Univariate and multivariate parameter estimates for milk production traits using an animal model. I. Description and results of REML analyses

PM Visscher R Thompson 0 Present address: Livestock Improvement Unit, Department of Food and Agriculture , 166-176 Wellington Parade, East Melbourne, Melbourne 3002 , Australia Summary - Using production records in lactations 1-3 from 100 large Holstein-F'riesian pedigree herds, parameters for milk, fat and protein yield in lactations 1-3 were estimated with REML using an animal model. The number of records for each lactation was 38 811, 26 223 and 16 542 for lactation 1, 2 and 3 respectively. Heritabilities for the 3 yield traits were similar: approximately 0.36 in lactation 1 and 0.30 in lactations 2 and 3. Genetic correlations between yield traits in lactations 1 and 2, for example between milk production in first and second lactations, were approximately 0.86. Genetic correlations between yield traits in lactations 2 and 3 were near unity. Genetic correlations between yield traits within lactations ranged from 0.58, for milk and fat yield in lactation 3, to 0.91, for milk and protein yield in lactation 1. Genetic correlations between yield traits between lactations ranged from 0.55, for milk yield in lactation 1 and fat yield in lactation 2, to 0.85, for milk yield in lactation 2 and protein yield in lactation 3. Environmental correlations between traits within lactations were approximately 0.95, and approximately 0.40 across lactations. dairy cattle / animal model / maximum likelihood / multivariate analyse / multitrait / multi-lactation Rsum - Utilisation du modle animal pour l'estimation des paramtres univariates et multivariates concernant les caractres de production laitire. I. Description et rsultats des analyses selon le maximum de vraisemblance restreint (REML). A partir des donnes obtenues pendant les lactations 1 3 dans 100 grands troupeaux HolsteinFreisian inscrits, les paramtres de production de lait, de matire grasse et de matire protique pour les lactations1 d ont t estims par maximum de vraisemblance restreint - (REML) selon le modle animal. Le nombre des donnes pour chaque lactation a t de 38 811, 26 223 et 16 542 pour les lactations 1,2 et 3 respectivement. Les hritabilits des3 critres de production ont t similaires: approximativement 0,36 en premire lactation et 0,30 en seconde et troisime lactation. Les corrlations gntiques entre les caractres de production en lactations1 et 2, par exemple la production laitire, ont t approximativement de 0,86. Les corrlations gntiques entre critres de production aux lactations2 et3 ont t pratiquement gaux 1. Les corrlations gntiques entre les critres de production intralactation ont vari de 0,58, pour la production laitire et la production de matire grasse en lactation 3, 0,91 pour la production laitire et la production de protine en lactation 1. Les corrlations entre les productions diffrentes lactations ont vari de 0,55, pour la production laitire en lactation1 et la production de matire grasse en lactation 2, 0,85 pour la production laitire en lactation2 et la production de protine en lactation 3. Les corrlations non gntiques entre caractres pour une mme lactation ont t approximativement de 0,95 et celles correspondant des lactations diffrentes ont t approximativement de 0,40. bovin laitier / modle animal / maximum de vraisemblance / analyse multivariate / multicaractre / multilactation Dairy cattle sire evaluation in many countries is carried out using best linear unbiased prediction (BLUP) (Interbull, 1988), while cows are usually evaluated separately using a selection index type approach (eg Hill and Swanson, 1983). Recently there has been a shift towards a joint evaluation of cows and bulls, using a so-called animal model (AM). Some countries have implemented an AM national evaluation for single traits (Wiggans et al, 1988a, b; Ducrocq et al, 1990; Jones and Goddard, 1990), others are in the process of doing so. Assumptions about the covariance structure of observations analysed with a linear model are often simplified to make computations feasible. For example, the USA (Wiggans et al, 1988a), France (Ducrocq et al, 1990; Bonaiti and Boichard, 1990) and Australia (Jones and Goddard, 1990) use a modified repeatability model for which a genetic correlation of unity is assumed between performances across lactations and some (pre)scaling is applied to later lactation records to account for higher phenotypic variances of traits in later lactations. Later lactation records are given lower weightings by adjusting the error structure of the observations, and milk, fat, and protein yield are analysed separately using this modified repeatability model. The potential loss in efficiency of selection by making these assumptions depends on the true, unknown, covariance structure of the data, and on the breeding goal. By estimating relevant (co)variances and assuming a particular combination of traits to select for, the potential loss in efficiency of selection by using simplified covariance structures may be quantified. For estimating (co)variance components it seems desirable to use the same model as is, or soon will be, used for the prediction of breeding values, ie an animal model. Few (co)variance estimates from AM analyses have been reported; Swalve and Van Vleck (1987) analysed milk yield in lactations 1-3, and Van Vleck and Dong (1988) performed a multivariate analysis on milk, fat and protein yield in the first lactation. The aims of this study were: 1) to estimate parameters for milk (M), fat (F) and protein (P) yield in lactations 1, 2 and 3 the implications of the estimates for prediction of breeding values when simplified assumptions are made regarding covariances structures. This part of the study is 2) to investigate reported separately (Visscher et al, 1992). Estimates of correlations between different traits in different lactations, for example between milk yield in lactation 1 have not been reported before. In the notation used, the number following M, F and fat yield in lactation 2 (Z)F or P refers to lactation number, and the combination above, be written as analysing Similarly, a multivariate (MV) analysis on 1M, F, and IP may MATERIAL First, second and third lactation production records for the period 1979-1987 from 100 large pedigree herds were extracted from the Milk Marketing Boards production files. Herds were selected on the number of heifers present in 1987, ie data were extracted from those herds which had the largest number of first lactation cows in 1987. Later lactation records, ie second or third, were included only from cows for which the previous lactations were present. All cows were pedigree Holstein-Friesian (HF). Some summary statistics of the data are presented Residual maximum likelihood (REML; Patterson and Thompson, 1971) was used to estimate (co)variances, using programs based on software written by Meyer (1988, 1989). Fixed effects in the mixed linear model were herd-year-seasons (HYS) and month of calving. Seasons were defined as 4-month periods, correspondin (...truncated)