Importantly, association with the strongest causal variant in individual simulations was more significant than with the strongest common synthetic association in 98% of the simulations, and for each combination of parameters, the proportion of simulations with genome-wide significant associations was always higher for the strongest causal variant than for synthetic associations when testing for association with individual variants. Of particular importance to note, except for the case of GRR = 2, all conditions considered here produced a nonnegligible proportion of simulations with significant common variants. It is also noteworthy that significant signals of association can be credited to common variants even when there is only a single rare causal site. A control simulation was run by testing the common variants from one genealogy against phenotypes generated by a separate genealogy with the same parameter settings and not a single test fell below genome-wide significance of 10−8 for all simulations. This shows that significant synthetic associations depend on the associations that occur within a single gene genealogy (or correlated ones in a recombination graph) and that sites undergoing free recombination cannot create genome-wide significant synthetic associations.
