1. Figure S6. Explanation of computer simulation used for calculating confidence intervals of Δ(SNP-index) under the null hypothesis. (A) Flow chart of simulation to derive confidence intervals of Δ(SNP-index) under null hypothesis (no QTL). (B) and (C) Δ(SNP-index) confidence intervals for different read depths under the null hypothesis (no QTL) as obtained by simulation test (10,000 replications for each read depth). x-axis: read depth. y-axis: Δ(SNP-index). Yellow, green and pink lines indicate 90, 95 and 99% confidential intervals, respectively. (B) Simulation result for RILs and 20 individuals per bulk. This corresponds to the RILs progeny derived from a cross between Nortai and Hitomebore (Figure 2). (C) Simulation results for F2 progeny and 50 individuals per bulk. This corresponds to the F2 progeny derived from a crosses between Hitomebore and Dunghan shali (Figure 3).

2. Start Determining genotypes Calculating the frequency of B allele Calculating Δ(SNP-index) Sampling alleles and calculating SNP-index Removing SNPs having SNP-index values less than 0.3 in both samples Obtaining the null distribution of ΔSNP-index in different depth Finish For each read depth, 90, 95 and 99% confidence intervals of Δ(SNP-index) were obtained by repeating the above sampling (progeny sampling and read sampling) 10,000 times and the relationship between the confidence intervals and read depth was depicted as in Figure S6B. This result was used to put the confidence interval lines in the Δ(SNP-index) plot in the actual experimental data (Figure 2, 3, S2, S3, S4). Progeny bulk 1 Progeny bulk 2 X 10,000 AA BB Crossing After crossing of two parents (genotype AA and BB), we obtained a large number of progeny (F2 or RILs). Next, we generated two bulks (Progeny bulk 1 and Progeny bulk 2) comprising equal number of progeny by randomly sampling a given number of individuals. The number of individuals was set to equal to that used for actual bulking experiments. Genotypes of sampled individuals were determined, and frequency of B allele [P(B)] in each bulk was calculated. Simulation for sampling progeny Simulation for calculating Δ(SNP-index) Generation of short reads were simulated by binomial sampling of alleles with the frequency of P(B). Sampling was repeated as many as the read depth, and resulting frequency of allele B was used as SNP- index. We tested a range of read depth, and for each read depth, Δ(SNP-index) was obtained by subtraction of SNP-index of Progeny bulk 2 from that of Progeny bulk 1. Calculation of null distribution A

3. 20 individuals of RIL50 individuals of F2 Δ(SNP-index) Depth -1.0-0.500.51.0 20406080100 -1.0-0.500.51.0 BC