1. Empirical analyses: exploration of the effect of ascertainment bias on real data

We assembled a set of diploid autosomal genotype calls for 352 individuals (S1 Table) sequenced at high coverage [36,67], including mostly present-day individuals from the Simons Genome Diversity Project (SGDP), several high-coverage ancient genomes with diploid genotype calls [68,69], and three archaic human genomes: the “Denisova 3” Denisovan [35], Vindija [33] and Altai Neanderthals [32]. Relying on this "SGDP+archaic" dataset, we explored a wide array of ascertainment schemes: 1) A/T and G/C SNPs (henceforth “AT/GC”) that are, unlike the other mutation classes, unaffected by biased gene conversion [70], and are also unaffected by deamination ancient DNA damage; 2) random thinning of the unascertained or "AT/GC" sets down to the size approximately equal to that of the 1240K SNP panel if missing data are not allowed on a given population set; 3) the 1240K panel [14]; 4) the 1000K panel composed of 997,780 SNPs comprising all transversion polymorphisms found in two African (Yoruba) individuals sequenced to high coverage and transversion polymorphisms found in the Altai Neanderthal genome [14]; 5) the union of the 1000K and 1240K panels termed 2200K [4]; 6) various components of the 1240K panel (the sites included in the Illumina 650Y and/or Human Origins SNP arrays, sites included exclusively in one of them, and the remaining sites); 7) the largest Human Origins sub-panels–panel 4 ascertained as sites heterozygous in a single San individual, panel 5 ascertained as sites heterozygous in a single Yoruba individual, their union (panels 4+5), and panel 13 including sites where a randomly chosen San allele is derived relative to the Denisovan [16] (abbreviated as, e.g., “HO panel 4”); 8) all sites polymorphic in a group uniting three high-coverage archaic genomes: the”Denisova 3” Denisovan, the Altai and Vindija Neanderthals (this ascertainment scheme is abbreviated in this study as “archaic asc.” and is similar to those proposed by Bergström et al. [30] and in the technical note published on the Daicel Arbor Biosciences product page); 9) transversion sites variable in the group comprising these three high-coverage archaic genomes (abbreviated as “archaic asc., transv.” or “archaic asc., tv.”); 10) restricting to SNPs that have high minor allele frequency (MAF >5%) in the whole "SGDP+archaic" dataset, i.e. high global MAF (abbreviated as “global MAF”); 11) restricting to SNPs having high global MAF combined with taking A/T and G/C SNPs only (abbreviated as “AT/GC, global MAF”); 12) restricting to SNPs that have >5% MAF in a selected African or non-African continental meta-population (abbreviated as, e.g., “AFR MAF”), irrespective of their frequency in the other meta-populations (there are nine such meta-populations in our dataset, and thus nine different ascertainments, see S1 Table); 13) restricting to SNPs that have >5% MAF in a selected continental meta-population, A/T and G/C SNPs only (abbreviated as, e.g., “AT/GC, AFR MAF”). For a list of SGDP-derived SNP sets explored in this study and their sizes in terms of groups, individuals, and SNPs see S2 Table. Although this list is surely not exhaustive, it includes all ascertainment schemes most popular in archaeogenetic publications.

To investigate the influence of SNP ascertainment on the ranking of admixture graph models according to their fits to data, we analyzed real data, considering sets of five populations, and as a way of evaluating the effect of SNP ascertainment on the ability to discriminate among different topologies, tested their fit to all possible admixture graph topologies with two admixture events (32,745 distinct topologies with no fixed outgroup; we considered graphs of this complexity as it was unfeasible to work with exhaustive collections of more complex graphs).

First, we explored such exhaustive collections of admixture graphs for three combinations of groups (Fig 1). Residuals of admixture graph model fits on all sites, on a random subset of them approximately equal to the size of the 1240K set, and on AT/GC sites, are tightly correlated (Pearson’s r approaches 1). Residuals of admixture graph models restricted to non-Africans only are also highly correlated on all sites and 1240K sites (r = 0.95–0.99, Fig 1). In contrast, the worst f₄-statistic residuals (WR) for graph models including one archaic human, three African groups, and one African group with ca. 60% of non-African ancestry [67] are poorly correlated on all sites and 1240K sites (r = 0.31–0.35). WR, also referred to as “admixture graph Z-score”, is one of two key metrics of admixture graph fit used in this study: it is the Z-score measuring deviation between observed and expected values of an f₄-statistic that is predicted most poorly by the admixture graph being tested [23,26]. WR is measured in standard error (SE) intervals, and, by convention, admixture graphs with WR below 3 SE are considered to fit the data well (see, e.g., [68,71–74]). Thus, WR is typically used in the literature to assess absolute fit of admixture graph models to data (e.g., [68,71–75]), and it is used for model ranking in some cases (strictly speaking, WR is just an approximation of absolute model fit, which is hard to calculate since many f-statistics for a given population set are correlated [23]). Log-likelihood score (LL score or simply LL) is another metric that is dependent on deviations of all f-statistics (for populations included in the model) from their predicted values and on their covariance, and thus more accurately reflects model fit to data [23,71]. However, unlike WR measured in SE units, LL is not easily comparable across admixture graph complexity classes, population sets, and SNP sets (but comparable across topologies of the same complexity on the same set of SNPs and populations), and thus WR is used as the primary admixture graph fit metric in this study.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. Scatterplots illustrating the effects of the 1240K ascertainment on worst f₄-statistic residuals of admixture graphs (WR), explored on exhaustive collections of simple graphs.

