Article
Extended Data Fig. 5 | Three examples of applying Twigstats. a Fine-scale 
population structure simulation emulating ref. 39  (see Methods for simulation 
details). First two principal components are computed from pairwise outgroup 
f3 statistics on the genotypes directly and on Relate trees inferred from the  
50 target individuals. Labels in plots show the average coordinates of members 
of that population. For each panel, we calculate a separation index (SI) as in 39, 
which we define as the proportion of individuals for which the closest 
individual (by the Euclidean distance in PC space) is in the same population.  
b, Fine-scale genetic structure in Neolithic Europe quantified using an MDS 
calculated on a symmetric matrix that contains all pairwise outgroup f 3 
statistics (outgroup: YRI) between individuals. These are either calculated 
directly on genotypes or calculated using Twigstats on Relate genealogies  
with a cutoff of 1000 generations. Individuals were selected by filtering based 
on Steppe and Western Hunter-gatherer ancestry (Methods). c , Admixture 
proportions inferred using qpAdm with three distal sources of Western 
Hunter-gatherers, early European farmers, and Yamnaya Steppe people 46.  
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 f4(outgroup, Altai, 
target, Mbuti)/ f4(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 Neanderthals 78,79. We also compute equivalent 
f4-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.