Removing data and using metafounders alleviates biases for all traits in Lacaune dairy sheep predictions.

Bias in dairy genetic evaluations, when it exists, has to be understood and properly addressed. The origin of biases is not always clear. We analyzed 40 yr of records from the Lacaune dairy sheep breeding program to evaluate the extent of bias, assess possible corrections, and emit hypotheses on its origin. The data set included 7 traits (milk yield, fat and protein contents, somatic cell score, teat angle, udder cleft, and udder depth) with records from 600,000 to 5 million depending on the trait, ∼1,900,000 animals, and ∼5,900 genotyped elite artificial insemination rams. For the ∼8% animals with missing sire, we fit 25 unknown parent groups. We used the linear regression method to compare "partial" and "whole" predictions of young rams before and after progeny testing, with 7 cut-off points, and we obtained estimates of their bias, (over)dispersion, and accuracy in early proofs. We tried (1) several scenarios as follows: multiple or single trait, the "official" (routine) evaluation, which is a mixture of both single and multiple trait, and "deletion" of data before 1990; and (2) several models as follows: BLUP and single-step genomic (SSG)BLUP with fixed unknown parent groups or metafounders, where, for metafounders, their relationship matrix gamma was estimated using either a model for inbreeding trend, or base allele frequencies estimated by peeling. The estimate of gamma obtained by modeling the inbreeding trend resulted in an estimated increase of inbreeding, based on markers, faster than the pedigree-based one. The estimated genetic trends were similar for most models and scenarios across all traits, but were shrunken when gamma was estimated by peeling. This was due to shrinking of the estimates of metafounders in the latter case. Across scenarios, all traits showed bias, generally as an overestimate of genetic trend for milk yield and an underestimate for the other traits. As for the slope, it showed overdispersion of estimated breeding values for all traits. Using multiple-trait models slightly reduced the overestimate of genetic trend and the overdispersion, as did including genomic information (i.e., SSGBLUP) when the gamma matrix was estimated by the model for inbreeding trend. However, only deletion of historical data before 1990 resulted in elimination of both kind of biases. The SSGBLUP resulted in more accurate early proofs than BLUP for all traits. We considered that a snowball effect of small errors in each genetic evaluation, combined with selection, may have resulted in biased evaluations. Improving statistical methods reduced some bias but not all, and a simple solution for this data set was to remove historical records.

Predicting the effect of reference population on the accuracy of within, across, and multibreed genomic prediction.

Genomic prediction is widely used to select candidates for breeding. Size and composition of the reference population are important factors influencing prediction accuracy. In Holstein dairy cattle, large reference populations are used, but this is difficult to achieve in numerically small breeds and for traits that are not routinely recorded. The prediction accuracy is usually estimated using cross-validation, requiring the full data set. It would be useful to have a method to predict the benefit of multibreed reference populations that does not require the availability of the full data set. Our objective was to study the effect of the size and breed composition of the reference population on the accuracy of genomic prediction using genomic BLUP and Bayes R. We also examined the effect of trait heritability and validation breed on prediction accuracy. Using these empirical results, we investigated the use of a formula to predict the effect of the size and composition of the reference population on the accuracy of genomic prediction. Phenotypes were simulated in a data set containing real genotypes of imputed sequence variants for 22,752 dairy bulls and cows, including Holstein, Jersey, Red Holstein, and Australian Red cattle. Different reference populations were constructed, varying in size and composition, to study within-breed, multibreed, and across-breed prediction. Phenotypes were simulated varying in heritability, number of chromosomes, and number of quantitative trait loci. Genomic prediction was carried out using genomic BLUP and Bayes R. We used either the genomic relationship matrix (GRM) to estimate the number of independent chromosomal segments and subsequently to predict accuracy, or the accuracies obtained from single-breed reference populations to predict the accuracies of larger or multibreed reference populations. Using the GRM overestimated the accuracy; this overestimation was likely due to close relationships among some of the reference animals. Consequently, the GRM could not be used to predict the accuracy of genomic prediction reliably. However, a method using the prediction accuracies obtained by cross-validation using a small, single-breed reference population predicted the accuracy using a multibreed reference population well and slightly overestimated the accuracy for a larger reference population of the same breed, but gave a reasonably close estimate of the accuracy for a multibreed reference population. This method could be useful for making decisions regarding the size and composition of the reference population.

