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Erratum to: Hybrid maize breeding with doubled haploids: V. Selection strategies for testcross performance with variable sizes of crosses and S1 families

Theoretical and Applied Genetics, 2010
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ERRATUM Erratum to: Hybrid maize breeding with doubled haploids: V. Selection strategies for testcross performance with variable sizes of crosses and S 1 families Thilo Wegenast H. Friedrich Utz C. Friedrich H. Longin Hans Peter Maurer Baldev S. Dhillon Albrecht E. Melchinger Published online: 3 September 2010 Ó Springer-Verlag 2010 Erratum to: Theor Appl Genet (2010) 120:699–708 DOI 10.1007/s00122-009-1187-y In the original version of the article, an error was detected in the simulation of breeding scheme S 1 TC-DHTC. This error led to an overestimation of the selection gain (D b G ) and the probability of selecting superior genotypes ( b PðqÞ ) in this breeding scheme. The corrected results for all selection strategies of breeding scheme S 1 TC-DHTC in Tables 2 and 3, as well as Fig. 1 are presented in the fol- lowing pages. The online version of the original article can be found under doi:10.1007/s00122-009-1187-y. T. Wegenast H. F. Utz B. S. Dhillon A. E. Melchinger (&) Institute of Plant Breeding, Seed Science, and Population Genetics, University of Hohenheim, 70593 Stuttgart, Germany e-mail: melchinger@uni-hohenheim.de T. Wegenast e-mail: wegenast@uni-hohenheim.de C. F. H. Longin Limagrain Verneuil Holding, BP 58 Route de Lavardac, 47600 Ne ´rac, France H. P. Maurer State Plant Breeding Institute, University of Hohenheim, 70593 Stuttgart, Germany 123 Theor Appl Genet (2010) 121:1391–1393 DOI 10.1007/s00122-010-1428-0
Table 2 Optimum allocation of test resources maximizing the optimization criteria (OC), selection gain (D b G ) and the probability of selecting superior genotypes ( b Pð0:1%Þ ), in two-stage selection with evaluation of testcross progenies of (1) DH lines at both stages (DHTC) and (2) S 1 families at first stage and DH lines of S 1 families at second stage (S 1 TC-DHTC) Breeding scheme/selection strategy Optimum allocation OC SD OC H N 1 *a N 2 *b L 1 * L 2 * Optimization criterion D b G DHTC–1 5,538 = 3 9 1,846 392 = 2 9 196 2 14 3.322 0.385 0.500 DHTC–2a 5,812 = 4 9 1,453 320 2 15 3.384 0.324 0.311 DHTC–2b 6,152 330 2 12 3.335 0.340 0.324 DHTC–2c 4,704 203 3 14 3.347 0.326 0.323 S 1 TC-DHTC–1 816 = 4 9 204 646 = 2 9 1 9 323 12 14 3.581 0.516 0.750 S 1 TC-DHTC–2a 800 = 5 9 160 660 = 3 9 1 9 220 12 14 3.610 0.485 0.663 S 1 TC-DHTC–2b 824 = 4 9 206 753 10 14 3.624 0.484 0.581 S 1 TC-DHTC–2c 725 = 5 9 145 781 11 14 3.612 0.494 0.584 Optimization criterion b Pð0:1%Þ DHTC–1 5,655 = 3 9 1,885 400 = 2 9 200 2 13 0.631 0.295 0.500 DHTC–2a 5,644 = 4 9 1,411 348 2 15 0.671 0.252 0.316 DHTC–2b 6,204 320 2 12 0.640 0.258 0.322 DHTC–2c 4,640 220 3 14 0.651 0.258 0.322 S 1 TC-DHTC–1 820 = 4 9 205 680 = 2 9 1 9 340 13 12 0.771 0.295 0.750 S 1 TC-DHTC–2a 775 = 5 9 155 735 = 3 9 1 9 245 11 14 0.773 0.265 0.566 S 1 TC-DHTC–2b 1,057 = 7 9 151 712 9 13 0.779 0.258 0.541 S 1 TC-DHTC–2c 828 = 6 9 138 804 11 12 0.775 0.262 0.576 Assumptions: a budget of 20,000 testcross plot equivalents, variance component ratios VC2, and a correlation q P = 0.71 between the mean performance of the parental lines and the mean genotypic value of the testcross performance of their progeny N j * = optimum number of test candidates in stage j, L j = optimum number of test locations in stage j, SD = the standard deviation, and H = the average coefficient of coancestry among the selected DH lines a DHTC–1 and 2a: number of crosses 9 DH lines within crosses, DHTC–2b and 2c: the number of DH lines within crosses depended on the rank of the cross; S 1 TC-DHTC: number of crosses 9 S 1 families within crosses b DHTC–1: number of crosses 9 DH lines within crosses, DHTC–2: number of DH lines; S 1 TC-DHTC–1 and 2a: number of crosses 9 S 1 families within crosses 9 DH lines within S 1 families; S 1 TC-DHTC–2b and 2c: the number of S 1 families within crosses and DH lines within S 1 families depended on the rank of the cross and the S 1 family Table 3 Optimum allocation of test resources maximizing the optimization criteria (OC), selection gain (D b G ) and the probability of selecting superior genotypes ( b Pð0:1%Þ ), in two-stage selection with evaluation of testcross progenies of (1) DH lines at both stages (DHTC–2a) and (2) S 1 families at first stage and DH lines of S 1 families at second stage (S 1 TC-DHTC–2c) and its dependence on the phenotypic correlation q P (between the mean performance of the parents and the mean genotypic value of the testcross performance of their progenies), the variance component ratios (VC), and the budget in terms of testcross plot equivalents Breeding scheme/selection strategy Assumptions Optimum allocation OC SD OC H Budget VC q P N 1 *a N 2 L 1 L 2 Optimization criterion D b G DHTC–2a 10,000 2 0.71 2,874 = 3 9 958 191 2 13 3.257 0.316 0.340 DHTC–2a 20,000 2 0.71 5,812 = 4 9 1,453 320 2 15 3.384 0.324 0.311 DHTC–2a 40,000 2 0.71 9,325 = 5 9 1,865 427 3 14 3.491 0.322 0.296 DHTC–2a 20,000 1 0.71 9,556 = 4 9 2,389 390 1 13 3.662 0.309 0.318 DHTC–2a 20,000 3 0.71 3,564 = 2 9 1,782 232 4 14 3.089 0.317 0.399 DHTC–2a 20,000 2 0.50 6,069 = 7 9 867 297 2 14 3.070 0.369 0.268 1392 Theor Appl Genet (2010) 121:1391–1393 123
Theor Appl Genet (2010) 121:1391–1393 DOI 10.1007/s00122-010-1428-0 ERRATUM Erratum to: Hybrid maize breeding with doubled haploids: V. Selection strategies for testcross performance with variable sizes of crosses and S1 families Thilo Wegenast • H. Friedrich Utz • C. Friedrich H. Longin • Hans Peter Maurer Baldev S. Dhillon • Albrecht E. Melchinger • Published online: 3 September 2010 Ó Springer-Verlag 2010 Erratum to: Theor Appl Genet (2010) 120:699–708 DOI 10.1007/s00122-009-1187-y In the original version of the article, an error was detected in the simulation of breeding scheme S1TC-DHTC. This b ) error led to an overestimation of the selection gain (D G b and the probability of selecting superior genotypes ( PðqÞ ) in this breeding scheme. The corrected results for all selection strategies of breeding scheme S1TC-DHTC in Tables 2 and 3, as well as Fig. 1 are presented in the following pages. The online version of the original article can be found under doi:10.1007/s00122-009-1187-y. T. Wegenast  H. F. Utz  B. S. Dhillon  A. E. Melchinger (&) Institute of Plant Breeding, Seed Science, and Population Genetics, University of Hohenheim, 70593 Stuttgart, Germany e-mail: melchinger@uni-hohenheim.de T. Wegenast e-mail: wegenast@uni-hohenheim.de C. F. H. Longin Limagrain Verneuil Holding, BP 58 Route de Lavardac, 47600 Nérac, France H. P. Maurer State Plant Breeding Institute, University of Hohenheim, 70593 Stuttgart, Germany 123 1392 Theor Appl Genet (2010) 121:1391–1393 Table 2 Optimum allocation of test resources maximizing the b ) and the probability optimization criteria (OC), selection gain (D G  b of selecting superior genotypes ( Pð0:1%Þ ), in two-stage selection Breeding scheme/selection strategy with evaluation of testcross progenies of (1) DH lines at both stages (DHTC) and (2) S1 families at first stage and DH lines of S1 families at second stage (S1TC-DHTC) Optimum allocation N*1 a N*2 b L*1 L*2 OC SDOC H 0.500 b Optimization criterion D G DHTC–1 5,538 = 3 9 1,846 392 = 2 9 196 2 14 3.322 0.385 DHTC–2a 5,812 = 4 9 1,453 320 2 15 3.384 0.324 0.311 DHTC–2b 6,152 330 2 12 3.335 0.340 0.324 DHTC–2c 4,704 203 3 14 3.347 0.326 0.323 S1TC-DHTC–1 