For a given number of studies, we observed that the effect CGR has on R2 is stronger than the effect it has on power. This observation is in line with the approximated theoretical R2 in Eq 2, indicating that R2 is quadratically proportional to CGR. However, an interesting observation is that this quadratic relation lessens as the number of studies grows large, despite the total sample size being fixed. For instance, at a CGR of a half, the R2 in the hold-out sample is expected to be 6.9% when there is only one discovery study. However, the expected R2 is 8.1% for two discovery studies, 9.3% for ten discovery studies, and 9.6% for 100 discovery studies. A likely reason for this pattern is that, in case of one discovery study, the PGS is influenced relatively strongly by the study-specific component of the genetic effects. This idiosyncrasy is not of relevance for the hold-out sample. As the number of studies increases—even though each study brings its own idiosyncratic contribution—each study consistently conveys information about the part of the genetic architecture which