Milk mid-infrared spectral data as a tool to predict feed intake in lactating Norwegian Red dairy cows.

Mid-infrared (MIR) spectroscopy of milk was used to predict dry matter intake (DMI) and net energy intake (NEI) in 160 lactating Norwegian Red dairy cows. A total of 857 observations were used in leave-one-out cross-validation and external validation to develop and validate prediction equations using 5 different models. Predictions were performed using (multiple) linear regression, partial least squares (PLS) regression, or best linear unbiased prediction (BLUP) methods. Linear regression was implemented using just milk yield (MY) or fat, protein, and lactose concentration in milk (Mcont) or using MY together with body weight (BW) as predictors of intake. The PLS and BLUP methods were implemented using just the MIR spectral information or using the MIR together with Mcont, MY, BW, or NEI from concentrate (NEIconc). When using BLUP, the MIR spectral wavelengths were always treated as random effects, whereas Mcont, MY, BW, and NEIconc were considered to be fixed effects. Accuracy of prediction (R) was defined as the correlation between the predicted and observed feed intake test-day records. When using the linear regression method, the greatest R of predicting DMI (0.54) and NEI (0.60) in the external validation was achieved when the model included both MY and BW. When using PLS, the greatest R of predicting DMI (0.54) and NEI (0.65) in the external validation data set was achieved when using both BW and MY as predictors in combination with the MIR spectra. When using BLUP, the greatest R of predicting DMI (0.54) in the external validation was when using MY together with the MIR spectra. The greatest R of predicting NEI (0.65) in the external validation using BLUP was achieved when the model included both BW and MY in combination with the MIR spectra or when the model included both NEIconc and MY in combination with MIR spectra. However, although the linear regression coefficients of actual on predicted values for DMI and NEI were not different from unity when using PLS, they were less than unity for some of the models developed using BLUP. This study shows that MIR spectral data can be used to predict NEI as a measure of feed intake in Norwegian Red dairy cattle and that the accuracy is augmented if additional, often available data are also included in the prediction model.

Strategies for implementing genomic selection for feed efficiency in dairy cattle breeding schemes.

Alternative genomic selection and traditional BLUP breeding schemes were compared for the genetic improvement of feed efficiency in simulated Norwegian Red dairy cattle populations. The change in genetic gain over time and achievable selection accuracy were studied for milk yield and residual feed intake, as a measure of feed efficiency. When including feed efficiency in genomic BLUP schemes, it was possible to achieve high selection accuracies for genomic selection, and all genomic BLUP schemes gave better genetic gain for feed efficiency than BLUP using a pedigree relationship matrix. However, introducing a second trait in the breeding goal caused a reduction in the genetic gain for milk yield. When using contracted test herds with genotyped and feed efficiency recorded cows as a reference population, adding an additional 4,000 new heifers per year to the reference population gave accuracies that were comparable to a male reference population that used progeny testing with 250 daughters per sire. When the test herd consisted of 500 or 1,000 cows, lower genetic gain was found than using progeny test records to update the reference population. It was concluded that to improve difficult to record traits, the use of contracted test herds that had additional recording (e.g., measurements required to calculate feed efficiency) is a viable option, possibly through international collaborations.

Improving production efficiency in the presence of genotype by environment interactions in pig genomic selection breeding programmes.

We simulated a genomic selection pig breeding schemes containing nucleus and production herds to improve feed efficiency of production pigs that were cross-breed. Elite nucleus herds had access to high-quality feed, and production herds were fed low-quality feed. Feed efficiency in the nucleus herds had a heritability of 0.3 and 0.25 in the production herds. It was assumed the genetic relationships between feed efficiency in the nucleus and production were low (rg  = 0.2), medium (rg  = 0.5) and high (rg  = 0.8). In our alternative breeding schemes, different proportion of production animals were recorded for feed efficiency and genotyped with high-density panel of genetic markers. Genomic breeding value of the selection candidates for feed efficiency was estimated based on three different approaches. In one approach, genomic breeding value was estimated including nucleus animals in the reference population. In the second approach, the reference population was containing a mixture of nucleus and production animals. In the third approach, the reference population was only consisting of production herds. Using a mixture reference population, we generated 40-115% more genetic gain in the production environment as compared to only using nucleus reference population that were fed high-quality feed sources when the production animals were offspring of the nucleus animals. When the production animals were grand offspring of the nucleus animals, 43-104% more genetic gain was generated. Similarly, a higher genetic gain generated in the production environment when mixed reference population was used as compared to only using production animals. This was up to 19 and 14% when the production animals were offspring and grand offspring of nucleus animals, respectively. Therefore, in genomic selection pig breeding programmes, feed efficiency traits could be improved by properly designing the reference population.

