These patterns make clear that so long as a given genomic region has one or more rare variants that contribute to disease, these rare variants can generate synthetic associations that are observed in much more common polymorphisms. Under ideal conditions for such synthetic associations, they can be detected with sample sizes far smaller than those routinely used in GWAS. Under less ideal conditions (for example, higher prevalence attributable to environment or to other genetic factors outside of the locus being considered or lower penetrance for the local rare variants), the sample size must be larger. One essential quality of synthetic associations is that although they are often likely to be created when multiple rare variants exist in a region, there are certain conditions under which very little association will be detected even with very large sample sizes and large effects of the causal variants because causal alleles will segregate to opposite common alleles. In other words, no common variant will be able to partition the rare variants on a genealogy to create a large enough imbalance to create association. We
