How pedigree errors affect genetic evaluations and validation statistics.

Pedigrees used in genetic evaluations contain errors. Because of such errors, assumptions regarding the relatedness among individuals in genetic evaluation models are wrong. Consequences of that have been investigated in earlier studies focusing on models that did not account for genomic information yet. The objective of this work was to investigate the effects of pedigree errors on the results from genetic evaluations using the single-step model, and the effect of such effects on results from validation studies with forward prediction. We used a real pedigree (n = 361,980) and real genotypes (n = 25,950) of Fleckvieh cattle, sampled in a way to provide a good consistency between pedigree and genomic relationships. Given the real pedigree and genotypes, true breeding values (TBV) were simulated to have a covariance structure equal to the matrix H assumed in a single-step model. Based on TBV, phenotypes were simulated with a heritability of 0.25. Genetic evaluations were conducted with a conventional animal model (i.e., without genomic information) and a single-step animal model under scenarios using either the correct pedigree or a pedigree containing 5%, 10%, or 20% of wrong records. Wrong records were simulated by randomly assigning wrong sires to nongenotyped females. The increasing rates of pedigree errors led to decreasing correlations between TBV and EBV and lower standard deviations of predictions. Less variation was observed because pedigree errors operate actually as a random exchange of daughters among bulls, making them look more similar to each other than they actually are. This occurs of course only when animals have progeny. Therefore, this decreased variation was more pronounced for progeny tested bulls than for young selection candidates. In a forward prediction validation scenario, the stronger decrease in variation when animals get progeny caused an apparent inflation of early predictions. This phenomenon may contribute to the usually observed problem of inflation of early predictions observed in validation studies.

Short communication: Calculating analytical reliabilities for single-step predictions.

It has been shown that single-step genomic BLUP (ssGBLUP) can be reformulated, resulting in an equivalent SNP model that includes the explicit imputation of gene contents of all ungenotyped animals in the pedigree. This reformulation reveals the underlying mechanism enabling ungenotyped animals to contribute information to genotyped animals via estimates of marker effects and consequently to the reliability of genomic predictions, a key feature generally associated with the single-step approach. Irrespective of which BLUP formulation is used for genomic prediction, with increasing numbers of genotyped animals, the marker-oriented model is recommended when calculating the reliabilities of genomic predictions. This approach has the advantage of a manageable and stable size of the model matrix that needs to be inverted to calculate analytical prediction error variances of marker effects, an advantage that also holds for prediction with the single-step model. However, when including imputed genotypes in the design matrix of marker effects, an additional imputation residual term has to be considered to account for the prediction error of imputation. We summarize some of the theoretical aspects associated with the calculation of analytical reliabilities of single-step predictions. Derivations are based on the equivalent reformulation of ssGBLUP as a marker-oriented model and the calculation of prediction error variances of marker effects. We propose 2 approximations that allow for a substantial reduction of the complexity of the matrix operations involved, while retaining most of the relevant information required for reliability calculations. We additionally provide a general framework for an implementation of single-step reliability approximation using standard animal model reliabilities as a starting point. Finally, we demonstrate the effectiveness of the proposed approach using a small example extracted from data of the routine evaluation on dual-purpose Fleckvieh (Simmental) cattle.

Technical note: Methods for interim prediction of single-step breeding values for young animals.

Single-step genomic evaluations have the advantage of simultaneously combining all pedigree, phenotypic, and genotypic information available. However, systems with a large number of genotyped animals have some computational challenges. In many genomic breeding programs, genomic predictions of young animals should become available for selection decisions in the shortest time possible, which requires either a very effective estimation or an approximation with negligible loss in accuracy. We investigated different procedures for predicting breeding values of young genotyped animals without setting up the full single-step system augmented for the additional genotypes. Methods were based on transmitting the information from single-step breeding values of genotyped animals that took part in the previous full run to young animals, either through genomic relationships or through a marker-based model. The different procedures were tested on real data from the April 2017 run of the German-Austrian official genomic evaluation for Fleckvieh. The data set included 62,559 genotyped animals and was used to run single-step evaluations for 23 conformation traits. A further data set comprising 1,768 young animals was used for interim prediction and we called it the validation set. The reference values for validation were the predicted breeding values of the young animals from a full single-step run containing the genotypes of all 64,327 animals. Correlations between the approximated predictions and those from the full single-step run also containing genotypes from young animals averaged 0.9932 for the best method (from 0.990 to 0.995 across traits). In conclusion, prediction of single-step breeding values for young animals can be well approximated using systems of size equal to the number of markers.

