The phase change is evident. Further, from [16, p. 1650ff] (also see [17, Equation 1.10]): above the BBP threshold we have that in probability as m,n → ∞. It then follows that above the BBP threshold, we can expect the TW statistic to be increasing with the number of individuals m if the data size mn is fixed. That is, increasing sample size, rather than marker number, is advantageous for detecting structure above the BBP threshold, but not below it. This effect is clearly visible in Figure 6 (note the behavior of the p-value for m = 256). We summarize:
