L.R. Schaeffer

Application of random regression models in animal breeding

Abstract Random regression models (RRM) have become common for the analysis of longitudinal data or repeated records on individuals over time. Applications in animal breeding research are emphasized while recognizing that RRM are used in many biological situations including human health. The best known application of RRM has been to genetic evaluation of dairy cattle using test day production records. The basic structure of a RRM is given. Other applications include growth traits in all species, genotype by environment interactions, and ad hoc proposals for the analysis of survival data and fertility data. RRM allow the researcher to study changes in genetic variability with time and allow selection of individuals to alter the general patterns of response over time.

Use of test day yields for genetic evaluation of dairy sires and cows

Abstract Genetic evaluations of dairy sires and cows for milk production based on 305-day lactation yields were compared to evaluations based on the corresponding test day yields from those lactations. First lactation data were from the Quebec Dairy Herd Analysis Service for 3094 cows calving from September 1983 to October 1989. There were 29462 test day yield records. Four animal models were studied for use with test day yields, and each model included four covariates to account for the shape of the lactation curve within eight age-season groups. Models contained either herd-year-season effects or herd-test date effects, and the residual variances were assumed to be either homogeneous or heterogeneous across days in milk. Herd-test date effects resulted in lower residual variances compared to models with herd-year-season effects. Correlations of test day evaluations with 305-day evaluations ranged from 0.87 to 0.97. Genetic evaluations based on test day yields offer many advantages over those based on 305-day lactations including better modeling of factors affecting yields, no need to extend records, and possibly greater accuracy of evaluations.

Body traits in rainbow trout: II. Estimates of heritabilities and of phenotypic and genetic correlations

Genetic parameters were estimated from data recorded at slaughter on 2–4-kg rainbow trout (Salmo gairdneri) from three year-classes. Observations were made on 4466 fish of 47 sires and 249 dams nested within sires (data set I). Some traits were recorded only on a sample of 662 fish of 37 sires and 111 dams included in data set I (data set II). No sire or dam was used in more than one year-class. Heritabilities based on the sire component of variance for traits in data set I were 0.21 for ungutted and gutted body weight, 0.18 for body length, 0.36 for dressing percentage, 0.19 for condition factor, 0.23 for gonad weight, 0.32 for belly thickness score and 0.40 for belly thickness measured, 0.25 for abdominal fat score and 0.28 for viscera weight, and 0.27 for meat colour score. Heritabilities for traits in data set II were 0.22–0.30 for body circumference, 0.19–0.34 for size and belly thickness measurements of the cross sections at the pelvic and dorsal fins, 0.13–0.25 for body shape, 0.00–0.31 for shape of the cross sections and 0.33, 0.47 and 0.03 for percent water, fat and protein in the meat, respectively. Genetic correlations of body weight with (a) body circumference traits and size measurements of the cross sections were all very high; (b) belly thickness, condition factor, abdominal fat score and meat colour score were low, but positive; (c) fat percentage was also low, but negative. Genetic correlations of belly thickness with abdominal fat score and fat percentage were −0.54 and 0.24, respectively, and −0.33 between fat percentage and abdominal fat score. Genetic correlations of condition factor with carcass fat percentage and body shape were 0.15 and 0.52, respectively, and the phenotypic correlations were 0.16 and 0.82, respectively. It was concluded that condition factor is an adequate measure of body shape. In conclusion, the possibilities for genetic improvement of body weight, belly thickness, body shape, abdominal fat, fat in the meat and meat colour are very good in rainbow trout. No strong unfavourable genetic correlation was found among the traits.

Multiple trait international bull comparisons

Abstract A multiple trait, multiple country, international evaluation model is described for dairy or beef cattle. Such a model is necessary so that countries with estimated breeding values for several subtraits from a within-country multiple trait model do not have to combine those values into one single trait. A multiple trait de-regression step is necessary before combining information from different countries coming from multiple trait models. An approximate Bayesian method is suggested for estimating the genetic covariances between traits between countries, while holding the genetic and residual covariance matrices for each country constant. The methods are illustrated by a small example.

MODEL FOR INTERNATIONAL EVALUATION OF DAIRY SIRES

Abstract A linear statistical model is put forward for use in comparing the genetic level of dairy sires based on their progeny test evaluations from one or more countries. Additive genetic relationships among bulls are included to provide more connections or comparisons among countries. Several definitions of genetic differences among countries are presented. A small example illustrates the use of this model.

Approximate accuracies of prediction from random regression models.

Abstract A procedure for obtaining approximate reliabilities of estimated breeding values under a random regression model is presented. The method is based on a concept of an equivalent number of progeny, with subsequent selection index approximation of reliability utilising equivalent progeny information on the animal and its parents. The accuracy of the proposed approximation was tested using a multiple trait random regression test day model for dairy production traits applied to Canadian Jersey data. Gibbs sampling method was used to generate exact reliabilities of genetic evaluations for several traits derived from the genetic random regression coefficients. The approximation was shown to be relatively unbiased for both bulls and cows. The method has been implemented in the Canadian test day model for dairy production traits.

