Increased inbreeding is an inevitable consequence of selection in livestock populations. The analysis of high-density single nucleotide polymorphisms (SNPs) facilitates the identification of long and uninterrupted runs of homozygosity (ROH) that can be used to identify chromosomal regions that are identical by descent. In this work, the distribution of ROH of different lengths in five Italian cattle breeds is described. A total of 4095 bulls from five cattle breeds (2093 Italian Holstein, 749 Italian Brown, 364 Piedmontese, 410 Marchigiana and 479 Italian Simmental) were genotyped at 54K SNP loci. ROH were identified and used to estimate molecular inbreeding coefficients (FROH ), which were compared with inbreeding coefficients estimated from pedigree information (FPED ) and using the genomic relationship matrix (FGRM ). The average number of ROH per animal ranged from 54 ± 7.2 in Piedmontese to 94.6 ± 11.6 in Italian Brown. The highest number of short ROH (related to ancient consanguinity) was found in Piedmontese, followed by Simmental. The Italian Brown and Holstein had a higher proportion of longer ROH distributed across the whole genome, revealing recent inbreeding. The FPED were moderately correlated with FROH > 1 Mb (0.662, 0.700 and 0.669 in Italian Brown, Italian Holstein and Italian Simmental respectively) but poorly correlated with FGRM (0.134, 0.128 and 0.448 for Italian Brown, Italian Holstein and Italian Simmental respectively). The inclusion of ROH > 8 Mb in the inbreeding calculation improved the correlation of FROH with FPED and FGRM . ROH are a direct measure of autozygosity at the DNA level and can overcome approximations and errors resulting from incomplete pedigree data. In populations with high linkage disequilibrium (LD) and recent inbreeding (e.g. Italian Holstein and Italian Brown), a medium-density marker panel, such as the one used here, may provide a good estimate of inbreeding. However, in populations with low LD and ancient inbreeding, marker density would have to be increased to identify short ROH that are identical by descent more precisely.

This review gives an overview of the mathematical modelling of lactation curves in dairy cattle. Over the last ninety years, the development of this field of study has followed the main requirements of the dairy cattle industry. Non-linear parametric functions have represented the preferred tools for modelling average curves of homogeneous groups of animals, with the main aim of predicting yields for management purposes. The increased availability of records per individual lactations and the genetic evaluation based on test day records has shifted the interest of modellers towards more flexible and general linear functions, as polynomials or splines. Thus the main interest of modelling is no longer the reconstruction of the general pattern of the phenomenon but the fitting of individual deviations from an average curve. Other specific approaches based on the modelling of the correlation structure of test day records within lactation, such as mixed linear models or principal component analysis, have been used to test the statistical significance of fixed effects in dairy experiments or to create new variables expressing main lactation curve traits. The adequacy of a model is not an absolute requisite, because it has to be assessed according to the specific purpose it is used for. Occurrence of extended lactations and of new productive and functional traits to be described and the increase of records coming from automatic milking systems likely will represent some of the future challenges for the mathematical modelling of the lactation curve in dairy cattle

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Selection is the major force affecting local levels of genetic variation in species. The availability of dense marker maps offers new opportunities for a detailed understanding of genetic diversity distribution across the animal genome. Over the last 50 years, cattle breeds have been subjected to intense artificial selection. Consequently, regions controlling traits of economic importance are expected to exhibit selection signatures. The fixation index (Fst ) is an estimate of population differentiation, based on genetic polymorphism data, and it is calculated using the relationship between inbreeding and heterozygosity. In the present study, locally weighted scatterplot smoothing (LOWESS) regression and a control chart approach were used to investigate selection signatures in two cattle breeds with different production aptitudes (dairy and beef). Fst was calculated for 42 514 SNP marker loci distributed across the genome in 749 Italian Brown and 364 Piedmontese bulls. The statistical significance of Fst values was assessed using a control chart. The LOWESS technique was efficient in removing noise from the raw data and was able to highlight selection signatures in chromosomes known to harbour genes affecting dairy and beef traits. Examples include the peaks detected for BTA2 in the region where the myostatin gene is located and for BTA6 in the region harbouring the ABCG2 locus. Moreover, several loci not previously reported in cattle studies were detected.

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