Considering dominance in reduced single-step genomic evaluations.

Single-step models including dominance can be an enormous computational task and can even be prohibitive for practical application. In this study, we try to answer the question whether a reduced single-step model is able to estimate breeding values of bulls and breeding values, dominance deviations and total genetic values of cows with acceptable quality. Genetic values and phenotypes were simulated (500 repetitions) for a small Fleckvieh pedigree consisting of 371 bulls (180 thereof genotyped) and 553 cows (40 thereof genotyped). This pedigree was virtually extended for 2,407 non-genotyped daughters. Genetic values were estimated with the single-step model and with different reduced single-step models. Including more relatives of genotyped cows in the reduced single-step model resulted in a better agreement of results with the single-step model. Accuracies of genetic values were largest with single-step and smallest with reduced single-step when only the cows genotyped were modelled. The results indicate that a reduced single-step model is suitable to estimate breeding values of bulls and breeding values, dominance deviations and total genetic values of cows with acceptable quality.

Short communication: The role of genotypes from animals without phenotypes in single-step genomic evaluations.

In a 2-step genomic system, genotypes of animals without phenotypes do not influence genomic prediction of other animals, but that might not be the case in single-step systems. We investigated the effects of including genotypes from culled bulls on the reliability of genomic predictions from single-step evaluations. Four scenarios with a constant amount of phenotypic information and increasing numbers of genotypes from culled bulls were simulated and compared with respect to prediction reliability. With increasing numbers of genotyped culled bulls, there was a corresponding increase in prediction reliability. For instance, in our simulation scenario the reliability for selection candidates was twice as large when all culled bulls from the last 4 generations were included in the analysis. Single-step evaluations imply the imputation of all nongenotyped animals in the pedigree. We showed that this imputation was increasingly more accurate as increasingly more genotypic information from the culled bulls was taken into account. This resulted in higher prediction reliabilities. The extent of the benefit from including genotypes from culled bulls might be more relevant for small populations with low levels of reliabilities.

Short communication: The effect of genotyping cows to improve the reliability of genomic predictions for selection candidates.

In this study we investigate the potential of enlarging the reference population for genomic prediction in dairy cattle by routinely genotyping a random sample of the first-crop daughters of every AI bull in the breeding program. We analyzed small nuclear pedigrees, each consisting of a genotyped selection candidate and 3 generations of genotyped male ancestors. Genotypes were taken from the genomic routine evaluation of Fleckvieh cattle in Germany and Austria. The phenotypic information of a daughter of any one male in each of these pedigrees was either considered to be part of the daughter yield deviation of the corresponding sire, or was assumed to be an individually observed genotyped daughter of this sire. Daughter genotypes in this case were simulated from phased haplotypes of their sires and random maternal gametes drawn from a haplotype library. We measured the gain from genotyping daughters as the increase in model-based theoretical reliability of the genomic prediction for a putative selection candidate. We expressed the improvements as a marginal increase, corresponding to an increase in reliability at a reliability baseline level of zero, to simplify comparisons. Results were encouraging with 2 to 40% of marginal reliability increase for selection candidates depending on the assumed heritability of the trait and the number of daughters modeled to be genotyped in the design.

How imputation errors bias genomic predictions.

