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A unified genealogy of modern and ancient genomes

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Abstract

The sequencing of modern and ancient genomes from around the world has revolutionised our understanding of human history and evolution. However, the general problem of how best to characterise the full complexity of ancestral relationships from the totality of human genomic variation remains unsolved. Patterns of variation in each data set are typically analysed independently, and often using parametric models or data reduction techniques that cannot capture the full complexity of human ancestry. Moreover, variation in sequencing technology, data quality and in silico processing, coupled with complexities of data scale, limit the ability to integrate data sources. Here, we introduce a non-parametric approach to inferring human genealogical history that overcomes many of these challenges and enables us to build the largest genealogy of both modern and ancient humans yet constructed. The genealogy provides a lossless and compact representation of multiple datasets, addresses the challenges of missing and erroneous data, and benefits from using ancient samples to constrain and date relationships. Using simulations and empirical analyses, we demonstrate the power of the method to recover relationships between individuals and populations, as well as to identify descendants of ancient samples. Finally, we show how applying a simple nonparametric estimator of ancestor geographical location to the inferred genealogy recapitulates key events in human history. Our results demonstrate that whole-genome genealogies are a powerful means of synthesising genetic data and provide rich insights into human evolution.
A unified genealogy of modern and ancient
genomes
Anthony Wilder Wohns1,2,*, Yan Wong1, Ben Jeffery1, Ali
Akbari2,3,6, Swapan Mallick2,4, Ron Pinhasi5, Nick Patterson2,3,4,6,
David Reich2,3,4,6, Jerome Kelleher1,+, and Gil McVean1,+
1Big Data Institute, Li Ka Shing Centre for Health Information and Discovery,
University of Oxford, Oxford, UK
2Broad Institute of MIT and Harvard, Cambridge, MA, USA
3Department of Human Evolutionary Biology, Harvard University, Cambridge, MA,
USA
4Howard Hughes Medical Institute, Boston, MA 02115, USA
5Department of Evolutionary Anthropology, University of Vienna, 1090 Vienna,
Austria
6Harvard Medical School Department of Genetics, Boston, MA 02115, USA
*Corresponding Author: awohns@broadinstitute.org
+These authors contributed equally to this work
Abstract
The sequencing of modern and ancient genomes from around the world has
revolutionised our understanding of human history and evolution1,2. However,
the general problem of how best to characterise the full complexity of ancestral
relationships from the totality of human genomic variation remains unsolved.
Patterns of variation in each data set are typically analysed independently, and
often using parametric models or data reduction techniques that cannot cap-
ture the full complexity of human ancestry3,4. Moreover, variation in sequencing
technology5,6, data quality7and in silico processing8,9, coupled with complexi-
ties of data scale10, limit the ability to integrate data sources. Here, we introduce
a non-parametric approach to inferring human genealogical history that over-
comes many of these challenges and enables us to build the largest genealogy
of both modern and ancient humans yet constructed. The genealogy provides
a lossless and compact representation of multiple datasets, addresses the chal-
lenges of missing and erroneous data, and benefits from using ancient samples
to constrain and date relationships. Using simulations and empirical analyses,
we demonstrate the power of the method to recover relationships between indi-
viduals and populations, as well as to identify descendants of ancient samples.
Finally, we show how applying a simple nonparametric estimator of ancestor ge-
ographical location to the inferred genealogy recapitulates key events in human
history. Our results demonstrate that whole-genome genealogies are a pow-
erful means of synthesising genetic data and provide rich insights into human
evolution.
1
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2
Main
Our ability to determine relationships among individuals, populations and species
is being transformed by population-scale biobanks of medical samples11,12, col-
lections of thousands of ancient genomes2, and efforts to sequence millions of eu-
karyotic species13. Such relationships, and the resulting distributions of genetic
and phenotypic variation, reflect the complex set of selective, demographic and
molecular processes and events that have shaped species and are consequently
a rich source of information about them1,9,14,15.
However, our ability to learn about evolutionary events and processes from
the totality of genomic variation, in humans or other species, is limited by
multiple factors. First, combining information from multiple data sets, even
within a species, is technically challenging; discrepancies between cohorts due
to error16, differing sequencing techniques5,6 and variant processing8lead to
noise that can easily obscure genuine signal. Second, few tools can cope with
the vast data sets that arise from the combination of multiple sources10. Third,
statistical analysis typically relies on data reduction techniques17,18 or the fitting
of parametric models4,19–21, which will inevitably provide an incomplete picture
of the complexities of evolutionary history. Finally, data access and governance
restrictions often limit the ability to combine data sources22.
Tree sequences represent a potential solution to many of these problems10,23.
Phylogenetic trees are fundamental to the evolutionary analysis of species; tree
sequences extend this concept to multiple correlated trees along the genome,
necessary when considering genealogies within recombining organisms24. Im-
portantly, the tree sequence, and the mapping of mutation events to it, reflects
the totality of what is knowable about genealogical relationships and the evo-
lutionary history of individual variants. Fig. 1a shows how the tree sequence
is defined as a graph with a set of nodes representing sampled chromosomes
and ancestral haplotypes, edges connecting nodes representing lines of descent,
and variable sites containing one or more mutations mapped onto the edges.
Recombination events in the ancestral history of the sample create different
edges and thus distinct, but highly correlated trees along the genome. Tree
sequences contain a comprehensive record of ancestral history and can not only
be used to compress genetic data10, but also lead to highly efficient algorithms
for calculating population genetic statistics25.
In this paper, we introduce, validate and apply nonparametric methods
for inferring time-resolved tree sequences from multiple heterogeneous sources,
building on previous work10 to efficiently infer a single, unified tree sequence
of ancient and contemporary human genomes. We validate this structure using
the known age and population affinities of ancient samples and demonstrate its
power through spatio-temporal inference of human ancestry. We note that while
humans are the focus of this study, the methods and approaches we introduce
are valid for most recombining organisms.
