بررسی اثر ناسازگاری ماتریس های واریانس- کواریانس در شاخص انتخاب

In selection index procedure, phenotype and genetic (co)variance matrices of traits are used for calculating different genetic parameters like index coefficients, index variance, genetic gain in selection goal and selection accuracy. Sometimes, it is possible that these matrices become inconsistent or they are not positive, nor definite. In the current study, for investigation of the effect of inconsistency of (co)variance matrices on the results of selection index procedure, 6 kinds of different selection indices: milk production (Milk) , fat percentage of milk (fat%) and herd life (HL) in selection goal were constructed The first to third indices included Milk, fat% and one of the type traits, i.e. rear udder height (Ruh), front teat placement (Ftp) or front udder attachment (Fua) respectively, as correlated traits with herd life. The fourth index included productive traits and the three mentioned type traits altogether, and the fifth and sixth indices as reduced indices, included milk production and fat percentage and just milk production, respectively. Also, the results of using mean of 3 individual records were taken into account. All of calculations were done for both consistent and inconsistent matrices. For making consistency in inconsistent matrices, “bending” method was used. Results showed that the use of inconsistent matrices in selection index calculations will lead to wrong selections and will decrease genetic gain. This conclusion was independent of different economic conditions of production system in different years. When using consistent matrices, index 4, that had the most information from selection goal, was the best index.