Background Animal breeding, i.e., the selective breeding for economically important traits, was traditionally based on phenotypic recordings. Best linear unbiased prediction (BLUP) combined individual records and those of relatives into estimates of breeding values (EBV). From 1990 onward, advances in molecular genetics held the promise that information at the DNA level would lead to more genetic improvement than using only phenotypic records. This resulted in research into MAS, which consists of two steps: 1) detect and (fine) map genes underlying the traits of interest, i.e., so called quantitative trait loci (QTL); 2) include the QTL information into the BLUP-EBV (Fernando and Grossman,1989). The QTL mapping step (1) was successful in the sense that most mapping studies detected QTL. But the repeatability of the mapping studies was low, i.e., QTL positions moved/(dis)appeared from one study to the next. One reason for this is that the majority of QTL have very small effects. When this is combined with testing a large number of markers, there is a marked "Beavis effect" in which the estimated effect of significant markers is overestimated (Beavis, 1994). For instance, if we test 100 markers for their statistical significance using a P-value of 1%, we expect one (false) positive result even if all true marker effects are zero. Conversely, if all of the markers have very small effects, few (randomly picked) markers will reach higher levels of significance and most will fail to reach the threshold and be declared nonsignificant. In genome-wide association studies (GWAS), the number of tests equals the number of genotyped independent SNPs, which is typically many thousands in livestock and hundreds of thousands in human genetics. With so many SNPs, the multiple-testing problem becomes so large that in human genetics, P-values of < 5 × 10-8 are commonly used. In addition, human genetics journals demand a confirmation of the QTL in an independent dataset. These very stringent tests resulted in only the largest QTL being found. For some traits, such large QTL were detected, e.g., DGAT1 affecting fat content in milk (Grisart et al., 2001) and CDH1 affecting infectious pancreatic necrosis virus (IPNV) resistance in Atlantic salmon (Moen et al., 2015). However, for many other traits, no reliable QTL were found, and less than 10% of the variation of the overall breeding objective, i.e., a combination of all the economically important traits, was explained by QTL. This was even the case for dairy cattle, where many powerful QTL mapping studies were conducted. Less than 10% of the genetic variance of the breeding objective explained by QTL implied that more than 90% of the genetic differences between animals had to be handled by traditional selection. Hence, by 2005, the uptake of MAS in livestock breeding was very limited. In human genetics, the result that very powerful GWAS studies (e.g., 160,000 individuals genotyped for 500,000 SNPs) explained only a (very) limited fraction of the total genetic variance was termed the ...