Estimation of individual animal SNP-BLUP reliability using full Monte Carlo sampling.

Calculation of individual animal reliability of estimated genomic breeding value by SNP-BLUP requires inversion of the mixed model equations (MME). When the SNP-BLUP model includes a residual polygenic (RPG) effect, the size of the MME will be at least the number of genotyped animals (n) plus the number of SNP markers (m). Inversion of the MME in SNP-BLUP involves computations proportional to the cube of the MME size; that is, (n + m)3, which can present a considerable computational burden. We introduce a full Monte Carlo (MC) sampling-based method for approximating reliability in the SNP-BLUP model and compare its performance to the genomic BLUP (GBLUP) model. The performance of the full MC approach was evaluated using 2 data sets, including 19,757 and 222,619 genotyped animals selected from populations with 231,186 and 13.35 million pedigree animals, respectively. Genotypes were available in the data sets for 11,729 and 50,240 SNP markers. An advantage of the full MC approximation method was its low computational demand. A drawback was its tendency to overestimate reliability for animals with low reliability, especially when the weight of the RPG effect was high. The overestimation can be lessened by increasing the number of MC samples.

Using Monte Carlo method to include polygenic effects in calculation of SNP-BLUP model reliability.

An SNP-BLUP model is computationally scalable even for large numbers of genotyped animals. When genetic variation cannot be completely captured by SNP markers, a more accurate model is obtained by fitting a residual polygenic effect (RPG) as well. However, inclusion of the RPG effect increases the size of the SNP-BLUP mixed model equations (MME) by the number of genotyped animals. Consequently, the calculation of model reliabilities requiring elements of the inverted MME coefficient matrix becomes more computationally challenging with increasing numbers of genotyped animals. We present a Monte Carlo (MC)-based sampling method to estimate the reliability of the SNP-BLUP model including the RPG effect, where the MME size depends on the number of markers and MC samples. We compared reliabilities calculated using different RPG proportions and different MC sample sizes in analyzing 2 data sets. Data set 1 (data set 2) contained 19,757 (222,619) genotyped animals, with 11,729 (50,240) SNP markers, and 231,186 (13.35 million) pedigree animals. Correlations between the correct and the MC-calculated reliabilities were above 98% even with 5,000 MC samples and an 80% RPG proportion in both data sets. However, more MC samples were needed to achieve a small maximum absolute difference and mean squared error, particularly when the RPG proportion exceeded 20%. The computing time for MC SNP-BLUP was shorter than for GBLUP. In conclusion, the MC-based approach can be an effective strategy for calculating SNP-BLUP model reliability with an RPG effect included.

Genealogical data of Boer and Nubian goats in Mexico.

The pedigree file of the Boer and Nubian goat breeds in Mexico was constructed using the national database provided by the Asociación Mexicana de Criadores de Ganado Caprino de Registro. Field technicians routinely updated the goat national database by recording information from flocks participating in the performance-recording system. Information on animal identification number, parents, birth date, sex, breed, and farm of origin were used to undertake pedigree analyses using the ENDOG program (version 4.8). This paper presents a pedigree data file, tables and figures of characteristics of pedigree data, pedigree analyses, pedigree integrity, effective population size and genetic conservation index. The data can be used to estimate other population parameters, to monitor the genetic diversity of the Boer and Nubian goat breeds in Mexico, and also to design balanced breeding programs, maintaining genetic variation at reasonable levels and maximizing genetic progress in these populations.