Estimation of genomic breed composition of individual animals in composite beef cattle.

Three statistical models (an admixture model, linear regression, and ridge-regression BLUP) and two strategies for selecting SNP panels (uniformly spaced vs. maximum Euclidean distance of SNP allele frequencies between ancestral breeds) were compared for estimating genomic-estimated breed composition (GBC) in Brangus and Santa Gertrudis cattle, respectively. Animals were genotyped with a GeneSeek Genomic Profiler bovine low-density version 4 SNP chip. The estimated GBC was consistent among the uniformly spaced SNP panels, and values were similar between the three models. However, estimated GBC varied considerably between the three methods when using fewer than 10 000 SNPs that maximized the Euclidean distance of allele frequencies between the ancestral breeds. The admixture model performed most consistently across various SNP panel sizes. For the other two models, stabilized estimates were obtained with an SNP panel size of 20 000 SNPs or more. Based on the uniformly spaced 20K SNP panel, the estimated GBC was 69.8-70.5% Angus and 29.5-30.2% Brahman for Brangus, and 63.9-65.3% Shorthorn and 34.7-36.1% Brahman in Santa Gertrudis. The estimated GBC of ancestries for Santa Gertrudis roughly agreed with the pedigree-expected values. However, the estimated GBC in Brangus showed a considerably larger Angus composition than the pedigree-expected value (62.5%). The elevated Angus composition in the Brangus could be due to the mixture of some 1/2 Ultrablack animals (Brangus × Angus). Another reason could be the consequences of selection in Brangus cattle for phenotypes where the Angus breed has advantages.

Structure-property relationships from universal signatures of plasticity in disordered solids.

When deformed beyond their elastic limits, crystalline solids flow plastically via particle rearrangements localized around structural defects. Disordered solids also flow, but without obvious structural defects. We link structure to plasticity in disordered solids via a microscopic structural quantity, "softness," designed by machine learning to be maximally predictive of rearrangements. Experimental results and computations enabled us to measure the spatial correlations and strain response of softness, as well as two measures of plasticity: the size of rearrangements and the yield strain. All four quantities maintained remarkable commonality in their values for disordered packings of objects ranging from atoms to grains, spanning seven orders of magnitude in diameter and 13 orders of magnitude in elastic modulus. These commonalities link the spatial correlations and strain response of softness to rearrangement size and yield strain, respectively.

Pathway-based genome-wide association analysis of milk coagulation properties, curd firmness, cheese yield, and curd nutrient recovery in dairy cattle.

It is becoming common to complement genome-wide association studies (GWAS) with gene-set enrichment analysis to deepen the understanding of the biological pathways affecting quantitative traits. Our objective was to conduct a gene ontology and pathway-based analysis to identify possible biological mechanisms involved in the regulation of bovine milk technological traits: coagulation properties, curd firmness modeling, individual cheese yield (CY), and milk nutrient recovery into the curd (REC) or whey loss traits. Results from 2 previous GWAS studies using 1,011 cows genotyped for 50k single nucleotide polymorphisms were used. Overall, the phenotypes analyzed consisted of 3 traditional milk coagulation property measures [RCT: rennet coagulation time defined as the time (min) from addition of enzyme to the beginning of coagulation; k20: the interval (min) from RCT to the time at which a curd firmness of 20 mm is attained; a30: a measure of the extent of curd firmness (mm) 30 min after coagulant addition], 6 curd firmness modeling traits [RCTeq: RCT estimated through the CF equation (min); CFP: potential asymptotic curd firmness (mm); kCF: curd-firming rate constant (% × min-1); kSR: syneresis rate constant (% × min-1); CFmax: maximum curd firmness (mm); and tmax: time to CFmax (min)], 3 individual CY-related traits expressing the weight of fresh curd (%CYCURD), curd solids (%CYSOLIDS), and curd moisture (%CYWATER) as a percentage of weight of milk processed and 4 milk nutrient and energy recoveries in the curd (RECFAT, RECPROTEIN, RECSOLIDS, and RECENERGY calculated as the % ratio between the nutrient in curd and the corresponding nutrient in processed milk), milk pH, and protein percentage. Each trait was analyzed separately. In total, 13,269 annotated genes were used in the analysis. The Gene Ontology and Kyoto Encyclopedia of Genes and Genomes pathway databases were queried for enrichment analyses. Overall, 21 Gene Ontology and 17 Kyoto Encyclopedia of Genes and Genomes categories were significantly associated (false discovery rate at 5%) with 7 traits (RCT, RCTeq, kCF, %CYSOLIDS, RECFAT, RECSOLIDS, and RECENERGY), with some being in common between traits. The significantly enriched categories included calcium signaling pathway, salivary secretion, metabolic pathways, carbohydrate digestion and absorption, the tight junction and the phosphatidylinositol pathways, as well as pathways related to the bovine mammary gland health status, and contained a total of 150 genes spanning all chromosomes but 9, 20, and 27. This study provided new insights into the regulation of bovine milk coagulation and cheese ability that were not captured by the GWAS.