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A unified genealogy of modern and ancient human genomes
To generate a unified genealogy of modern and ancient human genomes, we
integrated data from eight sources. This included three modern datasets: the
1000 Genomes Project (TGP) which contains 2,504 sequenced individuals from
26 populations1, the Human Genome Diversity Project (HGDP), which consists
of 929 sequenced individuals from 54 populations9, and the Simons Genome Di-
versity Project (SGDP) with 278 sequenced individuals from 142 populations15.
154 individuals appear in more than one of these datasets (see Supplementary
Note S3). In addition, we included data from three high-coverage sequenced
Neanderthal genomes26–28, the single Denisovan genome29, and newly reported
high coverage whole genome data from a nuclear family of four (a mother, a
father, and their two sons with average coverage of 21.2x, 25.3x, 10.8x, and
25.8x) from the Afanasievo Culture, who lived 4.1thousand years ago (kya).
Finally, we used 3,589 published ancient samples from over 100 publications
compiled by the Reich Laboratory (see Supplementary Note S3) to constrain
allele age estimates. These ancient genomes were not included in the final tree
sequence due to the lack of reliable phasing for the majority of samples, though
we later discuss a potential solution to this problem.
In this study, we illustrate our approach using Chromosome 20. We first
merged the modern datasets and inferred a tree sequence using tsinfer version
0.2 (see Methods). This approach uses a reference panel of inferred ancestral
haplotypes to impute missing data at the 96.7% of sites that have at least one
missing genotype. We then estimated the age of ancestral haplotypes with
tsdate (see Methods), a Bayesian approach that infers the age of ancestral
haplotypes with accuracy comparable to or greater than alternative approaches
and with unmatched scaling properties (see Fig. 1c, Extended Data Fig. 4-5).
We identified 159,504 variants present in both ancient and modern samples.
For each, a lower age bound is provided by the estimated archaeological date of
the oldest ancient sample in which the derived allele is found. Where this was
inconsistent with the initial inferred value (17,815, or 11% of variants) we used
the archaeological date as the variant age.
Next, we integrated the Afanasievo family and four archaic sequences with
the modern samples and re-inferred the tree sequence of Chromosome 20 using
the iterative approach outlined in Fig. 1b. In tsinfer, samples cannot directly
descend from other samples (which is highly unlikely in reality). Instead, we
create “proxy” ancestral haplotypes, which at non-singleton sites are identical
to each ancient sample, and insert them at a slightly older time than the ancient
sample. These proxies can act as ancestors of both modern and (younger) an-
cient samples. Thus, the ancient samples are never themselves direct ancestors
of younger ones, but their haplotypes may be. The integrated tree sequence
contains 626,133 ancestral haplotypes, 6,076,164 edges, 2,090,401 variable sites,
and 5,773,816 mutations. We infer that 39% of variant sites require more than
one change in allelic state in the tree sequence to explain the data. This may
indicate either recurrent mutations or errors in sequencing, genotype calling,
or phasing, all of which are represented by additional mutations in the tree
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sequence. If we discount mutations affecting only a single sample (indicative
of sequencing error) we find that 371,299 sites contain at least two mutations
affecting more than one sample, implying up to 17.8% of variable sites could be
the result of more than one ancestral mutation. Of these, we examined 3,314
sites with >100 mutations. Extended data Fig. 3 shows that a high proportion
of these outlier sites have sequencing or alignment quality issues as defined by
the TGP accessibility mask1, or are in minimal linkage disequilibrium to their
surrounding sites, suggesting they are largely erroneous. We chose to retain
such sites to enable recovery of input data sources; however, future iterative ap-
proaches to the removal of such probable errors are likely to improve use cases
such as imputation.
To characterise fine-scale patterns of relatedness between the 215 populations
of the constituent datasets, we calculated the time to the most recent common
ancestor (TMRCA) between pairs of haplotypes from these populations at the
122,637 distinct trees in the tree sequence (300 billion pairwise TMRCAs).
After performing hierarchical clustering on the average pairwise TMRCA values,
we find that samples do not cluster by data source (which would indicate major
data artefacts), but reflect known patterns of global relatedness (Fig. 2 and
interactive Supplementary Fig. 1). We conclude that our method of integrating
datasets is therefore robust to biases introduced by different datasets. Numerous
features of human history are immediately apparent, such as the deep divergence
of archaic and modern humans, the effects of the Out of Africa event (Fig. 2
(i)), and a subtle increase in Oceanian/Denisovan MRCA density from 2,000-
5,000 generations ago (Fig. 2 (ii)). Multiple populations show recent within-
group TMRCAs, suggestive of recent bottlenecks or consanguinity. The most
extreme cases are for “populations” for which only a single individual exists in
our dataset, such as the four archaic individuals, and a Samaritan individual
from the SGDP. We find the Samaritan has an logarithmic average within-
group TMRCA of 1,000 generations, which is caused by multiple MRCAs at
very recent times (Fig. 2 (iii)) and is consistent with documented evidence of a
severe bottleneck and extensive consanguinity in recent centuries30. Indigenous
populations in the Americas, an Atayal individual from Taiwan, and Papuans
also exhibit particularly recent within-group TMRCAs.
Tree-sequence based analysis of descent from ancient sam-
ples
To validate the dating methodology, we first used simulations to show that
the integration of ancient samples improves derived allele age estimates under
a range of demographic histories (Fig. 1d.). To provide empirical validation
of the method, we considered the ability of the method and alternatives to
infer allele ages that are consistent with observations from ancient samples.
We inferred and dated a tree sequence of TGP Chromosome 20 (without using
the ancient samples) and compared the resulting point estimates and upper and
lower bounds on allele age with results from GEVA31 and Relate32. This resulted
in a set of 659,804 variant sites where all three methods provide an allele age
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estimate. Of these, 76,889 derived alleles are observed within the combined set
of 3,734 ancient samples, thus putting a lower bound on allele age. We find that
estimated allele ages from tsdate and Relate showed the greatest compatibility
with ancient lower bounds, despite the fact that the mean age estimate from
tsdate is more recent than that of Relate (Fig. 3a and Supplementary Note
S5).
