Genomic predictions of growth curves in Holstein dairy cattle based on parameter estimates from nonlinear models combined with different kernel functions

Abstract

Availability of longitudinal body weight (BW) records allows the application of nonlinear models (NLINM) to predict phenotypic and genomic growth curves in dairy cattle. In this regard, we considered a data set including 31,722 BW records from 4,952 female Holstein cattle, during the period from birth (mo 0) to approximately age at first calving (mo 24). Parameters of the growth curves were estimated using 3 NLINM: the logistic (LOG), the Gompertz (GOM), and the Richards (RICH) functions. Residuals for the growth curve parameters from the NLINM applications were used as pseudo-phenotypes in the ongoing genomic analyses with different similarity matrices, including 2 genomic relationship matrices (G1 and G2), a combined pedigree and genomic relationship matrix (H), and 3 kernel matrices. The kernels were a weighted "alike by state" kernel function (K1), an exponential dissimilarity kernel (K2), and a Gaussian kernel (K3). On the basis of G1 and G2 matrices, genomic heritabilities for the growth curve parameters birth weight (W0), mature weight (Wm), and growth rate (k), and the shape parameter (m; only available from RICH) were moderate to large, in the range from 0.29 (m from RICH) to 0.46 (k from RICH). Fitting the similarity matrices based on kernel functions contributed to an increase of the ratio of the variance explained by the similarity matrix in relation to the total variance (compared with the heritability when modeling G1 or G2). Genetic correlations between W0, Wm, and k were always positive (>0.30), especially for the same growth curve parameters estimated from different NLINM (>0.90). The shape parameter m from RICH was negatively correlated with other growth curve parameters, from -0.29 to -0.95. In a next step, estimated genomic breeding values for growth curve parameters were input data for the respective NLINM, aiming to construct genomic growth curves. Prediction accuracies were correlations between genomic growth curves and genomic breeding values from random regression models for sires and female cattle. Considering all genotyped female cattle with pseudo-phenotypes, prediction accuracies were larger from RICH than from LOG and GOM. However, differences in prediction accuracies from the NLINM × similarity matrix combinations were quite small. Accordingly, in 5-fold cross-validations using heifer groups with masked phenotypes, very similar prediction accuracies across modeling approaches were identified. Especially for specific age months, genomic growth curve predictions were more accurate for sires than for female cattle, indicating that the relationships between animals in training and validation sets are more important than the selection of specific NLINM × similarity matrix combinations.