Estimation of genetic parameters of calving ease in first and second parities of Canadian Holsteins using Bayesian methods

Abstract Genetic parameters of calving ease in first and second parities of Canadian Holsteins were estimated using a Bayesian approach. Multiple-trait calving ease records on 94 925 cows (no missing records) were analyzed with a threshold model. The model included a fixed effect for sex of calf and random effects of herd–year–season, sire of cow, and sire of calf. Gibbs sampling was used to generate ten chains of 20 000 samples each, which were used to obtain posterior means for each parameter. Estimates of heritabilities were 0.26 and 0.17 for first and second lactations, respectively. Genetic correlations between lactations were 0.67, indicating that the scores were measures of distinct genetic traits. Direct heritabilities of 0.14 and 0.10 in first and second lactations, respectively, were approximately twice as large as the respective maternal heritabilities of 0.08 and 0.04. Estimates of genetic correlations among all combinations of direct and maternal genetic effects were positive, approximately 0.35, which conflicted with many previous studies. This positive correlation was confirmed by reanalyzing another sample of data with REML and by calculating correlations between official Canadian sire ETA for direct and maternal genetic effects on calving ease. Multiple trait genetic evaluation of calving ease should theoretically provide more precise predictions of breeding values than single-trait repeated records models.

Influence of population structure on estimates of direct and maternal parameters

The estimation of (co)variance components for multiple traits with maternal genetic effects was found to be influenced by population structure. Two traits in a closed breeding herd with random mating were simulated over nine generations. Population structures were simulated on the basis of different proportions of dams not having performance records (0, 0.1, 0.5, 0.8 and 0.9): three genetic correlations (-0.5, 0.0 and +0.5) between direct and maternal effects and three genetic correlations (0, 0.3 and 0.8) between two traits. Three ratios of direct to maternal genetic variances, (1:3, 1:1, 3:1), were also considered. Variance components were estimated by restricted maximum likelihood. The proportion of dams without records had an effect on the SE of direct-maternal covariance estimates when the proportion was 0.8 or 0.9 and the true correlation between direct and maternal effects was negative. The ratio of direct to maternal genetic variances influenced the SE of the (co)variance estimates more than the proportion of dams with missing records. The correlation between two traits did not have an effect on the SE of the estimates. The proportion of dams without records and the correlation between direct and maternal effects had the strongest effects on bias of estimates. The largest biases were obtained when the proportion of dams without records was high, the correlation between direct and maternal effects was positive, and the direct variance was greater than the maternal variance, as would be the situation for most growth traits in livestock. Total bias in all parameter estimates for two traits was large in the same situations. Poor population structure can affect both bias and SE of estimates of the direct-maternal genetic correlation, and can explain some of the large negative estimates often obtained.

Genetic and environmental relationships between body condition score and milk production traits in Canadian Holsteins.

The objective of this research was to estimate genetic parameters of first-lactation body condition score (BCS), milk yield, fat percentage (Fat%), protein percentage (Prot%), somatic cell score (SCS), milk urea nitrogen (MUN), lactose percentage (Lact%), and fat to protein ratio (F:P) using multiple-trait random regression animal models. Changes in covariances between BCS and milk production traits on a daily basis have not been investigated before and could be useful for determining which BCS estimated breeding values (EBV) might be practical for selection in the future. Field staff from Valacta milk recording agency (Sainte-Anne-de-Bellevue, QC, Canada) collected BCS from Québec herds several times per cow throughout the lactation. Average daily heritabilities and genetic correlations among the various traits were similar to literature values. On an average daily basis, BCS was genetically unfavorably correlated with milk yield (i.e., increased milk yield was associated with lower body condition). The unfavorable genetic correlation between BCS and milk yield became stronger as lactation progressed, but was equivalent to zero for the first month of lactation. Favorable genetic correlations were found between BCS with Prot%, SCS, and Lact% (i.e., greater BCS was associated with greater Prot%, lower SCS, and greater Lact%). These correlations were strongest in early lactation. On an average daily basis, BCS was not genetically correlated with Fat% or MUN, but was negatively correlated with F:P. Furthermore, BCS at 5 and 50 d in milk (DIM) had the most favorable genetic correlations with milk production traits over the lactation (at 5, 50, 150, and 250 DIM). Thus, early lactation BCS EBV shows potential for selection. Regardless, this study showed that the level of association BCS has with milk production traits is not constant over the lactation. Simultaneous selection for both BCS and milk production traits should be considered, mainly due to the unfavorable genetic correlation between BCS with milk yield.

Relationships between milk yield and somatic cell score in Canadian Holsteins from simultaneous and recursive random regression models

Multiple-trait random regression animal models with simultaneous and recursive links between phenotypes for milk yield and somatic cell score (SCS) on the same test day were fitted to Canadian Holstein data. All models included fixed herd test-day effects and fixed regressions within region-age at calving-season of calving classes, and animal additive genetic and permanent environmental regressions with random coefficients. Regressions were Legendre polynomials of order 4 on a scale from 5 to 305 d in milk (DIM). Bayesian methods via Gibbs sampling were used for the estimation of model parameters. Heterogeneity of structural coefficients was modeled across (the first 3 lactations) and within (4 DIM intervals) lactation. Model comparisons in terms of Bayes factors indicated the superiority of simultaneous models over the standard multiple-trait model and recursive parameterizations. A moderate heterogeneous (both across- and within-lactation) negative effect of SCS on milk yield (from -0.36 for 116 to 265 DIM in lactation 1 to -0.81 for 5 to 45 DIM in lactation 3) and a smaller positive reciprocal effect of SCS on milk yield (from 0.007 for 5 to 45 DIM in lactation 2 to 0.023 for 46 to 115 DIM in lactation 3) were estimated in the most plausible specification. No noticeable differences among models were detected for genetic and environmental variances and genetic parameters for the first 2 regression coefficients. The curves of genetic and permanent environmental variances, heritabilities, and genetic and phenotypic correlations between milk yield and SCS on a daily basis were different for different models. Rankings of bulls and cows for 305-d milk yield, average daily SCS, and milk lactation persistency remained the same among models. No apparent benefits are expected from fitting causal phenotypic relationships between milk yield and SCS on the same test day in the random regression test-day model for genetic evaluation purposes.