Five thousand best-fitting graphs (according to log-likelihood scores on all sites) of 32,745 possible graphs were selected for each combination of five populations, and correlation of WRs was explored for graphs fitted on all sites and on ascertained datasets. WR, also known as admixture graph Z-score, is the residual of an f₄-statistic that is fitted the worst by the admixture graph model. Log-likelihood score of an admixture graph model (LL [23]) reflects deviation of all relevant f-statistics from their values predicted under the model and their covariance. Results are shown for three population combinations indicated in plot titles. On x-axes results for all sites or for a randomly thinned site set are shown. Results for the 1240K ascertainment are shown in the upper row on the y-axes, and results for AT/GC sites are shown in the lower row on the y-axes. Linear trends fitted to the plotted points are shown in blue, along with Pearson correlation coefficient.

https://doi.org/10.1371/journal.pgen.1010931.g001

These results show that admixture graph fit rankings are severely affected by the 1240K ascertainment if certain population combinations are involved. We considered the possibility that this case of poor correlation was driven by admixture graph topologies that were obviously inconsistent with the data–that is, topologies that could be shown to be inconsistent with the data based on gold standard SNP sets without ascertainment bias. However, the lack of strong correlation for some combinations of populations is not just driven by graphs with poor fits to the data. For example, WRs of admixture graphs fitting the data well (WR <2.5 SE) on a random subsample of 840,000 sites range from nearly 0 SE to about 10 SE on ca. 845,000 sites included in the 1240K panel (Fig 1). Rejecting a model that fits on unascertained data runs the risk of rejecting the true model, as we show on simulated data in the next section. The converse problem also applies: some admixture graphs are well-fitting (WR <2.5 SE) on the 1240K sites but fit a random sample of sites poorly (WR >5 SE, Fig 1).

Next, we explored the same exhaustive set of admixture graph topologies including five groups and two admixture events on the wider collection of ascertainment schemes listed above and on a larger collection of populations. Twelve combinations of five groups including up to two archaic humans, up to five African groups, and up to five non-African groups were tested. In S1 Fig we compare various ways of looking at the effects of ascertainment on admixture graph fits, using the population quintuplet "Denisovan, Khomani San, Mbuti, Dinka, Mursi" as an example. In Table 1 we focus on the fraction of all graph topologies tested that are considered poorly-fitting under ascertainment (WR >3 SE) but well-fitting on all sites (WR <3 SE) as a metric appropriate for approximately quantifying the most serious effects of ascertainment bias, namely the probability of rejecting the true model. In the supplementary materials, we also show alternative ways of quantifying ascertainment bias: a metric reflecting the statistical power of ascertainment, namely the fraction of all graph topologies tested that are well-fitting under a given ascertainment (WR <3 SE) but poorly-fitting on all sites (WR >3 SE) (S3 Table), and squared Pearson correlation coefficient for fits (WR or LL) of admixture graphs on unascertained vs. ascertained data (S2 and S3 Figs, S4 and S5 Tables).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Performance of ascertainment schemes explored across 12 population quintuplets and assessed as the fraction of all possible admixture graph topologies that are rejected under ascertainment (fit poorly with WR >3 SE) but accepted on all sites (fit well with WR <3 SE).

We also applied the binary classifier to determine if an ascertainment scheme produces unbiased or biased results (the latter cases are highlighted in bold and underlined text). The numbers of population quintuplets or ascertainment schemes affected by bias, or by both bias and low statistical power, are shown in the two rightmost columns and in two bottom rows, respectively. The level of bias is approximated by the fraction of topologies that are rejected under ascertainment but accepted on all sites, and statistical power is approximated by the fraction of topologies that are, vice versa, accepted under ascertainment but rejected on all sites. The composition of the population sets is shown above the table in an abbreviated way: arch, archaic humans, followed by the number of archaic groups in admixture graph models tested; afr, Africans, followed by the number of African groups; nafr, non-Africans or Africans with substantial non-African admixture [67], followed by the number of such groups. The results for five population quintuplets (listed in the footnote) demonstrating no ascertainment bias are collapsed into one column. The SNP counts correspond to sites polymorphic in larger collections of groups from which the analyzed population quintuplets were taken, see S2 Table. SNP counts vary across the population sets, and minimal and maximal values are shown in separate columns.

https://doi.org/10.1371/journal.pgen.1010931.t001

Although we recognize that there can be no strict rule for classifying ascertainments into biased and unbiased ones since they form a continuum, for a high-throughput analysis a classifier is useful. Moreover, fits of a given admixture graph model vary even in the absence of ascertainment bias, due to random site sampling effects (Figs 2 and S1), as was shown in previous work [23]. In this study, we considered a SNP set biased if a bias metric (such as the fraction of topologies fitting poorly under ascertainment but well on all sites) was above (or below, as appropriate) the 2.5^th percentile of this metric’s distribution across 200 sets of randomly sampled SNPs equal to the size of the 1240K set for a given population combination (with no missing data allowed at the group level).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. The effect of ascertainment bias on admixture graph fits illustrated on a population combination "Altai Neanderthal, Ju|’hoan North, Biaka, Yoruba, Agaw".

Five thousand best-fitting graphs (according to log-likelihood scores on all sites) of 32,745 possible graphs were selected, and correlation of worst f₄-statistic residuals (WR) of admixture graphs was explored for models fitted on all sites and on ascertained sites. Results for ascertainment on variants common in Africans (either those having no detectable West Eurasian ancestry or all Africans in the SGDP dataset) are circled in red. Thirty eight site subsampling schemes were analyzed (see panel a): 1) AT/GC; 2) random thinning of the AT/GC dataset to the 1240K SNP count for a given combination of groups (no missing data allowed at the group level), results for 100 thinned replicates are shown; 3) random thinning of all sites to the 1240K SNP count, results for 100 thinned replicates are shown; 4) the 1240K enrichment panel; 5) major components of the 1240K panel: sites included in the Illumina 650Y and/or Human Origins (HO) SNP arrays, sites included exclusively in one of them, and remaining sites; 6) the 1000K and 2200K SNP panels; 7) archaic ascertainment (either all such sites or transversions only); 8) the largest HO panels (4, 5, 13) or their union (4+5); 9) MAF ascertainment in one of nine continental-scale groups; 10) the same procedure repeated on AT/GC sites. The size of the resulting SNP panels is coded by point size, and the ten broad ascertainment types are coded by color according to the legend. Squared Pearson correlation coefficients (R²) for admixture graph WR on unascertained vs. ascertained data are plotted. The 2.5^th WR percentile of all the thinned replicates combined, including those on all sites and AT/GC sites, is marked with the brown line. The area of the plot where ascertainments are considered biased according to this classifier is highlighted in red on the left. Scatterplots illustrating effects of selected ascertainment schemes on WR are shown in panels b–i. Dots on these scatterplots correspond to distinct admixture graph topologies. The corresponding ascertainment schemes are marked with letters b–i in panel a.

