NNLS with coalescence painting (true trees)
Twigstats (true trees)
Twigstats (Relate)
Twigstats mutations (Relate)
Source split time
Cut-off time (generations)
Best rare variant cut-off
5,0004,0003,0002,0001,0000
2
4
6
8
10
1,500
1,500
1,000
1,000
500
500
0
0
3. Twigstats
f2-Statistics f3, f4
qpAdm
qpgraph
α
c
d
Fig. 1 | Twigstats performance on simulated data. a, A diagram of the Twigstats 
approach. We first construct genealogies from genetic variation data and  
then use Twigstats to compute f 2-statistics between pairs of groups to be  
used by ADMIXTOOLS2. b , Admixture proportions inferred from an f 4-ratio 
statistic or non-negative least squares method. Source groups P1 and P2 split 
250 generations ago and mix 50 generations ago, where P2 contributes 
proportion  α and P1 contributes 1 − α. Effective population sizes are equal and 
constant except for a recent bottleneck in P2 (see Methods for simulation 
details). The Twigstats cut-off is set to 500 generations, the rare variant cut-off 
is set to 5%, and we additionally infer admixture proportions by generating 
‘first coalescence profiles’ for each population and modelling PX as a mixture 
of sources P1 and P2 using non-negative least squares (NNLS) (Methods).  
We sample 20 haploid sequences from each population. Data are mean ± 2 s.e. 
around the point estimate. c , The fold improvement of s.e. relative to the 
genotype case as a function of the Twigstats cut-off time, for the same simulation 
as in b and averaged across different true admixture proportions. The dashed 
line shows the best fold improvement of s.e. when ascertaining genotypes by 
frequency, when evaluated at different frequency cut-offs. d , The optimal 
Twigstats cut-off, defined as the largest reduction in s.e. relative to the genotype 
case, as a function of source split time in simulations using true trees. The dashed 
line indicates our theoretical prediction (Supplementary Note).