A method to approximate the inverse of a part of the additive relationship matrix

Variance estimates are similar using pedigree or genomic relationships with or without the use of metafounders or the algorithm for proven and young animals1

With an increase in the number of animals genotyped there has been a shift from using pedigree relationship matrices (A) to genomic ones. As the use of genomic relationship matrices (G) has increased, new methods to build or approximate G have developed. We investigated whether the way variance components are estimated should reflect these changes. We estimated variance components for maternal sow traits by solving with restricted maximum likelihood, with four methods of calculating the inverse of the relationship matrix. These methods included using just the inverse of A (A−1), combining A−1 and the direct inverse of G (HDIRECT−1), including metafounders (HMETA−1), or combining A−1 with an approximated inverse of G using the algorithm for proven and young animals (HAPY−1). There was a tendency for higher additive genetic variances and lower permanent environmental variances estimated with A−1 compared with the three H−1 methods, which supports that G−1 is better than A−1 at separating genetic and permanent environmental components, due to a better definition of the actual relationships between animals. There were limited or no differences in variance estimates between HDIRECT−1, HMETA−1, and HAPY−1. Importantly, there was limited differences in variance components, repeatability or heritability estimates between methods. Heritabilities ranged between <0.01 to 0.04 for stayability after second cycle, and farrowing rate, between 0.08 and 0.15 for litter weight variation, maximum cycle number, total number born, total number still born, and prolonged interval between weaning and first insemination, and between 0.39 and 0.44 for litter birth weight and gestation length. The limited differences in heritabilities suggest that there would be very limited changes to estimated breeding values or ranking of animals across models using the different sets of variance components. It is suggested that variance estimates continue to be made using A−1, however including G−1 is possibly more appropriate if refining the model, for traits that fit a permanent environmental effect.

Sparse single-step method for genomic evaluation in pigs

Background

In many animal breeding programs, with the increasing number of genotyped animals, estimation of genomic breeding values by the single-step method is becoming limited by excessive computing requirements. A recently proposed algorithm for proven and young animals (APY) is an approximation that reduces computing time drastically by dividing genotyped animals into core and non-core animals, with only computations for core animals being time-consuming. We hypothesized that choosing core animals based on representing all generations, minimizing the relatedness within the core group, or maximizing the number of genotyped offspring, would result in greater accuracies of estimated breeding values (EBV).

Methods

We compared eight different core groups for the three pig breeds DanAvl Duroc, DanAvl Landrace and DanAvl Yorkshire. These eight sparse approximations of the single-step method were evaluated based on correlations of EBV for genotyped animals obtained from the sparse methods with those obtained from the usual version of the single-step method. We used a single-trait model with daily gain as trait.

Results

For core groups that distributed animals across generations, correlations for genotyped animals (from 0.977 to 0.989) were higher than for those that did not distribute core animals across generations (from 0.934 to 0.956). For core groups that maximized the number of genotyped offspring, correlations for genotyped animals (from 0.983 to 0.989) were higher than for other core groups (from 0.934 to 0.981). There was no clear association between low relatedness within the core group and accuracy of approximations.

Conclusions

We found that for core groups that represent all generations and that maximize the number of genotyped offspring, accurate approximations of EBV were obtained. However, we did not find a clear association between accuracy and relatedness within the core group. For the APY method, this is the first study that reports systematic criteria for the creation of core groups that result in more accurate EBV than a similar-sized random core group. Random core groups only ensure across-generation representation. Therefore, we recommend choosing a core group that represents all generations and that maximizes the number of genotyped offspring for single-step genomic evaluation using the APY method.