“…We also emphasize that our simulated data provided results that are supported from field data. For example, the higher heterosis for the most contrasting populations (that can be assumed as heterotic groups; 1.4 and 10.5% for the heterosis involving populations 1x2 and 1x10, respectively, assuming a ratio of 1, 100% of epistatic genes, and an admixture of epistasis types), the higher heterosis for interpopulation single crosses relative to the intrapopulation heterosis (average intra-and interpopulation heteroses of 12.0 and 15.6%, also assuming a ratio of 1, 100% of epistatic genes, and an admixture of epistasis types), and the lower percent values of the average heterosis for populations (in the range 2.1 to 6.2) than for DHs (in the range 12.2 to 36.6), as observed in several studies (Lariepe et al 2017;Laude and Carena 2015;Punya et al 2019;Yu et al 2020) Table 2 Correlations between the average frequency for the genes that increase the trait expression, the average absolute allelic frequency differences between populations, the absolute average allelic frequency differences between a population and the other diallel parents, or the average frequency for the genes that increase the trait expression minus 0.5 and the genetic components of the heterosis and combining ability analyses, and average heterosis (g/plant), assuming no epistasis (No), seven types of digenic epistasis a and an admixture of these types (All), 25 and 100% of epistatic genes (% eg), and ratios V(I)/(V(A) + V(D)) of 1 and 10 Table 3 Correlations between the average frequency for the genes that increase the trait expression or the average allelic frequency differences between the DH lines and the genetic components of the combining ability analysis, and average heterosis (g/plant), assuming no epistasis (No), seven types of digenic epistasis a and an admixture of these types (All), 25 and 100% of epistatic genes (% eg), ratio V(I)/(V(A) + V(D)) of 1 and 10, and 20…”