Supporting Information S2. The expected genetic values of , and under the F2and the F∞ metric models in the F2-based TTC design

We assume that a quantitative trait is controlled by two QTL, A and B, each with two alleles (, and , ). The recombination fraction between A and B was . The genotypes of the two inbred lines (P1 and P2) and their F1 are , and , respectively. The F1produces four types of gametes , , and with frequencies , , and . The gametes from F1 are combined to produce F2 population with 10 type genotypes (Table S1). Note that the two double heterozygotes and , with different gametes constitutions under linkage disequilibrium, should be distinguished. Individuals from the F2 are cross to P1 (with gamete ), P2 (with gamete ) and F1 to produce L1, L2 and L3 families. The genetic constitutions of the three families aregiven in Table S1.

Thegenotypic values of the nine genotypes in L1i, L2i and L3i familiesunder the F2metric are defined asKao and Zeng [28],

where is model mean (mean genotypic values of F2 population when ); is additive effect of QTL A, i.e. one-half of the difference in genotypic value between the two homozygote means of (, and )and (, and ); is dominance effect of QTL A, i.e. the departure in genotypic value of the heterozygote mean of (,, and )from the midpoint between the two homozygote means of (, and )and (, and ); and are additive and dominance effects of QTL B, with similar definitions to QTL A; , , and are additive × additive, additive × dominance, dominance × additive and dominance × dominance epistatic effects. While under theF∞metric, genotypic values of the nine genotypesare defined asKao and Zeng [28],

where is model mean (mean genotypic values of four homozygotes, , , and ); is additive effect of QTL A, i.e. average substitution effect of (in and ) by ; is dominance effect of QTL A, i.e. the departure in genotypic value of the heterozygote mean of ( and )from the midpoint between the two homozygote means of ( and )and ( and ); and may be defined similarly; and , , and are additive × additive, additive × dominance, dominance × additive and dominance × dominance epistatic effects.Using the definitions above, the expected genetic values of L1i, L2i and L3i families can be calculated and are listed in Tables S2, S3 and S4. With these expected values, the expected values of the F2-based , and values can be further calculated and are presented in Table S5 for the F2metric model and Table S6 for the F∞metric model.

According to Table S5, genetic variance between families on , andunder the F2-metric model are:

Likewise, genetic variance of among F2 individuals and between F2:3 families under the F2-metric model are:

According to Table S6, genetic variance between families on, andunder the F∞-metric model are:

Likewise, genetic variance of among F2 individuals and between F2:3 families under the F∞-metric model are:

1