Approximating prediction error covariances among additive genetic effects within animals in multiple‐trait and random regression models

Tier, Bruce; Meyer, Karin

doi:10.1111/j.1439-0388.2003.00444.x

Cited by 81 publications

(95 citation statements)

References 14 publications

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“…They were used as validation criteria in the study by Su et al (2010). In conventional breeding value estimation (Misztal and Wiggans, 1988;Tier and Meyer, 2004), reliabilities of the estimated breeding values (EBVs) are also calculated from approximations of prediction error variances (PEVs) from the individual animal model solutions of genetic merit. Third, validation of the reliabilities of DGV for the group of the most recent bulls with EBV was used in the studies by Harris and Johnson (2010), Lund et al (2010) and VanRaden et al (2009).…”

Section: Introductionmentioning

confidence: 99%

Reliabilities of genomic estimated breeding values in Danish Jersey

Thomasen

Guldbrandtsen

et al. 2012

Animal

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In order to optimize the use of genomic selection in breeding plans, it is essential to have reliable estimates of the genomic breeding values. This study investigated reliabilities of direct genomic values (DGVs) in the Jersey population estimated by three different methods. The validation methods were (i) fivefold cross-validation and (ii) validation on the most recent 3 years of bulls. The reliability of DGV was assessed using squared correlations between DGV and deregressed proofs (DRPs). In the recent 3-year validation model, estimated reliabilities were also used to assess the reliabilities of DGV. The data set consisted of 1003 Danish Jersey bulls with conventional estimated breeding values (EBVs) for 14 different traits included in the Nordic selection index. The bulls were genotyped for Single-nucleotide polymorphism (SNP) markers using the Illumina 54 K chip. A Bayesian method was used to estimate the SNP marker effects. The corrected squared correlations between DGV and DRP were on average across all traits 0.04 higher than the squared correlation between DRP and the pedigree index. This shows that there is a gain in accuracy due to incorporation of marker information compared with parent index pre-selection only. Averaged across traits, the estimates of reliability of DGVs ranged from 0.20 for validation on the most recent 3 years of bulls and up to 0.42 for expected reliabilities. Reliabilities from the cross-validation were on average 0.24. For the individual traits, the reliability varied from 0.12 (direct birth) to 0.39 (milk). Bulls whose sires were included in the reference group had an average reliability of 0.25, whereas the bulls whose sires were not included in the reference group had an average reliability that was 0.05 lower.

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Section: Introductionmentioning

confidence: 99%

Reliabilities of genomic estimated breeding values in Danish Jersey

Thomasen

Guldbrandtsen

et al. 2012

Animal

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“…For most genetic evaluation schemes, however, this matrix is too large to be inverted. Approximation procedures for the inverse and 'accuracies' of estimated breeding values for RR analyses have been described by and Tier & Meyer (2004).…”

Section: Estimation Of Breeding Valuesmentioning

confidence: 99%

Up hill, down dale: quantitative genetics of curvaceous traits

Meyer

Kirkpatrick

2005

Phil. Trans. R. Soc. B

100

107

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'Repeated' measurements for a trait and individual, taken along some continuous scale such as time, can be thought of as representing points on a curve, where both means and covariances along the trajectory can change, gradually and continually. Such traits are commonly referred to as 'functionvalued' (FV) traits. This review shows that standard quantitative genetic concepts extend readily to FV traits, with individual statistics, such as estimated breeding values and selection response, replaced by corresponding curves, modelled by respective functions. Covariance functions are introduced as the FV equivalent to matrices of covariances.Considering the class of functions represented by a regression on the continuous covariable, FV traits can be analysed within the linear mixed model framework commonly employed in quantitative genetics, giving rise to the so-called random regression model. Estimation of covariance functions, either indirectly from estimated covariances or directly from the data using restricted maximum likelihood or Bayesian analysis, is considered. It is shown that direct estimation of the leading principal components of covariance functions is feasible and advantageous. Extensions to multidimensional analyses are discussed.

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“…These models present the advantage of using all records of the animal and of eliminating the need for the correction of weights for standard ages. In addition, it provides more accurate estimates of breeding values for any age within the interval of the records considered when compared with conventional multi-trait models (Tier and Meyer, 2004).…”

Section: Introductionmentioning

confidence: 99%

“…However, there are difficulties to include adult weights in genetic evaluations because of the scarcity of weight records at later ages and the lack of adequate models to estimate (co)variance components at mature ages. Apparently, RRMs on B-spline functions offer advantages over the Legendre polynomials and the traditional finite dimensional models (Tier and Meyer, 2004) and could be used for genetic evaluation of growth traits.…”

Section: Introductionmentioning

confidence: 99%

Random regression analyses using B-spline functions to model growth of Nellore cattle

Boligon

Mercadante

Lôbo

et al. 2012

Animal

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The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.Keywords: growth curve, covariance functions, segmented polynomials, Nellore cattle Implications Random regression models (RRMs) applying spline functions could be an option to model weights until mature age, as these functions are less susceptible to the problems frequently observed with orthogonal Legendre polynomials. However, to date there are no studies that have applied RRM on B-spline functions to estimate genetic parameters for weights in Nellore cattle. The results of this research showed that RRMs using Bspline functions revealed similar description of the trajectory of the variances and heritability estimates. Moreover, random regression on B-spline functions required lower computational requirement and faster convergence in relation to Legendre polynomials or multi-trait analysis. In genetic evaluation programs, with large data set, the application of RRMs using ...

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Approximating prediction error covariances among additive genetic effects within animals in multiple‐trait and random regression models

Cited by 81 publications

References 14 publications

Reliabilities of genomic estimated breeding values in Danish Jersey

Reliabilities of genomic estimated breeding values in Danish Jersey

Up hill, down dale: quantitative genetics of curvaceous traits

Random regression analyses using B-spline functions to model growth of Nellore cattle

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