The assumption that effects are normally distributed is necessary when markers are selected by their P-values but not otherwise. Similarly, allowing a proportion of markers to have no effect only makes a difference when selecting markers by P-values. Thus the present results are relevant even if one does not entirely accept the polygenic model proposed. The normal distribution simplifies some calculations, but various heavy-tailed distributions have also been proposed for GWAS data [38], [39] and would lead to improved prediction if such models held in truth. Furthermore the assumption of normality applies to effects on the standardised genotype scale, but there are plausible models for effect sizes as a function of allele frequency, leading to non-normal effects on the standardised scale. This may particularly affect the results for shrinkage estimation when the degree of shrinkage varies for markers with different allele frequencies. The numerical results presented are therefore not definitive but should be taken a guide to the likely magnitude of results in specific applications.