Genome-wide association study for cheese yield and curd nutrient recovery in dairy cows.

Cheese production and consumption are increasing in many countries worldwide. As a result, interest has increased in strategies for genetic selection of individuals for technological traits of milk related to cheese yield (CY) in dairy cattle breeding. However, little is known about the genetic background of a cow's ability to produce cheese. Recently, a relatively large panel (1,264 cows) of different measures of individual cow CY and milk nutrient and energy recoveries in the cheese (REC) became available. Genetic analyses showed considerable variation for CY and for aptitude to retain high proportions of fat, protein, and water in the coagulum. For the dairy industry, these characteristics are of major economic importance. Nevertheless, use of this knowledge in dairy breeding is hampered by high costs, intense labor requirement, and lack of appropriate technology. However, in the era of genomics, new possibilities are available for animal breeding and genetic improvement. For example, identification of genomic regions involved in cow CY might provide potential for marker-assisted selection. The objective of this study was to perform genome-wide association studies on different CY and REC measures. Milk and DNA samples from 1,152 Italian Brown Swiss cows were used. Three CY traits expressing the weight (wt) of fresh curd (%CYCURD), curd solids (%CYSOLIDS), and curd moisture (%CYWATER) as a percentage of weight of milk processed, and 4 REC (RECFAT, RECPROTEIN, RECSOLIDS, and RECENERGY, calculated as the % ratio between the nutrient in curd and the corresponding nutrient in processed milk) were analyzed. Animals were genotyped with the Illumina BovineSNP50 Bead Chip v.2. Single marker regressions were fitted using the GenABEL R package (genome-wide association using mixed model and regression-genomic control). In total, 103 significant associations (88 single nucleotide polymorphisms) were identified in 10 chromosomes (2, 6, 9, 11, 12, 14, 18, 19, 27, 28). For RECFAT and RECPROTEIN, high significance peaks were identified in Bos taurus autosome (BTA) 6 and BTA11, respectively. Marker ARS-BFGL-NGS-104610 (∼104.3 Mbp) was highly associated with RECPROTEIN and Hapmap52348-rs29024684 (∼87.4 Mbp), closely located to the casein genes on BTA6, with RECFAT. Genomic regions identified may enhance marker-assisted selection in bovine cheese breeding beyond the use of protein (casein) and fat contents, whereas new knowledge will help to unravel the genomic background of a cow's ability for cheese production.

Using the variability of linkage disequilibrium between subpopulations to infer sweeps and epistatic selection in a diverse panel of chickens.

A whole-genome scan for identifying selection acting on pairs of linked loci is proposed and implemented. The scan is based on , one of Ohta's 1982 measures of between-population linkage disequilibrium (LD). An approximate empirical null distribution for the statistic is suggested. Although the partitioning of LD into between-population components was originally used to investigate epistatic selection, we demonstrate that values of may also be influenced by single-locus selective sweeps with linkage but no epistasis. The proposed scan is implemented in a diverse panel of chickens including 72 distinct breeds genotyped at 538 298 single-nucleotide polymorphisms. In all, 1723 locus pairs are identified as putatively corresponding to a selective sweep or epistatic selection. These pairs of loci generally cluster to form overlapping or neighboring signals of selection. Known variants that were expected to have been under selection in the panel are identified, as well as an assortment of novel regions that have putatively been under selection in chickens. Notably, a promising pair of genes located 8 MB apart on chromosome 9 are identified based on as demonstrating strong evidence of dispersive epistatic selection between populations.

Bootstrap study of genome-enabled prediction reliabilities using haplotype blocks across Nordic Red cattle breeds.

