New Statistical Method Reveals Surprises About Our Ancestry: Inferring Human Colonization History Using a Copying Model
- From: Jack Linthicum <jacklinthicum@xxxxxxxxxxxxx>
- Date: Wed, 28 May 2008 11:41:23 -0700 (PDT)
Figures and other illustrations in the larger document at the cite
Inferring Human Colonization History Using a Copying Model
http://www.sciencedaily.com/releases/2008/05/080522210025.htm
New Statistical Method Reveals Surprises About Our Ancestry
ScienceDaily (May 24, 2008) — A statistical approach to studying
genetic variation promises to shed new light on the history of human
migration.
Scientists from the University of Oxford and University College Cork
have developed a technique that analyses shared parts of chromosomes
across the entire human genome. It can give much finer detail than
other methods and makes it possible to delve further back in time and
identify smaller genetic contributions.
Application of the method has already turned up such surprising
findings as a strong Mongolian contribution to the genes of the Native
American Pima people and gene flow from the north of Europe to Eastern
Siberia.
Previous methods of genome analysis have either concentrated on one
part of the human genome -- for example, just the Y-chromosome -- or
are based on "beanbag genetics" -- an oversimplified model of heredity
that does not fully consider chromosomal structure. The new technique
described by Hellenthal and colleagues was used to analyse 2000
genetic markers using Single Nucleotide Polymorphism data from the
2006 Human Diversity Project.
The researchers believe their method can cope with much larger
datasets with over 500,000 genetic markers.
Further developments of the technique should allow more finely
detailed reconstruction of human ancestry and give a perspective
independent of anthropological theory and interpretation.
Journal reference:
1. Hellenthal G, Auton A, Falush D. Inferring Human Colonization
History Using a Copying Model. PLoS Genet, 2008; 4(5): e1000078 DOI:
10.1371/journal.pgen.1000078
Adapted from materials provided by Public Library of Science, via
EurekAlert!, a service of AAAS.
The full article, minus figures, etc.
MLA
Public Library of Science (2008, May 24). New Statistical Method
Reveals Surprises About Our Ancestry. ScienceDaily. Retrieved May 28,
2008, from http://www.sciencedaily.com; /releases/
2008/05/080522210025.htm
Inferring Human Colonization History Using a Copying Model
Garrett Hellenthal1, Adam Auton1,2, Daniel Falush1,3*
1 Department of Statistics, University of Oxford, Oxford, United
Kingdom2 Department of Biological Statistics and Computational
Biology, Cornell University, Ithaca, New York, United States of
America3 Department of Microbiology, Environmental Research Institute,
Cork, Ireland
Abstract
Genome-wide scans of genetic variation can potentially provide
detailed information on how modern humans colonized the world but
require new methods of analysis. We introduce a statistical approach
that uses Single Nucleotide Polymorphism (SNP) data to identify
sharing of chromosomal segments between populations and uses the
pattern of sharing to reconstruct a detailed colonization scenario. We
apply our model to the SNP data for the 53 populations of the Human
Genome Diversity Project described in Conrad et al. (Nature Genetics
38,1251-60, 2006). Our results are consistent with the consensus view
of a single “Out-of-Africa” bottleneck and serial dilution of
diversity during global colonization, including a prominent East Asian
bottleneck. They also suggest novel details including: (1) the most
northerly East Asian population in the sample (Yakut) has received a
significant genetic contribution from the ancestors of the most
northerly European one (Orcadian). (2) Native South Americans have
received ancestry from a source closely related to modern North-East
Asians (Mongolians and Oroquen) that is distinct from the sources for
native North Americans, implying multiple waves of migration into the
Americas. A detailed depiction of the peopling of the world is
available in animated form.
Author Summary
Humans like to tell stories. Amongst the most captivating is the story
of the global spread of modern humans from their original homeland in
Africa. Traditionally this has been the preserve of anthropologists,
but geneticists are starting to make an important contribution.
However, genetic evidence is typically analyzed in the context of
anthropological preconceptions. For genetics to provide an accurate
and detailed history without reference to anthropology, methods are
required that translate DNA sequence data into histories. We introduce
a statistical method that has three virtues. First, it is based on a
copying model that incorporates the block-by-block inheritance of DNA
from one generation to the next. This allows it to capture the rich
information provided by patterns of DNA sharing across the whole
genome. Second, its parameter space includes an enormous number of
possible colonization scenarios, meaning that inferences are
correspondingly rich in detail. Third, the inferred colonization
scenario is determined algorithmically. We have applied this method to
data from 53 human populations and find that while the current
consensus is broadly supported, some populations have surprising
histories. This scenario can be viewed as a movie, making it
transparent where statistical analysis ends and where interpretation
begins.
Citation: Hellenthal G, Auton A, Falush D (2008) Inferring Human
Colonization History Using a Copying Model. PLoS Genet 4(5): e1000078.
doi:10.1371/journal.pgen.1000078
Editor: Molly Przeworski, University of Chicago, United States of
America
Received: November 1, 2007; Accepted: April 18, 2008; Published: May
23, 2008
Copyright: © 2008 Hellenthal et al. This is an open-access article
distributed under the terms of the Creative Commons Attribution
License, which permits unrestricted use, distribution, and
reproduction in any medium, provided the original author and source
are credited.
Funding: The authors were supported by Polygene grant LSHC-
CT-2005-018827 (GH), the Engineering and Physical Sciences Research
Council via the Life Sciences Interface doctoral training program
(AA), The Wellcome Trust and the Science Foundation of Ireland, grant
number 05/FE1/B882 (DF). The project also benefited greatly from
computing resources funded by a grant from the Wolfson Foundation.
Competing interests: The authors have declared that no competing
interests exist.
* E-mail: d.falush@xxxxxx
Introduction
According to current models, modern humans arose in Africa and spread
around the world, with little or no genetic contribution from the
hominid populations that they displaced [1],[2],[3]. Genetic diversity
decreases progressively with land distance from East Africa [4]
providing support for a “serial dilution” model in which diversity was
lost progressively in sequential bottlenecks associated with small
founder population sizes as new territories were colonized [5],[6].
However, the good fit of serial dilution models might principally
reflect recent admixture, which will tend to smooth diversity clines.
