text: **Extended Data Fig. 2 | Twigstats optimal cutoff. a**, Theoretically computed 
  z-score of*f*4(PO,P1,PX,P2) at a single genomic locus (Supplementary Note), 
  assuming PX is admixted between P1 and P2 at time 0.004 (in units of 2*N*e 
  generations), e.g. corresponding to 100 generations with 2*N*e of 25,000. 
  Sources split at time 0.02.**b**, The theoretical fold-improvement of the best 
  Twigstats z-score of*f*4(PO,P1,PX,P2) relative to the z-score obtained with  regular*f*4-statistics. We use the same parameters as in**a**, but vary source split 
  times to illustrate the improved power for mixtures involving more closely 
  related groups.**c**, The optimal Twigstats cutoff time as a function of the source 
  split time and the ratio between the optimal cutoff time and source split time. 
  **d**, Comparison of z-scores computed using Twigstats to the corresponding 
  theoretical values shown in**a**. 