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The objective was to simulate the response to selection by modifying the shape of the lactation curve to improve persistency in Israeli first-parity Holstein cattle using geometric morphometrics and multivariate quantitative genetics. The 2-dimensional Cartesian coordinates representing the shape of the lactation curve were characterized using geometric morphometrics. Genetic parameters of daily milk yield were estimated for the individual animal model using REML. Results of selection were simulated using the multivariate breeders' equation. We defined 6 selection regimens: (1) decrease in the third month in milk (MIM), (2) increase in the ninth MIM, (3) decrease in the third MIM and increase in the ninth MIM, (4) decrease in the first MIM, (5) decrease in the second MIM, and (6) decrease in the fourth MIM. The first 3 selection criteria targeted changes in the MIM of previous measurements of persistency in the Israeli Holstein population, and the last 3 targeted the months with the highest variability. All selection regimens attempted to modify the shape of the lactation curve while keeping total milk yield constant. The first 3 selection regimens showed greater total responses, with the highest response for decrease in the third MIM and increase in the ninth MIM. Magnitudes of correlated responses consistently surpassed direct responses in all selection criteria, suggesting that selection on specific parts of the lactation curve would produce correlated responses in other parts. Predicted responses to selections were depicted as shape changes from the mean shape in the data set. Most predicted responses demonstrated a fairly similar shape compared with the lactation curve. The predicted responses of lactation shapes of the last 3 selection regimens were overall lower in the first 3 MIM and decreased less in the last MIM, demonstrating a much flatter shape and thus improved persistency.
estimated persistency in the Israeli Holstein population as the ratio of milk yield at 270 DIM to milk yield at 90 DIM for first-parity cows. Although different measurements of persistency have been proposed [for reviews, see
) based on monthly test day records. These studies computed the eigenvectors and eigenvalues from either the additive genetic or environmental covariance matrices, and they were interpreted as measures of production level (PC1) and persistency (PC2).
) proposed an algorithm for genetic selection based on the eigenvectors. None of these studies considered daily production records even though these data are now available at least for milk production in many advanced production systems.
The response of shape to selection depends on the additive genetic (G) and phenotypic (P) covariance matrices among the different parts of the lactation curve (
) demonstrated the combination of geometric morphometric and multivariate quantitative genetic methods for the genetic evaluation of shape of the lactation curve as a whole and as a separate character, in which the parts of the lactation shape with the maximal response to selection were identified from the GP matrix (Figure 3 in
. The objective of this study was to simulate the response to selection by selection for the shape of the lactation curve of first-parity Israeli Holstein cattle. We hypothesized that applying selection regimens in different months of production may produce different shapes for the lactation curve. The predicted response to selection of the lactation curve shape was visualized as shape changes from the mean shape in the data set.
The G and P covariance matrices used to examine the predicted response to selection on shape were obtained from the analysis of Israeli Holstein cattle (
). The G and P matrices correspond to the shape of the lactation curve as depicted by orbital graphs. In the geometric morphometric literature, shape refers to all the geometrical information that remains after removing information on location, size, and orientation (
). Shape variables (Procrustes coordinates) were obtained from the geometric morphometric analysis on 2-dimensional landmark and semi-landmark coordinates representing lactation curves depicted by orbital graphs. Then, those shape variables were analyzed by the multitrait animal model using the MTC REML program (
), where Δμ denoted the response to selection (the difference between the mean shapes of the parental and offspring generations), s was a vector of selection differentials (the difference of the averages in the parental generation before and after selection), and the other terms were as defined previously. This equation was applied to the estimates of G and P covariance matrices of shape of the lactation curve (
: (1) decrease in the third month in milk (MIM), (2) increase in the ninth MIM, and (3) decrease in the third MIM and increase in the ninth MIM. The third MIM (or landmark) corresponded to peak milk yield of first-parity cows, and the ninth MIM was 180 DIM after peak production; the third selection criterion corresponds to previous selection for persistency implemented in the Israeli selection index (
). The other 3 selection differentials were also designed to improve persistency: (4) decrease in the first MIM, (5) decrease in the second MIM, and (6) decrease in the fourth MIM. To predict the response to selection, it is necessary to first identify the aspect of the shape with the greatest response to selection (
). The magnitude for each selection differential was chosen arbitrarily as a length of 0.02 Procrustes units; this shape change is within the values of variation observed in the sample, and the resulting response is visible without amplification. All 6 selection regimens corresponded to change the shape of the lactation curve with total milk yield held constant. The selection differentials were simulated as localized shape changes—that is, changes in a single or combined monthly yield of the lactation curve.
