Table 2.

Practical section on hybrid wheat: Optimum allocation of test resources maximizing annual selection gain (ΔG_a) under two alternative breeding strategies using three selection indices for the simultaneous improvement of two traits

Breeding strategy	Index	Optimum allocation of test resources								∆Ga Net merit	∆Ga Trait 1	∆Ga Trait 2
		Nini	N1	N2	N3	L2	L3	T2	T3
Goal 1: Simultaneous improvement of grain yield (Trait 1) and grain protein content (Trait 2)
PSstandard	ICL	2028		507	35	5	10	1	6	0.70	0.71	− 0.03
PSstandard	SH	2028	−	507	35	5	10	1	6	0.80	0.80	− 0.05
PSstandard	Base	1892	−	473	35	6	10	1	6	0.79	0.79	− 0.03
PSstandard	Restricted	1892	−	473	35	6	10	1	6	0.70	0.70	0.00
PSstandard	No Index	1892	−	473	35	6	10	1	6	−	0.79	0.09
GSrapid	ICL	2652	663	124.4	−	10	−	3	−	0.88	0.88	− 0.03
GSrapid	SH	2652	663	124.4	−	10	−	3	−	1.05	1.05	− 0.06
GSrapid	Base	2652	663	124.4	−	10	−	3	−	1.04	1.05	− 0.04
GSrapid	Restricted	2612	653	94.5	−	10	−	4	−	0.95	0.95	0.00
GSrapid	No Index	2644	661	124.7	−	10	−	3	−	−	1.05	0.13
Goal 2: Simultaneous improvement of grain yield (Trait 1) and sedimentation volume (Trait 2)
PSstandard	ICL	1892	−	473	35	6	10	1	6	0,68	0,68	0,00
PSstandard	SH	1892	−	473	35	6	10	1	6	0.78	0.76	0.13
PSstandard	Base	1892	−	473	35	6	10	1	6	0.78	0.76	0.10
PSstandard	Restricted	1892	−	473	35	6	10	1	6	0.78	0.78	0.00
PSstandard	No Index	1892	−	473	35	6	10	1	6	−	0.79	1.92
GSrapid	ICL	2652	663	124.4	−	10	−	3	−	0,86	0,86	0,02
GSrapid	SH	2652	663	124.4	−	10	−	3	−	1.03	1.01	0.21
GSrapid	Base	2652	663	124.4	−	10	−	3	−	1.03	1.01	0.17
GSrapid	Restricted	2652	663	124.4	−	10	−	3	−	1.03	1.03	0.00
GSrapid	No Index	2644	661	124.7	−	10	−	3	−	−	1.05	2.58

The allocation and ΔG_a correspond to the assumption of GS prediction accuracies of 0.3 for both traits. (ICL, independent culling levels; SH, Smith–Hazel; N_ini, number of lines entering the nursery assuming a selected fraction of ${\alpha }_{\mathit{ini}}$ = 0.25 after nursery assessment; N_j, L_j, T_j number of DH lines, test locations and testers in stages one, two, and three, respectively; No Index, maximum annual selection gain when optimization is based on trait 1 or trait 2 exclusively; only for “No Index”, ΔG_a for trait 1 and 2 is the maximum annual selection gain while for the other indices it is the annual selection gain for the individual traits when selected with the respective index; for further details see Suppl. Table 1)