This study compared the accuracy of genome-enabled prediction models using individual single nucleotide polymorphisms (SNP) or haplotype blocks as covariates when using either a single breed or a combined population of Nordic Red cattle. The main objective was to compare predictions of breeding values of complex traits using a combined training population with haplotype blocks, with predictions using a single breed as training population and individual SNP as predictors. To compare the prediction reliabilities, bootstrap samples were taken from the test data set. With the bootstrapped samples of prediction reliabilities, we built and graphed confidence ellipses to allow comparisons. Finally, measures of statistical distances were used to calculate the gain in predictive ability. Our analyses are innovative in the context of assessment of predictive models, allowing a better understanding of prediction reliabilities and providing a statistical basis to effectively calibrate whether one prediction scenario is indeed more accurate than another. An ANOVA indicated that use of haplotype blocks produced significant gains mainly when Bayesian mixture models were used but not when Bayesian BLUP was fitted to the data. Furthermore, when haplotype blocks were used to train prediction models in a combined Nordic Red cattle population, we obtained up to a statistically significant 5.5% average gain in prediction accuracy, over predictions using individual SNP and training the model with a single breed.

Assessment of bagging GBLUP for whole-genome prediction of broiler chicken traits.

Bootstrap aggregation (bagging) is a resampling method known to produce more accurate predictions when predictors are unstable or when the number of markers is much larger than sample size, because of variance reduction capabilities. The purpose of this study was to compare genomic best linear unbiased prediction (GBLUP) with bootstrap aggregated sampling GBLUP (Bagged GBLUP, or BGBLUP) in terms of prediction accuracy. We used a 600 K Affymetrix platform with 1351 birds genotyped and phenotyped for three traits in broiler chickens; body weight, ultrasound measurement of breast muscle and hen house egg production. The predictive performance of GBLUP versus BGBLUP was evaluated in different scenarios consisting of including or excluding the TOP 20 markers from a standard genome-wide association study (GWAS) as fixed effects in the GBLUP model, and varying training sample sizes and allelic frequency bins. Predictive performance was assessed via five replications of a threefold cross-validation using the correlation between observed and predicted values, and prediction mean-squared error. GBLUP overfitted the training set data, and BGBLUP delivered a better predictive ability in testing sets. Treating the TOP 20 markers from the GWAS into the model as fixed effects improved prediction accuracy and added advantages to BGBLUP over GBLUP. The performance of GBLUP and BGBLUP at different allele frequency bins and training sample sizes was similar. In general, results of this study confirm that BGBLUP can be valuable for enhancing genome-enabled prediction of complex traits.

Model averaging for genome-enabled prediction with reproducing kernel Hilbert spaces: a case study with pig litter size and wheat yield.

Predictive ability of yet-to-be observed litter size (pig) grain yield (wheat) records of several reproducing kernel Hilbert spaces (RKHS) regression models combining different number of Gaussian or t kernels was evaluated. Predictive performance was assessed as the average (over 50 replicates) predictive correlation in the testing set. Predictions from these models were combined using three different types of model averaging: (i) mean of predicted phenotypes obtained in each model, (ii) weighted average using mean squared error as weight or (iii) using the marginal likelihood as weight. (ii) and (iii) were obtained in a validation set with 5% of the data. Phenotypes consisted of 2598, 1604 and 1879 average litter size records from three commercial pig lines and wheat grain yield of 599 lines evaluated in four macro-environments. SNPs from the PorcineSNP60 BeadChip and 1447 DArT markers were used as predictors for the pig and wheat data analyses, respectively. Gaussian and univariate t kernels led to same predictive performance. Multikernel RKHS regression models overcame shortcomings of single kernel models (increasing the predictive correlation of RKHS models by 0.05 where 3 Gaussian or t kernels were fitted in the RKHS models simultaneously). None of the proposed averaging strategies improved the predictive correlations attained with single models using multiple kernel fitting.

Effect of allele frequencies, effect sizes and number of markers on prediction of quantitative traits in chickens.

