Separately considering the number of causal variants and the proportion of alleles that are disease causing (the disease class) makes clear that the latter is the key driver of the ease of creating synthetic associations. The intuition for this is obvious. Even when the frequency of disease-causing variants is very low individually, as the disease class grows, collectively they come closer to the frequency of common variants, allowing the possibility of a strong signal to be generated for one of the common variants. This is only prohibited when the causal variants are so numerous as to be distributed roughly evenly through the genealogy (or if an even distribution appears by chance for smaller numbers of causal variants).
