Imaginings of a Livestock Geneticist
As outlined in the previous pedigree-based algorithm sections (i.e. Recursive Method to Create L), when utilizing a relationship matrix in the mixed model equations, the inverse of the relationship matrix is needed (i.e. G-1 instead of the actual relationship (G). When genomic information was initially utilized in genetic evaluations, the number of animals was small and as a result generating G-1 was not a huge issue, although as the number of genotyped animals continued to increase computational issues started to manifest. Furthermore, the sparseness of A-1 and how you could restart from where you left off previously as new animals are generated was an attractive feature that the majority of programs exploited. As outlined in the previous section describing how to generate different G matrices), the G matrix is dense with all elements being nonzero. Therefore, a methods were developed in order to generate G-1 using recursions (Misztal et al. 2014) which is discussed in the current page or updating G-1 (Meyer et al. 2013) which is discussed in the next section. As a result G-1 can be updated without having to recompute the entire G-1 matrix.
A few major differences exist between recursion based on G versus A and they are outlined below:
As outlined below is a function that takes in as input a genomic relationship matrix utilizing the sequential update algorithm outlined in Misztal et al. (2014).
The following genomic relationship file from Misztal et al. (2014) can be utilized with the R code above. Outlined below is what G-1 looks like at the end of each iteration of the for loop.