Numerous questions remain about how many independent bottlenecks
occurred as new continents were colonized, the exact land routes
involved, and whether there have been genetically important migrations
that do not conform to a model of progressive outward expansion [7],
[8],[3].
Statistical inference of colonization history represents a
considerable challenge. A reasonably detailed description would
include (1) the times of major population splits, (2) the effective
sizes of each distinct population and/or a list of major bottlenecks
and (3) times of major admixture events, when previously distinct
populations met and the contributions of the distinct populations to
the new hybrid population. Even a complex population based history
does not fully describe migration patterns, since isolation by
distance can also be important. DNA is passed down through generations
in linear segments whose boundaries are determined by meiotic
crossovers. Modeling the segment-by-segment inheritance of genetic
material is technically challenging even assuming simple demographic
scenarios [9]. Adding modern and ancient population subdivision makes
computations more complex and introduces the problem of choosing
amongst a very large number of possible split and merger scenarios.
We take an approach that models the segmental pattern of human
inheritance and also allows comparison between numerous distinct
historical scenarios. The approach is predicated on populations
arising in an order that can be inferred from the data. For any given
ordering of the populations in the sample, we use the copying-with
recombination model of Li and Stephens [10] to reconstruct all of the
chromosomes. Different orderings of the populations can be compared
based on the overall likelihood of generating the entire set of
chromosomes in the sample.
Since all the data we analyze is from contemporaneous samples, the
assumption of an ordering is incorrect if interpreted literally.
However, under a serial dilution model, for example, it is natural to
think of populations arising sequentially during radiation from
Africa. Subseqent migrations and admixture have complicated this
picture but a sufficient signal of these early events remains that the
ordering our approach generates can for the most part be interpreted
reasonably easily. For example, the “Out of Africa” bottleneck has
left a signal of greater genetic diversity in Africans, both at the
nucleotide [11] and haplotype levels [12] in the great majority of
African and non-African populations, whatever their subsequent
demographic history. One of the properties of the Li and Stephens
model is that the likelihood of an ordering will generally be higher
if the most diverse haplotypes are created first. Our analysis finds
the same strong signal that is evident in the summary statistics of
diversity; for the dataset of Conrad et al [12] the likelihood of
generating two populations, one of which is African, is always higher
if the African population is first.
In addition to the order in which populations were founded, we would
also like to learn about patterns of ancestry. For each new
population, a subset of individuals from the previously formed
populations is designated as a “donor pool.” In the model, each new
haploid genome or “haploid” is formed by copying chromosomal segments
from the donor pool or from previously created haploids in the same
population (for notational simplicity we assume that every individual
consists of two haploids that each contain one of the two copies of
the 22 autosomes). The model allows different donor pool combinations
to be compared according to the likelihood of generating all the
chromosomes in the new population. The number of individuals from each
population in the donor pool with the highest likelihood provides an
indication of the relative importance of different ancestral sources.
For convenience, we refer to the donors using the labels of the modern
populations they come from, but they in fact represent surrogates for
the shared common ancestors of the donor and recipient populations.
The generation of individuals from a single population is illustrated
for a hypothetical example in Figure 1.
thumbnail
Figure 1. Formation of a new population using its donor pool.
The donor pool for population D consists of the red, blue and green
haploids from populations A, B and C. Gray haploids are not used as
donors. Haploids within population D are created in order, and
previously created haploids from population D can be used in the
formation of each new one (magenta). For example, haploid D1a is
copied from A1a, C2b and B2b, while haploid D1b is copied from C1b,
B2b, C1a and D1a. One of the two alleles at each locus is indicated by
a black cross, with differences from the copied haploid, i.e.
mutations, indicated by a white box around the mutated nucleotide.
doi:10.1371/journal.pgen.1000078.g001
Results
Simulated Data
We tested our inference method using data simulated under a coalescent
model [13],[14], with individuals sampled from five populations,
labelled A-E, that were generated by sequential bottlenecks (Figure 2-
(a)). Parameters were guided by previous demographic estimates [15],
with the first bottleneck approximately corresponding to the “Out of
Africa” event. In 10 independent realisations of the same scenario (5
with simulated recombinational hotspots, 5 without), the model
correctly inferred both the order in which the populations were
founded and which populations gave rise to each new one (Figure 2-(b))
and did not infer any additional, spurious sources of ancestry. We
then complicated the model by giving populations D and E ancestry from
two sources (Figure 2-(c)). The model continued to infer the correct
ordering for the formation of the populations and correctly identified
the single sources for populations B and C and the two sources for
population E in every case. However, in 7 of the 10 simulations, the
ancestry of population D was inferred incorrectly, with the model
either failing to include population A as an ancestor (as shown in
Figure 2-(d)), mistakenly including population B, or both (Table S1).
We conclude that, at least for relatively simple scenarios, the model
provides an accurate indication of historical relationships between
populations but does not always correctly identify minority sources of
ancestry, in particular when admixture is ancient.
thumbnail
Figure 2. Simulations description and results.
(a) and (c) A graphical representation of the simulation parameters.
The initial colonization times for each of populations B-E are denoted
with dashed lines, with the times t provided on the right in units of
generations. Each rectangle represents the demography of one of
populations A-E, as labeled, with the rectangle width scaled by the
population size at time t. Each arrow represents the sources of
colonization for populations B-E, pointing from source population to
sink population, with arrow widths pointing into D and E roughly
proportional to the proportion of genetic material coming from that
source. (b) and (d) A graphical representation of typical examples of
the results of our model applied to the simulated data, showing
inferred ordering and sources for each population (black arrows). The
widths of the rectangles are proportional to the number of sampled
individuals for each population, and the thickness of the arrow shafts
indicate how many of those chromosomes act as donors for subsequent
populations.
doi:10.1371/journal.pgen.1000078.g002
One potential confounding factor in SNP data is ascertainment bias.
The SNPs that are chosen for genotyping are often ascertained based on
a limited sample of individual who come from one or a small number of
ethnic groups (typically Europeans). For example, in the data of
Conrad et al., heterozygosity of the SNPs was actually highest in the
Middle East, Central and South Asia and Europe, although these
populations are known to be less diverse than Africans. Our method
reconstructs haplotypes and therefore we expect it to depend
principally on patterns of haplotype sharing and diversity, which a
priori should be less sensitive to the ascertainment protocols of
individual SNPs. Indeed, in the data of Conrad et al., the haplotype
diversity is highest in Africans [12].