The objective was to assess goodness of fit and predictive ability of subsets of single nucleotide polymorphism (SNP) markers constructed based on minor allele frequency (MAF), effect sizes and varying marker density. Target traits were body weight (BW), ultrasound measurement of breast muscle (BM) and hen house egg production (HHP) in broiler chickens. We used a 600 K Affymetrix platform with 1352 birds genotyped. The prediction method was genomic best linear unbiased prediction (GBLUP) with 354 564 single nucleotide polymorphisms (SNPs) used to derive a genomic relationship matrix (G). Predictive ability was assessed as the correlation between predicted genomic values and corrected phenotypes from a threefold cross-validation. Predictive ability was 0.27 ± 0.002 for BW, 0.33 ± 0.001 for BM and 0.20 ± 0.002 for HHP. For the three traits studied, predictive ability decreased when SNPs with a higher MAF were used to construct G. Selection of the 20% SNPs with the largest absolute effect sizes induced a predictive ability equal to that from fitting all markers together. When density of markers increased from 5 K to 20 K, predictive ability enhanced slightly. These results provide evidence that designing a low-density chip using low-frequency markers with large effect sizes may be useful for commercial usage.

Dissection of additive genetic variability for quantitative traits in chickens using SNP markers.

The aim of this study was to separate marked additive genetic variability for three quantitative traits in chickens into components associated with classes of minor allele frequency (MAF), individual chromosomes and marker density using the genomewide complex trait analysis (GCTA) approach. Data were from 1351 chickens measured for body weight (BW), ultrasound of breast muscle (BM) and hen house egg production (HHP), each bird with 354 364 SNP genotypes. Estimates of variance components show that SNPs on commercially available genotyping chips marked a large amount of genetic variability for all three traits. The estimated proportion of total variation tagged by all autosomal SNPs was 0.30 (SE 0.04) for BW, 0.33 (SE 0.04) for BM, and 0.19 (SE 0.05) for HHP. We found that a substantial proportion of this variation was explained by low frequency variants (MAF <0.20) for BW and BM, and variants with MAF 0.10-0.30 for HHP. The marked genetic variance explained by each chromosome was linearly related to its length (R(2) = 0.60) for BW and BM. However, for HHP, there was no linear relationship between estimates of variance and length of the chromosome (R(2) = 0.01). Our results suggest that the contribution of SNPs to marked additive genetic variability is dependent on the allele frequency spectrum. For the sample of birds analysed, it was found that increasing marker density beyond 100K SNPs did not capture additional additive genetic variance.

Mating programs including genomic relationships and dominance effects.

Computerized mating programs using genomic information are needed by breed associations, artificial-insemination organizations, and on-farm software providers, but such software is already challenged by the size of the relationship matrix. As of October 2012, over 230,000 Holsteins obtained genomic predictions in North America. Efficient methods of storing, computing, and transferring genomic relationships from a central database to customers via a web query were developed for approximately 165,000 genotyped cows and the subset of 1,518 bulls whose semen was available for purchase at that time. This study, utilizing 3 breeds, investigated differences in sire selection, methods of assigning mates, the use of genomic or pedigree relationships, and the effect of including dominance effects in a mating program. For both Jerseys and Holsteins, selection and mating programs were tested using the top 50 marketed bulls for genomic and traditional lifetime net merit as well as 50 randomly selected bulls. The 500 youngest genotyped cows in the largest herd in each breed were assigned mates of the same breed with limits of 10 cows per bull and 1 bull per cow (only 79 cows and 8 bulls for Brown Swiss). A dominance variance of 4.1 and 3.7% was estimated for Holsteins and Jerseys using 45,187 markers and management group deviation for milk yield. Sire selection was identified as the most important component of improving expected progeny value, followed by managing inbreeding and then inclusion of dominance. The respective percentage gains for milk yield in this study were 64, 27, and 9, for Holsteins and 73, 20, and 7 for Jerseys. The linear programming method of assigning a mate outperformed sequential selection by reducing genomic or pedigree inbreeding by 0.86 to 1.06 and 0.93 to 1.41, respectively. Use of genomic over pedigree relationship information provided a larger decrease in expected progeny inbreeding and thus greater expected progeny value. Based on lifetime net merit, the economic value of using genomic relationships was >$3 million per year for Holsteins when applied to all genotyped females, assuming that each will provide 1 replacement. Previous mating programs required transferring only a pedigree file to customers, but better service is possible by incorporating genomic relationships, more precise mate allocation, and dominance effects. Economic benefits will continue to grow as more females are genotyped.

An evaluation of a novel estimator of linkage disequilibrium.