The objective of this study was to investigate in detail the biasing effects of imputation errors on genomic predictions. Direct genomic values (DGV) of 3,494 Brown Swiss selection candidates for 37 production and conformation traits were predicted using either their observed 50K genotypes or their 50K genotypes imputed from a mimicked 6K chip. Changes in DGV caused by imputation errors were shown to be systematic. The DGV of top animals were, on average, underestimated and that of bottom animals were, on average, overestimated when imputed genotypes were used instead of observed genotypes. This pattern might be explained by the fact that imputation algorithms will usually suggest the most frequent haplotype from the sample whenever a haplotype cannot be determined unambiguously. That was empirically shown to cause an advantage for the bottom animals and a disadvantage for the top animals.

Implementation of genetic evaluation and mating designs for the endangered local pig breed 'Bunte Bentheimer'.

A pedigree including 1538 individuals of the endangered pig breed 'Bunte Bentheimer' and 3008 records of the fertility traits 'number of piglets born alive' (NBA) and 'number of piglets weaned' (NW) were used to i) characterize the population structure, ii) to estimate genetic (co)variance components and estimated breeding values (EBVs) and iii) to use EBVs for the application of the concept of optimal genetic contributions. The average coefficient of inbreeding increased from F = 0.103 to F = 0.121 within the two recent cohorts. Average rate of inbreeding amounted to 1.66%, which resulted in an effective population size of Ne  = 30 animals in the recent cohort. Average generation interval was 3.07 years considering the whole pedigree, and in total, only 612 sows and boars generated offspring. Estimated heritabilities for both traits NBA and NW were 0.12, and the estimated genetic correlation between both traits was 0.96. The variance component due to the service sire was higher than in commercial pig breeds, presumably due to the widespread use of natural service boars. The EBVs for NBA from 333 selection candidates (63 boars and 270 sows) were used to determine optimal genetic contributions. Based on selected animals and their optimal genetic contributions, specific mating designs were evaluated to minimize inbreeding in the next generation. Best results were achieved when using a simulated annealing algorithm and allowing artificial insemination.

Bos indicus introgression into (peri-)alpine cattle breeds - evidence from the analysis of bovine whey protein variants.

The major bovine whey proteins, α-lactalbumin (α-LA) and ß-lactoglobulin (ß-LG), exhibit breed-specific genetic variation. The aim of this study was to identify possible new protein variants and determine the distribution of variants across a variety of 18 taurine and indicine cattle breeds applying a DNA-based sequencing approach. To this end, the open reading frames of the respective genes (LALBA and LGB) were sequenced in 476 animals. Within the LALBA gene, a previously unknown synonymous and a previously undesignated non-synonymous nucleotide exchange were identified. Furthermore, two known α-LA variants (A and B) and four known ß-LG variants (A, B, C and W) were determined. The occurrence of typical indicine variants in some taurine cattle breeds, such as Suisse Eringer, German Hinterwälder and Hungarian Grey Steppe, further supports the hypothesis of ancient Bos indicus introgression into (peri-)alpine cattle breeds.

Footprints of recent selection and variability in breed composition in the Göttingen Minipig genome.

The Göttingen Minipig (GMP) developed at the University of Göttingen is a synthetic breed that is widely used in medical research and toxicology. It combines the high fertility of the Vietnamese potbellied pig, the low body weight of the Minnesota Minipig and the white coat colour of the German Landrace pig. The aim of this study was to find genomic regions that may have undergone selection since the creation of the breed in the 1960s. Therefore, the whole genome was screened for footprints of recent selection based on single nucleotide polymorphism (SNP) genotypes from the Illumina Porcine SNP60 BeadChip using two methods: the extended haplotype homozygosity (EHH) test and the estimation of the genomic proportion of the three original breeds at each SNP using a Bayesian approach. Local deviations from the average genome-wide breed composition were tested with a permutation-based empirical test. Results for a comprehensive whole-genome scan for both methods are presented. Several regions showing the highest P-values in the EHH test are related to breeding goals relevant in the GMP, such as growth (SOCS2, TXN, DDR2 and GRB10 genes) and white colour (PRLR gene). Additionally, the calculated proportion of the founder breeds diverged significantly in many regions from the pedigree-based expectations and the genome average. The results provide a genome-wide map of selection signatures in the GMP, which leads to a better understanding of selection that took place over the last decades in GMP breed development.