In order to test for an effect of ascertainment bias, we performed
inference in two extreme ascertainment schemes: one in which we
selected SNPs for all populations based only on those that were
heterozygous in population C, and one in which we selected SNPs for
all populations based only on those that were heterozygous in
population E. The former might represent ascertainment based only on
European or Middle Eastern populations. The latter would represent an
even more extreme and biased ascertainment, such as ascertaining SNPs
using only native Americans. We used 10 of the simulations described
above (the ones without recombination hotspots). In 9/10 cases,
results were not discernably different from those based on using all
SNPs. In the remaining simulation, population B and C were swapped in
the inferred ordering under both ascertainment schemes. We conclude
that even extremely biased ascertainment has a modest effect on
inference.
Our results might also be confounded by the incomplete nature of the
sample and by the many complexities of human population history. We
have performed additional simulations in order to assess how
complications to the scenarios shown in Figure 2 would affect
inference. We first evaluated the effect of leaving a population out
of the simulated datasets (population D). For all four simulations
(two as illustrated in Figure 2-a, one with and one without
recombination “hotspots,” and two as illustrated in Figure 2-c, one
with and one without recombination “hotspots”), population C was
chosen as a significant donor population for E. Remaining inference
was correct (i.e. no other spurious donors were detected, and for the
simulations illustrated in Figure 2-c, the model picked up the
additional contribution from population B.) This is what is expected:
with the appropriate donor population missing, our model chooses as
its replacement the population that contributed the majority of
genetic material to the missing donor population.
Complex patterns of admixture might considerably complicate inference.
We modified the scenarios shown in Figure 2-a and Figure 2-c by adding
recent admixture, either from D to C or from A to C. Examples are
shown in Figures 3-a and 3-c. A genetic contribution from population D
to C had little effect on inference in 10 different simulations
(Figure 3-d). These results show that “back admixture”, for example
migrations into Africa, will generally not be detectable by our
method. In this simulated example at least, the back admixture did not
affect the rest of the inference. The effect of a recent contribution
from population A to population C was more substantial. In 5/10 cases
(four for the scenario shown in Figure 3-a) the inferred order of
populations B and C were swapped (Figure 3-b). The swapping of the
populations leaves the genetic connections between the populations
correct but inferences on which are sources and which are sinks are
confused by the multi-layered migrational history.
thumbnail
Figure 3. Description and results for simulations with recent
admixture.
(a) and (c) A graphical representation of the simulation parameters,
comparable to Figure 2-a, with the addition of recent migration from
population A into C and recent back migration from population D into
C, respectively. (b) and (d) A graphical representation, as described
in Figure 2, of typical examples of the results of our model applied
to the simulated data. The recent back migration from population D
into C does not significantly alter inference, while recent migration
from population A into C results in mistakingly inferring that
population C is a source for B in this example.
doi:10.1371/journal.pgen.1000078.g003
Data of Conrad et al
We used the same approach to infer the order of birth and ancestral
sources of the 53 populations in the Human Genome Diversity Panel
using the data from 2,540 linked SNPs across 32 autosomal regions
genotyped by Conrad et al [12]. The highest likelihood scenario is
shown in Figure 4 and Movie S1. By visually inspecting these results,
we have identified nine phases in the colonization of the world. This
subdivision is subjective and the phases should not be thought of as
occurring strictly in chronological order. For example, East Asia and
Europe are peopled almost independently, making their relative
position in the ordering nearly arbitrary. Furthermore, Melanesia has
multiple sources that reflect ancient and recent migrations that
introduced very distinct genetic material (see [16] for a review). Its
inferred place in the ordering reflects the most recent of these
migrations. Nevertheless, the phases do reflect progressive outward
expansion, analogous to that implied by serial dilution models.
thumbnail
Figure 4. Summary of inferred history of the peopling of the world.
The formation of 53 populations has been condensed into 38 frames,
shown in full in Movie S1, by displaying the formation of each
population as soon as all of its donors are present. When 2 or more
populations are formed in the same frame, the connections from their
donors are shown in different colors. (A) Africa subsequent to San,
(B) initial colonization of central Eurasia, (C) initial colonization
of Far East and Europe, (D) Americas and Pacific Islands. The
thickness of each line is proportional to the mean estimated number of
donor individuals from each source (numerical values provided in Table
S2). Solid lines indicate that all or nearly all of the individuals in
the population were used as donors. Dashed lines indicate that on
average between four individuals and the number of available
individuals minus two were used.
doi:10.1371/journal.pgen.1000078.g004
1. Sub-Saharan Africa. The first population in the ordering are the
San, who are hunter gatherers that live in Southern Africa. Before the
Bantu expansion over the last 3,000 years, the ancestors of the San
occupied most of Southern Africa, but they have been progressively
displaced and currently are restricted to a few pockets [17]. The San
contributed ancestry to the next four populations (the Biaka Pygmies,
Bantu from South Africa and Kenya, and Mbuti Pygmies) but none
subsequent to that. The Bantu are inferred to have contributed to each
subsequent African population.
2. North Africa. The Mozabites are the only African population in the
sample from above the Sahara. In our analysis, they are the 8th and
final African population to arise and are also distinctive because
they represent the first population that uses less donor individuals
(46 from the Mandenka, Yoruba, and Kenyan Bantu) than their
predecessor the Mandeka, who used 64 donors from four populations. We
interpret the smaller number of donors as evidence for a bottleneck in
the history of the Mozabites, that is not shared by the other African
populations in the sample. The small number of donor populations
implies that only a subset of the human populations present at the
time of the bottleneck contributed to the Mozabite lineage.
3. Central Eurasia. There is no clear pattern to the order of
colonization of central Eurasia, with the initial Central Asian
populations (Makrani, Uygur) interspersed with those from the Near
East (Bedouin, Palestinians) and the eastern edge of Europe (the
Adygei). All of these populations have Mozabites as donors, with the
first three populations also using Kenyan Bantu. For these three, all
28 Mozabite individuals were used in generating each of the three
populations, making it possible that some of the Bantu chromosomes
would have been replaced by additional Mozabites or other North or
East Africans if they were present in the sample. Overall, non-African
populations can each trace approximately 3/4 of their ancestry via the
Mozabites (Movie S2, Table S4). The total number of donors increases
progressively from 39 for the Makrani to 141 for the Adygei. The high
interconnectedness of these populations presumably reflects the
absence of region-specific bottlenecks and/or multiple episodes of
gene flow between Eurasian populations subsequent to the initial
colonization event(s).
