Final answer:
Large-scale association studies, such as those employing GWAS, rely on the common disease-common variant hypothesis and need to consider a range of factors such as population-based sampling, accurate phenotyping, and evolutionary processes like genetic drift and gene flow.
Step-by-step explanation:
The assumption that must hold for large-scale association studies to be successful is not explicitly listed among the options provided in the question. However, one fundamental requirement for such studies, which often involves Genome-Wide Association Studies (GWAS), is the assumption of a common disease-common variant hypothesis. This hypothesis posits that common genetic variants contribute to the risk of developing common diseases. Therefore, while it is not necessary that the risk allele is in a coding region, or that only one gene is involved, or that the mutation occurred only once, or that the risk allele must not occur in the control group, it is critical that the studies rely on a range of other assumptions, including population-based sampling, accurate phenotyping, and the consideration of genetic drift, gene flow, and natural selection influencing allele frequencies.