https://doi.org/10.1371/journal.pgen.1010931.g002

Inspecting the key metric of ascertainment performance (the fraction of topologies that fit poorly under ascertainment but well on all sites), we found only three site sampling schemes that, following the above-mentioned rule, were classified as unbiased for all the population quintuplets tested: AT/GC, HO panel 4, and the union of HO panels 4 and 5 (Table 1). However, due to the small number of sites in the latter two panels, the union of HO panels 4 and 5, and especially panel 4, lack power to reject admixture graph models as compared to the 1240K panel and to AT/GC, as we show in S3 Table. Thus, the only ascertainment scheme that is problem-free according to both metrics is a random one: taking the A/T and G/C mutation classes.

Among the population quintuplets tested, "Altai Neanderthal, Ju|’hoan North, Biaka, Yoruba, Agaw" (Figs 2 and S2A) and "Altai Neanderthal, Ju|’hoan North, Luhya, Palestinian, Spanish" (S2B Fig) are most susceptible to ascertainment bias (Table 1). A very similar quintuplet "Altai Neanderthal, ancient South African hunter-gatherers, Biaka, Yoruba, Agaw" is encountered within more complex admixture graph models that occupy a central place in Lipson’s et al. [9,12] analyses based on 1240K data (see an investigation of bias affecting the admixture graphs from these studies in S1 Text and S4 and S5 Figs). As explored below on real and simulated data, a class of f₄-statistics that are strongly affected by non-outgroup SNP ascertainment underlies admixture graphs for both problematic population quintuplets: f₄(African_x, archaic; African_y, non-African). On the other hand, population sets including no archaic human were virtually unbiased (Table 1), but some ascertainment schemes showed limited power to reject admixture graph models in these cases (S3 Table).

Archaic ascertainment has been suggested in the literature [6,30] as a way to reduce ascertainment bias. However, this approach is guaranteed to work only if the outgroup or a related group is not included itself in admixture graphs or f-statistics, and if individuals used for ascertainment are not sole representatives of the respective groups in an analysis. Indeed, we show that archaic ascertainment is biased in the case of the most problematic population quintuplet "Altai Neanderthal, Ju|’hoan North, Biaka, Yoruba, Agaw" (Table 1); in fact, archaic ascertainment is by far the most biased ascertainment approach for population sets including both Neanderthal and Denisovan individuals (Table 1, see also results on simulated data below), and in our analysis it also emerged as the scheme with the lowest statistical power to reject admixture graph models (S3 Table).

If we combine both key metrics of ascertainment performance (the fraction of topologies fitting poorly under ascertainment but fitting well on all sites, and the fraction of topologies fitting well under ascertainment but poorly on all sites), the 1240K and archaic ascertainments are out-performed by many ascertainment schemes, and most notably by the following: 1) HO panels 4+5; 2) the 2200K panel, which combines various kinds of ascertainment such as the 1240K panel, ascertainment on two Yoruba individuals, and on the Altai Neanderthal [14]; and 3) restricting to variants that are common in the African meta-population in SGDP (abbreviated as “AFR MAF”, S1 Table), optionally followed by removal of all mutation classes except for A/T and G/C (Table 1). Squared Pearson correlation coefficient (R²) for admixture graph WR on unascertained vs. ascertained data is in some cases informative in a way that the fractions of poorly/well-fitting topologies are not. As illustrated in Fig 2, R² may differ substantially across ascertainment schemes while the fractions of topologies fitting poorly under ascertainment but well on all sites or vice versa stay nearly constant across most ascertainment schemes (Tables 1 and S3). Considering R² for admixture graph WR, the AFR MAF scheme emerges as the least biased form of ascertainment (S4 Table). We note that conclusions of this sort are not quantitative since our collection of 12 population quintuplets, although diverse, is just a small sample from the vast set of all possible population combinations. However, exploring all possible combinations is infeasible, and we consider our approach to be useful as a practical guide for assessing the performance of SNP ascertainment when admixture graphs including archaic humans, Africans, and non-Africans are fitted to genetic data.

2. Simulation studies confirm the qualitative patterns from exploration of empirical data

A major limitation of our empirical analyses of ascertainment bias is that fitting a model with two admixture events is almost certainly inadequate for the histories relating various sets of five populations being analyzed. Thus, it is almost certain that all fitted models will be wrong. When we fit wrong models, we have no guarantee that the (incorrect) admixture graph fit to the data will give the same signal of deviation for different SNP ascertainments. Different SNP ascertainments including random ascertainments will simply be sensitive to different aspects of the deviations between the wrong model and the true history. Thus, while the poor correlation between model fits on all sites and under different SNP ascertainment schemes for combinations of archaic humans, sub-Saharan Africans, and non-Africans is a potential signal of bias in analyses, it is valuable to analyze data where the truth is known, as is the case for simulations, to provide clear evidence that typical ascertainment schemes can cause false-positive inferences about history.

Using msprime v.1.1.1 [76], we simulated genetic data (a diploid genome composed of three 100 Mb chromosomes with recombination) that reproduce the F_ST values (S6A Fig) observed when comparing AMH groups, AMH and archaic humans, and AMH and chimpanzee [77]. First, ten independent simulations were performed under one admixture graph topology (Fig 3) serving as a case study, and then the analysis was expanded to dozens of random topologies (Fig 4). The former admixture graph (Fig 3A) reproduces some known features of the genetic history of anatomically modern and archaic humans, but differs in other respects from the widely accepted model [32,53]. The Neanderthal gene flow to the ancestors of non-Africans (via an unsampled proxy group) was either simulated or omitted.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Exploring the influence of non-outgroup ascertainment on fits of admixture graphs in the case of a single simulated history reproducing some known features of the genetic history of anatomically modern and archaic humans (but differing in other respects from the widely accepted model [53]).