4. Central Europe. Aside from the Adygei, the first European
populations to arise are the French, Tuscans, and Italians. These
three populations have an average of 260 donors, including those from
the Mozabites and several Near Eastern and Central Asian populations.
This is a larger number than for any non-European population in the
sample and highlights the diverse sources of European ancestry.
5. Pre-Han East Asia. The first 8 East Asian populations (Cambodia,
Mongolia, Oroqen, Xibo, Yi, Tu, Daur, Naxi) have 50-84 donors,
including all 32 individuals from two central Asian populations, the
Uygur and the Hazara (except the Tu who use 24/32). This represents an
entirely distinct source of ancestry from European populations, who
each receive less than 10% of their ancestry via the Uygur and almost
none via the Hazara (Movie S2, Table S3). The only other external
donors are the Pathan (contributing 12 chromosomes to Mongolians) and
the Burusho, Sindhi and Mozabites, who contribute 23, 15, and 4 donors
to the Cambodians respectively. We interpret the paucity of donors and
the consistence of ancestry patterns as evidence for a single East
Asian bottleneck.
6. The extremities of Europe. The final four European populations (the
Sardinians, Russians, Orcadians and Basque) all lie on the extremities
of the continent. As well as having many European donors, these
populations also have a large number from the Near East and Central
Asia, consistent with Europe absorbing multiple waves of migrants. The
Russians have 375 donors, more than for any other population,
including from the Yi, Tu, and Mongolians, indicative of admixture
with Far-Eastern populations. The Basque have 4 Hezhen donors but are
otherwise similar to other Europeans.
7. The Han expansion. The Han receive their ancestry exclusively from
other East Asian populations (including the more westerly Xibo) and
represent a principal source of ancestry for several subsequent
populations that also have principally East Asian ancestry (She,
Japanese, Dai, Lahu, Han from Northern China, and Miao).
8. The Americas. The Colombians are the first Amerind population. 47%
of their ancestry can be traced via the Hazara, which is marginally
less than typical East Asian populations such as the Han (54%) or Xibo
(59%) (Movie S2, Table S3). However, within the descendents of the
putative EastAsia bottleneck, their donor pool is diverse, implying
that none of the populations in the sample provides a good proxy for
the original group or groups that crossed the Bering straight. The
Colombians also have French donors, which may reflect post-Colombian
admixture. The second American population, the Pima, represents the
first North American population. As well as using all 7 Colombians as
donors, it uses 8 Mongolians and 4 Oroquen. Neither of these
populations acted as donors to the Colombians, suggesting distinct
colonization events from different sources. Subsequent American
populations did not have any non-Amerind donors, except for the Mayans
who have Bantu and Tuscan donors, presumably due to post-Columbian
admixture [18].
9. Pacific Islands. All but two of the East Asian populations that
donate to the Colombians also donate to the Melanesians, and the
Japanese are again the most numerically important with 20 donors.
However, the Melanesians have several additional sources of ancestry.
These include three populations which are products of the East Asian
bottleneck (Oroquen, Han, and Pima), in addition to Central Asian
populations (Burusho and Brahui) and Russians. Three Mozabite donors
are also estimated, which falls slightly below our conservative
threshold for significance (Methods). In total, the Melanesians trace
38% of their ancestry via the Hazara, which is less than East Asian or
Amerind populations and implies independent sources of ancestry. The
Papuans receive ancestry only from Melanesians and Cambodians,
suggesting a shared common bottleneck.
One concern for this dataset is that the number of individuals varies
widely among populations (from 6 to 45). We investigated whether this
might have a substantial effect on our results by correlating the
number of individuals in each population with both its position in the
inferred ordering (Figure S1) and the total number of donors it
received (Figure S2). Using simple linear regression, no strongly
significant correlation was found in either case (p-value > 0.05).
Discussion
We have inferred a scenario for the peopling of the world using SNP
data from 53 populations (Movie S1) by maximising a single likelihood
function (Equation 4, see “Ancestry model” section) that uses the
extensive information on ancestry provided by linkage between markers
in the same chromosomal region. Heuristic algorithms were needed in
order to search the very large space of possible scenarios for a high
likelihood solution (Methods) but the the scenario was generated
automatically and without the use of geographical information apart
from population labels. Because our model is simplified, this scenario
should not be interpreted as a full chronological colonization
history; automatic inference of such a history will require further
methodological advances. Nevertheless, because the scenarios our model
generates can be related to histories in a reasonably straightforward
and transparent fashion, our method is of immediate use in independent
hypothesis generation. We describe two such hypotheses below.
These hypotheses gain plausibility because our model also regenerates
hypotheses that are already well established in the anthropological
genetics literature. First, our results suggest a single major “out-of-
Africa” bottleneck. The African populations are all generated prior to
all of the non-African ones. Further the great majority of the
ancestry of non-Africans goes via a single African population, the
Mozabites. The only exceptions are Kenyan Bantu contributions to the
first three non-African populations, and South African Bantu
contributions to the Sindhi and the Maya. Admixture with descendents
of the slave trade can explain the Bantu contribution to the Maya and
possibly also to the Sindhi, who have coexisted with a small
ethnically African minority, the Sidi, for several hundred years [19].
There is no evidence of any ancient contribution to non-African humans
that are independent of the main source populations.
Second, our results are broadly consistent with serial dilution and
the peopling of the Americas via the Bering Strait. East Asians arise
from central Asians, as do Native Americans. Melanesians have broader
ancestry pool than East Asians, suggestive of multiple independent
waves of colonization [16]. Their late position in the ordering
reflects the ancestry they have derived from East Asians, while the
Cambodians precede all other East Asian populations consistent with
earlier migrations towards the South [8]. European populations all
have a strikingly diverse set of donors, consistent with admixture
during “demic diffusion” of near-Eastern DNA into Europe during the
spread of agriculture [20] and [21], and the many other documented
migrations into Europe, such as from North Africa [22]. Russians have
the most diverse sources of ancestry, including from East Asians,
consistent with admixture in the sprawling Russian empire.
