Accuracy of genomic BLUP when considering a genomic relationship matrix based on the number of the largest eigenvalues: a simulation study

Abstract

BackgroundThe dimensionality of genomic information is limited by the number of independent chromosome segments (Me), which is a function of the effective population size. This dimensionality can be determined approximately by singular value decomposition of the gene content matrix, by eigenvalue decomposition of the genomic relationship matrix (GRM), or by the number of core animals in the algorithm for proven and young (APY) that maximizes the accuracy of genomic prediction. In the latter, core animals act as proxies to linear combinations of Me. Field studies indicate that a moderate accuracy of genomic selection is achieved with a small dataset, but that further improvement of the accuracy requires much more data. When only one quarter of the optimal number of core animals are used in the APY algorithm, the accuracy of genomic selection is only slightly below the optimal value. This suggests that genomic selection works on clusters of Me.ResultsThe simulation included datasets with different population sizes and amounts of phenotypic information. Computations were done by genomic best linear unbiased prediction (GBLUP) with selected eigenvalues and corresponding eigenvectors of the GRM set to zero. About four eigenvalues in the GRM explained 10% of the genomic variation, and less than 2% of the total eigenvalues explained 50% of the genomic variation. With limited phenotypic information, the accuracy of GBLUP was close to the peak where most of the smallest eigenvalues were set to zero. With a large amount of phenotypic information, accuracy increased as smaller eigenvalues were added.ConclusionsA small amount of phenotypic data is sufficient to estimate only the effects of the largest eigenvalues and the associated eigenvectors that contain a large fraction of the genomic information, and a very large amount of data is required to estimate the remaining eigenvalues that account for a limited amount of genomic information. Core animals in the APY algorithm act as proxies of almost the same number of eigenvalues. By using an eigenvalues-based approach, it was possible to explain why the moderate accuracy of genomic selection based on small datasets only increases slowly as more data are added.

Changes in genomic predictions when new information is added

“…The stability of genomic evaluations depends on the amount of data and population parameters, provided that no changes are made to the model. When the data are large enough to estimate the value of nearly all independent chromosome segments, the accuracy of genomic predictions will be high ( Pocrnic et al, 2019 ); hence, their persistency and stability will also be high. Independent chromosome segments are DNA regions that are inherited together in linked blocks ( Stam, 1980 ) that are also called linkage disequilibrium blocks ( Muir, 2007 ).…”

“…The number of independent chromosome segments corresponds to the number of core animals in the algorithm for proven and young ( APY ; Misztal et al, 2014a ; Pocrnic et al, 2016b ). Pocrnic et al (2019) reported that accuracies were marginally smaller when using 25% instead of 100% of the optimal number of core animals in APY, suggesting that genomic selection acts on clusters of independent chromosome segments rather than on individual independent chromosome segments. In the same study, the authors also showed that a small amount of phenotypic data allowed only the estimation of the largest clusters (i.e., eigenvalues), and that the four largest clusters explained 10% of the variation in G .…”

Single-Step Genomic Evaluations from Theory to Practice: Using SNP Chips and Sequence Data in BLUPF90

“…When a large amount of information is available, the accuracy may be high enough; therefore, improvements from the incorporation of causative variants are likely to be small for large data sets. When the number of genotyped animals is larger than the number of independent chromosome segments, the accuracy is maximized without SNP weighting/selection [ 70 , 71 , 72 ].…”

Determining the stability of accuracy of genomic estimated breeding values in future generations in commercial pig populations

“…Although accuracy is dependent on the proportion of variance explained by the eigenvalues of the GRM, the distribution of eigenvalues is not consistent, and a small percentage of the largest eigenvalues explain the majority of the genetic variation ( Pocrnic et al, 2019 ). Additionally, the animals necessary to explain the largest eigenvalues carry almost the same genomic information.…”

“…Additionally, the animals necessary to explain the largest eigenvalues carry almost the same genomic information. Hence, selection by GBLUP-based models occurs on clusters of independent chromosome segments, not individual chromosome segments ( Pocrnic et al, 2019 ). In pig populations, the segments can be well estimated if there are around 5,000 animals available with very high accuracy (e.g., theoretical EBV accuracy based on prediction error variance) or an equivalent number of animals with less accuracy.…”