text: **Fig. 1 | Twigstats performance on simulated data. a**, A diagram of the Twigstats 
  approach. We first construct genealogies from genetic variation data and 
  then use Twigstats to compute*f*2-statistics between pairs of groups to be 
  used by ADMIXTOOLS2.**b**, Admixture proportions inferred from an*f*4-ratio 
  statistic or non-negative least squares method. Source groups P1 and P2 split 
  250 generations ago and mix 50 generations ago, where P2 contributes 
  proportion*α*and P1 contributes 1 −*α*. Effective population sizes are equal and 
  constant except for a recent bottleneck in P2 (see Methods for simulation 
  details). The Twigstats cut-off is set to 500 generations, the rare variant cut-off 
  is set to 5%, and we additionally infer admixture proportions by generating 
  ‘first coalescence profiles’ for each population and modelling PX as a mixture 
  of sources P1 and P2 using non-negative least squares (NNLS) (Methods). 
  We sample 20 haploid sequences from each population. Data are mean ± 2 s.e. 
  around the point estimate.**c**, The fold improvement of s.e. relative to the 
  genotype case as a function of the Twigstats cut-off time, for the same simulation 
  as in**b**and averaged across different true admixture proportions. The dashed 
  line shows the best fold improvement of s.e. when ascertaining genotypes by 
  frequency, when evaluated at different frequency cut-offs.**d**, The optimal 
  Twigstats cut-off, defined as the largest reduction in s.e. relative to the genotype 
  case, as a function of source split time in simulations using true trees. The dashed 
  line indicates our theoretical prediction (Supplementary Note). 