The idea of Mendelian inheritance, revered for more than a century, was initially about the inherently causal nature of dominance and recessiveness. The A allele always and, presumably, inherently, made its effects manifest, as in the accompanying figure. Even as late as 1995, an influential paper termed this 'physiological' dominance.
In the genetics of quantitative traits, one can look at the average trait value (say, stature or body fat content of pigs or oil content of corn) in AA's and aa's. If the 'A' were physiologically dominant, then the Aa's should have the same mean value as the AA's. These are clearly statistical statements because unlike green vs yellow peas, there is variation and there are sampling issues (in fact, even Mendel's classical traits had some variation, but little overlap between dominant and recessive plants).
What transpires as a rule, however, is that the Aa's are not exactly like the AA's. But a common alternative to Mendelian ideas was that rather than being dominant and recessive, the contributions of the alleles at a gene were additive, like doses of medicine: Each copy of, say, an A allele you have, is a jump in your trait value. In such situations, Aa's would be exactly intermediate between AA's and aa's. If instead they shift towards one of the two homozygote (AA or aa) individuals, this is called statistical dominance.
Unlike physiological dominance, statistical dominance has to be evaluated by sampling from a population, and that means in turn that the idea of estimating the net or 'actual' effects of the A and a alleles, depends on the frequencies of these in the population, and more importantly, that also means that environmental and other genomic effects will affect the mean values of the carriers of the 3 genotypes. Statistical geneticists now treat these two kinds of dominance differently, often ignoring the physiological because it is hard to identify in real-world situations of quantitatively variable traits, as opposed to experimental settings with only two clear states, that have been part of genetics ever since Mendel himself.
We can relate this to GWAS findings a simple way. If a given allele is common enough in cases for its effects to be found and reach statistical significance, relative to its frequency in controls, then it has a chance to be detected in a GWAS study. But this depends on its penetrance, that is, on the strength of its effects, on their own, on a trait measure like stature or blood pressure, or on the presence of a disease. Highly penetrant alleles will be found more frequently in cases than controls because they have a higher chance of 'causing' the trait. The greater the effect, the more likely if you have the allele you have the disease.
This is a kind of 'dominance', because the allele is being detected against the other allele at that gene in individuals, plus whatever other relevant variants they have in their genome. That typically only a few genes are identified in this way shows how relatively rare real dominance is--how far it is from being the baseline, basic nature of inheritance! In fact, most variants that contribute contribute so little--have so little 'dominance' in this context--that we simply cannot detect their individual effects (or those effects are not enough to generate a statistically 'significant' association with the trait). So, dominance is far from the general rule. We will see in the next installment why this should not be any kind of surprise.