Next, to assess the ability of the unified tree sequence to recover known rela-
tionships between ancient and modern populations, we considered the patterns
of descent to modern samples from Archaic proxy ancestral haplotypes on Chro-
mosome 20. Simulations, detailed in Supplementary Note S2.6, indicate that
this approach detects introgressed genetic material from Denisovans at a preci-
sion of 86% with a recall of 61%. We find that there are descendants among
non-archaic individuals, including both modern individuals and the Afanasievo,
for 13% of the span of the Denisovan proxy haplotypes on Chromosome 20. The
highest degree of descent among modern humans is in Oceanian populations as
previously reported29,33–35 (Fig. 3b). However, the tree sequence also reveals
how both the extent and nature of descent from the Denisovan proxy ances-
tors varies greatly among modern humans (Fig. 3c). In particular, we find that
Papuans and Australians carry multiple fragments of Denisovan haplotypes that
are largely unique to the individual. In contrast, other modern descendants of
Denisovan proxy ancestors have fewer Denisovan haplotype blocks which are
more widely shared, often between geographically distant individuals.
For the Afanasievo family, we find the greatest amount of descent from their
proxy ancestral haplotypes among individuals in Western Eurasia and South
Asia (Extended Data Fig. 6a), consistent with findings from the genetically
similar Yamnaya peoples36. Notably, the most frequent descendant blocks in
Extended Data Fig. 6b all contain geographically disparate modern samples.
These cosmopolitan patterns of descent support a contemporaneous diffusion of
Afanasievo-like genetic material via multiple routes36.
For the Neanderthal samples, where there are three samples of different age,
our simulations indicate that interpretation of the descent statistics is compli-
cated by varying levels of precision and recall among lineages. Nevertheless,
recall is highest at regions where introgressing and sampled archaic lineages
share more recent common ancestry and precision is higher for the most recent
samples. Examining patterns of descent from the Vindija on multiple chromo-
somes indicate that modern East Asian individuals carry roughly 40% more
Vindija-like material than West Eurasians (see Extended Data Fig. 8), support-
ing other reports of excess Neanderthal ancestry in East Asians relative to West
Eurasians27,37, and inconsistent with suggestions that the proportions are very
similar38.
Non-parametric inference of spatio-temporal dynamics in
human history
Tree-sequence based analysis of ancient samples demonstrates the power of the
approach for characterising patterns of recent descent. To assess whether we
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could use the tree sequence to capture wider patterns in human history we devel-
oped a simple estimator of ancestor spatial location. We use the location of de-
scendants of a node, combined with the structure of the tree sequence, to provide
an estimate of ancestor location (see Methods). The approach can use informa-
tion on the location of ancient samples, though it does not attempt to capture
the geographical plausibility of different locations and routes. The inferred lo-
cations are thus a model-free estimate of ancestors’ location, informed by the
tree sequence topology and geographic distribution of samples. Although the
relationships between genealogies and spatial structure has been an active area
of research in both phylogenetics and population genetics for many years39–44,
our approach is the first to infer ancestral locations incorporating recombina-
tion. More sophisticated methods which also use genome-wide genealogies are
currently in development, and show considerable promise (Osmond, M., and
Coop, G., personal communication).
We applied the method to the unified tree sequence, excluding TGP indi-
viduals (which lack precise location information). We find that the inferred
ancestor location recovers multiple key events in human history (Fig. 4, Sup-
plementary Video 1). Despite the fact that the geographic centre of gravity of
all sampled individuals is in Central Asia, by 72 kya the average location of
ancestral haplotypes is in Northeast Africa and remains there until the oldest
common ancestors are reached. Indeed, the inferred geographic centre of grav-
ity of the 100 oldest ancestral haplotypes (which have an average age of 2
million years) is located in Sudan at 19.4 N, 33.7 E. These findings reflect the
depth of African lineages in the inferred tree sequence and are compatible with
well-dated early modern human fossils from eastern and northern Africa45,46.
We caution that our sampling of Africa is inhomogenous, and it is likely that
if instead we analysed data from a grid sampling of populations in Africa the
geographic centre of gravity of independent lineages at different time depths
would shift. In addition, past major migrations such as the Bantu and Pastoral
Neolithic expansions, both occurring within the last few thousand years, mean
that present day distributions of groups in Africa and elsewhere may not repre-
sent ancestral ones, and thus the approach of using the present-day geographic
distribution to provide insight is likely to give a distorted picture of ancient
geographic distributions47. Nevertheless, this analysis demonstrates that the
deep tree structure is geographically centred in Africa in autosomal data, just
as it is for mitochondrial DNA and Y chromosomes48,49.
Traversing towards the present, by 280 kya, the centre of gravity of ancestors
is still located in Africa, but many ancestors are observed in the Middle East
and Central Asia and a few are located in Papua New Guinea. At 140 kya,
more ancestors are found in Papua New Guinea. This is almost 100 kya before
the earliest documented human habitation of the region50. However, our find-
ings are potentially consistent with the proposed timescales of deeply diverged
Denisovan lineages unique to Papuans35. At 56 kya, some ancestral lineages
are observed in the Americas, much earlier than the estimated migration times
to the Americas51. This effect is likely attributable to the presence of ances-
tors who predate the migration and did not live in the Americas, but whose
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descendants now exist solely in this region52; the same effect may also explain
the ancient ancestors within Papua New Guinea. Additional ancient samples
and more sophisticated inference approaches are required to distinguish between
these hypotheses. Nevertheless, these results demonstrate the ability of infer-
ence methods applied to tree sequences to capture key features of human history
in a manner that does not require complex parametric modelling.
Discussion
A central theme in evolutionary biology is how best to represent and analyse ge-
nomic diversity in order to learn about the processes, forces and events that have
shaped history. Historically, many modelling approaches focused on the tempo-
ral behaviour of individual mutation frequencies in idealised populations53,54.
In the last 40 years there has been a shift toward modelling techniques that
focus on the genealogical history of sampled genomes and that can capture the
correlation structures in variation that arise in recombining genomes24,55. Crit-
ically, while allele frequency is an idealised and unknowable quantity, there does
exist a single, albeit extremely complex, set of ancestral relationships that, cou-
pled with how mutation events have altered genetic material through descent,
describes what we observe today.
