The study of relationships between mathematical properties of functions used to model lactation curves is usually limited to the evaluation of the goodness of fit. Problems related to the existence of different lactation curve shapes are usually neglected or solved drastically by considering shapes markedly different from the standard as biologically atypical. A deeper investigation could yield useful indications for developing technical tools aimed at modifying the lactation curve in a desirable fashion. Relationships between mathematical properties and lactation curve shapes were analyzed by fitting several common functions (Wood incomplete gamma, Wilmink's exponential, Ali and Schaeffer's polynomial regression, and fifth-order Legendre polynomials) to 229,518 test-day records belonging to 27,837 lactations of Italian Simmental cows. Among the best fits (adjusted r(2) higher than 0.75), the 3-parameter models (Wood and Wilmink) were able to detect 2 main groups of curve shape: standard and atypical. Five-parameter models (Ali and Schaeffer function and the Legendre polynomials) were able to recognize a larger number of curve shapes. The higher flexibility of 5-parameter models was accompanied by increased sensitivity to local random variation as evidenced by the bias in estimated test-day yields at the beginning and end of lactation (border effect). Meaning of parameters, range of their values and of their (co) variances are clearly different among groups of curves. Our results suggest that analysis based on comparisons between parameter values and (co)variances should be done carefully. Comparisons among parameter values and (co)variances could yield more robust, reliable, and easy to interpret results if performed within groups based on curve shape.

The aim of this study was to investigate the effects of CSN2-CSN3 (beta-kappa-casein) haplotypes and BLG (beta-lactoglobulin) genotypes on milk production traits, content of protein fractions, and detailed protein composition of individual milk of Simmental cows. Content of the major protein fractions was measured by reversed-phase HPLC in individual milk samples of 2,167 cows. Protein composition was measured as percentage of each casein (CN) fraction to total CN and as percentage of beta-lactoglobulin (beta-LG) to total whey protein. Genotypes at CSN2, CSN3, and BLG were ascertained by reversed-phase HPLC, and CSN2-CSN3 haplotype probabilities were estimated for each cow. Traits were analyzed by using a linear model including the fixed effects of herd-test-day, parity, days in milk, and somatic cell score class, linear regressions on haplotype probabilities, class of BLG genotype, and the random effect of the sire of the cow. Effects of haplotypes and BLG genotypes on yields were weak or trivial. Genotype BB at BLG and haplotypes carrying CSN2 B and CSN3 B were associated with increased CN content and CN number. Haplotypes including CSN3 B were associated with increased kappa-CN content and percentage of kappa-CN to total CN and with decreased percentages of alpha(S1)- and gamma-CN to total CN. Allele CSN2 B had the effect of increasing beta-CN content and decreasing content of alpha(S1)-CN. Haplotypes including allele CSN2 A(1) exhibited decreased beta-, alpha(S2)-, and gamma-CN concentrations and increased alpha(S1)- and kappa-CN contents, whereas CSN2 I had positive effects on beta-CN concentration and trivial effects on content of other protein fractions. Effects of haplotypes on CN composition were similar to those exerted on content of CN fractions. Allele BLG A was associated with increased beta-LG concentration and percentage of beta-LG to total whey protein and with decreased content of other milk proteins, namely beta-CN and alpha(S1)-CN. Estimated additive genetic variance for investigated traits ranged from 14 to 39% of total variance. Increasing the frequency of specific genotypes or haplotypes by selective breeding might be an effective way to change milk protein composition.

Multivariate factor analysis and principal component analysis were used to decompose the correlation matrix of test-day milk yields of 48,374 lactations of 21,721 Italian Simmental cows. Two common latent factors related to level of production in early lactation and lactation persistency, and 2 principal components associated with the whole lactation yield and persistency were obtained. Factor and principal component scores were treated as new quantitative phenotypes related to prominent features of lactation curve shape. Genetic parameters were estimated by univariate and bivariate animal models. Estimates of heritability were moderately low for both latent factors (0.13 for persistency and yield early in lactation). Heritabilities of the principal component related to total lactation yield and 305-d yield were similar (0.19 and 0.20, respectively). Finally, heritability was quite low for the principal component related to lactation persistency (0.07). Repeatabilities between lactations were about 0.27 for both latent factors, around 0.4 for the first principal component and 305-d yield, and 0.11 for the second principal component. Moderate genetic correlation among common factors (0.26) and their high genetic correlation with total lactation yield (>0.60) suggest that selection can be used to change the shape of lactation curve as well as improve yield. Scores of the second principal component can be used to genetically improve persistency while maintaining constant total lactation yield.

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.

The aim of this study was to compare the common method of exploiting infrared spectral data in animal breeding; that is, estimating the breeding values for the traits predicted by infrared spectroscopy, and an alternative approach based on the direct use of spectral information (direct prediction, DP) to predict the estimated breeding values (EBV). Traits were pH, milk coagulation properties, contents of the main casein and whey protein fractions, cheese yield measured by micro-cheese making, lactoferrin, Ca, and fat composition. For the DP method, the number of spectral variables was reduced by principal components analysis to 8 latent traits that explained 99% of the original spectral variation. Restricted maximum likelihood was used to estimate variance components of the latent traits. (Co)variance components of the original spectral traits were obtained by back-transformation and EBV of all derived milk traits were then predicted as traits correlated with the genetic information of the spectra. The rank correlation between the EBV obtained for the infrared-predicted traits and those obtained from the DP method was variable across traits. Rank correlations ranged from 0.07 (for the content of saturated fatty acids expressed as g/100 g of fat) to 0.96 (for dry matter cheese yield, %) and, for most traits, was <0.5. This result can be explained by the nature of the principal components analysis: it does not take into account the covariance between the spectral variables and the reference traits but produces latent traits that maximize the spectral variance explained. Thus, the direct approach is more likely to be effective for traits more related to the main sources of spectral variation (i.e., protein and fat). More research is required to study spectral genetic variation and to determine the best way to choose spectral regions and the type and number of considered latent traits for potential applications.