Strategy for the simulation and analysis of longitudinal phenotypic and genomic data in the context of a temperature × humidity-dependent covariate.

A simulation study was conducted to evaluate the performance of genomic random regression models for the continuous environmental descriptor temperature-humidity index (THI). Statistically innovative aspects of the study included the combined simulation of both longitudinal phenotypic data representing the same trait in the course of THI and genomic data. The longitudinal trait was simulated (phenotypically expressed) at 5 different values of THI. For a moderate heritability trait, heritabilities were 0.30, 0.35, 0.40, 0.40, and 0.35 for THI of 15, 30, 45, 60 and 75, respectively. In a consecutive run, low heritabilities of 0.05, 0.1, 0.15, 0.15, and 0.10 were simulated, respectively. On the genomic level, simulation combined high and low linkage disequilibrium with 5,000-, 15,000-, and 50,000-SNP chip applications to simulate different scenarios of genomic architecture. With regard to data analyses, 2 strategies were applied to evaluate the accuracy of genomic predictions across THI, with special focus on the extreme ends of the environmental scale. In the first strategy, 100, 80, 50, or 20% of phenotypes at THI 75 were deleted randomly and the remaining data set was used to predict the breeding value at THI 75 for non-phenotyped, but genotyped cows. In the second strategy, 1,600 cows had complete information (genotypes and phenotypes) and 400 cows were genotyped, but with missing phenotypes for all THI. For the first strategy and without phenotypic observations at THI 75, accuracies of genomic predictions were lower than 0.34. When only 20% of cows had phenotypic records at THI 75, accuracies increased (~0.60). Such a small proportion of phenotyped cows was sufficient to predict reliable genomic breeding values for cows without phenotypes for extreme THI. For the second strategy, also for low linkage disequilibrium combined with a low density 5,000-SNP chip, the average accuracy of genomic predictions was 0.52, which is substantially higher than accuracies based on pedigree relationships. From a practical perspective, genomic random regression models can be used to predict genomic breeding values for scarce phenotypes (e.g., novel traits) traits measured in extreme environments, or traits measured late in life, such as longevity.

Interplay between heritability, genetic correlation and economic weighting in a selection index with and without genomic information.

The availability of genomic information demands proper evaluation on how the kind (phenotypic versus genomic) and the amount of information influences the interplay of heritability (h(2)), genetic correlation (r(GiGj)) and economic weighting of traits with regard to the standard deviation of the index (σI). As σI is directly proportional to response to selection, it was the chosen parameter for comparing the indices. Three selection indices incorporating conventional and genomic information for a two trait (i and j) breeding goal were compared. Information sources were chosen corresponding to pig breeding applications. Index I incorporating an own performance in trait j served as reference scenario. In index II, additional information in both traits was contributed by a varying number of full-sibs (2, 7, 50). In index III, the conventional own performance in trait j was combined with genomic information for both traits. The number of animals in the reference population (NP = 1000, 5000, 10,000) and thus the accuracy of GBVs were varied. With more information included in the index, σI became more independent of r(GiGj), h(j)(2) and relative economic weighting. This applied for index II (more full-sibs) and for index III (more accurate GBVs). Standard deviations of index II with seven full-sibs and index III with NP = 1000 were similar when both traits had the same heritability. If the heritability of trait j was reduced (h(j)(2) = 0.1), σI of index III with NP = 1000 was clearly higher than for index II with seven full-sibs. When enhancing the relative economic weight of trait j, the decrease in σI of the conventional full-sib index was much stronger than for index III. Our results imply that NP = 1000 can be considered a minimum size for a reference population in pig breeding. These conclusions also hold for comparing the accuracies of the indices.

DNA-based identification of novel bovine casein gene variants.