However, while the empirical generation of data has transformed our ability
to characterise genomic variation and relatedness structures in humans, includ-
ing that of ancient individuals, developing efficient methods for inferring the un-
derlying genealogy has proved challenging56,57. Recent progress in this area10,32,
on which we build, has been driven by using approximations that capture the
essence of the problem but enable scaling to population-scale and genome-wide
data sets. The methods described here produce high quality dated genealogies
that include thousands of modern and ancient samples. These genealogies can-
not be entirely accurate, nevertheless, they enable a wealth of novel analyses
that reveal features of human evolution25,58–60. That our highly simplistic es-
timator of spatio-temporal dynamics of ancestors of modern samples captures
key events, such as an East-African genesis of modern humans, introgression
from now-extinct archaic populations in Asia and historical admixture10, sug-
gests that more sophisticated approaches, coupled with the ongoing program
of sequencing ancient samples, will continue to generate new insights into our
history.
Moreover, because the tree sequence approach captures the structure of hu-
man relationships and genomic diversity, it provides a principled basis for com-
bining data from multiple different sources, enabling tasks such as imputing
missing data and identifying (and correcting) sporadic and systematic errors in
the underlying data. Our results identified different types of error common in
reference data sets (erroneous sites and genotyping error) as well as emphasis-
ing the importance of recurrent mutation in generating human genetic diver-
sity61,62. Although additional work is required to correct such errors, as well as
integrate other types of mutation, notably structural variation, a reference tree
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sequence for human variation - along with the tools to use it appropriately10,25
- potentially represents a basis for harmonising a much larger and wider set of
genomic data sources and enabling cross data-source analyses. We note that
such a reference tree-sequence could also enable data sharing and even privacy-
preserving forms of genomic analysis22 through compression of cohorts against
such a reference structure.
There exists much room for improvement in the methods introduced here, as
well as new opportunities for genomic analyses that use the dated tree-sequence
structure. For example, our approach requires phased genomes, which is a par-
ticular challenge for ancient samples that typically pick random reads to create
a “pseudo-haploid genome”63. However, it should be possible to use a diploid
version of the matching algorithm in tsinfer to jointly solve phasing and im-
putation. This also has the potential to alleviate biases introduced by using
modern and genetically distant reference panels for ancient samples64. Recent
work focusing on inferring genealogies for high-coverage ancient samples, and
using mutations dated in such a genealogy to infer relationships of lower cov-
erage samples through time, offers an alternative strategy for accommodating
the unique challenges of ancient DNA in this context (Speidel, L., Cassidy, L.,
Davies, R.W., Hellenthal, G., Skoglund, P., and Myers., S.R., personal com-
munication). In addition, our approach to age inference within tsdate only
provides an approximate solution to the cycles that are inherent in genealogical
histories65 and there are many possible approaches for improving the sophisti-
cation of spatio-temporal ancestor inference.
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5
(a)
6
4
4
2
= mutation
1
0
3
7
T1span
T2span
Graph Representation
Relative age
Tree Representation
3
6
4
4
2
1
0
3
5
4
4
2
1
0
3
7
3
6
4
4
2
1
0
3
= 2500!
generations
= 3000 !
generations
2
1
0
Ancient
Sample
Conflict
4
2
1
0
4
Freq. = 0.75
Freq. = 0.5
(b)
Infer Tree
Sequence Topology
Order by
Frequency
Constrain Ages with
Ancient Samples (if available)
Older
Older
Order by
Estimated Age
Step 0
Step 1
2
1
0
Date Tree
Sequence (Fig. 1)
Step 2
Step 3
Step 4
Modern Samples Only
Modern +
Ancient Samples (if
available)
(d)
(c)
CEU CHB YRI
5,600 Generations
Empirical Distribution of !
Sampled Ancient
Genomes
10,000 Generations
Fig. 1: Schematic overview and validation of the inference methodology. (a)
An example tree sequence topology with four samples (nodes 0-3), two marginal
trees, and two mutations. T1span and T2span measure the genomic span of each
marginal tree topology, with the dotted line indicating the location of a recombi-
nation event. The graph representation is equivalent to the tree representation.
(b) Schematic representation of the inference methodology. Step 0: alleles are
ordered by frequency; the mutation represented by the four-point star is thus
considered to be older than that represented by the five-point star. Step 1: the
tree sequence topology is inferred with tsinfer using modern samples. Step 2:
the tree sequence is dated with tsdate. Step 3: node date estimates are con-
strained with the known age of ancient samples. Step 4: ancestral haplotypes
are reordered by the estimated age of their focal mutation; the five pointed star
mutation is now inferred to be older than the four-point star mutation. The
algorithm returns to Step 1 to re-infer the tree sequence topology with ancient
samples. Arrows refer to modes of operation: Steps 0, 1 and 2 only (red); after
one round of iteration without ancient samples (green) and after one round of it-
eration with increasing numbers of ancient samples (blue). (c) Scatter plots and
accuracy metrics comparing simulated (x-axis) and inferred (y-axis) mutation
ages from neutral coalescent simulations from msprime, using tsdate with the
simulated topology (left) and inferred topology (right); see Methods for details.
(d) Accuracy metrics, root-mean squared log error (top) and Spearman rank
correlation coefficient (bottom), with modern samples only (first panel), after
one round of iteration (second panel) and with increasing numbers of ancient
samples (coloured arrows as in panel b). Three classes of ancient samples are
considered, reflecting where in history of humans they have been sampled from
(see schematic below). See Supplementary Note S2.3 for details.
