text: Hunter-gatherers, early European farmers, and Yamnaya Steppe people46. 
  We show results for Twigstats-5000. Bias is measured as the difference in 
  admixture proportions obtained from Twigstats-5000 and all SNPs, and 
  we show standard errors of the latter. We plot two standard errors around 
  the mean. The standard error improvement shown is one minus the ratio of 
  standard errors obtained from Twigstats-5000 and using all SNPs.**d**, Neanderthal 
  admixture proportion inferred using an*f*4-ratio of the form*f*4(outgroup, Altai, 
  target, Mbuti)/*f*4(outgroup, Altai, Vindija, Mbuti). We compute these on genetic 
  variation data from the Simon’s Genome Diversity Project (SGDP)75 and use the 
  high-coverage Altai and Vindija Neanderthals78,79. We also compute equivalent 
  *f*4-ratio statistics in a simulation emulating Neanderthal admixture 50,000 years 
  ago and a second simulation involving no Neanderthal admixture but deep 
  structure that leads to a similar inference unless deep coalescences are ignored 
  by Twigstats. We plot two standard errors around the mean. 