For each of the 6 examples, the vector of total response to selection (Δμ) was separated into 2 components: direct and correlated responses. The former corresponded to the direction of the shape feature under the selection gradient, and the latter corresponded to the change in the remaining shape features that were not under direct selection (
). The magnitude of the direct and correlated responses was quantified in units of Procrustes distance. In all other details, the analyses for the 6 selection differentials were conducted as described by
The magnitude of the predicted responses for the 6 selection regimens is presented in Table 1. Magnitude of predicted total responses for all selection criteria was much greater than the selection differential of magnitude 0.02 units of Procrustes distance; however, direct responses were lower than correlated responses. Among the first 3 selection regimens, the magnitude of total predicted response was the highest (0.098) for decrease in third MIM and increase in ninth MIM; the second highest (0.088) was decrease in third MIM, and the lowest (0.051) was increase in ninth MIM. The magnitudes of the predicted responses for the other 3 selection criteria were lower. Of these, the decrease in first MIM (0.055) produced the highest total response to selection, followed by decrease in fourth (0.025) and second (0.023) MIM.
Table 1Magnitude of predicted responses for 6 selections regimens (length unit of Procrustes distance)
The results of the predicted responses to selection depicted as shape changes from the mean shape in the data set are shown in Figure 1 for the first 3 regimens and in Figure 2 for the last 3 regimens. The first column of outlines (lactation shapes) represents the 3 selection differentials related to the measurement of persistency in the Israeli Holstein population, and the second column of outlines shows the result of simulated responses to selection. The total responses in the first 3 selection regimens included bigger changes in other regions of the lactation shape than in the selected month (black outline with solid-circle markers in the second column in Figure 1); changes were actually opposite with respect to the first and third selection differentials for third MIM. The overall patterns of variations of the responses to selections were very similar among the 3 selection regimens. For instance, they all showed the outward shift from the first to third months and the inward move in the sixth and 10th months.
The last 3 selection differentials were also intended to simulate decreases in production in the first, second, and fourth MIM, respectively (Figure 2). These MIM comprised the part of the shape identified with the highest response to selection by the first PC of the GM matrix (
), and they corresponded to the ascending phase of the lactation curve. Compared with the previous 3 patterns of responses to selection, the latter 3 were lower overall in the first 3 MIM and decreased less in the last MIM, demonstrating a much flatter shape and thus improved persistency. Selection differential D produced a response opposite to all the others (e.g., the decrease from first to third MIM and increase in sixth and 10th MIM). These results support the hypothesis that applying selection regimens in different months of lactation produced different responses in the shape of the lactation curve.
The localized shape changes used as selection differentials aimed to simulate selection for improving persistency by modifying shape and keeping constant the total production of the lactation curve. We obtained consistently greater correlated responses than the direct responses for all selection differentials, and the correlated responses constituted most of the total responses. This suggests that selection on localized parts of the shape of the lactation curve will produce correlated responses in other parts. The parts of the shape with greater responses coincide with the parts (beginning and end of lactation) presenting greater variation, as reported by
The pattern of variation reflected in the first 3 responses to selection shows increases in the ascending phase. In contrast, the pattern of variation of the other 3 responses to selection reflects a decrease in the ascending phase. Although the magnitudes of the total responses were greater overall for the first 3 regimens, the last 3 regimens were more effective at producing a flatter shape, and among the 3, targeting a decrease in the first MIM results in the flattest shape (selection differential D of Figure 2).
The combination of the 2 methods implemented in this study allowed the simulation of the response to selection for specific shape changes targeted to improve persistency of the lactation curve in Israeli first-parity Holstein cattle. Correlated responses were greater than direct responses for the 6 selection criteria. The criterion “decrease in the third MIM and increase in the ninth MIM” showed the highest magnitude of the predicted response to selection, and the predicted shape was a scaled version of the mean shape in the data set. The selection criterion “decrease in the first MIM” was effective in producing a flatter shape of the lactation curve.
This research was supported by grant number 58-8042-5-063F from the US-Israel Binational Agricultural Research and Development (BARD) Fund (Rishon LeZion, Israel) and by a grant from the Israel Dairy Board (Yehud, Israel). We thank Ignacy Misztal for use of the Multitrait REML Estimation of Variance Components Program by Canonical Transformation (University of Georgia, Athens) program, and the reviewers for many useful comments.
Genetic evaluation and best prediction of lactation persistency.