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.
Ancestry models of early medieval Europe
Having demonstrated that the Twigstats approach can effectively 
improve resolution and statistical power to test ancestry models and 
estimate proportions, we turn to the history of early medieval Europe.  
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.
T o develop an ancestry model for early medieval individuals (Supple-
mentary Table 1), we first need a broad characterization of the ancestry 
of the earlier sources from the early Iron Age (EIA) and Roman periods. 
We use hierarchical UPGMA clustering based on pairwise clade testing 
between all individuals, and formally test the cladality of proposed 
ancestry groups with qpWave5 (cladality in this sense means whether 
they are consistent with being symmetrically related to all other tested 
groups; Methods). This resulted in a set of model ancestry sources 
that included Iron Age and Roman Britain (n = 11), the Iron Age of cen-
tral European regions of mostly Germany, Austria and France (n = 10), 
Roman Portugal (n = 4), Roman Italy (n = 10), Iron Age Lithuania (n = 5), 
the EIA Scandinavian Peninsula (Sweden and Norway, n = 10) and several 
other more eastern groups dating to the Bronze Age and EIA (n = 25) 
(Fig. 2a and Extended Data Fig. 1). We then use a rotational qpAdm 
approach54 to narrow down the set of contributing sources from this 
larger pool of putative sources.
We additionally perform non-parametric multidimensional scaling 
(MDS) on outgroup-f3 statistics44 computed using Twigstats, the results 
of which do not depend on any modelling assumptions and which show 
increased resolution compared with conventional outgroup-f3 sta-
tistics (Fig. 2a,b, Extended Data Fig. 6 and Supplementary Table 2). 
Encouragingly, the MDS model supports regional fine-scale genetic 
structures reflected in our source groups, such as the separation of 
predominantly Norwegian and northern Swedish EIA individuals from 
southern Peninsular Scandinavia (Fig.  2a); this relationship is not 
detected without Twigstats. In this MDS analysis, we note a close affinity 
of wide-ranging individuals from Portugal, France, Germany, Austria 
and Britain. We hypothesize that this corresponds to areas associated 
with the Celtic-speaking world, and that their close genetic affinity is 
due to earlier expansions. Sparse sampling limits our understanding 
of the full extent of regional ancestry variation in central Europe and 
some other regions, but the continental ancestries differentiated in 
the MDS model suggests that major ancestry variation across Europe 
in this period is relatively well captured.
Expansions of Scandinavian-like ancestry
We assembled time transects using available aDNA data across several 
geographical regions in Europe, and infer their ancestry using a model 
with the EIA or Roman Iron Age sources previously defined (shown in 
Fig. 2a). Our modelling provides direct evidence of individuals with 
ancestry originating in northern Germany or Scandinavia appearing