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14
(i)
(ii)
(iii)
Fig. 2: Clustered heatmap showing the average time to the most recent com-
mon ancestor (TMRCA) on Chromosome 20 for haplotypes within pairs of the
215 populations in the HGDP, TGP, SGDP, and ancient samples. Each cell
in the heatmap is coloured by the logarithmic mean TMRCA of samples from
the two populations. Hierarchical clustering of rows and columns has been
performed using the UPGMA algorithm on the value of the pairwise average
TMRCAs. Row colours are given by the region of origin for each population,
as shown in the legend. The source of genomic samples for each population
is indicated in the shaded boxes above the column labels. Three population
relationships are highlighted using span-weighted histograms of the TMRCA
distributions: (i) average distribution of TMRCAs between all non-African pop-
ulations (black line) compared to African/African TMRCAs (solid yellow). (ii)
Denisovans and Papuan/Australian TMRCAs (solid line), compared to Deniso-
vans against all non-Archaic populations (solid white). The subtle but unique
signal is particularly evident in Supplementary Interactive Fig. 1 at https:
//awohns.github.io/unified_genealogy/interactive_figure.html).
(iii) TMRCAs between the two Samaritan chromosomes (solid line), compared
to the Samaritans/all other modern humans (solid white). Duplicate samples
appearing in more than one modern dataset are included in this analysis.
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Region
(a)
(b) (c)
Fig. 3: Validation of inference methods using ancient samples. (a) Comparison
of mutation age estimates from three methods (tsdate,Relate and GEVA) using
3,734 ancient samples at 76,889 variants on Chromosome 20. The radiocarbon-
dated age of the oldest ancient sample carrying a derived allele at each variant
site in the 1000 Genomes Project is used as the lower bound on the age of the
mutation (diagonal lines). Mutations below this line have an estimated age
that is inconsistent with the age of the ancient sample. Black lines on each
plot show the moving average of allele age estimates from each method as a
function of oldest ancient sample age. Plots to the left show the distribution
of allele age estimates for modern-only variants from each respective method.
Additional metrics are reported in each plot. (b) Percentage of Chromosome
20 for modern samples in each region that is inferred to descend from “proxy
ancestors” associated with the sampled Denisovan haplotypes, calculated using
the genomic descent statistic1. (c) Tracts of descent along Chromosome 20
descending from Denisovan “proxy ancestors” in modern samples with at least
100 kilobases (kb) of total descent (colour scheme as for Fig. 2).
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280 kya 840 kya
140 kya
25 kya2.5 kya
56 kya
(c)(a)
(b)
Fig. 4: Visualisation of the non-parametric estimator of ancestor geographic
location for HGDP, SGDP, Neanderthal, Denisovan, and Afanasievo samples.
(a) Geographic location of samples used to infer ancestral geography. The size
of each symbol is proportional to the number of samples in that population.
(b) The average location of the ancestors of each HGDP population from time
t=0 to 2million years ago. The width of lines is proportional to the number
of ancestors of each population over time. The ancestor of a population is
defined as an inferred ancestral haplotype with at least one descendant in that
population. (c) 2d-histograms showing the inferred geographical location of
HGDP ancestral lineages at six time-points. Histogram bins with fewer than 10
ancestors are not shown. Link to ancestral location video: https://www.yout
ube.com/watch?v=AvV0zBSdxsQ&feature=youtu.be.
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Methods
Novel algorithms are described in this section, while details of dataset prepara-
tion and simulations can be found in the Supplementary Notes.
Tree Sequence Inference Algorithm
tsinfer is a scalable method for inferring tree sequence topologies using genetic
variation data1, which we update to version 0.2 by incorporating two features:
provision for inexact matching in the copying process and support for missing
data.
Mismatch, error, and recurrent mutation
The tsinfer algorithm is a two-step process. First, partial ancestral haplo-
types for the sampled DNA sequences are constructed on the basis of shared,
derived alleles at a set of sites. Second, a Hidden Markov Model (HMM) is
employed from left to right along each haplotype to infer which, among the
array of older haplotypes, gives the closest match. This is based on the Li and
Stephens2(LS) copying model. In previous versions of tsinfer, we supported
only exact haplotype matching – if a haplotype matched perfectly against an
ancestor up to a certain position, but then a mismatch occurred, it could only
be explained by switching to a different ancestor via recombination. The new
algorithm now supports the full LS model including a mismatch term which
allows for inexact matching, where mismatches between a target haplotype and
its inferred ancestor are explained by additional mutations. The relative prob-
abilities of recombination versus mismatch are tuned via a “mismatch ratio”
parameter: high ratios lead to fewer inferred recombination events and more
additional mutations, while low ratios result in more recombination events and
fewer additional mutations (see Supplementary Note S1.1)
Probabilities of recombination between adjacent sites can be provided in the
form of a genetic map. However, optimal mismatch probabilities will depend
on factors such as sequencing error and variation in mutation rates along the
genome. To establish suitable mismatch ratios, we therefore evaluated inference
performance on both simulated and real data. Extended Data Fig. 1 shows the
effect of different mismatch probabilities, using a simulated 10 megabase (Mb)
region of 1,500 human genomes, both with and without added error in sequenc-
ing and ancestral state polarisation. Different metrics disagree slightly on the
optimal values used to minimise difference between the simulated and inferred
trees (see Supplementary Note S1.2). However, error metrics are consistently
low when mismatch ratios in both the ancestor and sample matching phases are
set to between 0.001 and 10. This range is also suggested as optimal by two dif-
ferent proxy measures of tree sequence complexity based on file size. Extended
Data Fig. 2 shows roughly the same pattern when inferring tree sequences from
real data, although in these cases only file size measures are available ––– no
ground truth exists for comparison. In all cases, good results are obtained by
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mismatch ratios close to unity, where the probability of a mismatch is set equal
to the median probability of recombination between adjacent inference sites
(marked as dashed and dotted lines on the plots). A mismatch ratio of 1 is
therefore used in all further analyses; the breadth of the plateau in parameter
space indicates similarly accurate results are obtained using mismatch ratios
within an order of magnitude either side of this value.
Missing data
Missing data is accommodated in tsinfer by using older ancestors as a “refer-
ence panel” for imputation. In the core tsinfer HMM, samples and ancestors
copy from older ancestors. If the sample or ancestor contains missing data at a
site, the missing genotypes are imputed from the most recent ancestor without
missing data. The approach provides a principled approach to imputing miss-
ing data for both contemporary and ancient genomes, as only older ancestral
haplotypes are used.
