The following dataset was generated:

- Figure 1—source data 1.

Download source data [figure-1—source-data-1.media-1.xlsx]**DOI:**http://dx.doi.org/10.7554/eLife.15266.004 - Figure 2—source data 1.
$TVD$ has been multiplied by 1000.

Download source data [figure-2—source-data-1.media-2.xlsx]**DOI:**http://dx.doi.org/10.7554/eLife.15266.009 - Figure 2—source data 2.
We used

*smartpca*to compute $F}_{ST$ for each pair of populations, upper right diagonal, together with standard errors computed using a block jacknife. $F}_{ST$ has been multiplied by 1000.

Download source data [figure-2—source-data-2.media-3.xlsx]**DOI:**http://dx.doi.org/10.7554/eLife.15266.010 - Figure 2—source data 3.
We used

*smartpca*to compute $F}_{ST$ for each pair of populations, upper right diagonal, together with standard errors computed using a block jacknife. $F}_{ST$ has been multiplied by 1000.

Download source data [figure-2—source-data-3.media-4.xlsx]**DOI:**http://dx.doi.org/10.7554/eLife.15266.011 - Figure 2—source data 4.
$TVD$ has been multiplied by 1000.

Download source data [figure-2—source-data-4.media-5.xlsx]**DOI:**http://dx.doi.org/10.7554/eLife.15266.012 - Figure 3—source data 1.
For each event in each ethnic group we show the largest inferred amplitude and date of an admixture event involving two reference populations (Pop1 and Pop2). We additionally provide the ancestry region identity of the two main reference populations, together with $Z$ scores for curve comparisons between this best curve and those containing populations from different ancestry regions. We use a cut-off of $Z<$ 2 to decide whether sources from multiple ancestries best describe the admixture source.

Download source data [figure-3—source-data-1.media-6.xlsx]**DOI:**http://dx.doi.org/10.7554/eLife.15266.015 - Figure 3—source data 2.
Columns as in Figure 3—source data 1.

Download source data [figure-3—source-data-2.media-7.xlsx]**DOI:**http://dx.doi.org/10.7554/eLife.15266.016 - Figure 3—source data 3.
Columns as in Figure 3—source data 1.

Download source data [figure-3—source-data-3.media-8.xlsx]**DOI:**http://dx.doi.org/10.7554/eLife.15266.017 - Figure 3—source data 4.
Columns are as in Figure 3—source data 1. Here we show the results for the MALDER analysis where we over-ride any short-range LD and define a minimum distance of 0.5cM from which to start computing admixture LD curves

Download source data [figure-3—source-data-4.media-9.xlsx]**DOI:**http://dx.doi.org/10.7554/eLife.15266.018 - Figure 4—source data 1.
$Analysis$ refers to whether the main or masked analysis was used to produce the final result. Admixture $P$-values are based on 100 bootstrap replicates of the NULL procedure. Our resulting inference, $res$ can be: 1D (two admixing sources at a single date); 1MW (multiple admixing sources at a single date); 2D (admixture at multiple dates); NA (no-admixture); U (uncertain). max($R}_{1$) refers to the $R}^{2$ goodness-of-fit for a single date of admixture, taking the maximum value across all inferred coancestry curves. $F{Q}_{1}$ is the fit of a single admixture event (i.e. the first principal component, reflecting admixture involving two sources) and $F{Q}_{2}$ is the fit of the first two principal components capturing the admixture event(s) (the second component might be thought of as capturing a second, less strongly-signalled event. $M$ is the additional $R}^{2$ explained by adding a second date versus assuming only a single date of admixture; we use values above 0.35 to infer multiple dates (although see Supplementary Text for details). As well as the final result, for each event we show the inferred dates, $\alpha$s and best matching sources for 1D, 1MW, and 2D inferences. Inferred dates are in years(+ 95% CI; B=BCE, otherwise CE); the proportion of admixture from the minority source (source 1) is represented by $\alpha$. Date confidence intervals are based on 100 bootstrap replicates of the date inference

Download source data [figure-4—source-data-1.media-10.xlsx]**DOI:**http://dx.doi.org/10.7554/eLife.15266.027 - Figure 4—source data 2.
$Analysis$ refers to whether the main or masked analysis was used to produce the final result. Admixture $P$-values are based on 100 bootstrap replicates of the NULL procedure. Our resulting inference, $res$ can be: 1D (two admixing sources at a single date); 1MW (multiple admixing sources at a single date); 2D (admixture at multiple dates); NA (no-admixture); U (uncertain). max($R}_{1$) refers to the $R}^{2$ goodness-of-fit for a single date of admixture, taking the maximum value across all inferred coancestry curves. $F{Q}_{1}$ is the fit of a single admixture event (i.e. the first principal component, reflecting admixture involving two sources) and $F{Q}_{2}$ is the fit of the first two principal components capturing the admixture event(s) (the second component might be thought of as capturing a second, less strongly-signalled event. $M$ is the additional $R}^{2$ explained by adding a second date versus assuming only a single date of admixture; we use values above 0.35 to infer multiple dates (although see Supplementary Text for details). As well as the final result, for each event we show the inferred dates, $\alpha$s and best matching sources for 1D, 1MW, and 2D inferences. Inferred dates are in years(+ 95% CI; B=BCE, otherwise CE); the proportion of admixture from the minority source (source 1) is represented by $\alpha$. Date confidence intervals are based on 100 bootstrap replicates of the date inference

Download source data [figure-4—source-data-2.media-11.xlsx]**DOI:**http://dx.doi.org/10.7554/eLife.15266.028 - Supplementary file 1.

Download source data [supplementary-file-1.media-12.zip]**DOI:**http://dx.doi.org/10.7554/eLife.15266.034 - Supplementary file 2.

Download source data [supplementary-file-2.media-13.xlsx]**DOI:**http://dx.doi.org/10.7554/eLife.15266.035 - Supplementary file 3.

Download source data [supplementary-file-3.media-14.zip]**DOI:**http://dx.doi.org/10.7554/eLife.15266.036