Background: Mathematical models are needed for the design of breeding programs using genomic prediction. While deterministic models for selection on pedigree-based estimates of breeding values (PEBV) are available, these have not been fully developed for genomic selection, with a key missing component being the accuracy of genomic EBV (GEBV) of selection candidates. Here, a deterministic method was developed to predict this accuracy within a closed breeding population based on the accuracy of GEBV and PEBV in the reference population and the distance of selection candidates from their closest ancestors in the reference population.
Methods: The accuracy of GEBV was modeled as a combination of the accuracy of PEBV and of EBV based on genomic relationships deviated from pedigree (DEBV). Loss of the accuracy of DEBV from the reference to the target population was modeled based on the effective number of independent chromosome segments in the reference population (Me). Measures of Me derived from the inverse of the variance of relationships and from the accuracies of GEBV and PEBV in the reference population, derived using either a Fisher information or a selection index approach, were compared by simulation.
Results: Using simulation, both the Fisher and the selection index approach correctly predicted accuracy in the target population over time, both with and without selection. The index approach, however, resulted in estimates of Me that were less affected by heritability, reference size, and selection, and which are, therefore, more appropriate as a population parameter. The variance of relationships underpredicted Me and was greatly affected by selection. A leave-one-out cross-validation approach was proposed to estimate required accuracies of EBV in the reference population. Aspects of the methods were validated using real data.
Conclusions: A deterministic method was developed to predict the accuracy of GEBV in selection candidates in a closed breeding population. The population parameter Me that is required for these predictions can be derived from an available reference data set, and applied to other reference data sets and traits for that population. This method can be used to evaluate the benefit of genomic prediction and to optimize genomic selection breeding programs.