Dating Algorithm
We use the tree sequence topology estimated by tsinfer as the basis for an
approximate Bayesian method to infer node age. This approach is implemented
in the open-source software package tsdate.
Conditional Coalescent Prior
The first step in the algorithm is to assign a prior distribution to the age of
ancestral nodes in the tree sequence. A coalescent prior is an obvious choice3–5.
However, rather than use a fully tree sequence-aware prior, we use an approxi-
mate approach based on assigning marginal priors to each node. Specifically, we
use the number of modern samples descending from each node to find a mean
age and associated variance under the coalescent6. In the tree sequence, a single
node may span many trees, and therefore be associated with several of these
means and variances: we take the average, weighted by tree span, resulting in
an average mean and average variance for each ancestral node. We then use mo-
ment matching to fit a lognormal distribution as a prior, πu, for the age of node
uin the tree sequence. Details of this approach can be found in Supplementary
Note S1.2.
Time Discretisation
Our inference approach requires a time grid for efficient computation. This
is constructed by taking the union of the quantiles of the prior distribution
of each ancestral node. The advantage of this approach is that inference is
focused on times with greater probability under the prior, outperforming a naive,
uniform grid. The density of the time grid is determined by the user-specified
number of quantiles to draw from each ancestral node as well as a value, ,
which establishes the minimum time distance between points in the grid. The
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conditional coalescent prior πufor a node uallows us to find a probability πu(t)
for each time-slice tin the grid.
Inside-Outside Algorithm
With a prior in place for ancestral nodes in the tree sequence and a time grid,
we infer the age of nodes using a belief propagation approach we call the inside-
outside algorithm, based on an HMM where the age of nodes are hidden states.
In the case of a single tree, this equates to the standard forward-backward
algorithm. In the case of a tree sequence, we must also consider the relative
genomic spans associated with edges and deal with cycles in the undirected
graph underlying the tree sequence. Cycles occur whenever a node has multiple
parents and present a general problem in belief propagation7.
The algorithm is efficient because it uses dynamic programming and the tree
sequence traversal methods implemented in tskit, the tree sequence toolkit.
Scaling is linear with the number of edges in the tree sequence (Extended Data
Fig. 5) and quadratic with the number of time slices used.
Inside pass
We seek to compute all values in the inside matrix Ifor all nodes and times
in the discretised time grid. Iu(t)is the probability of node uat time t, which
encompasses the probability of all nodes and edges in the subgraph beneath u.
We initialise the prior probability of a sample node to be 1 at its sampled time
and 0 elsewhere. We then proceed backwards in time, using the relationships
between nodes encoded in the tskit edge table until we reach the most recent
common ancestor (MRCA) nodes of the tree sequence. For each node, we visit
every child as well as every time tin the time grid using
Iu(t) = πu(t)Y
dC(u)X
t0t
Ldu(tt0+;Ddu , θ)Id(t0)wdu ,
where C(u)is the set of all child nodes of u, and as previously defined, πu(t)is
the prior probability of node uat time t.Ldu(tt0+;Ddu , θ)is the mutation-
based likelihood function of the edge from focal node uat time tto child node
dat time t0.is an arbitrarily small value that is used to prevent parent and
child nodes from existing at the same time slice. Ddu is the data associated
with the edge including the span of the edge and the number of mutations on
it. θis the population-scaled mutation rate. wdu is the span of the edge leading
from uto ddivided by sd, the total span of node din the tree sequence. Note
that the inside probability of node dis geometrically scaled by wdu to address
overcounting if dhas multiple parents.
The likelihood function gives the probability of observing kmutations on
an edge of length δt =tt0+with span ldu . It is Poisson distributed with
parameter (θldu δt)/2
Ldu(δt;Ddu, θ) = θldu δt
2k
k!e
θlduδt
2.
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We can factorise the inside probability as
Iu(t) = πu(t)Gu(t),
where Gu(t)is
Y
dC(u)
gd(t)
and gd(t)is
X
t0t
Ldu(tt0+;Ddu , θ)Id(t0)wdu .
This factorisation will be useful in describing the outside pass in the next section.
The equation terminates at the MRCA(s) of the tree sequence. The total
likelihood of the tree sequence is obtained by taking the product of the inside
matrix of each MRCA.
Outside pass
Once we have iterated up the tree sequence to find the inside matrix at every
node, the inside probability of the MRCAs contain all of the information encoded
in the tree sequence. To find the full posterior on node age, we now take
account of the information in the tree sequence “outside” of the subgraph of
each ancestral node. While this algorithm empirically performs well with a single
inside and outside pass, any cycles in the underlying undirected graph (which
occur when recombination causes a node to have more than one parent) will
result in overcounting. The alternative “outside-maximisation” pass introduced
in Supplementary Note S1.2.2 provides another approximate solution in these
cases, though we find that the outside pass performs better empirically (see
Fig. S2).
Beginning with the MRCA nodes in each marginal tree (the roots), we ini-
tialise the outside value of these nodes, OMRCAs, to be one at all non-zero time
points. There is no information “outside” the MRCAs because all information
in the tree has already been propagated to the node and is encoded in the MR-
CAs’ inside matrices. In a tree sequence, it is possible for a node uto be the
MRCA in some of the marginal trees in which it appears but not in other trees.
In these cases we find Ouby dividing the span of trees where the node is the
MRCA by su, the total span of uin the tree sequence.
We then proceed down the tree sequence (forwards in time), again using the
edge table sorted in descending order by the children’s age. At every node we
calculate:
Ou(t) = Y
pP(u)X
t0t
Op(t)wupLpu(t0t+;Dpu , θ)Ip(t0)
gup(t0)wup
,
where P(u)is the set of parents of node uand other terms are defined in the
previous section on the inside algorithm.
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Once the inside and outside passes are complete, the approximate posterior
can be calculated as
φu(t)Iu(t)Ou(t).
