text: We further confirm with simulations that genealogy-based*f*-statistics 
  estimates are robust to sequencing and phase-switch errors of expected 
  magnitude (Extended Data Fig. 3b). In fact, although sequence errors 
  can affect SNP-based population-genetic approaches substantially, 
  errors can be ‘corrected’ in genealogies as they take all variants in a 
  region into account32. 
  
  Previous studies have suggested ascertaining rare mutations as a 
  proxy for recent history3,4, but we show that this approach is prone to 
  bias when effective population sizes vary between populations, and 
  that using full time-restricted genealogies is both unbiased and more 
  powerful (Fig. 1b and Extended Data Fig. 3). We attribute this to the 
  observation that mutation age is not fully predictive of allele frequency 
  (Extended Data Fig. 4) and that the genealogy-based approach gains 
  power from the inclusion also of higher-frequency young mutations 
  that ‘tag’ recent coalescences by closely pre-dating them. We demon- 
  strate that a widely used ‘chromosome painting’ approach, and any 
  conceptually similar modelling based on identity by descent, that finds 
  the nearest neighbours between chromosomal segments in a sample 
  and model groups using a non-negative least squares of genome-wide 
  painting profiles2 is also prone to bias, when source groups have under- 
  gone strong drift since the admixture event (Fig. 1b and Extended Data 
  Fig. 3b). 