Results are presented for two topologies (with or without the Neanderthal to non-African gene flow simulated) and for eight types of SNP sets: 1) 10 sets of randomly selected variable sites matching the average size of the “HO one-panel” set, 500K sites (abbreviated as “subsampled non-asc.”); 2) unascertained sites (on average 5.55M polymorphic sites without missing data at the group level); 3) HO one-panel ascertainment based on the “African 2” group (500K sites on average across simulation iterations); 4) HO four-panel ascertainment, based on randomly selected individuals from four groups (“African 1”, “African 2”, “non-African 1”, and “non-African 2”, 1.34M sites on average); 5) archaic ascertainment (1.05M sites on average); 6) “AFR MAF”, that is restricting to sites with MAF >5% in the union of the “African 1” and “African 2” groups (1.85M sites on average); 7) global MAF ascertainment on the union of the “African 1”, “African 2”, “non-African 1”, and “non-African 2” groups (1.62M sites on average); 8) non-African MAF ascertainment on the union of the “non-African 1” and “non-African 2” groups (1.48M sites on average). (a) The simulated topology, with dates (in generations) shown on the y-axis (for the sake of visual clarity, the axis is not to scale). The Neanderthal to non-African gene flow was simulated either at 0% or at ~2% as shown in the figure. Effective population sizes and population split times are omitted for clarity (see S13 Table). The out-of-Africa bottleneck is marked with a star. (b) Boxplots illustrating the effects of various ascertainment schemes on fits (worst f₄-statistic residuals, WR) of the correct admixture graphs. The dashed line on the logarithmic scale marks a WR threshold often used in the literature for classifying models into fitting and non-fitting ones, 3 standard errors. The observation that common ascertainment schemes consistently produce much higher Z-scores than this threshold provides unambiguous evidence that ascertainment bias can profoundly compromise admixture graph fitting. The topologies fitted to the data are shown beside the boxplots. In the panels on the right, simple graphs including only one archaic lineage are fitted (with “Neanderthal 1” used as an example, but very similar results were obtained for the “Neanderthal 2” and “Denisovan” groups). In the panels on the left, results for the full simulated model fitted to the data are shown.

https://doi.org/10.1371/journal.pgen.1010931.g003

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. Effects of non-outgroup and true outgroup ascertainment on fits of admixture graphs explored on a collection of 80 random simulated histories.

The worst f₄-statistic residual (WR) of the correct admixture graph was used as a measure of bias. (a) WRs for unascertained data and four ascertainment schemes are summarized with boxplots: 1) HO one-panel; 2) HO four-panel; 3) MAF ascertainment on random sets of four populations (abbreviated as “MAF asc.”); 4) ascertainment on sites polymorphic in random sets of three individuals (one individual sampled per population; abbreviated as “3 groups poly asc.”). HO one-panel ascertainment was performed on various types of simulated populations: on non-outgroup populations (“non-OG groups”) or on more or less drifted phylogenetic outgroups (having effective population sizes of 1,000 or 100,000 diploid individuals, respectively) co-modelled with the other populations (abbreviated as “drifted OG” and “OG”, respectively). The individual that was used for HO one-panel ascertainment either acted as the only representative of its group for model fitting, or the whole group of 10 individuals was included in the fitted graph. Alternatively, the group used for HO one-panel ascertainment was not included in the fitted graph: it was either the more or less drifted outgroup, the true root, or the last common ancestor of non-outgroup populations (“non-OG root”). These details are reflected in the plot labels on the right and on the y-axis. The dashed vertical line corresponds to WR = 3 SE. (b) Correct admixture graphs under HO one-panel ascertainment are guaranteed to be well-fitting (WR < ca. 4 SE) if F_ST between the whole population sample used for ascertainment vs. the sample at the root of the simulation is below 0.12. (c) DAF spectra (derived allele count in a sample of 20 chromosomes vs. proportion of sites in square root scale) are summarized across simulated non-outgroup populations binned by the level of bias in admixture graph fits (approximated by WR of the true admixture graph) observed when HO ascertainment is performed on the respective population. DAF spectra in populations that are the last common ancestors of non-outgroup populations (abbreviated as “non-OG root”) are shown for comparison. The spectra shown here are based only on sites polymorphic in a sample of 20 chromosomes drawn at the root of the simulation (data for sites that are fixed derived or fixed ancestral are not shown, see complete results in S8 Fig). The boxplots summarize DAF across all the simulated admixture graph topologies, and are binned by derived allele counts from 1 to 19.

https://doi.org/10.1371/journal.pgen.1010931.g004

We tested several non-outgroup ascertainment schemes (Fig 3): 1) “HO, 1 panel”, ascertainment on heterozygous sites in a randomly selected individual from the “African 2” group (this ascertainment follows the scheme used for generating some of the 12 panels of sites comprising the Human Origins SNP array [16]); 2) “HO, 4 panels”, ascertainment on heterozygous sites in four randomly selected individuals, one per each “AMH” group (we consider the resulting SNP set to be qualitatively similar to the whole Human Origins SNP set); 3) archaic ascertainment (sites polymorphic in a group composed of one “Denisovan” individual and one individual per each “Neanderthal” group; the same individuals were subsequently used for calculating f-statistics); 4) “AFR MAF”, that is restricting to sites with MAF >5% in the union of two “African” groups; 5) similar MAF-based ascertainment on two “non-African” groups (“non-AFR MAF”) or 6) on all four “AMH” groups (“global MAF”).