Independent Sources of Ancestry for Northern and Southern Amerinds
In our inferred scenario, Pima are the first North American population
in the ordering and receive ancestry from the first South American
population, the Colombians. The Pima have two additional donor
populations, the Oroquen and Mongolians, both of whom reside in
Mongolia and neither of which are donors to Colombians. This result is
intruiging because it suggests independent sources for North and South
Americans and hence multiple waves of migration into the continent,
contradicting the current consensus based on available data [23].
We tested the robustness of this inference by swapping the two
populations in the ordering and re-inferring donors using the same
protocol. The Pima replaced their Colombian donors with a small number
of East Asians who were donors to the Colombians (4 donors each from
Naxi and She), but the Mongolians and Oroquen remained majority
donors. This result mirrors what is found in our simulations; if a
donor population is missing (or also present in insufficient numbers
in the sample) then it will typically be replaced by one or more of
its own donors. The Colombians gained the Pima and lost a substantial
number of other donor populations, but kept several from populations
that did not contribute to the Pima in either ordering (Daur, Hezhen,
Xibo and Burusho).
These results are consistent with substantial gene flow between North
and South America but also imply that these have not been strong
enough to overwhelm a clear signal of independent colonization. These
results also suggest a geographically and historically very plausible
scenario: The populations colonizing North East Asia whose members
crossed the Bering Strait and whose descendents eventually reached
South America were replaced by a population more closely related to
modern East Asians (and specifically modern Mongolians). This
population subsequently also crossed the Bering Strait and contributed
substantially to the ancestry of North American Amerinds. This second
wave of migration provides an explanation for the relationship between
distance from Siberia and genetic similarity to Siberians [23], which
was previously attributed to serial dilution [23]. It also explains
why an analysis of the population structure of the Pima and two South
American populations based on genome-wide SNP data, using the
admixture model of STRUCTURE [24], inferred that the South American
populations had a single source of ancestry but the Pima had received
approximately half of their ancestry from a second, additional source
[25]. Simulation results have shown that the admixture model of
STRUCTURE can be surprisingly successful in detecting ancient
admixture, even in the absence of source populations, if the number of
markers used is sufficiently large [26].
Gene Flow from Europe to East Asia around the Arctic Circle
In our inferred scenario there is little gene flow between East Asian
and Europeans and the Yakut is the only East Asian population to have
two European donors; the Russians and the Orcadians. The Russian
contribution is not surprising because the Yakut live in North East
Russia. The Orcadian contribution is particularly noteworthy because
removing these donors reduces the log-likelihood of generating the
Yakut chromosomes by 2.5 times more than removing donors from any
other population (Table S2). The Orcadians are also the only other
European population to donate to other East Asians, namely the Han
from Northern China and the Hezhen, who are also amongst the most
Northerly East Asian populations in the sample. On this basis we
hypothesize that there has been an episode of gene flow from Europe to
East Asia. We tested the robustness of this inference by putting
Orcadians last in the ordering. The Yakut replaced the Orcadians with
Sardinians, who are a major donor to the Orcadians. The Hezhen and the
Han from Northern China did not acquire new European donors,
consistent with the gene flow from Europe being less quantitatively
important to these two populations than to the more Northerly Yakut.
Orcadians did not gain any East Asian donors by being placed last in
the ordering, strengthening the inference that the direction of the
gene flow was from Europe to East Asia.
Our results provide evidence for two continent-scale bottlenecks, the
first affecting non-Africans and the second affecting East Asians,
with both groups having a small number of donors from outside the
region. Unfortunately, the limitation of both our method and the
sampled populations make it difficult for us to make detailed
inferences about the nature of these bottlenecks. Most of the ancestry
of non-Africans comes via the only only North African population in
the sample, the Mozabites, who are also the last African population to
be formed. However, their intermediate position might reflect back
migration from the Middle East and/or Europe[27],[28],[29]. Simulation
results suggest that our method is likely to miss this type of back
admixture. Indeed, if Mozabites are allowed to receive ancestry from
any populations and not only those that precede them in the ordering,
they get approximately 70% from these two regions, consistent with the
results of STRUCTURE for the same populations [30]. In any case, a
much better sample of East and North African populations would be
required to elucidate the nature of the bottleneck.
A similar problem of interpretation occurs for the East Asian
bottleneck. A majority of the ancestry of East Asians comes via two
central East Asian populations, the Uygur and the Hazara. However
these populations could have come to resemble East Asians through back
migration. Indeed, if these populations are placed last in the
ordering, then more than 40% of their donors are East Asian. If donors
for the East Asian populations are inferred while excluding the Uygur
and the Hazara from the dataset, the first populations have a somewhat
larger number of donors from a wider range of Central or West Asian
populations (Brahui, Makrani, Balochi, Sindhi and Adygei) than shown
in Movie S1, but populations later in the ordering revert to having
predominantly East Asian donors, supporting a strong East Asian
bottleneck that contrasts with the wide sources of ancestry of
Europeans.
The major simplification of our model is to assume that the
populations were founded in an order. Since the DNA samples came from
living humans, the ordering does not reflect age, but instead
bottlenecks and admixture events that distinguish more recently formed
populations from older ones. Complexities in human history make this
ordering somewhat arbitrary. For example, the Melanesians have been
founded by multiple waves of migrations. Their position late in our
ordering reflects the substantial proportion of their ancestry that
comes from East Asians. However they also have other, independent
sources of ancestry that reflect migrations that are likely to predate
those that gave rise to the modern East Asian populations. Information
on the timing of different waves of migration could potentially be
obtained from more extensive DNA sequence datasets by examining the
sizes of the blocks of DNA that are inherited from different donor
populations. Recent admixture would result in individuals sharing
large contiguous segments from particular donor populations [26],[31].
Recent shared ancestry would result in individuals receiving large
contiguous segments from particular donor haploids.
A fully realistic history would avoid any ordering of the modern
populations. One potential avenue for extending the current approach
to achieve this goal would be to impute chromosomes from “ancestral
populations,” which would both represent populations that existed in
the past and also act as efficient donors for the modern haplotypes.
