Genetic Evidence for Recent Population Mixture in India (2024)

Data Sets

To learn about population history in India at higher resolution than was previously possible, we assembled genome-wide data for 571 individuals from 73 well-defined ethno-linguistic groups from South Asia (71 Indian and 2 Pakistani groups). We refer to all these groups in what follows as “Indian.” For samples genotyped on Affymetrix 6.0 arrays, we required at least 99% completeness for all SNPs and samples; this resulted in 383 individuals from 52 groups (27 groups newly genotyped for this study)¹ genotyped at 494,863 SNPs. For samples genotyped on Illumina 650K arrays, we required at least 95% completeness, yielding 188 individuals from 21 groups^7,20 genotyped at 543,980 SNPs. Sample collection was in accordance with the ethical standards of the responsible committees on human experimentation (institutional and national), and informed consent consistent with genetic studies of population history was obtained from all participants.

We filtered the data set in two stages. First, we filtered out data from 49 individuals with the following characteristics: (1) duplicate individuals (for each pair of individuals that match at least 90% of genotypes, we remove one individual); (2) related individuals (for mother-father-child trios we exclude the child, and for first-degree relative pairs we remove one of the two individuals); (3) all individuals previously excluded by Metspalu etal.;⁷ and (4) six Pakistani groups (Hazara, Kalash, Burusho, Makrani, Balochi, and Brahui) that had previously been shown to have a complex history involving more than a simple mixture of two ancestral populations¹ (Table S1 available online). Second, we excluded an additional 194 individuals based on principal component analysis (PCA): (1) all individuals with evidence of recent ancestry from populations other than ANI and ASI^1,21 or visual identification of outliers in Figure1, which led us to exclude all Austro-Asiatic and Tibeto-Burman speakers; (2) all individuals from groups that were not hom*ogenous in PCA in the sense of having multiple clusters in the scatterplot; and (3) individuals who were ancestry outliers compared with the majority of individuals from their own group based on visual inspection of the PCA clusters (Table S1). After curation, we had 211 individuals (30groups) genotyped on Affymetrix arrays and 117 individuals (15 groups) genotyped on Illumina arrays.

We coanalyzed the Indian data with HGDP-CEPH data from 51 groups (257 individuals genotyped on Affymetrix 500K SNP arrays²² and 940 on Illumina 650K arrays²⁰); International Haplotype Map Phase 3 (HapMap) data from 11 groups (1,158 individuals genotyped on Affymetrix 6.0 arrays and Illumina 1M arrays²³); Behar etal.²⁴ data from 41 groups (466 individuals genotyped on Illumina 610K arrays); and Yunusbayev etal.²⁵ data from 13 groups (214 individuals genotyped on Illumina 610K arrays). Our “Affymetrix” merged data set consisted of 210,482 SNPs obtained by merging data from 211 Indians (30 groups) with data from non-Indians typed on Affymetrix arrays (HapMap and Affymetrix HGDP). Our “Illumina” merged data set consisted of 500,703 SNPs obtained by merging data from 117 Indians (15 groups) with data from non-Indians typed on Illumina arrays (HapMap, Illumina HGDP; Behar etal.,²⁴ and Yunusbayev etal.²⁵). Our “Illumina-Affymetrix” merged data set consisted of an intersection of these two data sets and included 328 Indian individuals (45 groups) genotyped at 86,213 SNPs.

F₄ Ratio Estimation

We use f₄ ratio estimation as implemented in ADMIXTOOLS²⁶ to estimate the proportion of ANI ancestry in Indian groups. Specifically, we compute the ANI ancestry proportion (α) as:

This assumes the model of FigureS1 with Pop1= Georgians and Pop2= Basque.

For f₄ ratio estimation to provide unbiased results, it requires access to four outgroup populations that branch off at four distinct positions on the ancestral lineage relating ANI and ASI.²⁶ We chose to work with Yoruba (YRI), Andamanese (Onge),²⁷ and two West Eurasian populations (Pop1 and Pop2) that are at successively increasing phylogenetic distances from the ANI (that is, the tree for West Eurasian populations is (Pop2, (Pop1, ANI))) (FigureS1). We first searched for a population to use as Pop1. For each Indian group (X), we compute D(Onge, X; YRI, Y) where Y = any West Eurasian population from a panel of 43 groups including Europeans, Central Asians, Middle Easterners, and Caucasians. For all 45 Indian groups on the Indian cline (described in the Results section), we find that Georgians along with other Caucasus groups are consistent with sharing the most genetic drift with ANI (Tables S2 and S3), as was also previously observed in Metspalu etal.⁷ based on clustering analysis. Therefore, we use Georgians as Pop1 (FigureS1). We next determined a second population to use as Pop2. We examined all possible West Eurasian populations to find groups that provide a good fit to the model (YRI, (Pop2, (Georgians, ANI)), [(ASI, Onge])) by using our admixture graph phylogeny testing software.²⁶ Within the limits of our resolution, we find six groups (Pop2= Italian, Tuscan, Basque, Kurd, Abhkasian, Spaniard) that are consistent with this model in the sense that none of the f statistics relating the groups are greater than three standard errors from expectation. To evaluate the uncertainty in the ANI ancestry proportions ranging over these six candidates for Pop2, we ran f₄ ratio estimation with two choices of Pop2 representing different geographic extremes (Pop2= Abhkasian and Pop2= Basque). We obtain similar ANI ancestry estimates (Table S4). Our ancestry estimates are also statistically consistent (within two standard errors) with those of Reich etal.¹ (Table S4).