Across population genomic prediction scenarios in which Bayesian variable selection outperforms GBLUP.

BACKGROUND: The use of information across populations is an attractive approach to increase the accuracy of genomic prediction for numerically small populations. However, accuracies of across population genomic prediction, in which reference and selection individuals are from different populations, are currently disappointing. It has been shown for within population genomic prediction that Bayesian variable selection models outperform GBLUP models when the number of QTL underlying the trait is low. Therefore, our objective was to identify across population genomic prediction scenarios in which Bayesian variable selection models outperform GBLUP in terms of prediction accuracy. In this study, high density genotype information of 1033 Holstein Friesian, 105 Groningen White Headed, and 147 Meuse-Rhine-Yssel cows were used. Phenotypes were simulated using two changing variables: (1) the number of QTL underlying the trait (3000, 300, 30, 3), and (2) the correlation between allele substitution effects of QTL across populations, i.e. the genetic correlation of the simulated trait between the populations (1.0, 0.8, 0.4). RESULTS: The accuracy obtained by the Bayesian variable selection model was depending on the number of QTL underlying the trait, with a higher accuracy when the number of QTL was lower. This trend was more pronounced for across population genomic prediction than for within population genomic prediction. It was shown that Bayesian variable selection models have an advantage over GBLUP when the number of QTL underlying the simulated trait was small. This advantage disappeared when the number of QTL underlying the simulated trait was large. The point where the accuracy of Bayesian variable selection and GBLUP became similar was approximately the point where the number of QTL was equal to the number of independent chromosome segments (M e ) across the populations. CONCLUSION: Bayesian variable selection models outperform GBLUP when the number of QTL underlying the trait is smaller than M e . Across populations, M e is considerably larger than within populations. So, it is more likely to find a number of QTL underlying a trait smaller than M e across populations than within population. Therefore Bayesian variable selection models can help to improve the accuracy of across population genomic prediction.

Genetic analysis of longevity in Dutch dairy cattle using random regression.

Longevity, productive life, or lifespan of dairy cattle is an important trait for dairy farmers, and it is defined as the time from first calving to the last test date for milk production. Methods for genetic evaluations need to account for censored data; that is, records from cows that are still alive. The aim of this study was to investigate whether these methods also need to take account of survival being genetically a different trait across the entire lifespan of a cow. The data set comprised 112,000 cows with a total of 3,964,449 observations for survival per month from first calving until 72 mo in productive life. A random regression model with second-order Legendre polynomials was fitted for the additive genetic effect. Alternative parameterizations were (1) different trait definitions for the length of time interval for survival after first calving (1, 3, 6, and 12 mo); (2) linear or threshold model; and (3) differing the order of the Legendre polynomial. The partial derivatives of a profit function were used to transform variance components on the survival scale to those for lifespan. Survival rates were higher in early life than later in life (99 vs. 95%). When survival was defined over 12-mo intervals survival curves were smooth compared with curves when 1-, 3-, or 6-mo intervals were used. Heritabilities in each interval were very low and ranged from 0.002 to 0.031, but the heritability for lifespan over the entire period of 72 mo after first calving ranged from 0.115 to 0.149. Genetic correlations between time intervals ranged from 0.25 to 1.00. Genetic parameters and breeding values for the genetic effect were more sensitive to the trait definition than to whether a linear or threshold model was used or to the order of Legendre polynomial used. Cumulative survival up to the first 6 mo predicted lifespan with an accuracy of only 0.79 to 0.85; that is, reliability of breeding value with many daughters in the first 6 mo can be, at most, 0.62 to 0.72, and changes of breeding values are still expected when daughters are getting older. Therefore, an improved model for genetic evaluation should treat survival as different traits during the lifespan by splitting lifespan in time intervals of 6 mo or less to avoid overestimated reliabilities and changes in breeding values when daughters are getting older.

Genetic contributions and their optimization.

