we generated 50 trios from each of the six subpopulations. Next, we generated unrelated controls from these six subpopulations to obtain, on average, a matching ratio of R. We vary R from 0 to 20. From Figure 6(b) we can see that the power increases as we add in controls to every case but it appears to plateau as R approaches 10. Adding many more controls does not add any new information to the model.