Using eigenvalues as variance priors in the prediction of genomic breeding values by principal component analysis.

Genome-wide selection aims to predict genetic merit of individuals by estimating the effect of chromosome segments on phenotypes using dense single nucleotide polymorphism (SNP) marker maps. In the present paper, principal component analysis was used to reduce the number of predictors in the estimation of genomic breeding values for a simulated population. Principal component extraction was carried out either using all markers available or separately for each chromosome. Priors of predictor variance were based on their contribution to the total SNP correlation structure. The principal component approach yielded the same accuracy of predicted genomic breeding values obtained with the regression using SNP genotypes directly, with a reduction in the number of predictors of about 96% and computation time of 99%. Although these accuracies are lower than those currently achieved with Bayesian methods, at least for simulated data, the improved calculation speed together with the possibility of extracting principal components directly on individual chromosomes may represent an interesting option for predicting genomic breeding values in real data with a large number of SNP. The use of phenotypes as dependent variable instead of conventional breeding values resulted in more reliable estimates, thus supporting the current strategies adopted in research programs of genomic selection in livestock.

Use of multivariate analysis to extract latent variables related to level of production and lactation persistency in dairy cattle.

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.

Detection of different shapes of lactation curve for milk yield in dairy cattle by empirical mathematical models.

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.

A multivariate approach to modeling shapes of individual lactation curves in cattle.

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.

Excretion of aflatoxin M1 in milk of dairy ewes treated with different doses of aflatoxin B1.

Two experiments were conducted to study the amount of aflatoxin M1 (AFM1) in milk in response to feeding aflatoxin B1 (AFB1). In experiment 1, four dairy ewes in early lactation received a single dose of pure AFB1 (2 mg). Individual milk samples were collected during the following 5 d to measure AFM1 concentration. The average excretion of AFM1 in milk followed an exponential decreasing pattern, with two intermediate peaks at 24 and 48 h. No AFM1 was detected in milk at 96 h after dosing. The mean rate of transfer of AFB1 into AFM1 in milk was 0.032%, with a high individual variability (SD = 0.017%). In experiment 2, 16 dairy ewes in midlactation were divided into four groups that received different daily doses of AFB1 (0, 32, 64, and 128 microgram for control and groups T1, T2, and T3, respectively) for 14 d. Pure AFB1 was administered to each animal divided in two daily doses. Individual milk samples were collected at 12, 24, 36, 48, 72, 96, 144, 216, and 312 h after the first AFB1 administration, during the intoxication period, and every 24 h for 7 d after the withdrawal of AFB1. AFM1 was detected in the milk of all animals of the treated groups at 12 h after the administration of AFB1. In all treated groups, milk AFM1 concentration increased from 12 to 144 h after the beginning of administration. It then decreased, reaching a stable concentration at 216 and 312 h after the first administration. No AFM1 was detected in milk 3 d after the last administration of AFB1. Milk AFM1 concentration measured at steady-state condition was significantly affected by the AFB1 dose (0.031, 0.095, and 0.166 in T1, T2, and T3 groups, respectively), with a linear relationship between AFB1 dose and milk AFM1 concentration (R2 = 77.2%). The carryover (AFM1/AFB1 ratio) was not significantly affected by treatment, and its mean value was 0.112% (SE = 0.011). The carryover was lower than that reported for dairy cattle and goats, suggesting a better ability of sheep to degrade AFB1.

Effects of age and calving season on lactation curves of milk production traits in Italian water buffaloes.

Test day (TD) records of milk production traits (milk yield, fat, and protein percentages) of 534 Italian buffalo cows were analyzed with a mixed linear model in order to estimate lactation curves pertaining to different ages at calving and different seasons of calving. Milk yield lactation curves of younger animals were lower than those of older animals until 20 wk from parturition. No effect of age at calving could be observed for fat and protein percentages. Season of calving affected milk yield only in the first phase of lactation, with the lowest production levels for summer calvings; no effect could be observed on fat and protein contents. Average correlations among TD measures within lactation were 0.59, 0.31, and 0.36 for milk yield, fat, and protein percentages, respectively. Five standard linear functions of time were able to reconstruct the average lactation curves. Goodness of fit was satisfactory for all models considered, although only the five-parameter model was flexible enough to fit all the three traits considered with excellent results.

Empirical and mechanistic mathematical models of temporal evolution of milk production in ruminants.

In the various sectors of animal science there has been little exploration of the theoretical mathematical aspects of data analysis and modelling. The dominant statistical methods used for the analysis of experimental data are rarely valuable for developing a deeper understanding of the problem. In addition they do not take account of the evolution over time of those variables of major interest to be studied. Only recently have more sophisticated methods of mathematical modelling begun to be used. Nonetheless attention tends to be focused exclusively on empirical models. Mathematical models with greater explanatory power, in particular those which use differential equations, are as yet little used. This work develops a mathematical approach to a problem that is of great interest in animal science: the development over time of milk production in economically important ruminant species.