Genetic contributions were first formalized in 1958 by James and McBride (Journal of Genetics, 56, 55-62) and have since been shown to provide a unifying framework for theories of gain and inbreeding. As such they have underpinned the development of methods that provide the most effective combination of maximizing gain whilst managing inbreeding and loss of genetic variation. It is shown how this optimum contribution technology can be developed from theory and adapted to provide practical selection protocols for a wide variety of situations including overlapping generations and multistage selection. The natural development of the theory to incorporate genomic selection and genomic control of inbreeding is also shown.

Genomic predictions based on a joint reference population for the Nordic Red cattle breeds.

The main aim of this study was to compare accuracies of imputation and genomic predictions based on single and joint reference populations for Norwegian Red (NRF) and a composite breed (DFS) consisting of Danish Red, Finnish Ayrshire, and Swedish Red. The single nucleotide polymorphism (SNP) data for NRF consisted of 2 data sets: one including 25,000 markers (NRF25K) and the other including 50,000 markers (NRF50K). The NRF25K data set had 2,572 bulls, and the NRF50K data set had 1,128 bulls. Four hundred forty-two bulls were genotyped in both data sets (double-genotyped bulls). The DFS data set (DSF50K) included 50,000 markers of 13,472 individuals, of which around 4,700 were progeny-tested bulls. The NRF25K data set was imputed to 50,000 density using the software Beagle. The average error rate for the imputation of NRF25K decreased slightly from 0.023 to 0.021, and the correlation between observed and imputed genotypes changed from 0.935 to 0.936 when comparing the NRF50K reference and the NRF50K-DFS50K joint reference imputations. A genomic BLUP (GBLUP) model and a Bayesian 4-component mixture model were used to predict genomic breeding values for the NRF and DFS bulls based on the single and joint NRF and DFS reference populations. In the multiple population predictions, accuracies of genomic breeding values increased for the 3 production traits (milk, fat, and protein yields) for both NRF and DFS. Accuracies increased by 6 and 1.3 percentage points, on average, for the NRF and DFS bulls, respectively, using the GBLUP model, and by 9.3 and 1.3 percentage points, on average, using the Bayesian 4-component mixture model. However, accuracies for health or reproduction traits did not increase from the multiple population predictions. Among the 3 DFS populations, Swedish Red gained most in accuracies from the multiple population predictions, presumably because Swedish Red has a closer genetic relationship with NRF than Danish Red and Finnish Ayrshire. The Bayesian 4-component mixture model performed better than the GBLUP model for most production traits for both NRF and DFS, whereas no advantage was found for health or reproduction traits. In general, combining NRF and DFS reference populations was useful in genomic predictions for both the NRF and DFS bulls.

Investigations on the pattern of linkage disequilibrium and selection signatures in the genomes of German Piétrain pigs.

The aim of this study was to study the population structure, to characterize the LD structure and to define core regions based on low recombination rates among SNP pairs in the genome of Piétrain pigs using data from the PorcineSNP60 BeadChip. This breed is a European sire line and was strongly selected for lean meat content during the last decades. The data were used to map signatures of selection using the REHH test. In the first step, selection signatures were searched genome-wide using only core haplotypes having a frequency above 0.25. In the second step, the results from the selection signature analysis were matched with the results from the recently conducted genome-wide association study for economical relevant traits to investigate putative overlaps of chromosomal regions. A small subdivision of the population with regard to the geographical origin of the individuals was observed. The extent of LD was determined genome-wide using r(2) values for SNP pairs with a distance ≤5 Mb and was on average 0.34. This comparable low r(2) value indicates a high genetic diversity in the Piétrain population. Six REHH values having a p-value < 0.001 were genome-wide detected. These were located on SSC1, 2, 6 and 17. Three positional candidate genes with potential biological roles were suggested, called LOC100626459, LOC100626014 and MIR1. The results imply that for genome-wide analysis especially in this population, a higher marker density and higher sample sizes are required. For a number of nine SNPs, which were successfully annotated to core regions, the REHH test was applied. However, no selection signatures were found for those regions (p-value < 0.1).

Reducing foreign genetic contributions to the YDH pig population by segment-based advanced optimum contribution selection.