First, we fitted the correct admixture graph as often practiced in the literature (e.g., [9,12,78]): including an “ape” outgroup, only one “archaic” individual, and all “AMH” groups. HO one-panel ascertainment always leads to rejection of the correct model in this case, both in the absence and in the presence of the Neanderthal gene flow to non-Africans, with WR ranging from 3.4 to 8.8 SE (Fig 3B). HO four-panel ascertainment is less problematic but led to rejection of the correct model (WR >3 SE) in 9 of 30 cases (in the presence of the Neanderthal gene flow to non-Africans), with WR up to 4.6 SE. Only the archaic and AFR MAF non-outgroup ascertainments (in the presence of the Neanderthal gene flow to non-Africans) did not lead to rejection of these simplified graph topologies, known to be correct since we simulated them. However, when the full simulated model (with the Neanderthal gene flow to non-Africans) including the outgroup and three “archaic” lineages is fitted to the data, all non-outgroup ascertainment schemes become problematic, except for the AFR MAF ascertainment (Fig 3B).

Next, we moved beyond fitting only one true admixture graph to ascertained data and used the exhaustive approach for exploring the stability of model ranking under ascertainment that was applied to the real data above. All possible graph topologies with two admixture events (32,745) were fitted to population quintuplets of the following composition: “Denisovan or Neanderthal 1 or Neanderthal 2”, “African 1”, “African 2”, “non-African 1”, “non-African 2”. The fractions of all topologies tested that were rejected/accepted under ascertainment but accepted/rejected on all sites (and the bias classifier) were then used to reveal simulation iterations and ascertainment schemes that demonstrated biased model fits (S6 Table). When no Neanderthal/non-African gene flow was simulated, only the non-AFR MAF ascertainment emerged as problematic (at least half of simulation iterations for at least one population quintuplet were classified as affected by bias) according to the fraction of topologies rejected under ascertainment but accepted on all sites (S6 Table). When the Neanderthal to non-African gene flow was simulated, all ascertainment schemes, except for the HO four-panel ascertainment, emerged as problematic according to the same metric (S6 Table). Summarizing these results on model ranking and on fits of the true model, we note that the HO four-panel ascertainment is relatively problem-free in this case study on one simulated topology, unlike archaic, MAF, and HO one-panel ascertainment, but it still led to rejection of the true model more often than on all sites or on random site subsamples (Fig 3B).

Finally, we explored non-outgroup ascertainment schemes that are similar to those presented in Fig 3B but are based on randomly chosen groups (see Methods for details) and were applied to SNP sets resulting from simulated genetic histories in the form of random admixture graphs. Graphs of four complexity classes including 9 or 10 populations and 4 or 5 admixture events were simulated using msprime v.1.1.1. Only simulations where pairwise F_ST for groups were in the range characteristic for anatomically modern and archaic humans were selected for further analysis, resulting in 20 random topologies per graph complexity class, each including an outgroup (see examples of the simulated histories and F_ST distributions in S7 Fig). Fits of the true admixture graph (WR) including an outgroup were compared on all sites and on ascertained SNP sets for each topology and ascertainment iteration (Fig 4A). We note that our simulation setup generated groups sampled at different dates in the past (from 0 to ca. 40,000 generations), and thus widely different levels of genetic drift with respect to the root (Fig 4B).

As illustrated by distributions of true admixture graph WRs in Fig 4A, ‘blindly’ ascertaining on individuals or sets of groups randomly sampled across the graph almost guarantees rejecting the true historical model by a wide margin. Ascertainment on sites polymorphic in randomly composed sets of three individuals (one individual per group) and restricting to variants common (MAF >5%) in randomly composed sets of four populations are two forms of ascertainment that are especially problematic (Fig 4A). One-panel and four-panel HO ascertainments often yield acceptable results (WR <3 SE), although median WR of the true graphs equals 4.6 SE for these ascertainment schemes across all graph topologies and all (non-root and non-outgroup) populations used for ascertainment (Fig 4A).

An illuminating result is that F_ST between the population used for Human Origins-like ascertainment and the root of the simulation influences WR of the true graph: all ascertainments with F_ST < 0.12 produce relatively unbiased fits of true graphs (WR <4 SE, see Fig 4B). In other words, ascertainment on heterozygous sites in a single individual taken from a population that is not an outgroup and is co-analyzed with other populations, but is relatively undrifted genetically compared to the root of the simulation, is unbiased, unlike ascertainment on a single individual from a more drifted population. We directly illustrate this effect by comparing results on outgroups co-analyzed with other populations that are more or less drifted with respect to the root (with effective population sizes differing by two orders of magnitude) (Fig 4A and 4B). We also show that co-analyzing the individual used for ascertainment with other groups does not exacerbate bias if that individual is a part of a wider population of 10 individuals. However, if that individual is the only representative of its group for model fitting, WRs are inflated drastically (Fig 4A). We finally illustrate the difference between ascertainment on an outgroup that is not co-modelled with the other groups (true outgroup ascertainment) and ascertainment on a phylogenetic outgroup that is included in the fitted model (Fig 4A). The former ascertainment is indeed unbiased even for highly drifted outgroups (Fig 4A), while the latter is not [16,37].

Another way of looking at this phenomenon is through derived allele frequency (DAF) spectra. Ascertainment schemes resulting in relatively unbiased fits of true models (WR <4 SE, Fig 4C) are most often based on populations where the DAF spectrum of sites that were polymorphic at the root is preserved relatively well (see a full version of this plot in S8 Fig). We note that some ascertainments may be unbiased with respect to the true graph but may have low power to reject incorrect admixture graph models due to the paucity of sites with high MAF in “present-day” populations. Indeed, ascertainments on the root itself or on groups genetically close to the root (such as outgroups with a large effective size) are unbiased (Fig 4A and 4B), but on average demonstrated lower power to reject incorrect models as compared to HO one-panel ascertainments on more drifted groups (S9 Fig). Summarizing these observations on a range of random simulated histories, we expect that it is difficult to find an ascertainment scheme that is optimal (at least for the purpose of admixture graph fitting), that is, demonstrates both low bias when testing the true model and high power to reject incorrect models. Our observations on the real data in the preceding section agree with this expectation.