Generation of such populations poses a number of statistical and
computational challenges but could potentially allow a chronological,
multi-layered history to be inferred. Accurate reconstruction of
historical migrations depends crucially on the use of appropriate
samples and any geographical interpretation can be confounded by major
population movements. Further, it should ideally be demonstrated that
the results are robust to which parts of the genome are used in
analysis. Further methodological innovation and genome-wide SNP
datasets from diverse human populations [25],[32] should allow
unprecedented detail in the reconstruction of the ancestry of extant
humans.
Materials and Methods
Genotype Data
We used the 32 autosomal regions in Conrad et al [12], each of which
consisted of approximately 80 biallelic SNPs across 330 kilobases of
the genome. SNP data were collected for a total of 927 individuals
sampled from 53 different populations, with sample sizes ranging from
6 to 45 individuals per population. Data were kindly provided to us as
haplotypes, which were phased using fastPHASE [33] on each region as
previously described [12].
Ancestry Model
Li and Stephens [10] described a likelihood based model that captures
the principal features of the genealogical process with recombination
while remaining computationally tractable for large datasets. Under
the model, the chromosomes are generated in order, with chromosomes
being copied segment-by-segment from those earlier in the ordering. In
our notation, every individual consists of two haploids, each
consisting of a single phased haplotype per genotyped region. The L
total SNPs in each haploid are listed one region at a time, in order
within each region.
Suppose that we wish to generate a particular haploid h*, using j pre-
existing donor haploids h1,…,hj. Let ρ represent the crossover
recombination rate per unit physical distance across the genome,
assumed fixed. The conditional probability Pr(h* | h1,…,hj; ρ) is
structured as a Hidden Markov model, where the hidden state Xl
represents the existing haploid from the set h1,…,hj that haploid h*
copies from at each site l = 1,…,L. The switches in copied-from
haplotype are modelled as a Poisson process with rate ρ/j. The
transition probabilities for X between sites l and l+1 are as follows:
(1)
where dl is the physical distance between SNPs l and l+1. If l and l+1
are on separate genetic regions, we set dl = ∞. The observed state
sequence component of the Hidden Markov Chain, the probability of
observing a particular allele given the haploid that h* is copying
from at a given SNP, allows for “imperfect” copying that depends on a
per site mutation parameter :
(2)
Here hj,l refers to the allelic type of haploid j at SNP l. The
mutation parameter is fixed, as in [10], as Watterson's estimate with
one expected mutation event per site, i.e. [34] for J total haploids.
To calculate Pr(h* | h1,…,hj; ρ), a summation is performed over all
permuations of the copying process, i.e. a summation over all possible
x, which can be accomplished efficiently using the forward algorithm
(e.g. [35]). In the analyses presented here, we used an alteration of
(1) above, using the “PAC-B” version described in [10].
Note that the probability of recombination events (i.e. switches) and
mutations goes down as the number of haploids j increases. This
mirrors a key property of data generated under the coalescent, that
the probability that a segment from an additional chromosome will be
identical by descent with a segment from chromosomes 1…j increases
with j. This property also means that different orderings will have
different likelihoods that at least in part reflect the demographic
history of the individuals in the sample. For example, if a subset of
individuals in the sample have a particularly high level of diversity,
then the overall likelihood will generally be higher if these
individuals are generated early rather than late in the ordering.
In previous implementations of the Li and Stephens algorithm, it has
been assumed that each new haplotype is made using all previous
haplotypes. This leads to the formula for the probability of observing
J haploids, conditional on ρ:
(3)
where as in [10].
However, in the context where individuals come from differentiated
populations, a higher likelihood may be obtained by using only a
subset of the pre-existing individuals as donors. In order for a donor
individual to increase the likelihood of generating h*, there needs to
be chromosomal segments, whether large or small, that are more similar
to h* than any of the others in the donor pool. Individuals from
populations that are more differentiated from h* than others in the
donor pool are likely to contain few such segments. Further, every
individual increases the value of j by 2, and for each segment that is
copied a 1/j term appears in the likelihood, corresponding to choosing
amongst the j donor haploids. Thus the presence of differentiated
individuals in the donor pool can decrease the overall likelihood.
Here we are interested in investigating ancestry at the population
level. We therefore make some assumptions about orderings and donors
that are justifiable if the individuals within each population share
the same demographic history. In practice, population labels are
initially defined based on geographic and ethnic criteria, and the
degree of homogeneity within the labelled populations can be assessed
on multilocus genetic data [18]. These assumptions considerably reduce
the computational complexity of the problem. Within each population,
haploids are assumed to be generated – and donors are used in
generating them – in the order they appear in the input file. In
generating a set of haploids H across K populations, we further assume
that:
1. The K populations are generated in sequence according to an order
of colonization U = (u1,…,uK), where uk denotes the kth population in
the order. To simpify notation, we subscript each population by its
position in the ordering, with 1 representing the initial population
and K the final population to be colonized.
2. Each population k has a fixed set of donor individuals from
previous populations in the order, Dk. The membership of Dk is
determined by k−1 integers, , reflecting the number of individuals
from previous populations 1,…, k−1 that donate genetic material to
population k.
3. Within a population k, haploids are made in order using the
previous haploids as donors, i.e. for , the ith haploid genome of
population k, the total donor pool .
4. The formation of each population k involves a single genome-wide
recombination rate, ρk.
Let represent the number of donor individuals from populations 1,…,K−1
for each of populations 2 to K, and let Φ = (ρ1,…,ρK) denote the set
of recombination rates involved in forming all populations K. Then the
probability of the haploid data of all populations, H, conditional on
U, M, and Φ, is:
(4)
where nk denotes the number of individuals in population k.
We want to maximise (4) across all possible orderings of populations,
donor sets and recombination rates. This represents a very large
search space. We used a hill climbing approach and some MCMC updates
to find a good solution.