The analysis of systems involving many loci is important in population and quantitative genetics. An important problem is the study of linkage disequilibrium (LD), a concept relevant in genome-enabled prediction of quantitative traits and in exploration of marker-phenotype associations. This article introduces a new estimator of a LD parameter (ρ(2)) that is much easier to compute than a maximum likelihood (or Bayesian) estimate of a tetra-choric correlation. We examined the conjecture that the sampling distribution of the estimator of ρ(2) could be less frequency dependent than that of the estimator of r(2), a widely used metric for assessing LD. This was done via an empirical evaluation of LD in 806 Holstein-Friesian cattle using 771 single-nucleotide polymorphism (SNP) markers and of HapMap III data on 21,991 SNPs (chromosome 3) observed in 88 unrelated individuals from Tuscany. Also, 1600 haplotypes over a region of 1 Mb simulated under the coalescent were used to estimate LD using the two measures. Subsequently, a simulation study compared the new estimator with that of r(2) using several scenarios of LD and allelic frequencies. From these studies, it is concluded that ρ(2) provides a useful metric for the study of LD as the distribution of its estimator is less frequency dependent than that of the standard estimator of r(2).

Assets of imputation to ultra-high density for productive and functional traits.

The aim of this study was to evaluate different-density genotyping panels for genotype imputation and genomic prediction. Genotypes from customized Golden Gate Bovine3K BeadChip [LD3K; low-density (LD) 3,000-marker (3K); Illumina Inc., San Diego, CA] and BovineLD BeadChip [LD6K; 6,000-marker (6K); Illumina Inc.] panels were imputed to the BovineSNP50v2 BeadChip [50K; 50,000-marker; Illumina Inc.]. In addition, LD3K, LD6K, and 50K genotypes were imputed to a BovineHD BeadChip [HD; high-density 800,000-marker (800K) panel], and with predictive ability evaluated and compared subsequently. Comparisons of prediction accuracy were carried out using Random boosting and genomic BLUP. Four traits under selection in the Spanish Holstein population were used: milk yield, fat percentage (FP), somatic cell count, and days open (DO). Training sets at 50K density for imputation and prediction included 1,632 genotypes. Testing sets for imputation from LD to 50K contained 834 genotypes and testing sets for genomic evaluation included 383 bulls. The reference population genotyped at HD included 192 bulls. Imputation using BEAGLE software (http://faculty.washington.edu/browning/beagle/beagle.html) was effective for reconstruction of dense 50K and HD genotypes, even when a small reference population was used, with 98.3% of SNP correctly imputed. Random boosting outperformed genomic BLUP in terms of prediction reliability, mean squared error, and selection effectiveness of top animals in the case of FP. For other traits, however, no clear differences existed between methods. No differences were found between imputed LD and 50K genotypes, whereas evaluation of genotypes imputed to HD was on average across data set, method, and trait, 4% more accurate than 50K prediction, and showed smaller (2%) mean squared error of predictions. Similar bias in regression coefficients was found across data sets but regressions were 0.32 units closer to unity for DO when genotypes were imputed to HD density. Imputation to HD genotypes might produce higher stability in the genomic proofs of young candidates. Regarding selection effectiveness of top animals, more (2%) top bulls were classified correctly with imputed LD6K genotypes than with LD3K. When the original 50K genotypes were used, correct classification of top bulls increased by 1%, and when those genotypes were imputed to HD, 3% more top bulls were detected. Selection effectiveness could be slightly enhanced for certain traits such as FP, somatic cell count, or DO when genotypes are imputed to HD. Genetic evaluation units may consider a trait-dependent strategy in terms of method and genotype density for use in the genome-enhanced evaluations.

Genome-enabled methods for predicting litter size in pigs: a comparison.

Predictive ability of models for litter size in swine on the basis of different sources of genetic information was investigated. Data represented average litter size on 2598, 1604 and 1897 60K genotyped sows from two purebred and one crossbred line, respectively. The average correlation (r) between observed and predicted phenotypes in a 10-fold cross-validation was used to assess predictive ability. Models were: pedigree-based mixed-effects model (PED), Bayesian ridge regression (BRR), Bayesian LASSO (BL), genomic BLUP (GBLUP), reproducing kernel Hilbert spaces regression (RKHS), Bayesian regularized neural networks (BRNN) and radial basis function neural networks (RBFNN). BRR and BL used the marker matrix or its principal component scores matrix (UD) as covariates; RKHS employed a Gaussian kernel with additive codes for markers whereas neural networks employed the additive genomic relationship matrix (G) or UD as inputs. The non-parametric models (RKHS, BRNN, RNFNN) gave similar predictions to the parametric counterparts (average r ranged from 0.15 to 0.23); most of the genome-based models outperformed PED (r = 0.16). Predictive abilities of linear models and RKHS were similar over lines, but BRNN varied markedly, giving the best prediction (r = 0.31) when G was used in crossbreds, but the worst (r = 0.02) when the G matrix was used in one of the purebred lines. The r values for RBFNN ranged from 0.16 to 0.23. Predictive ability was better in crossbreds (0.26) than in purebreds (0.15 to 0.22). This may be related to family structure in the purebred lines.