In cattle, at least 39 variants of the 4 casein proteins (α(S1)-, ß-, α(S2)- and κ-casein) have been described to date. Many of these variants are known to affect milk-production traits, cheese-processing properties, and the nutritive value of milk. They also provide valuable information for phylogenetic studies. So far, the majority of studies exploring the genetic variability of bovine caseins considered European taurine cattle breeds and were carried out at the protein level by electrophoretic techniques. This only allows the identification of variants that, due to amino acid exchanges, differ in their electric charge, molecular weight, or isoelectric point. In this study, the open reading frames of the casein genes CSN1S1, CSN2, CSN1S2, and CSN3 of 356 animals belonging to 14 taurine and 3 indicine cattle breeds were sequenced. With this approach, we identified 23 alleles, including 5 new DNA sequence variants, with a predicted effect on the protein sequence. The new variants were only found in indicine breeds and in one local Iranian breed, which has been phenotypically classified as a taurine breed. A multidimensional scaling approach based on available SNP chip data, however, revealed an admixture of taurine and indicine populations in this breed as well as in the local Iranian breed Golpayegani. Specific indicine casein alleles were also identified in a few European taurine breeds, indicating the introgression of indicine breeds into these populations. This study shows the existence of substantial undiscovered genetic variability of bovine casein loci, especially in indicine cattle breeds. The identification of new variants is a valuable tool for phylogenetic studies and investigations into the evolution of the milk protein genes.

Genomic selection for the improvement of meat quality in beef.

Selection index theory was used to compare different selection strategies aiming at the improvement of meat quality in beef cattle. Alternative strategies were compared with a reference scenario with three basic traits in the selection index: BW at 200 d (W200) and 400 d (W400) and muscling score (MUSC). These traits resemble the combination currently used in the German national beef genetic evaluation system. Traits in the breeding goal were defined as the 3 basic traits plus marbling score (MARB), to depict a situation where an established breeding program currently selecting for growth and carcass yield intends to incorporate meat quality in its selection program. Economic weights were either the same for all 4 traits, or doubled or tripled for MARB. Two additional selection criteria for improving MARB were considered: Live animal intramuscular fat content measured by ultrasound (UIMF) as an indicator trait and a genomic breeding value (GEBV) for the target trait directly (gMARB). Results were used to estimate the required number of genotyped animals in an own calibration set for implementing genomic selection focusing on meat quality. Adding UIMF to the basic index increased the overall genetic gain per generation by 15% when the economic weight on MARB was doubled and by 44% when it was tripled. When a genomic breeding value for marbling could be estimated with an accuracy of 0.5, adding gMARB to the index provided larger genetic gain than adding UIMF. Greatest genetic gain per generation was obtained with the scenario containing GEBV for 4 traits (gW200, gW400, gMUSC, and gMARB) when the accuracies of these GEBV were ≥0.7. Adding UIMF to the index substantially improved response to selection for MARB, which switched from negative to positive when the economic weight on MARB was doubled or tripled. For all scenarios that contained gMARB in the selection index, the response to selection in MARB was positive for all relative economic weights on MARB, when the accuracy of GEBV was >0.7. Results indicated that setting up a calibration set of ∼500 genotyped animals with carcass phenotypes for MARB could suffice to obtain a larger response to selection than measuring UIMF. If the size of the calibration set is ∼2,500, adding the ultrasound trait to an index containing already the GEBV would bring little benefit, unless the relative economic weight for marbling is much larger than for the other traits.

Controlling inbreeding and maximizing genetic gain using semi-definite programming with pedigree-based and genomic relationships.

