K.A. Weigel

Semi-parametric genomic-enabled prediction of genetic values using reproducing kernel Hilbert spaces methods

Prediction of genetic values is a central problem in quantitative genetics. Over many decades, such predictions have been successfully accomplished using information on phenotypic records and family structure usually represented with a pedigree. Dense molecular markers are now available in the genome of humans, plants and animals, and this information can be used to enhance the prediction of genetic values. However, the incorporation of dense molecular marker data into models poses many statistical and computational challenges, such as how models can cope with the genetic complexity of multi-factorial traits and with the curse of dimensionality that arises when the number of markers exceeds the number of data points. Reproducing kernel Hilbert spaces regressions can be used to address some of these challenges. The methodology allows regressions on almost any type of prediction sets (covariates, graphs, strings, images, etc.) and has important computational advantages relative to many parametric approaches. Moreover, some parametric models appear as special cases. This article provides an overview of the methodology, a discussion of the problem of kernel choice with a focus on genetic applications, algorithms for kernel selection and an assessment of the proposed methods using a collection of 599 wheat lines evaluated for grain yield in four mega environments.

Predictive ability of direct genomic values for lifetime net merit of Holstein sires using selected subsets of single nucleotide polymorphism markers

The objective of the present study was to assess the predictive ability of subsets of single nucleotide polymorphism (SNP) markers for development of low-cost, low-density genotyping assays in dairy cattle. Dense SNP genotypes of 4,703 Holstein bulls were provided by the USDA Agricultural Research Service. A subset of 3,305 bulls born from 1952 to 1998 was used to fit various models (training set), and a subset of 1,398 bulls born from 1999 to 2002 was used to evaluate their predictive ability (testing set). After editing, data included genotypes for 32,518 SNP and August 2003 and April 2008 predicted transmitting abilities (PTA) for lifetime net merit (LNM

Technical note: an R package for fitting generalized linear mixed models in animal breeding.

), the latter resulting from progeny testing. The Bayesian least absolute shrinkage and selection operator method was used to regress August 2003 PTA on marker covariates in the training set to arrive at estimates of marker effects and direct genomic PTA. The coefficient of determination (R(2)) from regressing the April 2008 progeny test PTA of bulls in the testing set on their August 2003 direct genomic PTA was 0.375. Subsets of 300, 500, 750, 1,000, 1,250, 1,500, and 2,000 SNP were created by choosing equally spaced and highly ranked SNP, with the latter based on the absolute value of their estimated effects obtained from the training set. The SNP effects were re-estimated from the training set for each subset of SNP, and the 2008 progeny test PTA of bulls in the testing set were regressed on corresponding direct genomic PTA. The R(2) values for subsets of 300, 500, 750, 1,000, 1,250, 1,500, and 2,000 SNP with largest effects (evenly spaced SNP) were 0.184 (0.064), 0.236 (0.111), 0.269 (0.190), 0.289 (0.179), 0.307 (0.228), 0.313 (0.268), and 0.322 (0.291), respectively. These results indicate that a low-density assay comprising selected SNP could be a cost-effective alternative for selection decisions and that significant gains in predictive ability may be achieved by increasing the number of SNP allocated to such an assay from 300 or fewer to 1,000 or more.

Accuracy of direct genomic values derived from imputed single nucleotide polymorphism genotypes in Jersey cattle

Mixed models have been used extensively in quantitative genetics to study continuous and discrete traits. A standard quantitative genetic model proposes that the effects of levels of some random factor (e.g., sire) are correlated accordingly with their relationships. For this reason, routines for mixed models available in standard packages cannot be used for genetic analysis. The pedigreemm package of R was developed as an extension of the lme4 package, and allows mixed models with correlated random effects to be fitted for Gaussian, binary, and count responses. Following the method of Harville and Callanan (1989), a correlation between levels of the grouping factor (e.g., sire) is induced by post-multiplying the incidence matrix of the levels of this random factor by the Cholesky factor of the corresponding (co)variance matrix (e.g., the numerator relationship matrix between sires). Estimation methods available in pedigreemm include approximations to maximum likelihood and REML. This note describes the classes of models that can be fitted using pedigreemm and presents examples that illustrate its use.

Evaluation of inbreeding depression in Holstein cattle using whole-genome SNP markers and alternative measures of genomic inbreeding