We first set out to generate an inital order of colonization, U(0),
using a pairwise analysis. For each of the K(K−1) permutations of
pairs of populations, we calculated the probability of forming all
haploids in both populations using (3). Specifically, for each
pairwise combination, we calculated (3) twice, once using a haploid
ordering where all of one population's haploids are formed first and
the other where they are formed last. For each calculation, we
maximized over ρ using 200 iterations of Markov Chain Monte Carlo
(MCMC). In particular, for each MCMC iteration r, a new proposal of
log10 ρ, log10ρ(r), was selected from a uniform(−1,1) distribution
shifted to be centered on the previous value of log10 ρ. This new
value of ρ was then accepted or rejected via a Metropolis-Hastings
step, i.e. ρ(r) was accepted with probability min(a1), where , or
otherwise rejected. (Here we take a uniform prior on log10 ρ between
−7 and 3.) We compared the final probability values at r = 200 for
each of the two orderings, awarding 1 point to the population that was
first in the highest likelihood ordering. Our initial ordering U(0)
was based on the number of points received by each population, with
the highest scoring population considered the first population formed.
Ties were broken randomly; in the data of Conrad et al [12], there
were nine instances where two populations had the same number of
points and two instances where three populations had the same number
of points (Table S5).
We calculated the likelihood for U(0) and for subsequent orderings
using a greedy algorithm for each k to obtain values of M and Φ. For
each k, first (4) was evaluated using all possible individuals as
donors, i.e. , maximizing over ρk using 200 iterations of MCMC as
described above, giving . Next, the change in the likelihood obtained
by setting , fixing , was evaluated for each for which . If each of
these changes decreased the likelihood, the algorithm stopped.
Otherwise, for the p which resulted in the highest increase in
likelihood, was set to 0 and ρk was re-maximised conditional on this
new value of Dk using a further 200 MCMC iterations, and the algorithm
continued.
We used an iterative procedure to obtain orderings with progressively
higher overall likelihood. Specifically, for each , we calculated the
likelihood of the ordering U* = (u1…,uk+1,uk,…,uK). In each iteration,
we accepted all changes in ordering that increased the likelihood or
left it the same, the only exeptions being where two or more such
changes were incompatable with each other. In these cases, we accepted
those changes that improved the likelihood the most. This procedure
was repeated until the changes either decreased the likelihood or
reversed a change that had previously been made. For the data of
Conrad et al [12], 13 such iterations were performed, providing the
ordering U(13) (Table S5). The overall log-likelihood improved by 344
in these 13 iterations. For the simulated data, no changes in ordering
were accepted. For the data of Conrad et al [12] but not the simulated
data, we performed an analogous procedure to generate U(14) but
comparing all possible conFigure urations of triplets of orderings,
i.e. U* = (u1,…,uk,uk+1,uk+2,…,uK), U* = (u1,…,uk,uk+2,uk+1,…,uK), U*
= (u1,…,uk+1,uk+2,uk,…,uK), U* = (u1,…,uk+1,uk,uk+2,…,uK), U* = (u1,
…,uk+2,uk,uk+1,…,uK), and U* = (u1,…,uk+2,uk+1,uk,…,uK). We accepted 4
such changes, improving the log-likelihood by a further 67. We then
recalculated new optimal values of ρk for this ordering, which
improved the log-likelihood by a further 60, and checked pairwise
population swaps based on these new values. None of the proposed swaps
increased the likelihood further, so this gave us our final ordering
(Table S5).
The greedy algorithm assumes that for each population k, the
preceeding populations contribute either all or none of their
chromosomes to the donor pool Dk. In order to find a solution which
allowed fractional contributions from donor populations, we used an
MCMC approach, conditional on this final ordering and final values of
ρk, . Let be the donor pool at iteration r, with the number of donor
haploids from population p to population k at iteration r. Initially,
we set for all and . We then performed the following steps at each
iteration r = 1,…,R:
1. randomly choose one of k's donor populations 1,…,(k−1) with uniform
probability; call this population p
2. randomly choose with uniform probability
3. if r is an even number, set
4. if r is an odd number, set
5. if or then reject the change, i.e. .
6. Otherwise, accept the change with probability min(a,1), where .
For both the simulated data and our application to the data of Conrad
et al [12], contributions were deemed significant if the average
number of donors exceeded 2. For our simulated data, we used the
results of a single MCMC run with 5,000 iterations, including 1,000
Burn-in iterations. For the data of Conrad et al [12], different MCMC
runs converged on slightly different local optima, as a result of the
complexity of the search space. We therefore used a consensus of the
results of the greedy solution and two independent MCMC solutions. For
each MCMC run, we initially ran the algorithm for 10,000 iterations,
including 2,000 iterations of burn-in. In 17 cases (both runs of
Japanese, Lahu, Maya, Pima and Papuan and one run of Dai, Italian,
Sardinian, Surui, Tujia, Karitiana and She) the algorithm initially
got stuck in a local optimum but then jumped to a significantly better
solution (>30 improvement in log-likelihood) after the burn-in was
complete. We therefore continued the run for a further 10,000
iterations, using the last 8,000 to estimate the posterior. In each of
these 17 instances no further large improvement in likelihood occurred
during these 10,000 iterations, indicating convergence on a local
optimum. The consensus (Table S2) included donor populations that were
significant in at least two of the three solutions and for which the
number of donor individuals, averaged across the three solutions, was
also greater than 4.
Simulations
To test our method's performance under simple demographic scenarios,
we performed several sets of simulations using the coalescent-based
simulation software msHOT [14],[13]. In particular, we performed
simulations under a sequential bottleneck model, using five
populations and four bottleneck events (Figure 2). We performed
simulations for two different scenarios, as shown in Figure 2-a and
Figure 2-c. For both scenarios, the population size of A beyond t =
3500 generations is 10,000 chromosomes, bottleneck size is 2,000 for
the initial colonizations of each of B-E, and present-day population
size is 25,000 for A-E. In the simulatons with admixture, D has 75%
contribution from C and 25% from A; E has 75% contribution from D and
25% from B. The number of sampled individuals ranged between 6 (for
population A) and 45 (for population B). This range was chosen to
match that found in the data of Conrad et al [12].
For each scenario, we performed ten independent simulations. In each
we simulated 32 genetic regions of size ≈330kb and 80 SNPs for each
population. We considered two different models of recombination (five
simulations under each model). The first model consisted of a constant
recombination rate ρsim across all 32 regions, with ρsim = 1.0/kb.