Estimating Admixture Dates via Rolloff

For each pair of SNPs (x,y) separated by a distance d Morgans, we compute the covariance between (x,y), which we use to measure the linkage disequilibrium (LD) resulting from population mixture. Specifically, we use the rolloff^26,28,29 statistic

where z(x,y) is the covariance between SNPs x and y, and w(x,y) is a weight function. The weight can be either (1) the allele frequency difference between the two groups we use as surrogates for the ancestors (Europeans, Onge), (2) the allele frequency difference between a tested Indian group and one reference group (Europeans), or (3) the PCA-based loadings for SNPs (x, y) computed by performing PCA with Europeans and various Indian cline groups. We plot the weighted covariance with distance and obtain a date by fitting an exponential function with an affine term y =Ae^−nd +c, where d is the distance in Morgans and we interpret n as the number of generations since admixture. We compute standard errors with a weighted block jackknife,³⁰ with one chromosome dropped perrun.

Admixture Dates and Their Difference inIndo-European and Dravidian Speakers

For many analyses in this study, we cluster Indians into two categories based on their linguistic affiliation: “Indo-Europeans” toindicate groups that speak Indo-European languages and “Dravidians” to indicate groups that speak Dravidian languages. For the dating analysis shown in Figure2, we applied rolloff to the merged Illumina-Affymetrix data set of 86,213 SNPs, with weights from PCA-based SNP loadings computed with Basque and speakers of the language group other than the one being analyzed (for example, for estimating the dates of mixture for Indo-Europeans, we use Dravidians and Basque to compute the PCA-based SNP loadings). To compute the significance of the difference in the date estimates, we leave out each of the 22 chromosomes in turn and use a weighted block jackknife procedure to convert the variability into a standard error. As a robustness check, we repeat this analysis with the Affymetrix data set of 210,482 SNPs for the four Indo-European and five Dravidian groups that we found were consistent with a simple ANI-ASI mixture (described in the Results section). For this analysis we use Basque and all other Indian cline groups to compute SNP loadings. We confirm a younger date for Indo-Europeans than for Dravidians, with the difference of 44 ± 18 generations being statistically significant at Z = 2.4 standard errors from zero.

Identifying Groups Consistent with Simple ANI-ASI Admixture

For each of the 37 Indian groups including Onge (this is less than the total number of groups on the Indian cline because we applied aminimum sample size requirement of 5), we tested whether they are consistent with deriving all their ancestry from the same ANI and ASI ancestral populations by studying the matrix of all possible statistics of the form f₄(Indian_base, Indian_other; NonIndian_base, NonIndian_other) with a panel of 38 non-Indian populations. Many f₄ statistics can be written as linear combinations of each other, and therefore we need to pick a basis for the space of f₄ statistics. In practice, we fix one Indian group as “Indian_base” and compute the f₄ statistic for each of the 36 remaining Indian groups as “Indian_other.” We use an African group (YRI) as “NonIndian_base” and the “NonIndian_other” groups include Dai, Papuans, Karitiana, and diverse West Eurasian groups including Europeans, Middle Easterners, and Caucasians (the choice of base has no mathematical impact on the test). To identify sets of Indian groups consistent with having the same relationship to the panel of non-Indians, we use a Hotelling T test as in Reich etal.³¹ to evaluate whether the matrix of all f₄ statistics has exactly one linearly independent component (rank 1). For sets of Indian groups that are consistent with being rank 1, we also run the admixture graph testing software to evaluate whether the relationships in FigureS1 (where Pop1= Georgians, Pop2= Basque) are consistent with the data. We began by applying this procedure to all possible sets of three Indian groups. For the sets that passed, we added each possible fourth Indian group in turn and tested the consistency with a simple ANI-ASI mixture. We applied this process iteratively until no additional Indian groups could be added to the rank 1 set.

