Selection for milk production and persistency using eigenvectors of the random regression coefficient matrix

The purpose of this study was to investigate the relationships of the eigenvectors of the additive genetic random regression coefficient matrix (K) to selection responses and to determine how many eigenvectors are necessary in the breeding goal to explain the variation. The construction of various eigenvector indexes was based on the K matrix estimated from test-day records of Japanese Holstein cattle. The first (leading) eigenvector index produced constant responses for each day of lactation, indicating that the first eigenvector is responsible for scaling the lactation curve without altering its shape. Daily genetic responses to the second eigenvector index increased linearly as DIM increased. Genetic responses to the third eigenvector index were negative in mid-lactation but were positive in early and late lactation (concave curve). Genetic responses to the fourth and fifth eigenvector indexes hovered around zero across the lactation. The results suggest that both second and third eigenvectors account for the change in the shape of the lactation curve and there is little utility of the fourth and fifth eigenvectors in improving lactation milk or persistency. When the goal is to increase lactation milk yield alone, the index based on the first eigenvector produced a similar response to the index based on all 5 eigenvectors. When the goal is to improve both lactation milk yield and persistency, the index based on the first 3 eigenvectors achieved more than 99.9% of the genetic response to an index based on all 5 eigenvectors. The advantage of an eigenvector index over conventional selection based on total lactation milk yield increases with increasing economic weight assigned to persistency.