Because of the relatively high levels of genetic relationships among potential bull sires and bull dams, innovative selection tools should consider both genetic gain and genetic relationships in a long-term perspective. Optimum genetic contribution theory using official estimated breeding values for a moderately heritable trait (production index, Index-PROD), and a lowly heritable functional trait (index for somatic cell score, Index-SCS) was applied to find optimal allocations of bull dams and bull sires. In contrast to previous practical applications using optimizations based on Lagrange multipliers, we focused on semi-definite programming (SDP). The SDP methodology was combined with either pedigree (a(ij)) or genomic relationships (f(ij)) among selection candidates. Selection candidates were 484 genotyped bulls, and 499 preselected genotyped bull dams completing a central test on station. In different scenarios separately for PROD and SCS, constraints on the average pedigree relationships among future progeny were varied from a(ij)=0.08 to a(ij)=0.20 in increments of 0.01. Corresponding constraints for single nucleotide polymorphism-based kinship coefficients were derived from regression analysis. Applying the coefficient of 0.52 with an intercept of 0.14 estimated for the regression pedigree relationship on genomic relationship, the corresponding range to alter genomic relationships varied from f(ij) = 0.18 to f(ij) = 0.24. Despite differences for some bulls in genomic and pedigree relationships, the same trends were observed for constraints on pedigree and corresponding genomic relationships regarding results in genetic gain and achieved coefficients of relationships. Generally, allowing higher values for relationships resulted in an increase of genetic gain for Index-PROD and Index-SCS and in a reduction in the number of selected sires. Interestingly, more sires were selected for all scenarios when restricting genomic relationships compared with restricting pedigree relationships. For example, at constraint of f(ij)=0.185 and selection on Index-PROD, the number of selected sires was 35. In contrast, only 21 sires were selected at the comparable constraint on additive genetic relationship of a(ij)=0.09. A further reduction in relationships is possible when using SDP output (i.e., suggested genetic contributions of selected parents) and applying a simulated annealing algorithm to define specific mating plans. However, the advantage of this strategy is limited to a short-term perspective and probably not successful in the period of genomic selection allowing a substantial reduction of generation intervals.

Power and robustness of three whole genome association mapping approaches in selected populations.

Selection is known to influence the linkage disequilibrium (LD) pattern in livestock populations. Spurious LD may lead to a higher number of false-positive signals in whole genome association mapping experiments. We compared three approaches for whole genome association mapping in a simulation study: single marker regression (SMR), a two-step approach, which analyses residuals corrected for family effects with an SMR (GRAMMAR), and a combined linkage and LD approach, which applies the quantitative transmission disequilibrium test to the Mendelian sampling term (MTDT). Three different scenarios were simulated: idealized random mating, limited number of parents and directional selection. The number of false-positive associations increased when the number of parents was limited. Mapping accuracy was the worst in the scenario with directional selection for all approaches. As SMR produced a high number of false-positive signals in small populations, results of whole genome scans in livestock analysed with SMR should be considered with caution. GRAMMAR was the most accurate approach, but also the least powerful one. The Bonferroni-corrected significance threshold seemed to be too stringent for this approach. Results obtained with MTDT changed only slightly with selected populations. MTDT combined sufficient power with a manageable number of false-positive associations in all scenarios.

Exploration of relationships between production and fertility traits in dairy cattle via association studies of SNPs within candidate genes derived by expression profiling.

The objective of this work was to integrate findings from functional genomics studies with genome-wide association studies for fertility and production traits in dairy cattle. Association analyses of production and fertility traits with SNPs located within or close to 170 candidate genes derived from two gene expression studies and from the literature were performed. Data from 2294 Holstein bulls genotyped for 39557 SNPs were used. A total of 111 SNPs were located on chromosomal segments covered by a candidate gene. Allele substitution effects for each SNP were estimated using a mixed model with a fixed effect of marker and a random polygenic effect. Assumed covariance was derived either from marker or from pedigree information. Results from the analysis with the kinship matrix built from marker genotypes were more conservative than from the analysis with the pedigree-derived relationship matrix. From sixteen SNPs with significant effects on both classes of traits, ten provided evidence of an antagonistic relationship between productivity and fertility. However, we found four SNPs with favourable effects on fertility and on yield traits, one SNP with favourable effects on fertility and percentage traits, and one SNP with antagonistic effects on two fertility traits. While most quantitative genetic studies have proven genetic antagonisms between yield and functional traits, improvements in both production and functionality may be possible when focusing on a few relevant SNPs. Investigations combining input from quantitative genetics and functional genomics with association analysis may be applied for the identification of such SNPs.

A genome-wide scan for signatures of recent selection in Holstein cattle.