Admixture Graph Analysis

We applied the admixture graph²⁶ formal phylogeny testing software to evaluate whether the model of simple ANI-ASI admixture in rank 1 Indo-European and Dravidian groups provides a fit to the data. Admixture graph studies the correlations in allele frequency differentiation statistics (f₂, f₃, and f₄)²⁶ among groups, comparing the observed values to those specified by the model (with a standard error from a block jackknife) to test hypotheses about population relationships. To test whether a proposed model provides a fit to the data, the software examines individual f statistics and considers statistics more than three standard errors from expectation to be indicative of a poor fit. We also use this method to estimate the internal genetic drift lengths required by ALDER for estimating admixture proportions (on the lineages separating (ANI, X”) and (ASI, X”) in FigureS2).

Estimating the Date and Proportion of Mixture via ALDER

We run ALDER³² with one reference population (a West Eurasian group; we tried seven diverse West Eurasian groups). The ALDER statistic for measuring admixture LD is similar to the rolloff statistic:

As before, z(x,y) is the covariance between SNPs x and y. Here w(x,y) is the product of the allele frequency differences at x and y between the two reference groups (in this case, a West Eurasian group and the admixed group itself), and S(d) ={(x,y):|x−y|<d−ε/2} (where ε is a discretization parameter).

We plot the weighted covariance against genetic distance and perform a least-squares fit by y =Ae^−nd +c, where n is the number of generations since admixture and d is the genetic distance in Morgans. Under a single-wave mixture model, the amplitude ofadmixture LD decay defined as a_o =A +c/2 is analytically predicted by the ANI ancestry proportion (α):

Here, X″ is the common ancestor of the reference West Eurasian group (X) and the ANI lineage (FigureS2). We estimate f₂(ANI,X^″) and f₂(ASI,X^″) via our admixture graph software with one West Eurasian outgroup (because we do not have access to Georgians in the 210,482 SNP Affymetrix data set). Having only a single West Eurasian outgroup in the admixture graph makes the model poorly constrained, but we address this limitation by fixing thevalue of the admixture proportion to be equal to the ANI ancestry inferred from f₄ ratio estimation. We compare the expected amplitude a_o (from Equation 4) and the observed amplitude â_o (from the weighted LD curve) to test whether the model of a single wave of mixture between ANI and ASI provides a good fit to the data. The entire procedure is repeated, dropping each chromosome in turn to generate block jackknife standard errors on the quantities of interest.

95% Confidence Interval on the ANI Ancestry Proportion prior to Mixture

Consider the model that an Indian group derives its ancestry from two waves of admixture involving ANI-related populations (assumed to have the same allele frequencies), where the older wave is old enough that its contribution to the measured LD is negligible. If so, the group would have ancestry from three sources: old ANI ancestry (α_old), recent ANI ancestry (α_new), and ASI ancestry (1− α_total = 1− (α_old + α_new)). The expected one-reference ALDER amplitude is then

We estimate the internal drift lengths by using admixture graph and estimate α_total by using f₄ ratio estimation. Substituting â₀ (inferred from the weighted LD curve) and solving the above equation for each jackknife run, we estimate the range of α_old. We find that the central 95% confidence intervals always include zero. Therefore, we instead compute a one-sided 95% confidence interval ranging from 0% to the mean plus 1.65 times the standard error.

Principal Component Analysis of 73 Indian Groups

We assembled the most comprehensive sampling of Indian genetic variation to date: genome-wide SNP data collected from 571 individuals belonging to 73 well-defined ethno-linguistic groups. Figure1 presents the PCA showing the qualitative relationships of these individuals to West Eurasians (Northern Europeans, Basque, Georgians, and Iranians) and East Asians (Han Chinese). Almost all groups speaking Indo-European or Dravidian languages lie along a gradient of varying relatedness to West Eurasians in PCA (referred to as “Indian cline”), which we have previously shown reflects variable proportions of ANI-ASI ancestry.¹ Groups speaking Austro-Asiatic and Tibeto-Burman languages fall away from the Indian cline, consistent with ancestry from distinct populations; the history of these groups is important but is not our focus here. We curated our data by using PCA, removing individuals who did not cluster with others from the same group, and restricting the analysis to 45 groups that fall on the Indian cline, all of which speak Indo-European or Dravidian languages (Table S1; Material and Methods).

