a, Inferring admixture in a population of 1,044 UK individuals from central and southern England. Left hand plot: the bold red squares show mean grandparental birthplace for each individual in this cluster. Central three plots: example curves constructed by GLOBETROTTER to infer admixture times, and infer details of admixing groups (see Methods and Supplementary Note). For each pair of populations A and B (A can be the same as or different from B) the points show the empirical probability, relative to under independence, as a function of genetic distance x, that two positions separated by distance x correspond to ancestry donated by population A, and by population B, respectively. The green line shows GLOBETROTTER fitted exponential decay curves for the underlying (that is, expected) value of this relative probability estimate. Under a model of a single admixture event occurring g generations ago, this probability decays at a rate g according to theory, providing an estimate of the admixture time (and 95% CI) shown overlaying curves SFS31 versus GER3 and SFS31 versus SFS31. If ancestries A and B associate with the same admixing group, for example, whenever A = B the fitted curve will have negative slope, as seen for the GER3 versus GER3 plot. If a positive slope is seen, as for the SFS31 versus GER3 plot, this implies these populations contribute to the two different respective admixing groups. Right bar-plot, and map: GLOBETROTTER inference shows one possibility for the genetic composition of (haplotypes carried by) the two unsampled historical admixing groups, as a mixture of (haplotypes carried by) populations actually sampled. This mixture inference jointly uses curves for pairs of sampled populations, and the overall haplotypic makeup of different sampled populations, including the admixed group. The bar-plot shows the inferred mixture representation (with largest contributions in each case by GER3/DEN18, sampled most frequently from northern Germany and Denmark, and SFS31/ITA52, sampled mainly from southern France and Spain and northern Italy) and estimated admixture proportion (34%), with more intense red/blue populations respectively implying a larger contribution. The map shows populations inferred as contributing to the first (pink/red shades) or second (blue shades) admixing group respectively, with populations coloured according to the bar-plot. We caution that in this setting of admixture between genetically similar European groups, estimation of admixture fraction is very uncertain (see Methods and Supplementary Note) (for example, contributing populations are often impossible to definitively assign to a side of the event), so that other closely related scenarios, for example, a somewhat lower admixture fraction from a more completely ‘GER3’-like group than that inferred, are likely consistent with the GLOBETROTTER results seen. b, Inferring admixture in a population of 51 UK individuals from Orkney. Left hand plot: the bold purple squares show mean grandparental birthplace for each individual in this cluster. Central three plots: example curves constructed by GLOBETROTTER to infer admixture times, and infer details of admixing groups (see Methods and Supplementary Note). For each pair of populations A and B (A can be the same as or different from B) the points show the empirical probability, relative to under independence, as a function of genetic distance x, that two positions separated by distance x correspond to ancestry donated by population A, and by population B, respectively. The green line shows GLOBETROTTER fitted exponential decay curves for the underlying (that is, expected) value of this relative probability estimate. Under a model of a single admixture event occurring g generations ago, this probability decays at a rate g according to theory, providing an estimate of the admixture time (and 95% CI) shown overlaying curves NOR90 versus FRA12 and NOR90 versus NOR90. If ancestries A and B associate with the same admixing group, for example, whenever A = B the fitted curve will have negative slope, as seen for the NOR90 versus NOR90 plot. If a positive slope is seen, as for the NOR90 versus FRA12 plot, this implies these populations contribute to the two different respective admixing groups. Right bar-plot, and map: GLOBETROTTER inference shows one possibility for the genetic composition of (haplotypes carried by) the two unsampled historical admixing groups, as a mixture of (haplotypes carried by) populations actually sampled. This mixture inference jointly uses curves for pairs of sampled populations, and the overall haplotypic makeup of different sampled populations, including the admixed group. The bar-plot shows the inferred mixture representation (with largest contribution in each case by GER3/NOR90, sampled most frequently from northern Germany and Norway, and FRA12/FRA14, both sampled mainly from France) and estimated admixture proportion (42%), with more intense red/blue populations respectively implying a larger contribution. The map shows populations inferred as contributing to the first (pink/red shades) or second (blue shades) admixing group respectively, with populations coloured according to the bar-plot. We caution that in this setting of admixture between genetically similar European groups, estimation of admixture fraction is very uncertain (see Methods and Supplementary Note) (for example, contributing populations are often impossible to definitively assign to a ‘side’ of the event). In particular, inspection of curves involving GER3 does not yield a clear ‘side’ of the event for this population, unlike the NOR90 versus FRA12 case that implies French-like and Norwegian-like haplotype presence must occur mainly in distinct admixing groups. Therefore the GER3 component might in fact capture haplotypes for either (or both) the French-like or Norwegian-like admixing groups, and the inferred scenario shows only one possibility. 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