Nature | Vol 637 | 2 January 2025 | 119
single-nucleotide polymorphism (SNP) markers, but this informa -
tion has not been accessible in combination with the advantages of 
f-statistics2,6,25,26. Furthermore, the overwhelming majority of available 
aDNA is from a panel of 1.2 million SNPs27, and few clear advantages 
have been demonstrated for analysis of the more than 50 million SNPs 
available with whole-genome shotgun data.
One class of methods that use haplotype information is full genea-
logical tree inference28,29, which can now readily be applied to many 
thousands of modern and ancient whole genomes 30–35. Such meth-
ods have been successfully applied to boost the detection of positive 
selection32,36–38, population structure31,33,35,39, geographical locations of 
ancestors34,40, demography31,32 and mutation rate changes31. Genealogi-
cal trees can be thought of as containing essentially full, time-resolved 
information about genetic ancestry, including information typically 
captured by recent haplotype sharing or identity by descent. Genetic 
ancestry here refers to the full collection of genetic ancestors of indi-
viduals41, and genealogical trees reveal how and when these are shared 
across individuals. By contrast, rare variant ascertainment, haplotypes 
or chromosome blocks can be thought of as subsets or summaries of 
the information available in genealogies.
Here, we propose an approach that we refer to as ‘time-stratified 
ancestry analysis’ to boost the statistical power of f -statistics 
several-fold by using inferred genome-wide genealogies (Fig. 1a) and 
apply our method to reconstruct the genetic history of northern and 
central Europe from around 500 bce to 1000 ce.
 
Genealogies improve ancestry modelling
By definition, f-statistics count the occurrence of local genealogical 
relationships that are implied by how mutations are shared between 
individuals42. This inherent relationship between f-statistics and local 
genealogies makes it straightforward to compute f-statistics directly on 
inferred genealogies43. Instead of computing f-statistics on observed 
mutations, they are now calculated on the inferred branches of these 
genealogies, some of which may not be directly tagged by mutations 
but are inferred by resolving the local haplotype structure (Methods).
We develop mathematical theory and simulate a simple admixture 
model, in which the ancestry proportion is constrained in a single ratio of 
two f4-statistics19, to test this approach (Fig. 1b and Supplementary Note). 
While unbiased, we find that using f-statistics computed on genealogies 
by itself does not yet yield a large improvement in statistical power to 
quantify admixture events. However, we show, through both theoretical 
prediction and simulation, that large improvements in power can be 
gained without bias by restricting to recent coalescences, which are most 
informative for recent admixture events (Fig. 1c,d and Extended Data 
Figs. 2 and 3). We show that coalescences older than the time of diver-
gence of the sources carry no information with respect to the admixture 
event and only add noise to the f-statistics. Excluding these therefore 
increases statistical power, without introducing bias, in principle.
We implement this idea of studying the ‘twigs’ of gene trees in a tool, 
Twigstats (Fig. 1a and Methods), which we demonstrate in simulations 
2. Whole-genome
   genealogies
a
b
1. Genetic variation
0POP2PXP1PI
α =
 1 – α
0.2
0.4
0.6
0.8
1.0
Inferred proportion
0
0.2
0.4
0.6
0.8
1.0
Inferred proportion
0
0.2
0.4
0.6
0.8
1.0
Inferred proportion
Bottleneck
0 (no admixture)
f4 (P0, PI, PX, P1)
f4 (P0, PI, PX, P1)
1 – D
0.2 0.4
4. ADMIXTOOLS2
Genotype
Optimal Twigstats cut-off
Theo
retical prediction
Fold reduction in s.e.
Rare variant cut-off
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