjusts based on the average difference between all elements of G$$ \mathbf{G} $$ and A22$$ {\mathbf{A}}_{22} $$. Over 6 million Angus growth records and 5.9 million Holstein udder depth records were available. Genomic information was available on 51,478 Angus and 105,116 Holstein animals. Average realized relationship estimates among groups of animals were similar across scenarios. Scatterplots show that GEBV, SNP effects and IP did not noticeably change for all animals in the evaluation regardless of the order of computations and when using blending parameter of 0.05. Formulas were derived to determine the blending parameter that maximizes changes in the genomic relationship matrix and GEBV when changing the order of blending and tuning. Algebraically, the change is maximized when the blending parameter is equal to 0.5. Overall, tuning G$$ \mathbf{G} $$ before blending, regardless of blending parameter used, had a negligible impact on genomic predictions and SNP effects in this study. [ABSTRACT FROM AUTHOR]

Abstract Background Using a multi-breed reference population might be a way of increasing the accuracy of genomic breeding values in small breeds. Models involving mixed-breed data do not take into account the fact that marker effects may differ among breeds. This study was aimed at investigating the impact on accuracy of increasing the number of genotyped candidates in the training set by using a multi-breed reference population, in contrast to single-breed genomic evaluations. Methods Three traits (milk production, fat content and female fertility) were analyzed by genomic mixed linear models and Bayesian methodology. Three breeds of French dairy cattle were used: Holstein, Montbéliarde and Normande with 2976, 950 and 970 bulls in the training population, respectively and 964, 222 and 248 bulls in the validation population, respectively. All animals were genotyped with the Illumina Bovine SNP50 array. Accuracy of genomic breeding values was evaluated under three scenarios for the correlation of genomic breeding values between breeds (rg): uncorrelated (1), rg = 0; estimated rg (2); high, rg = 0.95 (3). Accuracy and bias of predictions obtained in the validation population with the multi-breed training set were assessed by the coefficient of determination (R2) and by the regression coefficient of daughter yield deviations of validation bulls on their predicted genomic breeding values, respectively. Results The genetic variation captured by the markers for each trait was similar to that estimated for routine pedigree-based genetic evaluation. Posterior means for rg ranged from −0.01 for fertility between Montbéliarde and Normande to 0.79 for milk yield between Montbéliarde and Holstein. Differences in R2 between the three scenarios were notable only for fat content in the Montbéliarde breed: from 0.27 in scenario (1) to 0.33 in scenarios (2) and (3). Accuracies for fertility were lower than for other traits. Conclusions Using a multi-breed reference population resulted in small or no increases in accuracy. Only the breed with a small data set and large genetic correlation with the breed with a large data set showed increased accuracy for the traits with moderate (milk) to high (fat content) heritability. No benefit was observed for fertility, a lowly heritable trait.

Abstract Background Genetic relatedness or similarity between individuals is a key concept in population, quantitative and conservation genetics. When the pedigree of a population is available and assuming a founder population from which the genealogical records start, genetic relatedness between individuals can be estimated by the coancestry coefficient. If pedigree data is lacking or incomplete, estimation of the genetic similarity between individuals relies on molecular markers, using either molecular coancestry or molecular covariance. Some relationships between genealogical and molecular coancestries and covariances have already been described in the literature. Methods We show how the expected values of the empirical measures of similarity based on molecular marker data are functions of the genealogical coancestry. From these formulas, it is easy to derive estimators of genealogical coancestry from molecular data. We include variation of allelic frequencies in the estimators. Results The estimators are illustrated with simulated examples and with a real dataset from dairy cattle. In general, estimators are accurate and only slightly biased. From the real data set, estimators based on covariances are more compatible with genealogical coancestries than those based on molecular coancestries. A frequently used estimator based on the average of estimated coancestries produced inflated coancestries and numerical instability. The consequences of unknown gene frequencies in the founder population are briefly discussed, along with alternatives to overcome this limitation. Conclusions Estimators of genealogical coancestry based on molecular data are easy to derive. Estimators based on molecular covariance are more accurate than those based on identity by state. A correction considering the random distribution of allelic frequencies improves accuracy of these estimators, especially for populations with very strong drift.