Yuedonghei (YDH) is the only local pig breed with full black hair among the four well-known local pig breeds originated and distributed in Guangdong province, China, which caters to the consumers' preference of the local market of 127 million residents and thus brings a significantly above-average price. However, considerable genetic introgression (GI) has been reported for the YDH population, i.e., gene flow into YDH from other pig breeds, which is mainly due to the recent crossbreeding with several mainstream breeds for upgrading reasons. Therefore, this study aimed to evaluate the GI as well as the conservation status in the current YDH population and test the feasibility of advanced optimum contribution selection (aOCS) in alleviating GI in YDH. We first analysed the genetic diversity, ancestral structure, population structure, and phylogeny of 360 YDH relative to 782 publicly downloaded pigs of 42 Eurasian or American breeds and wild boars, based on single nucleotide polymorphism chip data. Then, we selected 304 initial YDH and stochastically simulated a practical conservation programme that spanned 10 discrete generations and implemented haplotype segment-based aOCS in every generation. The expected and observed heterozygosity of 360 YDH were 0.344 and 0.336. The linkage disequilibrium-based recent effective population size (Ne) was 32.89. Considerable GI amounting to 32.9% foreign ancestry was found in 28 lowly related YDH individuals using admixture analysis. In the simulated YDH conservation programme, the average native genomic contribution was increased from 50.4 to 71.4% while maintaining a Ne of 100 by controlling classic kinship and native kinship. Our study showed that segment-based aOCS that required only genomic data can be used to alleviate GI in the current YDH population and meanwhile increase its Ne, which provided strategic insights into the sustainable conservation of local genetic resources of livestock.

Genetic components of milk Fourier-transform infrared spectra used to predict breeding values for milk composition and quality traits in dairy goats.

The usual practice today is that milk component phenotypes are predicted using Fourier-transform infrared (FTIR) spectra and they are then, together with pedigree information, used in BLUP for calculation of individual estimated breeding values. Here, this is referred to as the indirect prediction (IP) approach. An alternative approach-a direct prediction (DP) method-is proposed, where genetic analyses are directly conducted on the milk FTIR spectral variables. Breeding values of all derived milk traits (protein, fat, fatty acid composition, and coagulation properties, among others) can then be predicted as traits correlated only to the genetic information of the spectra. For the DP, no need exists to predict the phenotypes before calculating breeding values for each of the traits-the genetic analysis is done once for the spectra, and is applicable to all traits derived from the spectra. The aim of the study was to compare the effects of DP and IP of milk composition and quality traits on prediction error variance (PEV) and genetic gain. A data set containing 27,927 milk FTIR spectral observations and milk composition phenotypes (fat, lactose, and protein) belonging to 14,869 goats of 271 herds was used for training and evaluating models. Partial least squares regression was used for calibrating prediction models for fat, protein, and lactose percentages. Restricted maximum likelihood was used to estimate variance components of the spectral variables after principal components analysis was applied to reduce the spectral dimension. Estimated breeding values were predicted for fat, lactose, and protein percentages using DP and IP methods. The DP approach reduced the mean PEV by 3.73, 4.07, and 7.04% for fat, lactose, and protein percentages, respectively, compared with the IP method. Given the reduction in PEV, relative genetic gains were 2.99, 2.78, and 4.85% for fat, lactose, and protein percentages, respectively. We concluded that more accurate estimated breeding values could be found using genetic components of milk FTIR spectra compared with single-trait animal model analyses on phenotypes predicted from the spectra separately. The potential and application is not only limited to milk FTIR spectra, but could also be extended to any spectroscopy techniques implemented in other species and for other traits.

A comparison of dairy cattle breeding designs that use genomic selection.

Different dairy cattle breeding schemes were compared using stochastic simulations, in which the accuracy of the genomic breeding values was dependent on the structure of the breeding scheme, through the availability of new genotyped animals with phenotypic information. Most studies that predict the gain by implementing genomic selection apply a deterministic approach that requires assumptions about the accuracy of the genomic breeding values. The achieved genetic gain, when genomic selection was the only selection method to directly identify elite sires for widespread use and progeny testing was omitted, was compared with using genomic selection for preselection of young bulls for progeny testing and to a conventional progeny test scheme. The rate of inbreeding could be reduced by selecting more sires every year. Selecting 20 sires directly on their genomic breeding values gave a higher genetic gain than any progeny testing scheme, with the same rate of inbreeding as the schemes that used genomic selection for preselection of bulls before progeny testing. The genomic selection breeding schemes could reduce the rate of inbreeding and still increase genetic gain, compared with the conventional breeding scheme. Since progeny testing is expensive, the breeding scheme omitting the progeny test will be the cheapest one. Keeping the progeny test and use of genomic selection for preselection still has some advantages. It gives higher accuracy of breeding values and does not require a complete restructuring of the breeding program. Comparing at the same rate of inbreeding, using genomic selection for elite sire selection only gives a 13% increase in genetic gain, compared with using genomic selection for preselection. One way to reduce the costs of the scheme where genomic selection was used for preselection is to reduce the number of progeny tested bulls. This was here achieved without getting lower genetic gain or a higher rate of inbreeding.

