Table 1.

Quantitative-genetic expectations of means and genetic variances for per se (PP) and testcross (TP) performance in the sample of the ancestral landrace (LS), derived DH, and GC lines

Population	Coefficient of parameters†
	Population mean‡ $\overline{x}$				Genetic variances
					Primary variance		Variance within families		Total variance
	$a+\mathrm{\Delta }$	$\left(p-(1-p)\right)a$	$\left[d\right]=$ $2p(1-p)d_{12}$	$\left[d^{*}\right]=$ $p{d}_{1x}+(1-p)d_{2x}$	${\sigma }_A^2$	${\sigma }_{A^{\mathrm{*}}}^2$	${\sigma }_A^2$	${\sigma }_{A^{\mathrm{*}}}^2$	${\sigma }_A^2$	${\sigma }_{A^{\mathrm{*}}}^2$
LS	0	1	1	0	1	0	—	—	1	0
DH	0	1	0	0	2	0	0	0	2	0
GC-S1:2	1/2	1/2	0	1/4	3/4	1/4	1/8	1/8	7/8	3/8
GC-S1:∞	1/2	1/2	0	0	3/4	1/4	1/4	1/4	1	1/2
FV2	1	0	0	0	—	—	—	—	—	—

For GC lines, the total genetic variance is decomposed into the primary variance between families as observed for GC-S_1:2 lines in this study and the variance within families.

^†Parameters $[d]$ and $[d^{*}]$ are not required for TP.

^‡$p$ and $(1-p)$ refer to the frequencies of alleles $A_1$ and $A_2$ in LS, respectively. $a$ and $a+\mathrm{\Delta }$ refer to the additive effects in LS and the capture line, respectively, with different meanings for PP and TP. $\left[d\right]$ and $\left[d^{*}\right]$ refer to the contribution of dominance effects to the PP of LS and GC-S_1:2, respectively, where $d_{12}$, $d_{1x}$, and $d_{2x}$ refer to the dominance effect of genotypes $A_1{A}_2$, $A_1{A}_x$, and $A_2{A}_x$, respectively, with $A_x$ being the allele of the capture line. ${\sigma }_A^2$ refers to the additive variance inherent in the ancestral landrace, with ${\sigma }_A^2=2p(1-p)a^2$. ${\sigma }_{A^{\mathrm{*}}}^2$ refers to the additive variance resulting from the effects of the capture line alleles, with ${\sigma }_{A^{\mathrm{*}}}^2=2{\left(\left(1-p\right)a+\text{Δ}/2\right)}^2$ (details are in SI Appendix, SI Text A2).