Abstract Background Since 2001, the use of more and more dense maps has made researchers aware that combining linkage and linkage disequilibrium enhances the feasibility of fine-mapping genes of interest. So, various method types have been derived to include concepts of population genetics in the analyses. One major drawback of many of these methods is their computational cost, which is very significant when many markers are considered. Recent advances in technology, such as SNP genotyping, have made it possible to deal with huge amount of data. Thus the challenge that remains is to find accurate and efficient methods that are not too time consuming. The study reported here specifically focuses on the half-sib family animal design. Our objective was to determine whether modelling of linkage disequilibrium evolution improved the mapping accuracy of a quantitative trait locus of agricultural interest in these populations. We compared two methods of fine-mapping. The first one was an association analysis. In this method, we did not model linkage disequilibrium evolution. Therefore, the modelling of the evolution of linkage disequilibrium was a deterministic process; it was complete at time 0 and remained complete during the following generations. In the second method, the modelling of the evolution of population allele frequencies was derived from a Wright-Fisher model. We simulated a wide range of scenarios adapted to animal populations and compared these two methods for each scenario. Results Our results indicated that the improvement produced by probabilistic modelling of linkage disequilibrium evolution was not significant. Both methods led to similar results concerning the location accuracy of quantitative trait loci which appeared to be mainly improved by using four flanking markers instead of two. Conclusions Therefore, in animal half-sib designs, modelling linkage disequilibrium evolution using a Wright-Fisher model does not significantly improve the accuracy of the QTL location when compared to a simpler method assuming complete and constant linkage between the QTL and the marker alleles. Finally, given the high marker density available nowadays, the simpler method should be preferred as it gives accurate results in a reasonable computing time.

Abstract Background Ranks have been used as phenotypes in the genetic evaluation of horses for a long time through the use of earnings, normal score or raw ranks. A model, ("underlying model" of an unobservable underlying variable responsible for ranks) exists. Recently, a full Bayesian analysis using this model was developed. In addition, in reality, competitions are structured into categories according to the technical level of difficulty linked to the technical ability of horses (horses considered to be the "best" meet their peers). The aim of this article was to validate the underlying model through simulations and to propose a more appropriate model with a mixture distribution of horses in the case of a structured competition. The simulations involved 1000 horses with 10 to 50 performances per horse and 4 to 20 horses per event with unstructured and structured competitions. Results The underlying model responsible for ranks performed well with unstructured competitions by drawing liabilities in the Gibbs sampler according to the following rule: the liability of each horse must be drawn in the interval formed by the liabilities of horses ranked before and after the particular horse. The estimated repeatability was the simulated one (0.25) and regression between estimated competing ability of horses and true ability was close to 1. Underestimations of repeatability (0.07 to 0.22) were obtained with other traditional criteria (normal score or raw ranks), but in the case of a structured competition, repeatability was underestimated (0.18 to 0.22). Our results show that the effect of an event, or category of event, is irrelevant in such a situation because ranks are independent of such an effect. The proposed mixture model pools horses according to their participation in different categories of competition during the period observed. This last model gave better results (repeatability 0.25), in particular, it provided an improved estimation of average values of competing ability of the horses in the different categories of events. Conclusions The underlying model was validated. A correct drawing of liabilities for the Gibbs sampler was provided. For a structured competition, the mixture model with a group effect assigned to horses gave the best results.

Abstract Background Populational linkage disequilibrium and within-family linkage are commonly used for QTL mapping and marker assisted selection. The combination of both results in more robust and accurate locations of the QTL, but models proposed so far have been either single marker, complex in practice or well fit to a particular family structure. Results We herein present linear model theory to come up with additive effects of the QTL alleles in any member of a general pedigree, conditional to observed markers and pedigree, accounting for possible linkage disequilibrium among QTLs and markers. The model is based on association analysis in the founders; further, the additive effect of the QTLs transmitted to the descendants is a weighted (by the probabilities of transmission) average of the substitution effects of founders' haplotypes. The model allows for non-complete linkage disequilibrium QTL-markers in the founders. Two submodels are presented: a simple and easy to implement Haley-Knott type regression for half-sib families, and a general mixed (variance component) model for general pedigrees. The model can use information from all markers. The performance of the regression method is compared by simulation with a more complex IBD method by Meuwissen and Goddard. Numerical examples are provided. Conclusion The linear model theory provides a useful framework for QTL mapping with dense marker maps. Results show similar accuracies but a bias of the IBD method towards the center of the region. Computations for the linear regression model are extremely simple, in contrast with IBD methods. Extensions of the model to genomic selection and multi-QTL mapping are straightforward.