Prediction of additive genetic variances of descendants for complex families based on Mendelian sampling variances

The ability to predict the outcome of selection and mating decisions enables breeders to make strategically better selection decisions. To improve genetic progress, those individuals need to be selected whose offspring can be expected to show high genetic variance next to high breeding values. Previously published approaches enable to predict the variance of descendants of 2 future generations for up to 4 founding haplotypes, or 2 outbred individuals, based on phased genotypes, allele effects, and recombination frequencies. The purpose of this study was to develop a general approach for the analytical calculation of the genetic variance in any future generation. The core development is an equation for the prediction of the variance of double haploid lines, under the assumption of no selection and negligible drift, stemming from an arbitrary number of founder haplotypes. This double haploid variance can be decomposed into gametic Mendelian sampling variances (MSVs) of ancestors of the double haploid lines allowing usage for non-double haploid genotypes that enables application in animal breeding programs as well as in plant breeding programs. Together with the breeding values of the founders, the gametic MSV may be used in new selection criteria. We present our idea of such a criterion that describes the genetic level of selected individuals in 4 generations. Since breeding programs do select, the assumption made for predicting variances is clearly violated, which decreases the accuracy of predicted gametic MSV caused by changes in allele frequency and linkage disequilibrium. Despite violating the assumption, we found high predictive correlations of our criterion to the true genetic level that was obtained by means of simulation for the "corn" and "cattle" genome models tested in this study (0.90 and 0.97). In practice, the genotype phases, genetic map, and allele effects all need to be estimated meaning inaccuracies in their estimation will lead to inaccurate variance prediction. Investigation of variance prediction accuracy when input parameters are estimated was not part of this study.