Mixture Proportions

By using f₄ ratio estimation²⁶ that analyzes allele frequency correlation patterns to infer mixture proportions, we estimate that ANI ancestry along the Indian cline ranges from as low as 17% (Paniya) to as high as 71% (Pathan) (Table S4). Traditionally lower caste, Dravidian, and tribal groups tend to have lower proportions of ANI ancestry than traditionally upper caste and Indo-European groups (p < 0.001).¹ Our estimates of ANI ancestry are lower than we previously reported (although within two standard errors),¹ because of the fact that wepreviously used Papuans, Adygei, and Northwest Europeans as outgroups for ancestry estimation, whereas here we use YRI, Basque, and Georgians (FigureS1, Table S4). Since the publication of that study, we have found that some of the groups used in the statistic have a more complex history than is captured by the assumed model.³³ The reason for replacing the Papuans with YRI is that Papuans are now known to harbor gene flow from archaic humans (Denisovans),³³ which could bias ancestry estimates. We use different West Eurasians because the Adygei derive a small proportion of their ancestry from an East Asian-related source, which could again bias estimates, and because a model in which Georgians are the most closely related West Eurasian group to the ANI provides a good fit to the data for many models that we tested, whereas models with Europeans in their place do not provide as good a fit. Although we believe that the Onge are only distantly related to ASI, we do not replace the Onge in our analysis because this is the only group we have data from that is consistent with forming a clade with the ASI (the only requirement for our method to work is for the outgroup to form a clade with the ASI).

Admixture Dates

To date ANI-ASI mixture, we capitalized on the fact that admixture between two populations generates allelic association (linkage disequilibrium [LD]) between pairs of SNPs.³⁴ The LD decays at a constant rate as recombination breaks down the contiguous chromosomal blocks inherited from the ancestral mixing populations. The expected value of the admixture LD is related to the genetic distance between SNPs (the probability of recombination per generation between them) and the time that has elapsed since mixture.³⁴ We previously reported simulations showing that dating population mixture based on the scale of admixture LD is robust to the use of imperfect surrogates for the ancestral populations, fine-scale errors in the genetic map, and a history of founder events in the admixed population, and is able to provide unbiased estimates for the dates of events up to 500 generations ago.^26,28,29 We confirmed this by using new simulationswith demographic parameters relevant to India (Appendix A).

We estimated admixture dates for all the groups on the Indian cline with more than five samples (a minimum sample size is important for measuring LD with precision). We observe a decay of LD with genetic distance for all groups (Figures 2 and S3). By fitting an exponential function using least-squares (via rolloff), our point estimates for the dates range from 64 to 144 generations ago, or 1,856 to 4,176 years assuming 29 years per generation.³⁵

We highlight two implications of these dates. First, nearly all groups experienced major mixture in the last few thousand years, including tribal groups like the Bhil, Chamar, and Kallar that might be expected to be more isolated. Second, the date estimates are typically more recent in Indo-Europeans (average of 72 generations) compared to Dravidians (108 generations). A jackknife estimate of the difference is highly significant at 35 ± 8 generations (Z = 4.5 standard errors from zero) (Table 1). A possible explanation is a secondary wave of mixture in the history of many Indo-European groups, which would decrease the estimated admixture date.

Testing for Multiple Layers of Admixture in the History of Indian Groups

A caveat for these dating analyses is that they assume that the entire admixture occurred instantaneously (or over a small number of generations). However, population mixture can be noninstantaneous, such that the date we obtain from our method may actually be an average of multiple dates spread out over a substantial period. One way to detect a history of noninstantaneous gene flow is to fit a sum of exponential functions to the decay of admixture LD and to show that this provides a better fit to the data than a single exponential function, as we in fact find for the Kashmiri Pandit, Kshatriya, Sindhi, and Pathan (Table 2, Appendix B). However, even if we fail to detect a nonexponential decay, we cannot rule out noninstantaneous gene flow, because the decay can be noisy, making the statistical detection of a mixture of exponential functions difficult.³⁶ A particularly important scenario we could not rule out by this method is that several thousand years ago, Indian groups were already admixed, and thus the LD decay we detect is the result of mixture of already admixed ancestral groups with different proportions of ANI ancestry. If the initial admixture was more than 10,000 years old, the associated admixture LD would have decayed to such a short distance that our methods would have poor power to detect it. The LD we measure might in this case reflect only the final admixture events, complicating interpretation of the results.

To assess whether the admixture LD we are detecting could plausibly account for all the ANI-ASI mixture in an Indian group’s history, we compared the observed amplitude of the LD curves (the amount observed at short genetic distances) to what would be expected if the dated LD accounts for the entire ANI-ASI admixture. We took advantage of our recently developed method ALDER,³² which computes weighted LD statistics and also provides a theoretical expectation for the amplitude under the model of a single wave of mixture, even in cases where the populations used as surrogates for the ancestral populations are highly genetically drifted from the true ancestral populations.^32,37 The ALDER expected-amplitude formula requires estimates of the admixture proportion (which we have from f₄ ratio estimation) as well as the genetic drift separating the true ancestral populations and the surrogates we use for the analysis, which we obtain by fitting a model of population relationships to our data via admixture graph²⁶ (Material and Methods). By comparing the observed and the expected values of the amplitude, we can evaluate whether the admixture LD we are dating can account for the entire ANI-ASI admixture in the group’s history. Our simulations show that for asingle-wave admixture history, the weighted LD amplitude measured by ALDER is consistent with the expectation (Table S5).