Technical note: An R package for fitting Bayesian regularized neural networks with applications in animal breeding.

In recent years, several statistical models have been developed for predicting genetic values for complex traits using information on dense molecular markers, pedigrees, or both. These models include, among others, the Bayesian regularized neural networks (BRNN) that have been widely used in prediction problems in other fields of application and, more recently, for genome-enabled prediction. The R package described here (brnn) implements BRNN models and extends these to include both additive and dominance effects. The implementation takes advantage of multicore architectures via a parallel computing approach using openMP (Open Multiprocessing) for the computations. This note briefly describes the classes of models that can be fitted using the brnn package, and it also illustrates its use through several real examples.

Prediction of clinical mastitis outcomes within and between environments using whole-genome markers.

The objective of this study was to evaluate genome-enabled predictions of daughter yield deviations for clinical mastitis in Norwegian Red cows within and between environments according to mastitis pathogen status. Genome-based predictions of daughter yield deviations for clinical mastitis for 1,126 bulls within and between 5 environments were performed using Bayesian ridge regression. The environments were defined as herd-5-yr classes with the following prevalence of bacteriological milk samples found positive for contagious mastitis pathogens: <50% (L50), ≥ 50% (H50), ≤ 25% (L75), >25% and <75% (M75), and ≥ 75% (H75). In addition, predictions based on all data across environment groups (the full data set, FD) were calculated to provide a benchmark for comparison. Predictive ability was evaluated using a 10-fold cross validation. A bootstrap procedure was used to obtain 95% confidence intervals for the cross-validation distribution of predictive ability for each data set. Predictive ability ranged from 0.04 for L75 to 0.19 for FD. Similar predictions within and between environments showed no evidence of genotype by environment interaction. The 95% confidence interval for all 5 environmental data sets included zero and ranged from 0.02 to 0.35 for FD. The bootstrap distribution showed large variation within each data set and small variation between data sets. Although we found no evidence of genotype by environment interaction, rank correlations of the single nucleotide polymorphism effects between different environments ranged from 0.15 (L75 - H75) to 0.92 (M75 - FD), indicating that single nucleotide polymorphisms may have a differential contribution to predictive ability in environments with distinct pathogen loads.

An assessment of linkage disequilibrium in Holstein cattle using a Bayesian network.

Linkage disequilibrium (LD) is defined as a non-random association of the distributions of alleles at different loci within a population. This association between loci is valuable in prediction of quantitative traits in animals and plants and in genome-wide association studies. A question that arises is whether standard metrics such as D' and r(2) reflect complex associations in a genetic system properly. It seems reasonable to take the view that loci associate and interact together as a system or network, as opposed to in a simple pairwise manner. We used a Bayesian network (BN) as a representation of choice for an LD network. A BN is a graphical depiction of a probability distribution and can represent sets of conditional independencies. Moreover, it provides a visual display of the joint distribution of the set of random variables in question. The usefulness of BN for linkage disequilibrium was explored and illustrated using genetic marker loci found to have the strongest effects on milk protein in Holstein cattle based on three strategies for ranking marker effect estimates: posterior means, standardized posterior means and additive genetic variance. Two different algorithms, Tabu search (a local score-based algorithm) and incremental association Markov blanket (a constraint-based algorithm), coupled with the chi-square test, were used for learning the structure of the BN and were compared with the reference r(2) metric represented as an LD heat map. The BN captured several genetic markers associated as clusters, implying that markers are inter-related in a complicated manner. Further, the BN detected conditionally dependent markers. The results confirm that LD relationships are of a multivariate nature and that r(2) gives an incomplete description and understanding of LD. Use of an LD Bayesian network enables inferring associations between loci in a systems framework and provides a more accurate picture of LD than that resulting from the use of pairwise metrics.

Genome-enabled prediction of genetic values using radial basis function neural networks.