Here ρsim = 4N0c, where c is the rate of crossover recombination as
before and N0 is the present-day population size of each population,
i.e. N0 = 25000. This rate closely matches the observed average rate
of recombination in humans, assuming a present-day population size of
25,000. The second model included recombination hotspots, or narrow
areas of the genome with intense recombination activity relative to
the surrounding region. For the latter recombination model, hotspot
parameters were chosen to mimic current observations on typical
hotspot characteristics [36],[37],[38],[39]. The number of hotspots
was selected from a Poisson distribution such that they occured
genomewide every 40kb on average. Each hotspot's width in kilobases
was sampled from a uniform(1,2). Its intensity λ, or relative rate of
recombination compared to regions outside of hotspots, was sampled
such that log10λ~Uniform(1.0,2.5). This intensity distribution
restricts hotspots to have recombination rates between 10-316 times
that of background rates, with 50% of hotspots expected to have
intensities between 10 and 32. Outside of hotspots, the rate of
recombination in all regions was fixed at ρsim = 0.2325/kb. Finally,
we imposed an additional restriction that hotspots had to be at least
5kb apart in a region. These parameters resulted in a genomewide
average recombination rate of ≈1.0/kb, with 15 maximum hotspots per
region and roughly 78% of the total recombination occuring in the 3.7%
of the sequence genomewide designated as hotspots. These numbers match
– or are slightly more extreme than – current observations [38].
After simulating the haplotypes for each region based on the above
parameters using msHOT, SNPs were randomly chosen to mimic allele
frequencies present in the data of Conrad et al [12] in the following
manner. The 0th, 10th, … , 90th, and 100th quantile values of SNP
allele frequencies for all populations combined were found for the
Conrad et al [12] data across all regions. SNPs were then selected in
the simulated data such that, for 80 total SNPs per region, ≈10% were
between the 0 and 10th quantile values of the real data, ≈10% were
between the 10th and 20th quantile values of the real data, etc.
Histograms of the allele frequencies of our simulated data after
ascertaining in this manner were roughly comparable to that of the
data of Conrad et al [12] (data not shown).
The data we analyzed consisted of haplotypes estimated by the authors
of Conrad et al [12] using the program fastPHASE [33]. Therefore we
used fastPHASE to estimate the haplotypes of our simulated data after
selecting SNPs based on the ascertainment strategy described above.
That is, we pretended the haplotype information from the msHOT
simulations was unknown and phased the genotype data using fastPHASE v.
1.2.0 on each region, for each of the five simulated populations
separately. We used roughly the same fastPHASE parameters as [12],
using H = 500, T = 20, and C = 25, with K = 20 clusters for
populations with more than 40 haplotypes and K = 10 clusters otherwise
(see the fastPHASE documentation for a full description of these
parameters and [12] for a full description of their phasing strategy).
For the scenarios with recent forwards or backwards admixture, recent
admixture was added such that 0.25% of the “sink” population was
comprised of new migrants from the donor population each generation,
starting 20 generations ago and continuing until present-day.
Otherwise the simulations were the same as those based on Figure 2-a
and Figure 2-c described above (five for each under each recent
admixture scenario), without recombination hotspots.
Supporting Information
Figure S1.
Number of individuals per population versus our model's inferred
ordering. Note that there is no clear correlation between the two.
(0.003 MB PDF)
Figure S2.
Number of individuals per population versus our model's inferred total
number of donors. Note that there is no clear correlation between the
two.
(0.003 MB PDF)
Table S1.
Results of simulations shown. Shows inferred order and mean number of
donor individuals contributed from donor to recipient. Contributions
are treated as significant if more than two individuals on average are
inferred as donors. Red indicates inference of a genuine source,
orange indicates inference of a genuine source that highlights the
recent admixture, blue indicates a genuine source that is not
inferred, green indicates an incorrect source that is inferred, and
purple indicates an incorrect swap in the ordering.
(0.06 MB XLS)
Table S2.
Summary of results for Conrad et al [12] dataset. Shows the mean
number of donors for each of the sources shown in Movie S1 and also
totals. The last column shows the reduction in log-likelihood by
excluding the population in the greedy solution.
(0.06 MB XLS)
Table S3.
Ancestry of particular populations. For each recipient population,
gives proportion of donor chromosomes that went via each existing
population. Values were estimated recursively, working backwards from
the labelled population to the first (San) by assuming that the amount
of genetic material passed on by each population was proportional to
the number of donor individuals it contributed.
(0.09 MB XLS)
Table S4.
Ancestral routes for particular populations. Shows values for
particular lines as shown in Movie S2.
(0.68 MB XLS)
Table S5.
Inference of ordering. First column gives score for each population
based on pairwise comparisons. The second to fifth columns give
details of the initial ordering chosen based on those scores (U(0)),
including the inferred value of the recombination rate ρ and the
likelihood of generating the haploids for each population, both of
which are calculated based on the greedy approach. For subsequent
iterations, ρ is kept fixed, but the likelihoods for particular
populations change. After the final iteration, new ρ values are
calculated for each population, shown in the final column of the
table.
(0.04 MB XLS)
Movie S1.
Inferred history of the peopling of the world. Donors are listed at
the bottom in order according to the mean number of individuals that
are used. See Figure 4 for further details. Numerical values are given
in Table S2.
(0.94 MB CDR)
Movie S2.
Inferred history of chromosomes for individual populations. Each frame
shows the path that chromosomes took from their origin in Southern
Africa in reaching the population labelled in each frame. The width of
each line indicates the proportion of the chromosomes that travelled
by that route, with the diameter of the circle indicating the total
proportion of chromosomes that went via that location (diameter of San
= 1.0). Values were estimated recursively, working backwards from the
labelled population to the first by assuming that the amount of
genetic material passed on by each population was proportional to the
number of donor individuals it contributed. Numerical values are given
in Table S3 and Table S4.
(1.23 MB CDR)
Acknowledgments
Christian Capelli, Peter Donnelly, David Jackson, Simon Myers,
Jonathan Pritchard, Mark Thomas and Damjan Vukcevic each provided
numerous helpful comments, as did two anonymous reviewers.
Author Contributions
Conceived and designed the experiments: DF. Performed the experiments:
GH. Contributed reagents/materials/analysis tools: AA. Wrote the
paper: GH DF.
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