Using geometric morphometrics for the genetics analysis of shape and size of lactation curves in Israeli first-parity Holstein cattle

Abstract

Our objective was to combine the methods of geometric morphometrics and multivariate quantitative genetics to genetic evaluation of the size and shape of lactation curves of milk of 3,492 Israeli first-parity Holstein cattle. Lactation records were treated as morphological data, for which 2 different lactation shape functions were evaluated, one depicted by a line graph and the other by an orbital graph. The lactation curves from both shape functions were represented by 2-dimensional Cartesian landmark coordinates. The 2 sets of landmarks were then analyzed individually for each shape function with geometric morphometrics to separate variation into components of size and shape. The analysis yielded 2 size measures and 2 sets of shape variables, and they were the inputs to estimate variance components using the MTC REML individual animal model program. Variance components were also estimated for the 305-d lactation production as a reference. Shape variables showed negligible correlation with 305-d production, providing evidence of size and shape of lactation curve as separate characters. The size measure derived from the orbital-depicted lactation curve had equal heritability (0.39 ± 0.01; ± standard error) and complete genetic and environmental correlations with 305-d production, whereas the size measure derived from the line-depicted lactation curve showed low heritability (0.09 ± 0.01) and environmental correlation (0.02 ± 0.004) and relative high genetic correlation with 305-d production (0.48 ± 0.04). This may validate both the orbital graph to depict lactation records and the use of geometric morphometrics to split variation of lactation curve into size and shape components. The maximal heritability for shape of lactation curve was 0.55 for orbital-and 0.56 for line-depicted lactation curves. The respective patterns of variations were visualized as shape changes from the mean shape in the data set. Geometric morphometrics are well grounded within the theory of shape analysis and can be paired with conventional methods in the field to characterize the patterns of phenotypic and genetic variation of shape and size of lactation curve in dairy cattle.

Short communication: Selection for persistency by changing the shape of lactation curves with geometric morphometrics

“…Angel-Amed Durón-Benítez, 1 * Joel Ira Weller, 1 † and Ephraim Ezra 2 metric 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 Durón-Benítez et al, 2018a). Using the GP matrix, the response to selection of shape can be predicted with the multivariate breeders' equation as implemented by Klingenberg and Leamy (2001).…”

“…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 (Durón-Benítez et al, 2018a). The G and P matrices correspond to the shape of the lactation curve as depicted by orbital graphs.…”

“…They used the multivariate version of the breeders' equation Δμ = GP −1 s (Lande, 1979), 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 (Durón-Benítez et al, 2018a).…”

“…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 (Klingenberg and Leamy, 2001); for lactation curve shape, the last 3 MIM were previously identified with the maximal response to selection from the GP matrix (Figure 3 in Durón-Benítez et al, 2018a). 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.…”

“…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 (Durón-Benítez et al, 2018a), 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.…”