The availability of high density panels of molecular markers has prompted the adoption of genomic selection (GS) methods in animal and plant breeding. In GS, parametric, semi-parametric and non-parametric regressions models are used for predicting quantitative traits. This article shows how to use neural networks with radial basis functions (RBFs) for prediction with dense molecular markers. We illustrate the use of the linear Bayesian LASSO regression model and of two non-linear regression models, reproducing kernel Hilbert spaces (RKHS) regression and radial basis function neural networks (RBFNN) on simulated data and real maize lines genotyped with 55,000 markers and evaluated for several trait-environment combinations. The empirical results of this study indicated that the three models showed similar overall prediction accuracy, with a slight and consistent superiority of RKHS and RBFNN over the additive Bayesian LASSO model. Results from the simulated data indicate that RKHS and RBFNN models captured epistatic effects; however, adding non-signal (redundant) predictors (interaction between markers) can adversely affect the predictive accuracy of the non-linear regression models.

Predictive ability of alternative models for genetic analysis of clinical mastitis.

Mastitis in cows can be defined as a binary trait, reflecting presence or absence of clinical mastitis (CM), or as a count variable, number of mastitis cases (NCM), within a defined time interval. Many different models have been proposed for genetic analyses of mastitis, and the objective of this study was to evaluate the predictive ability and sire predictions of a set of models for genetic evaluation of CM or NCM. Linear- and threshold liability models for CM, and linear, censored ordinal threshold, and zero-inflated Poisson (ZIP) models for NCM were compared in a cross-validation study. To assess the ability of these models to predict future data, records from 620492 first-lactation Norwegian Red cows, which were daughters of 3064 sires, were evaluated in a fourfold cross-validation scheme. The mean squared error of prediction was used for model comparison. All models but ordinal threshold model equally performed when comparing the overall predictive ability. This result was on average, across sick and healthy cows; however, the models behaved differently for each category of animals. For example, healthy cows were predicted better by the threshold and linear models for binary data and ZIP model, whereas for mastitic cows, the ordinal threshold model was by far the best model. Predicted sire effects and rankings of sires were highly correlated across all models. For practical purposes, the linear models are very competitive with the nonlinear models.

Comparison of selective genotyping strategies for prediction of breeding values in a population undergoing selection.

Genomewide marker information can improve the reliability of breeding value predictions for young selection candidates in genomic selection. However, the cost of genotyping limits its use to elite animals, and how such selective genotyping affects predictive ability of genomic selection models is an open question. We performed a simulation study to evaluate the quality of breeding value predictions for selection candidates based on different selective genotyping strategies in a population undergoing selection. The genome consisted of 10 chromosomes of 100 cM each. After 5,000 generations of random mating with a population size of 100 (50 males and 50 females), generation G(0) (reference population) was produced via a full factorial mating between the 50 males and 50 females from generation 5,000. Different levels of selection intensities (animals with the largest yield deviation value) in G(0) or random sampling (no selection) were used to produce offspring of G(0) generation (G(1)). Five genotyping strategies were used to choose 500 animals in G(0) to be genotyped: 1) Random: randomly selected animals, 2) Top: animals with largest yield deviation values, 3) Bottom: animals with lowest yield deviations values, 4) Extreme: animals with the 250 largest and the 250 lowest yield deviations values, and 5) Less Related: less genetically related animals. The number of individuals in G(0) and G(1) was fixed at 2,500 each, and different levels of heritability were considered (0.10, 0.25, and 0.50). Additionally, all 5 selective genotyping strategies (Random, Top, Bottom, Extreme, and Less Related) were applied to an indicator trait in generation G(0,) and the results were evaluated for the target trait in generation G(1), with the genetic correlation between the 2 traits set to 0.50. The 5 genotyping strategies applied to individuals in G(0) (reference population) were compared in terms of their ability to predict the genetic values of the animals in G(1) (selection candidates). Lower correlations between genomic-based estimates of breeding values (GEBV) and true breeding values (TBV) were obtained when using the Bottom strategy. For Random, Extreme, and Less Related strategies, the correlation between GEBV and TBV became slightly larger as selection intensity decreased and was largest when no selection occurred. These 3 strategies were better than the Top approach. In addition, the Extreme, Random, and Less Related strategies had smaller predictive mean squared errors (PMSE) followed by the Top and Bottom methods. Overall, the Extreme genotyping strategy led to the best predictive ability of breeding values, indicating that animals with extreme yield deviations values in a reference population are the most informative when training genomic selection models.