Dimensionality of Genomic Information in Cattle and Other Species

The dimensionality of the additive information in SNP information can be defined as 1) the number of causative SNP if all causative SNP are identified, 2) the number of effective SNP if only generic SNP are available, 3) the number of independent chromosome segments. Measures 2) and 3) are due to large LD blocks and may be identical, with 3) being a linear function of the effective population size.  In practice, the number of effective SNP can be computed from eigenvalue decomposition of SNP BLUP matrix or the genomic relationship matrix when both the number of genotyped individuals and SNP markers are large enough. In particular, with SNP50k, that dimensionality approximately corresponds to the number of the largest eigenvalues explaining about 98% of the matrix variation, with the reminder 2% attributed to noise; the fraction due to noise decreases with more SNP and increases with less SNP quality control.  Analyses with large number of genotypes indicate approximately 10k effective SNP in Holstein and Angus, about 4k in commercial pigs, and about 3k in commercial broilers. Small number of effective SNP limit the resolution of GWAS but allow for GBLUP based genomic predictions with arbitrary number of animals at a small cost.