The data from the newly available 50 K SNP chip was used for tagging the genome-wide footprints of positive selection in Holstein-Friesian cattle. For this purpose, we employed the recently described Extended Haplotype Homozygosity test, which detects selection by measuring the characteristics of haplotypes within a single population. To assess formally the significance of these results, we compared the combination of frequency and the Relative Extended Haplotype Homozygosity value of each core haplotype with equally frequent haplotypes across the genome. A subset of the putative regions showing the highest significance in the genome-wide EHH tests was mapped. We annotated genes to identify possible influence they have in beneficial traits by using the Gene Ontology database. A panel of genes, including FABP3, CLPN3, SPERT, HTR2A5, ABCE1, BMP4 and PTGER2, was detected, which overlapped with the most extreme P-values. This panel comprises some interesting candidate genes and QTL, representing a broad range of economically important traits such as milk yield and composition, as well as reproductive and behavioural traits. We also report high values of linkage disequilibrium and a slower decay of haplotype homozygosity for some candidate regions harbouring major genes related to dairy quality. The results of this study provide a genome-wide map of selection footprints in the Holstein genome, and can be used to better understand the mechanisms of selection in dairy cattle breeding.

The pattern of linkage disequilibrium in German Holstein cattle.

This study presents a second generation of linkage disequilibrium (LD) map statistics for the whole genome of the Holstein-Friesian population, which has a four times higher resolution compared with that of the maps available so far. We used DNA samples of 810 German Holstein-Friesian cattle genotyped by the Illumina Bovine SNP50K BeadChip to analyse LD structure. A panel of 40 854 (75.6%) markers was included in the final analysis. The pairwise r(2) statistic of SNPs up to 5 Mb apart across the genome was estimated. A mean value of r(2) = 0.30 +/- 0.32 was observed in pairwise distances of <25 kb and it dropped to 0.20 +/- 0.24 at 50-75 kb, which is nearly the average inter-marker space in this study. The proportion of SNPs in useful LD (r(2) > or = 0.25) was 26% for the distance of 50 and 75 kb between SNPs. We found a lower level of LD for SNP pairs at the distance < or =100 kb than previously thought. Analysis revealed 712 haplo-blocks spanning 4.7% of the genome and containing 8.0% of all SNPs. Mean and median block length were estimated as 164 +/- 117 kb and 144 kb respectively. Allele frequencies of the SNPs have a considerable and systematic impact on the estimate of r(2). It is shown that minimizing the allele frequency difference between SNPs reduces the influence of frequency on r(2) estimates. Analysis of past effective population size based on the direct estimates of recombination rates from SNP data showed a decline in effective population size to N(e) = 103 up to approximately 4 generations ago. Systematic effects of marker density and effective population size on observed LD and haplotype structure are discussed.

Robust QTL fine mapping by applying a quantitative transmission disequilibrium test to the Mendelian sampling term.

In many farm animal populations, high-density single nucleotide polymorphism (SNP) genotypes are becoming available on a large scale, and routine estimation of breeding values is implemented for a multiplicity of traits. We propose to apply the basic principle of the quantitative transmission disequilibrium test (QTDT) to estimated Mendelian sampling terms. A two-step procedure is suggested, where in the first step additive breeding values are estimated with a mixed linear model and the Mendelian sampling terms are calculated from the estimated breeding values. In the second step, the QTDT is applied to these estimated Mendelian sampling terms. The resulting test is expected to yield significant results if the SNP is in sufficient linkage disequilibrium and linkage with quantitative trait loci (QTL). This principle is illustrated with a simulated data set comprising 4665 individuals genotyped for 6000 SNP and 15 true QTL. Thirteen of the fifteen QTL were significant on a genome-wide 0.1% error level. Results for the empirical power are derived from repeated samples of 1000 and 3000 genotyped individuals, respectively. General properties and potential extensions of the methodology are indicated. Owing to its computational simplicity and speed, the suggested procedure is well suited to scan whole genomes with high-density SNP coverage in samples of substantial size and for a multiplicity of different traits.