120 | Nature | Vol 637 | 2 January 2025
Article
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.
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).
We next test the Twigstats time-restricted genealogy approach 
on a range of empirical examples. First, we boost pairwise outgroup 
f3-statistics44 to quantify fine-scale population structure; we demon-
strate this improvement using a previously proposed simulation 39 
(Extended Data Fig. 5a). When applied to published genomes from 
Neolithic Europe (Methods and Supplementary Table 1), we can repli-
cate the previously suggested fine-scale structure between individuals 
buried in megalithic structures in Ireland compared with others45, a 
relationship that is not apparent from SNP data alone (Extended Data 
Fig. 5b). For the well-studied example of three major ancestries contrib-
uting to prehistoric Europe, that is, Mesolithic hunter-gatherers, early 
farmers and steppe populations13–16, we obtain unbiased estimates and 
an approximately 20% improvement in standard errors in an already 
well-powered qpAdm model46 (Extended Data Fig. 5c).
Finally, we demonstrate that Twigstats can be used to resolve com-
peting models of punctual admixture and long-standing gene flow, or 
constrain the time of admixture. For instance, it has previously been 
suggested that long-standing deep structure and gene flow between 
Neanderthals and early modern humans in Africa may produce genetic 
patterns that resemble a punctual admixture event some 60,000 years 
ago47–49, casting doubt on the model of Neanderthal admixture into 
ancestors of Eurasians49–51. However, whereas such long-standing deep 
substructure would confound SNP-based f-statistics to produce pat-
terns similar to Neanderthal admixture, we demonstrate, in simula-
tions, that Twigstats can clearly distinguish this history from recent 
admixture (Extended Data Fig. 5d). Application of Twigstats on empiri-
cal whole genomes produces results inconsistent with deep substruc-
ture alone, but consistent with punctual admixture.