Indeed, ASReml uses sparse matrix methods for most of the calculations. This means that it is stored (and used) as a half-diagonal matrix, and only the non-zero values are kept and used for calculations. ASReml-R (and also ASReml-SA) generates the inverse of the A matrix in sparse form. In order to understand this, let’s first see why the old A matrix worked so well. But to my surprise, the analysis often takes hours, or does not work because of insufficient RAM memory.
Typically my analyses consider only two to four thousand genotyped individuals (a much smaller matrix than my old pedigree-based A matrix with half a million genotypes). However, the biggest shock comes once I use this ‘tuned-up’ G matrix in my GBLUP analysis using the library ASReml-R v. But even after I obtain it, I still need to use more tricks (such as blending, or bending) in order to tune-up my G matrix to be invertible and well-conditioned. First, I have to deal with many tricks on pre-processing my molecular data (often SNPs) in order to calculate my G matrix. My first surprise was the level of complexity associated with the generation of the G matrix. So, the process seems simple and straightforward, but it is not! The theory is simple: just replace your numerator relationship matrix A with a genomic-based relationship matrix G and you are now doing what is known as GBLUP. Now with the genomics era here, I have been moving from this pedigree-based animal model to a genomic-based animal model.
Nowadays, this takes even less time, given that computers have more memory and computing power. This, back then, took a few minutes, and I was always excited to see a large file with all the breeding value estimates.
I started in the pre-genomics era and I recall fitting an animal model during my PhD with more than half a million records in my pedigree file without any issues. I have been a user of ASReml-R for more than 10 years.
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