Short communication: evidence for a major gene by polygene interaction for milk production traits in German Holstein dairy cattle.

The present study investigated putative interaction effects between the DGAT1 K232A mutation and the polygenic term (i.e., all genes except DGAT1) for 5 milk production traits in the German Holstein dairy cattle population. Mixed models were used, and the test for interaction relied on the comparison of polygenic variance components depending on the sire's genotypes at DGAT1 K232A. Substitution effects were highly significant for all traits. Significant interaction effects were found for milk fat and protein percentage.

Use of female information in dairy cattle genomic breeding programs.

Genomic selection has the potential to increase the accuracy of selection and, therefore, genetic gain, as well as reducing the rate of inbreeding, yet few studies have evaluated the potential benefit of the contribution of females in genomic selection programs. The objective of this study was to determine the effect on genetic gain, accuracy of selection, generation interval, and inbreeding, of including female genotypes in a genomic selection breeding program. A population of approximately 3,500 females and 500 males born annually was simulated and split into an elite and commercial tier representation of the Irish national herd. Several alternative breeding schemes were evaluated to quantify the potential benefit of female genomic information within dairy breeding schemes. Results showed that the inclusion of female phenotypic and genomic information can lead to a 3-fold increase in the rate of genetic gain compared with a traditional BLUP breeding program and decrease the generation interval of the males by 3.8 yr, while maintaining a reasonable rate of inbreeding. The accuracy of the selected males was increased by 73% in the final 3 yr of the genomic schemes compared with the traditional BLUP scheme. The results of this study have several implications for national breeding schemes. Although an investment in genotyping a large population of animals is required, these costs can be offset by the greater genetic gain achievable through the increased accuracy of selection and decreased generation intervals associated with genomic selection.

Maximization of total genetic variance in breed conservation programmes.

The preservation of the maximum genetic diversity in a population is one of the main objectives within a breed conservation programme. We applied the maximum variance total (MVT) method to a unique population in order to maximize the total genetic variance. The function maximization was performed by the annealing algorithm. We have selected the parents and the mating scheme at the same time simply maximizing the total genetic variance (a mate selection problem). The scenario was compared with a scenario of full-sib lines, a MVT scenario with a rate of inbreeding restriction, and with a minimum coancestry selection scenario. The MVT method produces sublines in a population attaining a similar scheme as the full-sib sublining that agrees with other authors that the maximum genetic diversity in a population (the lowest overall coancestry) is attained in the long term by subdividing it in as many isolated groups as possible. The application of a restriction on the rate of inbreeding jointly with the MVT method avoids the consequences of inbreeding depression and maintains the effective size at an acceptable minimum. The scenario of minimum coancestry selection gave higher effective size values, but a lower total genetic variance. A maximization of the total genetic variance ensures more genetic variation for extreme traits, which could be useful in case the population needs to adapt to a new environment/production system.

Using the genomic relationship matrix to predict the accuracy of genomic selection.

Estimated breeding values (EBVs) using data from genetic markers can be predicted using a genomic relationship matrix, derived from animal's genotypes, and best linear unbiased prediction. However, if the accuracy of the EBVs is calculated in the usual manner (from the inverse element of the coefficient matrix), it is likely to be overestimated owing to sampling errors in elements of the genomic relationship matrix. We show here that the correct accuracy can be obtained by regressing the relationship matrix towards the pedigree relationship matrix so that it is an unbiased estimate of the relationships at the QTL controlling the trait. This method shows how the accuracy increases as the number of markers used increases because the regression coefficient (of genomic relationship towards pedigree relationship) increases. We also present a deterministic method for predicting the accuracy of such genomic EBVs before data on individual animals are collected. This method estimates the proportion of genetic variance explained by the markers, which is equal to the regression coefficient described above, and the accuracy with which marker effects are estimated. The latter depends on the variance in relationship between pairs of animals, which equals the mean linkage disequilibrium over all pairs of loci. The theory was validated using simulated data and data on fat concentration in the milk of Holstein cattle.