In Some Groups, the ANI-ASI Admixture Is Multilayered

To make this analysis maximally robust, we restricted it to sets of Indian groups that are consistent with a model of mixture between the same ANI and ASI ancestral populations to within the limits of our resolution. To evaluate formally whether this model fits the data for a proposed set of Indian groups, we compared the allele frequency differences among the Indian groups to the allele frequency differences among a set of 38 non-Indian groups including many West Eurasians, searching for differences that would be expected if the Indian groups did not derive all their ancestry from the same two ancestral populations (Appendix C). Specifically, we computed f₄ statistics measuring the correlation in allele frequencies between each possible pair of Indian groups in the set and diverse pairs of non-Indian groups. If the ANI ancestry in all the Indian groups in the tested set derives from the same ancestral population(s), then the f₄ statistics measuring the correlations are expected to be proportional, and thus the matrix of all f₄ statistics is expected to have one linearly independent component (rank 1). We tested this null hypothesis (rank = 0) with a Hotelling T test as described in Reich etal.³¹ Our simulations show that this test has power to detect a history of multiple ancestral ANI populations even when they are closely related and that genetic drift in the admixed groups cannot increase the rank (Appendix C). For all the sets that pass as rank 1, we performed a further level of testing, running admixture graph to evaluate whether the relationships in FigureS1 (with Georgians forming a clade with ANI and Basque as a second West Eurasian outgroup) are supported by the data in the sense that no f statistic measuring allele frequency correlation is more than three standard errors from model expectation (Appendix C).

Applying this procedure to all possible sets of three Indian groups, and adding in additional Indian groups until we could add no more (without increasing the rank), we identified previously undetected complexity in Indian history, with many sets of Indian groups not consistent with a simple ANI-ASI admixture. This analysis produces two notable findings. First, although aboriginal Andaman Islanders (Onge) are consistent with being asister group of ASI for many sets of Indian groups,¹ the Onge cannot be added to the model for other sets of Indian groups. Such a pattern would be expected if there was ancient gene flow into the Andaman Islanders from a group more closely related to the ASI ancestry of some present-day Indian groups than others. This would also be consistent with the finding that the closest known matches to Andamanese mitochondrial DNA haplotypes in Eurasia are rare haplotypes found in India.³⁸ Second, we find that the Indian groups consistent with simple ANI-ASI mixture are most often from tribal and traditionally lower-caste groups. Middle- and upper-caste groups tend to have evidence of more complex histories, with signals of multiple layers of ANI ancestry from slightly different ANI ancestral populations (Appendix C). Further evidence for multiple waves of admixture in the history of many traditionally middle- and upper-caste groups (as well as Indo-European and northern groups) comes from the more recent admixture dates we observe in these groups (Table 1) and the fact that a sum of two exponential functions often produces a better fit to the decay of admixture LD than does a single exponential (as noted above for some northern groups; Appendix B). Evidence for multiple components of West Eurasian-related ancestry in northern Indian populations has also been reported by Metspalu etal.⁷ based on clustering analysis.

In Some Groups, the ANI Admixture Is Consistent with Being Simple and All due to Events in the Last Few Thousand Years

Focusing on the largest set of Indo-Europeans (four groups) and the largest set of Dravidians (five groups) consistent with mixture of the same ANI and ASI ancestral populations, we find that the expected and observed admixture LD amplitudes are equivalent to within the limits of our resolution. We restricted this analysis to Indian groups genotyped on Affymetrix arrays because this allowed us to analyze about 2.5 times more SNPs (n = 210,482), which improves the accuracy of inferences based on admixture LD. Limiting our analysis to samples genotyped on Affymetrix arrays raised the challenge that we could not use Georgians as part of our admixture graph fitting (we need a second West Eurasian outgroup to obtain tight constraints on the absolute estimates of ANI-ASI admixture), but in Appendix D we show that we can accurately infer the difference between the two amplitude values (observed− expected) even without access to Georgians by constraining the admixture proportions estimated via f₄ ratio estimation. For both the Indo-European and Dravidian rank 1 sets, the observed amplitudes are statistically consistent with the expected values (Table 3). Thus, our data are consistent with all of the ANI ancestry in some selected sets of Indians (including groups speaking both Indo-European and Dravidian languages) being due to admixture events that we can date to within the past few thousand years. Accounting for statistical uncertainty, we estimate that the ANI ancestry that cannot be explained by a single wave of admixture in the last few thousand years has a 95% confidence interval (truncated to 0) of 0%–19% for Indo-Europeans and 0%–16% for Dravidians. Thus, all the ANI ancestry in some groups is consistent with deriving from admixture events that have occurred in the past few thousand years.