Our results on randomized ascertainment schemes (not to be confused with random site sampling) and simulated histories in the form of random admixture graphs show that ascertainment on groups that are highly drifted with respect to the root of the groups being co-analyzed is problematic. Thus, if proper outgroup ascertainment is impractical (if an outgroup shares few polymorphisms with the other populations analyzed, or if an outgroup is needed for constraining the analysis), unascertained or randomly sampled sets of sites should be treated as a gold standard for admixture graph inference. The 1240K ascertainment is much more complex [14,15] than the ascertainment schemes we explored on simulated data, but its effects are possibly intermediate between the effects of a MAF-based ascertainment (since all common SNP panels are more or less depleted for rare variants) and ascertainment on heterozygous sites in single individuals from several groups (since approximately half of the 1240K sites are derived from the Human Origins SNP array ascertained this way [14]). Thus, we expect an accurate admixture graph including at least one archaic human, at least two African groups, and at least one non-African group (Fig 3A) to fit the data poorly under the 1240K ascertainment.

We also checked if non-outgroup ascertainment could bias the simplest cladality tests in the absence of gene flow. f₄-statistics are tests for treeness that are essentially the same [16] as the ABBA-BABA test (D-statistic [24,25]) which was used to detect Neanderthal admixture in non-Africans [24]. A tree of four groups conforming to the f₄-statistic (A, B; C, O) was simulated using msprime v.1.1.1, with a tree depth of 4,000 generations (S10A Fig). All the groups had a uniform effective population size of 100,000 diploid individuals, except for a 10x to 10,000x size reduction immediately after the A-B divergence (1,999 generations in the past). While the dramatic drop in the effective population size of group A yields a complex shape of the derived allele frequency spectrum in {A, B} [79], two of three ascertainment schemes explored here (HO one-panel and MAF ascertainment, but not removal of the derived end of the allele frequency spectrum; see Methods) increase the noise in the f₄-statistic (A, B; C, O), but do not shift the statistic away from its expectation at 0 (S10 Fig). These results confirm an observation by Patterson et al. [16] that in the case of perfect trees non-outgroup SNP ascertainment does not lead to false rejection of cladality. However, as demonstrated in Figs 3 and 4, non-outgroup ascertainment is generally problematic in the case of complex demographic histories with multiple admixture events. This is due to biases on f-statistics that have non-zero expected values, which are not relevant to the f₄-symmetry test but are very important in admixture graph fitting.

3. An overview of f₄-statistic biases caused by non-outgroup ascertainment

We explored various classes of f₄-statistics exhaustively to obtain a "bird’s-eye view" of ascertainment biases that was previously difficult to obtain due to technical challenges in calculating millions of f-statistics [30]. Another motivation for this analysis was the fact that it is infeasible to explore fits of large collections of admixture graphs on thousands of population sets, ascertainment schemes and random site subsamples. However, if an exhaustively sampled class of f-statistics is demonstrated to be unbiased, all admixture graph fits based on those statistics are expected to be unbiased too.

For this analysis we used residual standard deviation ("residual SE") of a linear trend as a way of measuring correlation between f₄-statistic Z-scores on all sites and under ascertainment. We found this metric more convenient than the squared Pearson correlation coefficient (R²) since it is expressed in the same units as Z-scores and thus is an intuitive way of representing deviation of f₄-statistic sets on ascertained data from those on unascertained data. We note that it reflects both bias introduced by ascertainment and variance generated by random site sampling. In S7 Table and S11 and S12 Figs we show residual SE values for a collection of 27 exhaustively sampled f₄-statistic classes and for the large collection of ascertainment schemes introduced in section 1. The f₄-statistic classes explored here can be described concisely as African(all SGDP populations)_x;archaic_y;chimpanzee₁, African(unadmixed with West Eurasians)_x;archaic_y;Mediterranean/Middle Eastern (abbreviated as Med/ME or ME)_z, African(unadmixed with West Eurasians)_x;East Asian_y(y>0), American/Siberian_x;European_y;Papuan_z. Here, x, y, and z stand for the number of groups in the population quadruplet; thus, “African₃;East Asian₁” would mean three Africans and one East Asian. All possible distinct f₄-statistics composed of those "ingredients” were considered. Although this analysis is by no means exhaustive, the chosen classes of f₄-statistics underly a very wide array of admixture graph and qpAdm models from the archaeogenetic literature.

The effects of SNP ascertainment vary dramatically across the classes of f₄-statistics, but ascertainment schemes based on one or two African individuals (HO panels 4, 5, 13, 4 and 5 combined), on the three archaic individuals (either all sites or transversions only), and components of the 1240K panel such as Illumina 650Y emerged as the worst-performing when results across all the f₄-statistic classes were considered (S7 Table, S11 Fig). Ascertainment schemes based on a global MAF threshold or on a MAF threshold in a single non-African continental meta-population, and the 1000K and 2200K panels are similar in their effects to the 1240K ascertainment (S7 Table, S11 Fig). We recognize that there is a continuum between unbiased and biased ascertainment schemes, and that for nearly all schemes and f₄-statistic classes a majority of statistics remain unaffected by ascertainment, but for describing our results in a concise way and for partially factoring out effects of SNP panel size, we applied the criterion similar to that employed above for admixture graph fits: residual SE for an f₄-statistic class is higher than the 97.5^th percentile across 200 randomly thinned datasets matching the 1240K panel in size. According to this criterion, the 1240K ascertainment is problematic in the case of the following nine f₄-statistic classes (S7 Table): 1) f₄(African_w, African_x; African_y, African_z), 2) f₄(African_x, African_y; African_z, Med/ME), 3) f₄(African_x, African_y; African_z, East Asian), 4) f₄(African_x, African_y; African_z, archaic), 5) f₄(African_x, African_y; African_z, chimpanzee), 6) f₄(African_x, archaic; African_y, non-African), 7) f₄(African_x, archaic; African_y, chimpanzee) and f₄(African_x, African_y; archaic, chimpanzee), 8) f₄(archaic_x, archaic_y; archaic_z, Med/ME), 9) f₄(archaic_x, archaic_y; archaic_z, African), and unproblematic for the remaining 18 classes exhaustively explored in this analysis. Unlike all the other classes explored here (S7 Table, S11 Fig), statistics of the form f₄(African_x, archaic; African_y, non-African) are substantially biased under all types of SNP ascertainment (Fig 5A). The classes f₄(African_x, African_y; African_z, X) are problematic under all ascertainment schemes except for AFR MAF (S7 Table, see an example in Fig 5B), and the class f₄(African_w, African_x; African_y, African_z) is problematic under all ascertainment schemes except for the 1000K, 2200K, and AFR MAF (S7 Table). Scatterplots underlying these residual SE estimates are also shown in Fig 6 (for some of the most problematic classes highlighted above) and in S13–S15 Figs (for all classes). Importantly, the classes of statistics most affected by ascertainment (f₄(African_x, archaic; African_y, non-African), f₄(African_x, archaic; African_y, chimpanzee), f₄(African_x, African_y; African_z, X), and f₄(African_w, African_x; African_y, African_z)) are often relevant for fitting admixture graph models of African population history (see S1 Text). However, for most classes of f₄-statistic Z-scores that were classified as problematic, i.e., if residual SE of a linear trend under ascertainment exceeds residual SE under random site sub-sampling to the size of the 1240K panel, absolute residual SE values are below 1 SE (S7 Table and S11 Fig), and thus these statistics are probably not problematic in practice.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 5. Variance in f₄-statistic Z-scores resulting from ascertainment and random site subsampling expressed as residual standard deviation of a linear trend fitted to a scatterplot of Z-scores on unascertained vs. ascertained data (abbreviated as “residual SE” and expressed in the same units as f₄-statistic Z-scores).