The objective of the present study was to evaluate the predictive ability of direct genomic values for economically important dairy traits when genotypes at some single nucleotide polymorphism (SNP) loci were imputed rather than measured directly. Genotypic data consisted of 42,552 SNP genotypes for each of 1,762 Jersey sires. Phenotypic data consisted of predicted transmitting abilities (PTA) for milk yield, protein percentage, and daughter pregnancy rate from May 2006 for 1,446 sires in the training set and from April 2009 for 316 sires in the testing set. The SNP effects were estimated using the Bayesian least absolute selection and shrinkage operator (LASSO) method with data of sires in the training set, and direct genomic values (DGV) for sires in the testing set were computed by multiplying these estimates by corresponding genotype dosages for sires in the testing set. The mean correlation across traits between DGV (before progeny testing) and PTA (after progeny testing) for sires in the testing set was 70.6% when all 42,552 SNP genotypes were used. When genotypes for 93.1, 96.6, 98.3, or 99.1% of loci were masked and subsequently imputed in the testing set, mean correlations across traits between DGV and PTA were 68.5, 64.8, 54.8, or 43.5%, respectively. When genotypes were also masked and imputed for a random 50% of sires in the training set, mean correlations across traits between DGV and PTA were 65.7, 63.2, 53.9, or 49.5%, respectively. Results of this study indicate that if a suitable reference population with high-density genotypes is available, a low-density chip comprising 3,000 equally spaced SNP may provide approximately 95% of the predictive ability observed with the BovineSNP50 Beadchip (Illumina Inc., San Diego, CA) in Jersey cattle. However, if fewer than 1,500 SNP are genotyped, the accuracy of DGV may be limited by errors in the imputed genotypes of selection candidates.

Prediction of unobserved single nucleotide polymorphism genotypes of Jersey cattle using reference panels and population-based imputation algorithms

The effects of increased pedigree inbreeding in dairy cattle populations have been well documented and result in a negative impact on profitability. Recent advances in genotyping technology have allowed researchers to move beyond pedigree analysis and study inbreeding at a molecular level. In this study, 5,853 animals were genotyped for 54,001 single nucleotide polymorphisms (SNP); 2,913 cows had phenotypic records including a single lactation for milk yield (from either lactation 1, 2, 3, or 4), reproductive performance, and linear type conformation. After removing SNP with poor call rates, low minor allele frequencies, and departure from Hardy-Weinberg equilibrium, 33,025 SNP remained for analyses. Three measures of genomic inbreeding were evaluated: percent homozygosity (FPH), inbreeding calculated from runs of homozygosity (FROH), and inbreeding derived from a genomic relationship matrix (FGRM). Average FPH was 60.5±1.1%, average FROH was 3.8±2.1%, and average FGRM was 20.8±2.3%, where animals with larger values for each of the genomic inbreeding indices were considered more inbred. Decreases in total milk yield to 205d postpartum of 53, 20, and 47kg per 1% increase in FPH, FROH, and FGRM, respectively, were observed. Increases in days open per 1% increase in FPH (1.76 d), FROH (1.72 d), and FGRM (1.06 d) were also noted, as well as increases in maternal calving difficulty (0.09, 0.03, and 0.04 on a 5-point scale for FPH, FROH, and FGRM, respectively). Several linear type traits, such as strength (-0.40, -0.11, and -0.19), rear legs rear view (-0.35, -0.16, and -0.14), front teat placement (0.35, 0.25, 0.18), and teat length (-0.24, -0.14, and -0.13) were also affected by increases in FPH, FROH, and FGRM, respectively. Overall, increases in each measure of genomic inbreeding in this study were associated with negative effects on production and reproductive ability in dairy cows.

Assessment of environmental descriptors for studying genotype by environment interaction

The availability of dense single nucleotide polymorphism (SNP) genotypes for dairy cattle has created exciting research opportunities and revolutionized practical breeding programs. Broader application of this technology will lead to situations in which genotypes from different low-, medium-, or high-density platforms must be combined. In this case, missing SNP genotypes can be imputed using family- or population-based algorithms. Our objective was to evaluate the accuracy of imputation in Jersey cattle, using reference panels comprising 2,542 animals with 43,385 SNP genotypes and study samples of 604 animals for which genotypes were available for 1, 2, 5, 10, 20, 40, or 80% of loci. Two population-based algorithms, fastPHASE 1.2 (P. Scheet and M. Stevens; University of Washington TechTransfer Digital Ventures Program, Seattle, WA) and IMPUTE 2.0 (B. Howie and J. Marchini; Department of Statistics, University of Oxford, UK), were used to impute genotypes on Bos taurus autosomes 1, 15, and 28. The mean proportion of genotypes imputed correctly ranged from 0.659 to 0.801 when 1 to 2% of genotypes were available in the study samples, from 0.733 to 0.964 when 5 to 20% of genotypes were available, and from 0.896 to 0.995 when 40 to 80% of genotypes were available. In the absence of pedigrees or genotypes of close relatives, the accuracy of imputation may be modest (generally <0.80) when low-density platforms with fewer than 1,000 SNP are used, but population-based algorithms can provide reasonably good accuracy (0.80 to 0.95) when medium-density platforms of 2,000 to 4,000 SNP are used in conjunction with high-density genotypes (e.g., >40,000 SNP) from a reference population. Accurate imputation of high-density genotypes from inexpensive low- or medium-density platforms could greatly enhance the efficiency of whole-genome selection programs in dairy cattle.

