Extended Data Fig. 3: Simulations.
From: High-resolution genomic history of early medieval Europe
a, Theoretically computed r2 stratified by minor allele frequency between true genotypes and genotypes with randomly introduced errors (Methods), emulating imputation accuracy plots. b, Admixture simulation where sources P1 and P2 split 250 or 500 generations ago and a pulse admixture event gives rise to a target population PX 50 generations ago. We vary demographic history, error rates, and sample sizes and simulate 20 replicates for each scenario (see Methods for simulation details). Admixture proportions are computed using an f4-ratio statistic and the Twigstats cutoff is set to twice the source split time and the rare variant cutoff is 5%. We plot two standard errors around the mean. c, qpAdm simulation taken from21,23, as well as an adapted version where all population split times and the admixture date are divided by 5. The Twigstats cutoff time is chosen to be 1200 generations (top) and 600 generations (bottom). We simulate 10 replicates and plot two standard errors around the mean. d, Simulation adapted from23 of a stepping stone model with 9 populations organised on a 1-dimensional grid as shown, where individuals are able to migrate between adjacent fields. We run a rotational qpAdm to fit population 4 using other pairs of populations to the left and right as sources. We run 50 replicates and set the p-value of models with inferred proportions outside of [0,1] to 0. We then compute the proportion where a given pair achieves the best p-value (top) and show the median p-value across these replicates (bottom). In all simulations in b, c, d, we sample N = 20 haploid sequences per population, except for one simulation in b, where we sample N = 100 sequences.
