Erosion of estimated genomic breeding values with generations is due to long distance associations between markers and QTL

Most validation studies of genomic evaluations on candidates (prior to observing phenotypes) present inflation of their predicted breeding values, i.e., regression coefficients of their later observed phenotypes on the early predictions are smaller than one. The aim of this study was to show that this inflation pattern reflects at least partly long-distance associations between markers and quantitative trait loci (QTL) in the reference population and to propose methods to estimate the corresponding “erosion” coefficient. Across-chromosome linkage disequilibrium (LD) is observed in different dairy cattle breeds, being a result from limited effective population size and from relationships within the reference population. Due to this long distance LD, the estimated SNP effects capture non-zero contributions from distant QTLs, some located on other chromosomes than the SNP itself. Therefore, corresponding SNP effects are partly lost in the next generations and we refer to this loss as “erosion”. With the concept of QTL contribution to SNP effects derived from mixed model equations, we show with simulation that this long range LD explains 6–25% of the variance of the estimated genomic breeding values, a proportion that is unchanged when the evaluation model includes a residual polygenic effect. Two methods are proposed to predict this erosion factor assuming known simulated QTL effects. In Method 1, one generation of progeny is simulated from the reference population and the GEBV of these progeny based on SNP effects estimated in this newly simulated generation are regressed on the GEBV of the same progeny based on SNP effects estimated in the reference population. In Method 2 all the QTL contributions to SNP effects are regressed based on SNP-QTL recombination rates and summed to predict the GEBV at the next generation. The regression coefficient of the GEBV based on eroded contributions on the raw GEBV is also an estimate of erosion. An illustration is given with the French Normande female reference bovine population in 2021, showing erosion factors ranging from 0.84 to 0.87. Accounting for erosion is important to avoid inflation and biased predictions. The ways to both reduce inflation and to correct for it in the prediction are discussed.