Mathematical methods in the breeding evaluation of small  horned ruminants

Aim. Traditionally, prediction of breeding values of male small horned ruminants   (rams) by referring to levels of economically useful traits of their progeny is carried  out by methods of statistical analysis. However, at the same time, there is a forecasting method based on the use of a mixed biometric model. The solution of the system  of equations constituting a mixed biometric model is associated with certain difficulties caused by the peculiarity of the system matrix. It is proposed to use integrated  mathematical packages in the forecast, by which the system of equations can be  solved in several ways, followed by analysis of the results. The prediction of progeny  values is carried out by statistical methods using three statistical tests, as well as with  the use of a mixed biometric model. It is of interest to compare estimates obtained  by using statistical methods with estimates using a mixed biometric model. 

Material and Methods. The initial data set was the live weight of Qigai rams, the  progeny of a group of sixteen rams belonging to eight genetic groups.   Results. It was found that the forecast of breeding values of each animal using a  mixed biometric model substantially clarifies the rank of each animal in the group  being evaluated.   

Conclusion. The refinement of the estimation of breeding value is related to the  effects of the genetic groups to which the animals belong in the mixed model, as well  as the degree of relationship between them. Also the mixed model also allows one to  isolate environmental effects from the overall assessment. Solving the system of  equations in several ways will improve the reliability of the forecast.

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