A(d)=∑|x−y|≈dz(x,y)w(x,y)∑|x−y|≈dz(x,y)2∑|x−y|≈dw(x,y)2.

(Equation A1)

Simulations with Demographic Parameters Relevant to Indian Groups

Moorjani etal.²⁸ reported that rolloff estimates can be upwardly biased in the cases of low admixture proportion and small sample sizes. To evaluate how this might affect our results in India, we created simulated chromosomes of mixed European and Asian ancestry for demographic parameters relevant to Indian groups (Table S7). The choice of Europeans and East Asians as the ancestral populations for these simulations was motivated by the factthatF_st(ANI, ASI) is approximately equivalent to F_st(CEU,CHB) = 0.09.¹

We simulated data based on the framework described in Moorjani etal.²⁸ For each Indian group (Brahmins, Mala, Pathan, Dravidian rank 1, and Indo-European rank 1), we ran 100 simulations where we set the mixture proportion, time since mixture, and number of samples to match the parameters estimated for the specific group. Table S7 shows that the average date of mixture from the 100 simulations is consistent with the expected date (within one standard error).

−N2(loge(2π)+1−loge(N)+loge(∑i=1nεi2)),

(Equation A2)

f₄(Indian_base, Indian_other; NonIndian_base, NonIndian_other).

Simulations

To test the method for demographic parameters relevant to Indian groups, we performed coalescent simulations by ms.⁴⁶ For each simulation, we generated data for ∼250K independent SNPs for 15 groups (Pop1–15, 10 samples for each group). We set the effective population size (N_e) for all groups to be 12,500 and the mutation and recombination rates at 2× 10⁻⁸ and 1× 10⁻⁸ per base pair per generation, respectively. Pop1 is the outgroup that diverged from Pop2 and Pop3 about 1,800 generations ago. Pop2 and Pop3 diverged 900 generations ago. The relationship of Pop1, Pop2, and Pop3 can be considered analogous to the relationship of YRI, Onge, and CEU, respectively. Pop4–9 are related to Pop3 analogously to the relationship of West Eurasians to ANI, and these populations diverged from Pop3 200–450 generations ago (FigureS5).

Simulation 1: Single Gene-Flow Event with the Same Admixing Populations

Consider the model in FigureS5. Pop10–15 are admixed and derive between 20% and 80% ancestry from Pop2′, which is closely related to Pop2 (the remaining ancestry is from Pop3′, which is related to Pop3). The date of admixture for all groups (Pop10–15) is 100 generations ago. These groups are analogous to the Indian cline with the range of admixture proportions and dates set to be similar to those inferred from real data. We estimate the rank of the f₄ relationship matrix, f₄(Pop10–15; Pop1–9). Here, Pop10 is analogous to Indian_base and Pop1 (anoutgroup to Pop2–15) is analogous to NonIndian_base. We infer that the number of independent components is 1 (rank 1 at p > 0.05).

Simulation 2: Two Gene-Flow Events Involving Different Ancestral Populations

Pop10–15 are admixed and Pop10–14 have ancestry from Pop2′ and Pop3′, with Pop3′ ancestry varying between 20% and 80% (the remaining ancestry is from Pop2′). Pop15 has 35% Pop4′ and 65% Pop2′ ancestry. All admixture events occurred 100 generations ago. We estimate the rank of the f₄ relationship matrix as f₄(Pop10–15; Pop1–9) and infer the number of independent components to be 2. If we remove Pop15 from the analysis, that is f₄(Pop10–14; Pop1–9), the inferred rank is 1, as expected.

Simulation 3: Three Independent Gene Flows with Different Mixing Populations

Pop10–15 are admixed and Pop10–13 have ancestry from populations 2′ and 3′, with Pop3′ ancestry between 20% and 80% (the remaining ancestry is from Pop2′). Pop14 has 70% Pop5′ and 30% Pop2′ ancestry, and Pop15 has 35% Pop4′ and 65% Pop2′ ancestry. All admixture events occurred 100 generations ago. We estimate the rank of the f₄ relationship matrix f₄(Pop10–15; Pop1–9) and infer the number of independent components is 3.