Importantly, the mean value of the posterior distribution may not be con-
sistent with the tree sequence topology. We provide the option to “constrain”
node age estimates by forcing each node to be older than the estimated age of
its children. The unconstrained mean and variance of each node are retained as
metadata in the tree sequence. The full posterior can also be retained separately
if desired.
We observe that mutations mapping to edges descending from the single
oldest root in tree sequences inferred by tsinfer are generally of lower quality,
so in our implementation of the outside pass we include an option to avoid
traversing such edges. We use this setting in all analyses using tsdate in this
work. Additionally, results from tsdate do not include estimates for mutations
appearing on these edges.
Iterative Approach for Inferring Tree Sequences with An-
cient and Modern Samples
We combined tsinfer and tsdate in an iterative approach that allows for
the incorporation of ancient samples and improves inference accuracy in many
settings.
The first step of the iterative approach is to order derived alleles appearing
in the sample by their frequency. tsinfer requires a relative ordering of derived
alleles to both build ancestral haplotypes and infer copying paths. Frequency
is a largely accurate and highly efficient means of providing an ordering for
these ancestors1. Once alleles are ordered, it is possible to infer a tree sequence
topology with tsinfer (Fig. 1b Step 1).
With an inferred tree sequence topology, we next estimate the age of inferred
ancestral haplotypes with tsdate (Fig. 1b Step 2). If using tsdate’s outside
pass, we do not constrain the resulting date estimates by the topology.
If ancient samples are present, we can use them to constrain the estimated
age of derived alleles. The previous step (Fig. 1b Step 2) provides date estimates
for the inferred ancestors as well as for mutations. Since we estimate the age
of the ancestral nodes above and below a mutation, the child node of an edge
hosting a mutation is constrained by the ancient sample-informed lower bound
on derived allele age. This bound is determined by gathering the haplotypes of
ancient samples (either sequenced or genotyped) and examining derived alleles
that can be called in these ancient samples with high confidence. If multiple an-
cient samples carry the same derived allele, we use the oldest sample as the lower
bound on its age. Once lower bounds have been collected for all derived alleles
observed in ancient samples, we compare these with our statistically inferred
lower bounds on allele age, adjusting our age estimates where necessary to en-
sure consistency with ancient samples. Any radiocarbon-dated ancient samples
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with high-confidence variant calls may provide constraints in this step, includ-
ing unphased and/or low-coverage samples. Although a substantial fraction of
radiocarbon dates are likely inaccurate, we note that there is a low probability
that errors on the order of a few thousand years will meaningfully affect tree se-
quences inferred using this approach. Only a subset of erroneously dated alleles
will be older than the true age of the mutation, which would affect allele age
estimation accuracy, and still fewer will be older than the ancestral haplotype
from which they descend, which would affect topological estimation accuracy.
With allele age estimates from step 2, possibly constrained by ancient sam-
ples in step 3, we are now able to re-infer the tree sequence topology. The revised
age estimates are used to order the age of derived alleles when re-estimating
ancestral haplotypes with tsinfer; if they are more accurate than frequency
in determining a relative ordering of mutations, topological inference accuracy
should be improved. Indeed, we find that the iterative approach improves ac-
curacy when re-inferring tree sequences from variation data simulated with a
uniform recombination map and without error (Fig. 1d). When reinferring tree
sequences from data simulated with error or with a variable recombination map,
less improvement is observed (Fig. S4).
Ancient samples can be included in tree sequences that are (re)-inferred
with estimated allele ages. This is accomplished by inserting ancient samples
at their correct relative ordering among ancestors generated by tsinfer. Only
phased ancient samples with an age estimate may be included, although we
note that extending tsinfer’s HMM to handle diploid individuals may allow
for phasing of ancient samples in this step. We additionally produce “proxy
ancestors” associated with ancient samples at a slightly older time than the
ancient sample. These are composed of all non-singleton sites carried by the
ancient sample, and may serve as ancestors to younger ancestors and samples.
Finally, we infer copying paths between ancestors and samples to produce a tree
sequence of modern and ancient samples.
Inferring the Location of Ancestors in a Tree Sequence
We use a naive, non-parametric approach to gain insight into the geographic lo-
cation of ancestral haplotypes based on the known locations of sampled genomes.
The latitude and longitude coordinates of individual samples are provided for
SGDP individuals, while the location of sampling centres were used for the
HGDP individuals. No geographic information was provided for TGP individu-
als, so these were not used in location inference. We also used the coordinates of
the archaeological sites associated with the Afanasievo and Archaic individuals.
The weighted centre of gravity is determined for each ancestral node by
iterating up the tree sequence, visiting child nodes before their parents using
the same traversal pattern as for the previously described inside algorithm. At
each focal ancestral node, we find the geographic midpoint between each of
the children of that node. The following simple approach was used to find the
geographic midpoints. For a node u, the latitude and longitude coordinates
of the child node of each edge descending from uwere converted to Cartesian
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23
coordinates. We find the average of the children’s coordinates and convert this
back to latitude and longitude. We then continue up the tree sequence using
this location to calculate the coordinates of u’s parents.
This method is highly efficient, requiring less than 1 minute to compute on
the combined tree sequence of Chromosome 20.
Code and Data Availability
tsinfer is available at https://tsinfer.readthedocs.io/ under the GNU
General Public License v3.0, tsdate at https://tsdate.readthedocs.io/
under the MIT License, and tskit at https://tskit.readthedocs.io/ under
the MIT License. All code used to perform analyses in this paper can be found
at https://github.com/awohns/unified_genealogy_paper.
All publicly available datasets used in this paper are available from their
original publications. See Supplementary Note for details.
Acknowledgements
Funded by the Wellcome Trust (grant 100956/Z/13/Z to GM), the Li Ka Shing
Foundation (to GM), the Robertson Foundation (to JK), the Rhodes Trust (to
AWW), the NIH (NIGMS grant GM100233 to DR), the Paul Allen Foundation
(to DR), the John Templeton Foundation (grant 61220 to DR) and the Howard
Hughes Medical Institute (to DR). The computational aspects of this research
were supported by the Wellcome Trust (Core Award 203141/Z/16/Z) and the
NIHR Oxford BRC. The views expressed are those of the authors and not nec-
essarily those of the NHS, the NIHR or the Department of Health. We thank
the Oxford Big Data research computing team, specifically Adam Huffman and
Robert Esnouf, and Daniel Lieberman and E. Castedo Ellerman for comments.
