text: reduces standard errors (s.e.) by up to tenfold and potentially more, 
  depending on sample sizes and details of the genetic history model. The 
  approach does not produce detectable bias in estimates of admixture 
  proportions (Fig. 1b–d and Extended Data Fig. 3). Furthermore, we 
  demonstrate that computing*f*-statistics on genotypes ascertained 
  for young mutation ages produce a power gain nearly equal to that 
  produced when using full genealogies in many examples, while add- 
  ing flexibility by allowing lower-quality genomes to be grafted onto a 
  genealogy reconstructed with higher-quality genomes31. 
  
  In the first half of the first millennium ce, Roman historians such as 
  Tacitus and Ammianus Marcellinus described the geographical dis- 
  tribution and movements of groups beyond the imperial frontier and 
  suggested a potential role for them in the fall of the western Roman 
  Empire52. However, the exact nature and scale of these historically 
  attested demographic phenomena—and their genetic impact— 
  have been questioned53, and have been difficult to test with genetic 
  approaches owing to the close relations shared between many groups 
  that were ostensibly involved. Less is understood at further distances 
  from the Roman frontier owing to a lack of historical accounts. The 
  improved statistical power of time-restricted ancestry in Twigstats 
  thus offers an opportunity to revisit these questions. 