Simulation 4: Two Independent Gene-Flow Events at Different Time Periods

Pop10–15 are admixed and have ancestry from Pop2′ and Pop3′, with Pop3′ ancestry between 20% and 80%. Admixture occurred 100 generations ago. Pop15 also has ancestry from an older gene-flow event that occurred 150 generations ago with 50% Pop2′ and 50% Pop3′ ancestry. Thus overall, Pop15 has 70% Pop2′ and 30% Pop3′ ancestry. We estimate the rank of the f₄ relationship matrix f₄(Pop10–15; Pop1–9) and infer the number of independent components is 2.

Simulation 5: Multiple Independent Gene-Flow Events at Different Time Periods

Pop10–15 are admixed with ancestry from Pop2′ and Pop3′. Pop3′ ancestry is between 20% and 80%. Admixture occurred 50–300 (intervals of 50) generations ago (such that Pop10 was admixed 50 generations ago, Pop11 was admixed 100 generations ago, etc.). We estimate the rank of the f₄ relationship matrix, f₄(Pop10–15; Pop1–9), and infer the number of independent components is 3.

In conclusion, our simulations demonstrate that we can accurately estimate the minimum number of gene flow events and that postadmixture drift alone does not change the rank of the f₄ relationship matrix.

Results

We performed a systematic analysis to identify groups that have a similar history of ANI-ASI mixture, meaning that all their ancestry is consistent with deriving from the same ANI and ASI ancestral populations to within the limits of our resolution. We restrict this analysis to Indian groups with at least five samples and non-Indian groups that have at least ten samples, including groups from East Asia, Europe, the Middle East, the Caucasus, and Africa. We remove Central Asian and South Asian populations from the list of non-Indian groups because these have an increased likelihood of back-migration from India in the recent past that can complicate interpretation. We include Vedda (four samples), an aboriginal population from Sri Lanka, they appeared to have a relatively simple history of ANI-ASI mixture in our preliminary analysis. The analyzed data thus consists of m = 37 Indian groups (including Onge) and n = 38 non-Indian groups.

To identify sets of Indian populations that are consistent with deriving all their ancestry from exactly the same ANI-ASI ancestral populations, we systematically explored sets of these Indian groups. We used an iterative procedure, as follows.

(1) Testing all possible sets of three Indian groups. We start by computing

and estimate the ranks of the resulting 2× (n − 1) matrix by a likelihood ratio test. We repeat this for all (37× 36× 35)/6 possible triples of Indian groups.

For each set of three Indian groups consistent witha simple mixture of ANI and ASI (rank 1 at p > 0.05), we performed a further level of testing for whether the model is consistent with our data. Specifically, we run the admixture graph phylogeny-testing software^1,26 to test whether the relationships shown in FigureS1 with Pop1= Georgians, Pop2= Basque, and India = set of three Indian groups being tested is consistent with the data to within the limits of our resolution (this is the same set of reference populations we use for estimating ancestry proportions in f₄ ratio estimation and thus we are formally testing whether the model underlying the estimation is valid). To evaluate significance, we use the criterion than none of the f₂, f₃, and f₄ statistics relating the seven analyzed groups in the admixture graph is more than three standard errors from expectation.

(2) Testing sets of four Indian groups. For all sets of three Indian groups that pass these two tests, we advanced to the next round, testing sets of four Indian groups for consistency with being a simple mix of exactly the same ANI and ASI ancestral populations. Specifically, we took each of the passing sets of three Indian groups and added in turn each of the remaining groups that were part of at least one set that was rank 1. We applied the same two tests for consistency with a simple ANI-ASI mixture, leading to passing quadruples.

(3) Testing sets of five, six, and seven Indian groups. We applied the same procedure to test larger sets of groups. The results of each round are recorded in Tables S8 and S9. We stopped finding sets of groups that pass the test after m = 6.

We highlight two qualitative results that emerge from this analysis:

• •

  Onge is often included in the sets of groups consistent with rank 1, consistent with their being an ancient sister group for ASI.¹ However, for some sets of Indian groups qualifying as rank 1, we cannot add in Onge, suggesting that there also might be differences in ASI ancestry within India.

• •

  A higher proportion of sets including lower-caste and tribal groups have rank 1 than is the case for sets including upper-caste groups.

(αold(1−αnew))∗A+(1−(αold(1−αnew)))∗B

(Equation A3)

ao=2αnew(1−αnew)(1−αtotal)2(1−αnew)2(αtotalf2(ANI,X″)−(1−αtotal)f2(ASI,X″))2,

(Equation A4)

Simulations

We tested the accuracy of the methodology in scenarios simulated to resemble hypothetical admixture histories of India. To capture some of the complexities of real human populations, we built our simulated data sets by using phased haplotypes from real groups from HGDP and HapMap via the method described in Moorjani etal.²⁸ Specifically, we simulated two sets of admixed groups. Set 1 consisted of three groups with [30%, 50%, 70%] ancestry from Europeans (HapMap CEU) and the remaining ancestry from East Asians (HGDP Han). Set 2 consisted of three groups with [20%, 30%, 40%] ancestry from Europeans and the remaining ancestry from East Asians.

