Mendelian sampling covariability of marker effects and genetic values

Measures of the expected genetic variability among full-sibs are of practical relevance, such as in the context of mating decisions. An important application field in animal and plant breeding is the selection and allocation of mates when large or small amounts of genetic variability among offspring are desired, depending on user-specific goals. Estimates of the Mendelian sampling variance can be obtained by simulating gametes from parents with known diplotypes. Knowledge of recombination rates and additive marker effects is also required. In this study, we aimed at developing an exact method that can account for both additive and dominance effects.

We derived parent-specific covariance matrices that exactly quantify the within-family (co-)variability of additive and dominance marker effects. These matrices incorporate prior knowledge of the parental diplotypes and recombination rates. When combined with additive marker effects, they allow the exact derivation of the Mendelian sampling (co-)variances of (estimated) breeding values for several traits, as well for the aggregate genotype. A comparative analysis demonstrated good average agreement between the exact values and the simulation results for a practical dataset (74,353 German Holstein cattle).

The newly derived method is suitable for calculating the exact amount of intra-family variation of the estimated breeding values and genetic values (comprising additive and dominance effects).