In quantitative genetics, the degree of resemblance between parents and offspring is described in terms of the additive variance (VA) relative to genetic (VG) and phenotypic (VP) variance. For populations with extreme allele frequencies, high VA/VG can be explained without considering properties of the genotype–phenotype (GP) map. We show that randomly generated GP maps in populations with intermediate allele frequencies generate far lower VA/VG values than empirically observed. The main reason is that order-breaking behaviour is ubiquitous in random GP maps. Rearrangement of genotypic values to introduce order-preservation for one or more loci causes a dramatic increase in VA/VG. This suggests the existence of order-preserving design principles in the regulatory machinery underlying GP maps. We illustrate this feature by showing how the ubiquitously observed monotonicity of dose–response relationships gives much higher VA/VG values than a unimodal dose–response relationship in simple gene network models.