A Multivariate Approach to Modeling Shapes of Individual Lactation Curves in Cattle

Abstract

Milk test-day records of 5728 lactations of Italian Simmental cows were analyzed with multivariate factor analysis in order to extract 2 common factors, whose scores were used as quantitative measures of 2 main features of lactation curve shape-i.e., the increasing rate of yield in the first part of lactation and the rate of decline of milk yield after the lactation peak. The 2 indices, objectively derived from the correlation matrix of original test-day records, showed a high discriminant power in separating lactation curves with different shapes. The weak correlation between the 2 factors (0.11), together with the high correlation of factors and the total 305-d yield (about 0.70), suggests that an increase in lactation yield could be achieved by acting only on one of the 2 factors related to lactation-curve shape, with the other kept constant at a medium or low value. The suitability of the 2 factors as descriptors of lactation patterns has been confirmed by the relationships found between factor scores and the main environmental effects known to affect the shape of the lactation curve, such as parity and season of calving.

Factor analysis for genetic evaluation of linear type traits in dual-purpose autochthonous breeds

“…Consequently, considering that genetic correlation in a selected population is mainly due to the pleiotropic effects of genes, that is, the involvement of the same genes in the expression of two or more traits, the factor score could become a useful method of removing redundancies among traits of interest for animal selection (Crawford and DeFries, 1978). This is particularly interesting when a biological significance could be attributable to single factors on the basis of the loading coefficients of the single factorized traits (Macciotta et al, 2004 and2012).…”

“…milk composition and coagulation properties, lactation curve; Macciotta et al, 2004 and2012). Often these traits require different models, are difficult to estimate, and the reduction in factors is a effective strategy to simplify the genetic analysis (Macciotta et al, 2012).…”

“…Factor analysis was then computed separately for the two breeds using the raw data (Chu and Shi, 2002 FACTOR Procedure;SAS Institute Inc., 2009). The varimax rotation as described by Kaiser (1958) was carried out to obtain latent factors that accounted only for the traits with large absolute value of loadings (Ali et al, 1998, Macciotta et al, 2004and 2012. The varimax rotation method was chosen in order to obtain orthogonal loading coefficients that maximize the variance of the loadings, that is, to maximize independencies among factors (Kaiser, 1958).…”

“…Ali et al (1998) presented four reasons for which applying factor analysis to type trait data is considered to be an important innovation: (1) summarizing information from the observed type traits into a few unobserved and relatively uncorrelated derived factors; (2) partitioning each trait response into a covariant and a specific part the variance of each component can be estimated; (3) grouping type traits such that correlated traits could be isolated in the same factor and each factor will include traits with common biological and/or physiological characters; (4) the magnitude of each loading in the factor pattern reflects the importance of each type trait within the derived factor. Previously, factor analysis was applied in scientific disciplines during most of the 20th century, like in socio-biology (Crawford and DeFries, 1978;Crawford and Anderson, 1989) and it has been also used in animal sciences to find indicators of management and production levels for dairy cattle herds (Enevoldsen et al, 1996), to evaluate relationships between longevity and type traits (Vukasinovic et al, 1997), to model the shape of the lactation curve (Macciotta et al, 2004), and to study the structure of relationships between milk yield, milk composition and milk coagulation properties (Macciotta et al, 2012). Applications in animal and veterinary science, however, are scant and in most of cases outdated, but these and other examples confirm the usefulness of the analytical approach (Sieber et al, 1988).…”

Fitting lactation curves in a Colombian Holstein herd using nonlinear models

“…The trends observed in first calving cows, with lower total and peak milk production, an increase in peak time and greater persistence, could be explained, according to Dijkstra et al (1997), for the lower rate of proliferation of mammary secretory cells in primiparous, which can affect the speed to reach the peak, and, according to Stanton et al (1992), counteract the normal decline of the lactation curve, generating greater persistence. In addition, the greatest productive increase between the first and the second may (2004,2011). Differences between calving seasons evidenced a small but significant increase (P<0.05) in MY305d and PP traits for cows calving during the rainy season, and this peak of production was obtained earlier during the lactation period (Table 3).…”