PMC

a-d Accuracy of imputation relying on the coalescent (black) and with IMPUTE2 (gray) represented by mean concordance rates with the corresponding 95% confidence intervals (shown as error bars). a 1000 haplotypes were simulated under the basic coalescent. Genotypes were imputed based on the basic coalescent and with IMPUTE2 without recombination. Results are presented for all variants and stratified by minor allele frequency. b Different total numbers of haplotypes were simulated under the basic coalescent. Genotypes were imputed based on the basic coalescent and with IMPUTE2 without recombination. c Haplotypes were simulated under the basic coalescent extended to accommodate different exponential growth rates (α). Genotypes were imputed based on the coalescent with growth, and with IMPUTE2 without recombination. d Haplotypes were simulated under the coalescent extended to consider different numbers of subpopulations (β). Genotypes were imputed based on the coalescent with population structure and with IMPUTE2 without recombination

Illustrations of possible coalescent event vectors for a sample when and There are possible sequences of coalescent events. The vector elements are ordered according to the order of coalescent events; “” stands for the coalescent event on major branches and “” for the coalescent event on minor branches. Each coalescent event on major branches corresponds to an index where is the number of lineages in the major part right before the coalescent event, and is the number of lineages in the whole tree right before this event.

Expected coalescent times with different reproductive systems. The population size for all plots is N = 10,000. (A) Expected mean coalescent time according to in coalescent time units as a function of sex σ. The blue line represents between-individual mean coalescent time , and the red line is within-individual mean coalescent time . The vertical line represents (), and the horizontal solid lines show the predicted mean coalescent times for this value (; on the coalescent timescale), whereas the horizontal dashed line shows . (B and C) Expected coalescent time if selfing is also included, according to . Line colors are the same as in A, with (B) σ = 1 or (C) σ = 1/N ().

Inferred asymmetry of migration and coalescent rates. Here we show the inferred median coalescent (upper row) and migration (lower row) rate ratios under different conditions. In the first column, the coalescent rate ratios (x-axis) are varied while the migration rates ratios are kept constant. In the second column, the migration rate ratios (x-axis) are varied, whereas the coalescent rate ratios are kept constant. We simulated a total of 2,000 trees using MASTER with 100 tips from each of the two different states sampled uniformly between times t = 0 and t = 10. Of these trees, 1,000 were simulated with pairwise coalescent rate ratios λ₁/λ₂ from 0.01 to 1, λ₁ + λ₂ = 4 and migration rates in both directions equal to 1. The other 1,000 trees were simulated with migration rate ratios from m₁₂/m₂₁ from 0.01 to 1, m₁₂ + m₂₁ = 2 and pairwise coalescent rates in both states equal to 2, using exponential priors with mean 2 for the coalescent rates and mean 1 for the migration rates. Both coalescent rates and both migration rates are estimated. The red line indicates where the estimates should lie.