Results are shown for three classes of f₄-statistics: f₄(African_x, archaic; African_y, Mediterranean/Middle Eastern), f₄(African_x, African_y; African_z, archaic), and f₄(African, Med/ME_x; Med/ME_y, Med/ME_z). The following abbreviations are used for naming the f₄-statistics classes: AFR, African populations; ARCH, archaic human individuals (Neanderthals and Denisovans); Med/ME or ME, Mediterranean and Middle Eastern populations. Results for ascertainment on variants common in Africans (either those having no detectable West Eurasian ancestry according to Fan et al. [67] or on all Africans in the SGDP dataset) are circled in red. Residual SE values for f₄-statistic Z-scores lying not far from 0 (absolute Z-scores on all sites < 15) are plotted. The 97.5% percentiles of all the thinned replicates combined, including those on all sites and AT/GC sites, are marked by the brown lines. Size of the SNP panels is coded by point size, and the broad ascertainment types are coded by color according to the legend. Thirty eight ascertainment schemes were explored, identical to those in Fig 2.

https://doi.org/10.1371/journal.pgen.1010931.g005

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 6. Scatterplots illustrating the effects of two ascertainment schemes on Z-scores of f₄-statistics of four classes including African (abbreviated as AFR) and/or archaic (ARHC) and/or Mediterranean/Middle Eastern (ME) groups.

The f₄-statistic classes were selected to represent severe ascertainment bias (leftmost panels), moderate level of bias (two middle panels) and no bias (rightmost panels). The ascertainments selected are 1240K (a SNP enrichment panel most widely used in the archaeogenetic literature) and the new “African MAF” ascertainment scheme proposed in this study to mitigate bias for nearly all f₄-statistic classes. For results on other f₄-statistic classes see S13 Fig, and results for a wider range of ascertainment schemes are summarized in S11 and S12 Figs. Labels of f₄-statistic classes and numbers of statistics plotted are shown above the panels. Instead of individual points, heatmaps illustrating point density are shown. Z-scores on all sites (10 million sites, as indicated on the x-axes) are compared to Z-scores on ascertained datasets on the y-axes. Ascertainment schemes and site counts are shown on the y-axes. All plots include only statistics with absolute Z-scores below 15 on all sites. A linear model fitted to the data and lines representing ± 2 SE are shown in red. Residual standard deviations (residual SE) for those linear trends are shown in each plot in red.

https://doi.org/10.1371/journal.pgen.1010931.g006

If we consider f₄-statistics instead of their Z-scores and R² instead of residual SE, results remain virtually the same (S8 Table). For additional details on f₄-statistic classes see S2 Text (and S12–S15 Figs), and for a dissection of effects of ascertainment on few selected f₄-statistics see S3 Text (and S9–S12 Tables). In contrast to the f₄-statistic classes relevant for modelling African population history, f₄-statistics including non-Africans only, or one or two African groups and non-Africans (see an example in Figs 5C and 6), are unproblematic under the 1240K, 2200K, AFR MAF and other MAF-based ascertainments (but demonstrate increased variance due to paucity of sites with high MAF under some other ascertainment types such as HO panels 4 & 5 and archaic ascertainment, S7 Table).

The AFR MAF ascertainment (restricting to variants common across 68 African individuals with little or no Holocene-era ancestry derived from West Eurasians, or across 94 African individuals, S1 Table), emerged as the best-performing non-outgroup ascertainment scheme. Unlike the other ascertainment schemes explored in this study, this type of ascertainment demonstrates a bias only in the case of the (African_x, archaic; African_y, non-African) class of f₄-statistics (when only statistics with |Z| <15 SE on all sites were considered, S7 Table, S11 Fig). Another class of f₄-statistics is biased under this ascertainment scheme when all statistics are considered: f₄(non-African_x, archaic; African, non-African_y) (S11 Fig), and AFR MAF ascertainment is unbiased in the case of the other 25 classes of f₄-statistics explored in this study (S7 Table, S11 Fig), which also translates into downstream analyses such as fits of admixture graph models (Figs 2 and S2, Tables 1 and S3–S5).

