Dimensionality of genomic information and performance of the Algorithm for Proven and Young for different livestock species

Abstract

BackgroundA genomic relationship matrix (GRM) can be inverted efficiently with the Algorithm for Proven and Young (APY) through recursion on a small number of core animals. The number of core animals is theoretically linked to effective population size (N e). In a simulation study, the optimal number of core animals was equal to the number of largest eigenvalues of GRM that explained 98% of its variation. The purpose of this study was to find the optimal number of core animals and estimate N e for different species.MethodsDatasets included phenotypes, pedigrees, and genotypes for populations of Holstein, Jersey, and Angus cattle, pigs, and broiler chickens. The number of genotyped animals varied from 15,000 for broiler chickens to 77,000 for Holsteins, and the number of single-nucleotide polymorphisms used for genomic prediction varied from 37,000 to 61,000. Eigenvalue decomposition of the GRM for each population determined numbers of largest eigenvalues corresponding to 90, 95, 98, and 99% of variation.ResultsThe number of eigenvalues corresponding to 90% (98%) of variation was 4527 (14,026) for Holstein, 3325 (11,500) for Jersey, 3654 (10,605) for Angus, 1239 (4103) for pig, and 1655 (4171) for broiler chicken. Each trait in each species was analyzed using the APY inverse of the GRM with randomly selected core animals, and their number was equal to the number of largest eigenvalues. Realized accuracies peaked with the number of core animals corresponding to 98% of variation for Holstein and Jersey and closer to 99% for other breed/species. N e was estimated based on comparisons of eigenvalue decomposition in a simulation study. Assuming a genome length of 30 Morgan, N e was equal to 149 for Holsteins, 101 for Jerseys, 113 for Angus, 32 for pigs, and 44 for broilers.ConclusionsEigenvalue profiles of GRM for common species are similar to those in simulation studies although they are affected by number of genotyped animals and genotyping quality. For all investigated species, the APY required less than 15,000 core animals. Realized accuracies were equal or greater with the APY inverse than with regular inversion. Eigenvalue analysis of GRM can provide a realistic estimate of N e.

208 Crossbred evaluations using single-step genomic BLUP and algorithm for proven and young with different sources of data

“…This was successfully demonstrated for several purebred Table 4. Regression coefficients (b1) of adjusted phenotypes on genomic EBV, for different groups of validation animals (purebred animals L1 and L2, and their crosses C) with a different source of phenotypes available, shown for traits 1 (T1) and 2 (T2), under the first model (M1; 2-trait animal model without the distinction between the lines) and second model (M2; when that trait was separated into 3 traits based on the line of the animals) populations in different species (e.g., Pocrnic et al, 2016b); however, the application of this concept for crossbred/multibreed contexts was unclear. Bradford et al (2017) found, by simulating a purebred population, that any core definition is robust in populations with complete pedigree; otherwise, selecting core animals randomly across multiple generations gives desirable accuracies.…”

“…Me seems to be the key parameter of the algorithm for proven and young (APY) (Misztal et al, 2014), which reduces the computational cost of the inversion of genomic relationship matrix (G) by shrinking the dimensionality of genomic information (Misztal, 2016). For large populations, such dimensionality was close to 4NeL and corresponded to the number of eigenvalues explaining 98% variability of G (Pocrnic et al, 2016a(Pocrnic et al, , 2016b. The same study showed that Me varies from about 4k for pigs and chickens to over 10k for cattle.…”

Predicting the effect of reference population on the accuracy of within, across, and multibreed genomic prediction

“…Misztal (2016) and Pocrnic et al (2016a,b) propose that the number of animals required to explain almost all GRM variance equals M e and can be estimated as the number of largest Eigen values explaining nearly all variance. Pocrnic et al (2016b) applied this to Holstein and Jersey cattle populations, where they required more than 10,000 Eigen values to explain 98% of the variance. This number was substantially larger than values for M e obtained in our study by either the GRM or cross-validation and would have resulted in an underestimation of the prediction accuracy.…”

Genomic Predictions for Muscle Yield and Fillet Firmness in Rainbow Trout using Reduced-Density SNP Panels

“…An average Ne of 145 was reported in the early generations of the NCCCWA rainbow trout selective breeding program and was expected to decline with selection [45]. The estimated Ne in this population is comparable to that estimated in other livestock species; Jersey cattle (Ne = 101), Angus cattle (Ne = 113), Holstein cattle (Ne = 149) [46] and a commercial rainbow trout population (Ne = 155) [24], and it is considerably larger than the Ne estimated for cat sh (Ne = 27) [22], swine (Ne = 32), and chicken (Ne = 44) [46]. Chromosome 22 had the largest effective population size (Ne = 180) followed by chromosome 24 (Ne = 171).…”