Competing Interests
GM is a director of and shareholder in Genomics plc and a partner in Peptide
Groove LLP.
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(a) No added error
(b) Empirical sequencing error + 1% ancestral state polarisation error
Extended Data Fig. 1: The effect of varying the mismatch ratio on accuracy met-
rics for tsinfer. Results from 1,500 simulated human-like genome sequences
of 10 Mb in length. (a) Simulations without error. (b) Simulations with an
empirically calibrated genotyping error model and 1% error in ancestral state
assignment. For each panel, the upper (coloured contour) plots show accuracy
metrics as a function of the mismatch ratio in ancestor matching (x-axis) and
in sample matching (y-axis) algorithms. Slices through contour plots indicated
by the dashed and dotted lines are plotted in the lower (line) plots. The to-
tal number of edges plus mutations, and filesize relative to the simulated tree
sequence (first 2 columns) are indirect measures of accuracy. Direct measures
of inference accuracy provided via the Kendall-Colijn (KC) or Robinson-Foulds
(RF) tree-distance metrics (middle columns) which can, however, be influenced
by polytomy size (i.e. node arity: last column); breaking polytomies at random
may reduce this influence. Metrics are normalised against maximum expected
distances. See Supplementary Note S2.1 for further details.
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(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
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26
(a) 1000 Genomes Project (TGP), inference performed on a
4 Mb region from 5,008 genomes with no missing data
(b) Human Genome Diversity Project (HGDP), inference
performed on 4.6 Mb region from 1,858 genomes with 1.2%
missing data
Extended Data Fig. 2: Effect of mismatch ratio parameter on tsinfer results
from empirical sequence data (based on a subset of 100,000 sites on the short
arm of Chromosome 20). Dotted and dashed lines as for Extended Data Fig. 1.
See Supplementary Note S2.1 for further details.
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(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
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27
Extended Data Fig. 3: The relationship between metrics of variant-calling error
and the number of mutations on the inferred tree sequence. For the combined
tree sequence of HGDP, TGP, SGDP, and ancient samples, the proportion of
sites in two categories - low quality and low linkage, binned by the number of
mutations at the site. Low quality is defined by the TGP strict accessibility
mask. Sites that fail any of the accessibility mask filters such as low coverage
or low mapping quality are marked as low quality. Low linkage is defined by
summing the linkage disequilibrium (r2) for the 50 sites either side of the focal
site. If this quantity is less than 10 the site is marked as low linkage.
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(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
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28
Extended Data Fig. 4: Accuracy of variant age inference. Evaluation of the ac-
curacy of tsdate,tsinfer,GEVA and Relate on 5 Mb sections of Chromosome
20 simulated using the OutOfAfrica_3G09 model implemented in stdpopsim2–4
with the Chromosome 20 GRCh37 recombination map and 100 samples each
from YRI, CEU, and CHB. 30 replicates were performed. The top row shows
the accuracy of tsdate on the simulated topology. The second row shows the
results of inferring tree sequences with tsinfer, dating the tree sequence with
tsdate, and then re-inferring and re-dating the tree sequence (using the Chro-
mosome 20 recombination map and a mismatch ratio of 1). The third row shows
the results of Relate using a script provided by the authors to re-infer branch
lengths and Ne. The fourth row shows the results of GEVA with default param-
eters. The first column shows simulations without genotype error, the second
shows simulations with an empirical error model and the third shows an empir-
ical error model and 1% ancestral state error. In each column, only sites dated
by all three methods are shown. Summary metrics are shown in each subplot.
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29
Extended Data Fig. 5: Scaling properties of tsdate compared to tsinfer,
Relate, and GEVA. The left column shows the CPU and memory requirements
for inference using the three methods on msprime simulations of 1 Mb, with
Ne= 104,µ=r= 108and sample sizes from 10 to 2000 (Relate continues
to scale quadratically with larger sample sizes). Five replicates were performed
at each sample size. The column on the right shows results of ten msprime
simulations with sample size fixed at 250 and simulated lengths of 100 kb to
10 Mb. The main axes compare results for tsdate,tsinfer, and Relate. The
inset plots show the same data with the addition of GEVA, which otherwise
obscures the differences between other methods.
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30
(a) Descent from proxy Afanasievo ancestors on Chromosome 20 among HGDP, SGDP,
and TGP populations. The upper panel shows the proportion of genetic material in
each population that descends from the proxy Afanasievo ancestors (using the genomic
descent statistic1). Only populations with at least two individuals and a mean genomic
descent value of 0.01% are shown. Boxplots in the lower panel show the distribution
of descendant material among samples from the corresponding population.
(b) Patterns of descent among samples with at least 100 kb of material descending
from Afanasievo proxy ancestors. Each row is a sample and each column is a 1 kb
section of Chromosome 20. The region of origin of each sample is coloured on the left
side of the row.
Extended Data Fig. 6: Inferred patterns of descent from Afanasievo proxy an-
cestors on Chromosome 20. The colour scheme for each region is the same as
in Fig. 2.
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31
Extended Data Fig. 7: Descent from Denisovan proxy ancestors on Chromo-
some 20. The upper portion shows the proportion of genetic material in each
population that descends from the proxy Denisovan ancestors (the genomic de-
scent statistic1). Boxplots in the lower panel show the distribution of descendant
material among samples from the corresponding population. Only populations
with a mean genomic descent value of 0.04% are shown. See Fig. 3 for details
of the modern haplotypes inherited from Denisovan proxy ancestors.
Extended Data Fig. 8: Descent from Vindija Neanderthal proxy haplotypes
on Chromosome 17-22. Genomic descent1results from each chromosome are
plotted for each region. The boxplot indicates the inter-quartile range, the
whiskers extend to the minimum and maximum genomic descent values across
the five chromosomes within each population.
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