1. Simulating genetic data

2. Constructing the set of real data

We used the cteam-lite dataset described Mallick et al. [36], composed of the full SGDP set (300 high-coverage genomes from present-day populations), the chimpanzee genome (pseudo-haploid genotype calls, see http://hgdownload.cse.ucsc.edu/goldenPath/panTro2/bigZips/), and the Altai Neanderthal, “Denisova 3” Denisovan, Ust’-Ishim, WHG Loschbour, and LBK Stuttgart ancient genomes (see SI section 3 in Mallick et al. [36]). We supplemented cteam-lite by 44 present-day African genomes sequenced using the SGDP protocols by Fan et al. [67], the Vindija Neanderthal’s genome [33], and the genome of an ancient African forager individual I10871 sequenced by Lipson et al. [9] (S1 Table). Sites polymorphic in this set of 352 individuals were extracted from the cteam-lite files of the “hetfa” format using the cpoly tool [36]: alleles were grouped into derived and ancestral (polarized) according to the chimpanzee genome; missing data and heterozygous sites were allowed. For each genome, we used individual base quality masks included in cteam-lite or constructed using the same protocol for other genomes (Vindija Neanderthal and those sequenced by Fan et al. [67]): minimum base quality was set by default at 1, as recommended by Mallick et al. ([36], see SI section 3 in that study), which discarded lowest-quality regions marked as “0”, “?”, or “N”. The individual I10871 was not included in most analyses in this study (except for the complex admixture graphs in S1 Text, and S4 and S5 Figs) due to its relatively high rate of deamination errors.

The resulting dataset prior to missing data removal and ascertainment includes 94,691,841 biallelic autosomal SNPs (S2 Table). To keep the polarity of alleles, all data manipulations and ascertainments were performed using PLINK v.2.0 alpha [86]. For calculating f₄-statistics, sets of continental-level meta-populations were selected (e.g., Africans and East Asians or Africans and archaic humans) and then f₄-statistics were calculated for all possible combinations of populations in the resulting subset of the “SGDP+archaic” dataset, with no missing data (at the population level) allowed within the selected subset. This was done to avoid potential biases associated with data missing non-randomly across groups. Alternatively, f₄-statistics were drawn randomly from a certain class of statistics, and no missing data (at the population level) were allowed in the resulting population quadruplets.

3. Influence of ascertainment on fits of admixture graphs to real data

First, we fitted all possible graphs including two admixture events (32,745 distinct topologies with no fixed outgroup) for three combinations of groups: 1) one archaic individual, three African groups, and one African group with substantial West Eurasian-related ancestry (Altai Neanderthal, Ju|’hoan North, Biaka, Yoruba, and Agaw, respectively); 2) five deeply-divergent ancient and present-day non-African groups (Ust’-Ishim, Papuan, Onge, LBK Stuttgart, Even); and 3) five deeply-divergent present-day non-African groups (Papuan, Onge, Palestinian, Even, Mala). These three sets of simple graphs were fitted to all sites, AT/GC sites, and 1240K sites (no missing data were allowed at the group level within these sets of five populations); 5,000 best-fitting models were selected according to LL scores on all sites and WRs of those models were compared across SNP sets (Fig 1).

Next, we explored the same exhaustive set of admixture graph topologies including five groups and two admixture events on the wider collection of ascertainment schemes. Twelve combinations of five groups including up to two archaic humans, up to five African groups, and up to five non-African groups were tested. To ensure fair comparison across at least a subset of population combinations, as a starting point for generating ascertained site sets we used either 11,706,773 sites (with no missing data at the group level) polymorphic in a set of 48 archaic and African groups composed of 97 individuals in total; or 10,051,585 such sites in a set of 59 archaic, African, European, and Middle Eastern groups composed of 120 individuals in total; or 5,296,653 such sites in a set of 51 Papuan, Native American/Siberian, European, Anatolian, and Caucasian groups composed of 112 individuals in total (S1 and S2 Tables).

We examined fits of these collections of admixture graphs to the real data from different perspectives. (1) We considered just 5,000 topologies per each population quintuplet that are best-fitting on the unascertained site set (Figs 1, S1 and S2) or all 32,745 topologies tested (S3 Fig). (2) We also considered alternative admixture graph fit metrics, LL or WR. LL as a fit metric (see left-hand panels in S2 and S3 Figs) is more accurate than WR, but difficult to compare across different population sets. Finally, in addition to (squared) Pearson correlation coefficient of admixture graph fits on ascertained vs. unascertained data (Figs 1, 2 and S1–S3) as a way of measuring ascertainment bias, we considered the fraction of all possible admixture graph models of a certain complexity that are fitting the data poorly (“rejected”) under ascertainment (WR >3 SE) but fitting well (“accepted”) on all sites (WR <3 SE). The fraction of all possible models that are fitting the data well under ascertainment (WR <3 SE) but fitting poorly on all sites (WR >3 SE) was used to measure the power to reject incorrect admixture graph topologies.

4. Automated inference of fitting admixture graphs on real data

The 12-population admixture graph published by Lipson et al. [9] (and later used as a skeleton graph in Lipson et al. [12]) and simpler 7- and 10-population intermediate graphs presented in the former study were revisited by Maier et al. [23], and thousands of alternative well-fitting graphs of the same complexity were found using the find_graphs function from the ADMIXTOOLS 2 package (https://uqrmaie1.github.io/admixtools/articles/graphs.html). Maier et al. [23] used the 1240K dataset only, and in the current study we re-fitted the admixture graphs found by the algorithm on the 1240K SNP panel to the AT/GC and unascertained datasets derived from the “SGDP+archaic” dataset, and also repeated automated admixture graph inference on these two additional SNP sets. Advantages and pitfalls of automated admixture graph inference are described in detail in Maier et al. [23], along with justifications for the specific protocol used in that study, and here we used the protocols identical to those employed by Maier et al. [23]. We first calculated all possible f₂-statistics for 4 Mbp-sized genome blocks (with the “maxmiss = 0”, “adjust_pseudohaploid = FALSE”, and “minac2 = 2” settings, see Maier et al. [23] for details on the settings) and then used them for fitting admixture graphs (with the “numstart = 100” and “diag = 0.0001” settings) and for automated admixture graph inference with the find_graphs function (see the Methods section in Maier et al. [23] for a complete list of arguments for this function). Only one topology constraint was used at the graph space exploration step: chimpanzee was assigned as an outgroup.