Time series autoregressive integrated moving average modeling of test-day milk yields of dairy ewes.

Monthly test-day milk yields of 1200 dairy Sarda ewes were analyzed by time-series methods. Autocorrelation functions were calculated for lactations within parity classes and altitude of location of flocks. Spectral analysis of the successions of data was developed by Fourier transformation, and different Box-Jenkins autoregressive integrated moving average models were fitted. The separation of deterministic and stochastic components highlighted the autoregressive feature of milk production pattern. The forecasting power of autoregressive integrated moving average models was tested by predicting total milk production for a standardized lactation length of 225 d from only a few test-day records. Results indicated a greater forecasting capacity in comparison with standard methods and suggested further development of time-series analysis for studying lactation curves with more sophisticated methods, such as wavelet decomposition and neural network models.

Analysis of environmental effects on test day milk yields of Sarda dairy ewes.

Temporal evolution of Sarda ewes milk production was analyzed with mixed linear models and factor analysis to investigate environmental effects on the shape of lactation curves and on milk yields during different lactation stages. Parity, year of production, level of altitude, and flock within altitude affected milk yield, whereas the effect of type of lambing was not significant. Lactation curves pertaining to the three altitudes were clearly different. Factor analysis suggested an independence among yields recorded during different phases of lactation and a specific behavior of (co)variances structure among test day yields obtained in mountains compared with hills and plains.

Enzymes (isoenzyme system) as homeostatic mechanisms the isoenzyme (ADA2) of adenosine deaminase of human monocytes-macrophages as a regulator of the 2'deoxyadenosine.

Regarding homeostatic mechanisms in the enzyme (isoenzymes) and substrate system we show through a simulation model obtained by STELLA II software that: (i) a pair of isoenzymes (Is1 and Is2) that have different affinity for the substrate (Is2 affinity < Is1 affinity), can constitute an efficient homeostatic mechanism: by varying the relative concentration of the isoenzymes in the system, the levels of the substrate can be controlled; (ii) the isoenzymes ADA1 and ADA2 of adenosine deaminase (ADA) that have different affinity for the substrate 2'deoxyadenosine (ADA2 has very weak affinity for 2'deoxyadenosine) constitute, inside human Monocytes-Macrophages, a homeostatic mechanism that assures an up-regulation of 2'deoxyadenosine and a down-regulation of a second substrate (adenosine) for which the affinity of the two isoenzymes is similar.

Lactation curves of Valle del Belice dairy ewes for yields of milk, fat, and protein estimated with test day models.

Test day models were used to estimate the lactation curves for Valle del Belice ewes and to study the main environmental effects on milk yield and on percentage of fat and protein. Environmental effects were treated as fixed. A random effect was associated with each lactation to evaluate the mean correlation among all test day records of an individual ewe. Lactation curves were constructed by adding solutions for classes of either days in milk nested within parity or days in milk nested within season of lambing to appropriate general means. Parity primarily affected the lactation curve for milk yield, which was lower and flatter for first lambing ewes; effects on fat and protein were smaller. Season of lambing affected all traits. Seasonal productivity had the greatest effect on milk composition, resulting in an imbalance between fat and protein percentages. Flock and feed supplementation affected only the lactation curve for milk yield. The lactation curve of Valle del Belice ewes stood at a relatively high level. However, the presence of notable, perturbative effects (environmental and random variation) on milk yield and composition suggests that management is unable to meet the requirements of ewes consistently.

Morphometric analysis of Sardinian breed donkeys.

The main somatometric characteristics of 15 Sardinian breed adult donkeys (6 male and 9 female) were studied. Analysis of the somatic measurements and zoometric indexes show subjects of small build of a mesomorph constitutional type. Dimorphism between the sexes is slight and is limited to the rump area. The number of donkeys still to be found in Sardinia is greatly reduced and urgent measures are needed to safeguard its animal genetic resource.

Morphology of adult white donkeys of Asinara.

The phenotype of the Asinara white donkey has the following somatic characteristics: white coat, pink skin and glabrous areas, straight profile, body not very rounded on account of relatively slight muscular development, large head, eyes with irises of a pink-blue colour, short thin neck, not very pronounced withers, straight, average length dorsolumbar region, prominent angular rump higher than the withers, short chest, wide hind quarters, well developed abdomen, short sturdy limbs, light-coloured hooves. The somatometric measurements and the zoometric indexes show small-sized subjects with a hardy bone structure, of compact build with morphological homogeneity between the sexes. The donkeys are of the mesomorph type, more developed lengthwise than in height.