For each group, we generated 14 diploid individuals under two alternative admixture histories: (1) a single CEU-Han admixture event 100 generations ago and (2) two waves of CEU admixture into Han, 300 and 75 generations ago, that together produce the same total fraction of CEU ancestry as shown above.

To perform the admixture graph analysis, we require additional outgroups. For this we use real data from HGDP French, Basque, Yoruba, and Dai and use the model shown in FigureS6. We use the drift lengths and admixture proportions estimated by admixture graph to compute the expected amplitude (note that the constraint of fixing the admixture proportion from f₄ ratio estimation is not required because we have two West Eurasian outgroups here). We performed ALDER single-reference analysis for each set of admixed groups with the Basque and Dai as single reference populations (independently). We note that we do not reuse the CEU or Han populations (used for generating the simulated data) in our inference procedure, to account for the fact that we do not have access to the true ancestral populations (ANI and ASI) for India. We created simulated populations in groups of three to allow us to infer the necessary f₂ values in the amplitude formula.

We designed our simulations to qualitatively match the scenario relevant to India. In FigureS6, the four outgroups (French, Basque, Yoruba, and Dai) take the place of Georgians, Basque, YRI, and Onge in FigureS1. For the simulated histories, we chose a date of 100 generations ago to be similar to the observed average age of ANI-ASI admixture in India. The two-wave dates of 300 and 75 generations ago provide a plausible alternative scenario yielding an ALDER curve similar to the expectation for a single-wave mixture 100 generations ago. Finally, the two simulated population sets covered distinct ranges of admixture proportion space, one with larger CEU ancestry components and higher ancestry proportion variation than the other. For both sets, our inference methods provide reliable results (Table S5).

Our simulation results demonstrate that for a single-wave admixture history, the weighted LD amplitude measured by ALDER is consistent with the expectation of our formula, whereas in the case of two-wave admixture, the measured ALDER amplitude is smaller than the expectation of Equation 4 (Table S5). Out of the 12 population-reference pairs, the difference in the amplitudes is statistically consistent with zero (|Z| < 3) for all single-wave simulations, whereas the difference is significantly different from zero in 8 of the 12 two-wave simulations, including all 6 with Basque as the reference population. The estimates of the mixture proportion α_old required to explain the amplitude discrepancy under the alternate model are considerably smaller for the single-wave simulated data, with zero always within the confidence interval (Table S5).

Results

(1) Indo-European rank 1 set: For all West Eurasian groups, the model of relationships shown in FigureS2 provides a good fit to the Indo-European rank 1 data as assessed by admixture graph (such that none of the f statistics are greater than three standard errors from expectation). Therefore we substitute the admixture proportions and drift lengths f₂(ANI,X^″) and f₂(ASI,X^″) computed by admixture graph in Equation 4 to estimate the expected amplitude. We observe that the expected amplitude is consistent with the observed amplitude (|Z| < 3 for a difference between the two estimates over all seven West Eurasian groups we tested) (Table 3).

For the constrained analysis, we focused on Basque as the reference population and fixed the ANI ancestry proportionfrom f₄ ratio estimation as described above. We compute thedifference in amplitude (observed − expected) and find that the two estimates are statistically consistent (Z = −0.35). This suggests that the model of a single wave of ANI-ASI admixture is consistent with ourdata.

Applying the alternate two-wave amplitude formula (Equation 5), we estimate α_old to be 4.5% ± 8.5%, giving a 95% confidence interval of 0%–18.6%. Therefore we find no evidence to reject a single-wave model with all ancestry contributing to the measured admixture LD.

(2) Dravidian rank 1 set: Similar to the Indo-European rank 1 set, we applied admixture graph and ALDER to the Dravidian rank 1 data with various West Eurasian groups as references and found that the expected and observed amplitudes are consistent (|Z| < 3) for all reference populations tested (Table 3).

We focused next on Basque as the reference population and used the ANI estimate from f₄ ratio estimation. The expected amplitude is consistent with the observed amplitude in ALDER (Z = −1.06), suggesting that the model of a single wave of ANI-ASI ancestry provides a fit to the data. The proportion of ANI ancestry unexplained by our model (α_old) is 7.1% ± 5.5%, with a 95% confidence interval of 0%–16.2% (truncated at 0).

In conclusion, our data are consistent with the null model of a single wave of ANI-ASI admixture in selected Indo-European and Dravidian groups in India.

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