One essential question about synthetic associations is whether they are expected to be robust to the presence of recombination. Surprisingly, not only does recombination fail to eliminate synthetic associations, but low rates of recombination can enhance them compared with no recombination (Figure 2B). For example, for GRR = 4 and 9 risk alleles, and a sample size of 3,000 cases and 3,000 controls, we find the proportion of trees showing significance for zero recombination is 0.66. When we introduce a recombination rate of 5×10−5 (ten times the genome-wide average for 500 bp) between segments, however, we find that the proportion increases to 0.92. When recombination is increased further, the expected decline in the synthetic association is observed. Importantly, however, even at exceptionally high recombination through the region (5×10−4 between segments), we find that almost 30% of the simulations show a significant common variant, and recombination must increase to 5×10−3 to reduce the proportion to below 1%. Importantly, the simulations involving recombination prohibit evaluation of any common variant that has a rare causal site within the same segment. Thus the synthetic