The unified approach to the use of genomic and pedigree information in genomic evaluations revisited.

Previous proposals for a unified approach for amalgamating information from animals with or without genotypes have combined the numerator relationship matrix A with the genomic relationship G estimated from the markers. These approaches have resulted in biased genomic EBV (GEBV), and methodology was developed to overcome these problems. Firstly, a relationship matrix, G(FG) , based on linkage analysis was derived using the same base population as A, which (i) utilizes the genomic information on the same scale as the pedigree information and (ii) permits the regression coefficients used to propagate the genomic data from the genotyped to ungenotyped individuals to be calculated in the light of the genomic information, rather than ignoring it. Secondly, the elements of G were regressed back towards their expected values in the A matrix to allow for their estimation errors. These developments were combined in a methodology LDLAb and tested on simulated populations where either parents were phenotyped and offspring genotyped or vice versa. The LDLAb method was demonstrated to be a unified approach that maximized accuracy of GEBV compared to previous methodologies and removed the bias in the GEBV. Although LDLAb is computationally much more demanding than MLAC, it demonstrates how to make best use the marker information and also shows the computational problems that need to be solved in the future to make best use of the marker data.

Incorporating desirable genetic characteristics from an inferior into a superior population using genomic selection.

Resistance to specific diseases may be improved by crossing a recipient line with a donor line (a distantly related strain) that is characterized by the desirable trait. However, considerable losses in the total merit index are expected when crossing recipient and donor lines. Repeated backcrossing with the recipient line will improve total merit index, but usually at the expense of the newly introgressed disease resistance, especially if this is due to polygenic effects rather than to a known single major QTL. This study investigates the possibilities for a more detailed introgression program based on marker-trait associations using dense marker genotyping and genomic selection. Compared with classical selection, genomic selection increased genetic gain, with the largest effect on low heritability traits and on traits not recorded on selection candidates (due to within-family selection). Further, within a wide range of economic weights and initial differences in the total merit index between donor and recipient lines, genomic selection produced backcrossed lines that were similar or better than the purebred lines within three to five generations. When using classical selection in backcrossing schemes, the long-term genetic contribution of the donor line was low. Hence, such selection schemes would usually perform similarly to simple purebreeding selection schemes.

Fine mapping and detection of the causative mutation underlying Quantitative Trait Loci.

The effect on power and precision of including the causative SNP amongst the investigated markers in Quantitative Trait Loci (QTL) mapping experiments was investigated. Three fine mapping methods were tested to see which was most efficient in finding the causative mutation: combined linkage and linkage disequilibrium mapping (LLD); association mapping (MARK); a combination of LLD and association mapping (LLDMARK). Two simulated data sets were analysed: in one set, the causative SNP was included amongst the markers, while in the other set the causative SNP was masked between markers. Including the causative SNP amongst the markers increased both precision and power in the analyses. For the LLD method the number of correctly positioned QTL increased from 17 for the analysis without the causative SNP to 77 for the analysis including the causative SNP. The likelihood of the data analysis increased from 3.4 to 13.3 likelihood units for the MARK method when the causative SNP was included. When the causative SNP was masked between the analysed markers, the LLD method was most efficient in detecting the correct QTL position, while the MARK method was most efficient when the causative SNP was included as a marker in the analysis. The LLDMARK method, combining association mapping and LLD, assumes a QTL as the null hypothesis (using LLD method) and tests whether the 'putative causative SNP' explains significantly more variance than a QTL in the region. Thus, if the putative causative SNP does not only give an Identical-By-Descent (IBD) signal, but also an Alike-In-State (AIS) signal, LLDMARK gives a positive likelihood ratio. LLDMARK detected less than half as many causative SNPs as the other methods, and also had a relatively high false discovery rate when the QTL effect was large. LLDMARK may however be more robust against spurious associations, because the regional IBD is largely corrected for by fitting a QTL effect in the null hypothesis model.