International genetic evaluations for feed intake in dairy cattle through the collation of data from multiple sources

Abstract Access to individual performance records opens up possibilities for treatment of genotype by environment interaction in international genetic evaluations. The ability to distinguish similar from dissimilar environments is thus important. Reaction norms were used in this study to evaluate several variables for their suitability to classify production environments for studies on genotype by environment interaction. Reaction norms describe the phenotypic expression of a genotype as a function of the environment, and can be modelled by random regression on environmental descriptors. Fifteen variables that measure aspects of management, genetic composition and climate were computed on herd level. Suitability of each variable to detect genotype by environment interaction was assessed through likelihood ratio tests for significant linear or quadratic random regression terms. First lactation records from approximately 40 000 Guernsey cows in four countries (Australia, Canada, USA and Republic of South Africa) were used. Variables with significant effect were: herd size, within-herd standard deviation of lactation yield, peak milk yield, persistency, days to peak production, calving pattern, age at first calving, rate of maturity, and annual rainfall. Genetic correlation between extreme environments for milk peak yield, within-herd standard deviation and annual rainfall were lower than 0.91, indicating that re-ranking of animals may occur.

Assessment of Poisson, logit, and linear models for genetic analysis of clinical mastitis in Norwegian Red cows

Feed represents a large proportion of the variable costs in dairy production systems. The omission of feed intake measures explicitly from national dairy cow breeding objectives is predominantly due to a lack of information from which to make selection decisions. However, individual cow feed intake data are available in different countries, mostly from research or nucleus herds. None of these data sets are sufficiently large enough on their own to generate accurate genetic evaluations. In the current study, we collate data from 10 populations in 9 countries and estimate genetic parameters for dry matter intake (DMI). A total of 224,174 test-day records from 10,068 parity 1 to 5 records of 6,957 cows were available, as well as records from 1,784 growing heifers. Random regression models were fit to the lactating cow test-day records and predicted feed intake at 70 d postcalving was extracted from these fitted profiles. The random regression model included a fixed polynomial regression for each lactation separately, as well as herd-year-season of calving and experimental treatment as fixed effects; random effects fit in the model included individual animal deviation from the fixed regression for each parity as well as mean herd-specific deviations from the fixed regression. Predicted DMI at 70 d postcalving was used as the phenotype for the subsequent genetic analyses undertaken using an animal repeatability model. Heritability estimates of predicted cow feed intake 70 d postcalving was 0.34 across the entire data set and varied, within population, from 0.08 to 0.52. Repeatability of feed intake across lactations was 0.66. Heritability of feed intake in the growing heifers was 0.20 to 0.34 in the 2 populations with heifer data. The genetic correlation between feed intake in lactating cows and growing heifers was 0.67. A combined pedigree and genomic relationship matrix was used to improve linkages between populations for the estimation of genetic correlations of DMI in lactating cows; genotype information was available on 5,429 of the animals. Populations were categorized as North America, grazing, other low input, and high input European Union. Albeit associated with large standard errors, genetic correlation estimates for DMI between populations varied from 0.14 to 0.84 but were stronger (0.76 to 0.84) between the populations representative of high-input production systems. Genetic correlations with the grazing populations were weak to moderate, varying from 0.14 to 0.57. Genetic evaluations for DMI can be undertaken using data collated from international populations; however, genotype-by-environment interactions with grazing production systems need to be considered.

Whole-genome scan for quantitative trait loci associated with birth weight, gestation length and passive immune transfer in a Holstein × Jersey crossbred population

Clinical mastitis is typically coded as presence/absence during some period of exposure, and records are analyzed with linear or binary data models. Because presence includes cows with multiple episodes, there is loss of information when a count is treated as a binary response. The Poisson model is designed for counting random variables, and although it is used extensively in epidemiology of mastitis, it has rarely been used for studying the genetics of mastitis. Many models have been proposed for genetic analysis of mastitis, but they have not been formally compared. The main goal of this study was to compare linear (Gaussian), Bernoulli (with logit link), and Poisson models for the purpose of genetic evaluation of sires for mastitis in dairy cattle. The response variables were clinical mastitis (CM; 0, 1) and number of CM cases (NCM; 0, 1, 2, ..). Data consisted of records on 36,178 first-lactation daughters of 245 Norwegian Red sires distributed over 5,286 herds. Predictive ability of models was assessed via a 3-fold cross-validation using mean squared error of prediction (MSEP) as the end-point. Between-sire variance estimates for NCM were 0.065 in Poisson and 0.007 in the linear model. For CM the between-sire variance was 0.093 in logit and 0.003 in the linear model. The ratio between herd and sire variances for the models with NCM response was 4.6 and 3.5 for Poisson and linear, respectively, and for model for CM was 3.7 in both logit and linear models. The MSEP for all cows was similar. However, within healthy animals, MSEP was 0.085 (Poisson), 0.090 (linear for NCM), 0.053 (logit), and 0.056 (linear for CM). For mastitic animals the MSEP values were 1.206 (Poisson), 1.185 (linear for NCM response), 1.333 (logit), and 1.319 (linear for CM response). The models for count variables had a better performance when predicting diseased animals and also had a similar performance between them. Logit and linear models for CM had better predictive ability for healthy cows and had a similar performance between them.