text: The optimal Twigstats time cut-off is a priori unknown; however, we 
  develop a theory that predicts the optimal choice in a simple two-way 
  admixture as a function of the admixture date, source split time and 
  admixture proportion (Supplementary Note). In this case, the optimal 
  cut-off equals approximately 1.4 times the split time between admixing 
  source groups, depending on exact parameters in the model (Fig. 1b,c 
  and Extended Data Fig. 2). 
  
  In real settings, we are additionally required to computationally 
  phase genomes. We emulate this by combining two haploid sequences 
  to construct a diploid individual. We then computationally rephase 
  these diploid individuals without a reference panel. This approach is 
  expected to result in suboptimal phasing and should therefore be well 
  suited to test robustness to phase-switch errors. 
  
  **Non-negative least squares ancestry modelling.**We implement 
  an approach that uses genealogies to emulate the chromosome 
  painting technique of identifying closest genetic relatives along the 
  genome1,2 to fit admixture weights. When applied to true genea- 
  logies in simulations, this approach represents an idealized version of 
  this idea. 