%0 Journal Article
%T Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse
%A Takuro Oikawa
%A Kazuhiro Yasuda
%J Genetics Selection Evolution
%D 2009
%I BioMed Central
%R 10.1186/1297-9686-41-25
%X Cloning animals is regarded as a means to multiply genetically identical animals (GIAs). In Japan, clones of bulls are routinely produced to test bulls' performance and in some cases to multiply fattening animals. A survey conducted by the Japanese Ministry of Agriculture, Forestry and Fisheries, and published on October 31, 2007, has recorded calves cloned from somatic cells of 535 animals and from embryonic cell nuclei of 716 animals.In animal breeding, analysis of quantitative traits using a mixed model is essential to predict the breeding value of an individual and to estimate the genetic parameters of the traits. When applying an animal model to perform the genetic analysis, it is necessary to include the inverse of the numerator relationship matrix (NRM) in order to connect all the animals included in the mixed model; however, calculating the inverse of a large NRM requires exceptionally large computing power. On the one hand, Henderson [1] has developed a method of calculating directly A-1, without calculating the A matrix itself in a non-inbred population. This innovation has made it possible to use a model in which the data set includes a large number of animals. On the other hand, Quaas [2] has extended the method for the application to inbred populations by including the inbreeding coefficients in the model. A faster computing method of inbreeding coefficients has been developed by Tier [3] and Meuwissen and Luo [4], where inbreeding coefficients are computed as a subset of the A matrix. In addidion, Famula [5] has proposed a simplified algorithm for inbred populations, incorporating parental uncertainty to the model.Inclusion of GIAs in the model raises the problem of a singular A matrix because of perfect additive genetic relationships between pairs of GIAs. In the case of an analysis with a singular A, Henderson [6] presented a method to solve a mixed model without inversion of the G matrix, where G = A     ¦Ò a 2    MathType@MTEF@5@5@+=feaagaart1ev2aaa
%U http://www.gsejournal.org/content/41/1/25