816 = 4 9 204 646 = 2 9 1 9 323 12 14 3.581 0.516 0.750 S1TC-DHTC–2a 800 = 5 9 160 660 = 3 9 1 9 220 12 14 3.610 0.485 0.663 S1TC-DHTC–2b 824 = 4 9 206 753 10 14 3.624 0.484 0.581 S1TC-DHTC–2c 725 = 5 9 145 781 11 14 3.612 0.494 0.584 0.500  b Optimization criterion Pð0:1%Þ DHTC–1 5,655 = 3 9 1,885 400 = 2 9 200 2 13 0.631 0.295 DHTC–2a 5,644 = 4 9 1,411 348 2 15 0.671 0.252 0.316 DHTC–2b 6,204 320 2 12 0.640 0.258 0.322 DHTC–2c 4,640 220 S1TC-DHTC–1 S1TC-DHTC–2a 820 = 4 9 205 775 = 5 9 155 680 = 2 9 1 9 340 735 = 3 9 1 9 245 S1TC-DHTC–2b 1,057 = 7 9 151 712 9 13 0.779 0.258 0.541 S1TC-DHTC–2c 828 = 6 9 138 804 11 12 0.775 0.262 0.576 3 14 0.651 0.258 0.322 13 11 12 14 0.771 0.773 0.295 0.265 0.750 0.566 Assumptions: a budget of 20,000 testcross plot equivalents, variance component ratios VC2, and a correlation qP = 0.71 between the mean performance of the parental lines and the mean genotypic value of the testcross performance of their progeny N*j = optimum number of test candidates in stage j, Lj = optimum number of test locations in stage j, SD = the standard deviation, and H = the average coefficient of coancestry among the selected DH lines a DHTC–1 and 2a: number of crosses 9 DH lines within crosses, DHTC–2b and 2c: the number of DH lines within crosses depended on the rank of the cross; S1TC-DHTC: number of crosses 9 S1 families within crosses b DHTC–1: number of crosses 9 DH lines within crosses, DHTC–2: number of DH lines; S1 TC-DHTC–1 and 2a: number of crosses 9 S1 families within crosses 9 DH lines within S1 families; S1TC-DHTC–2b and 2c: the number of S1 families within crosses and DH lines within S1 families depended on the rank of the cross and the S1 family Table 3 Optimum allocation of test resources maximizing the b ) and the probability optimization criteria (OC), selection gain (D G  b of selecting superior genotypes ( Pð0:1%Þ ), in two-stage selection with evaluation of testcross progenies of (1) DH lines at both stages (DHTC–2a) and (2) S1 families at first stage and DH lines of S1 Breeding scheme/selection strategy families at second stage (S1TC-DHTC–2c) and its dependence on the phenotypic correlation qP (between the mean performance of the parents and the mean genotypic value of the testcross performance of their progenies), the variance component ratios (VC), and the budget in terms of testcross plot equivalents Assumptions Optimum allocation Budget N*1 a VC qP OC N2 L1 SDOC H L2 b Optimization criterion D G DHTC–2a 10,000 2 0.71 2,874 = 3 9 958 191 2 13 3.257 0.316 0.340 DHTC–2a 20,000 2 0.71 5,812 = 4 9 1,453 320 2 15 3.384 0.324 0.311 DHTC–2a 40,000 2 0.71 9,325 = 5 9 1,865 427 3 14 3.491 0.322 0.296 DHTC–2a 20,000 1 0.71 9,556 = 4 9 2,389 390 1 13 3.662 0.309 0.318 DHTC–2a DHTC–2a 20,000 20,000 3 2 0.71 0.50 3,564 = 2 9 1,782 6,069 = 7 9 867 232 297 4 2 14 14 3.089 3.070 0.317 0.369 0.399 0.268 123 Theor Appl Genet (2010) 121:1391–1393 1393 Table 3 continued Breeding scheme/selection strategy Assumptions Optimum allocation Budget VC qP N*1 a OC N2 L1 SDOC H L2 S1TC-DHTC–2c 10,000 2 0.71 267 = 3 9 89 686 9 10 3.434 0.505 0.592 S1TC-DHTC–2c 20,000 2 0.71 725 = 5 9 145 781 11 14 3.639 0.494 0.584 S1TC-DHTC–2c 40,000 2 0.71 848 = 4 9 212 2,391 10 12 3.751 0.484 0.561 S1TC-DHTC–2c 20,000 1 0.71 888 = 4 9 222 980 10 11 3.991 0.498 0.601 S1TC-DHTC–2c 20,000 3 0.71 522 = 3 9 174 856 13 14 3.224 0.476 0.605 S1TC-DHTC–2c 20,000 2 0.50 794 = 12 9 66 720 11 14 3.376 0.524 0.551  b Optimization criterion (OC) Pð0:1%Þ DHTC–2a 10,000 2 0.71 3,153 = 3 9 1,051 149 2 12 0.595 0.273 0.338 DHTC–2a DHTC–2a 20,000 40,000 2 2 0.71 0.71 5,644 = 4 9 1,411 9,375 = 5 9 1,875 348 447 2 3 15 13 0.671 0.730 0.252 0.225 0.316 0.296 DHTC–2a 20,000 1 0.71 9,728 = 4 9 2,432 371 1 13 0.833 0.197 0.315 DHTC–2a 20,000 3 0.71 3,222 = 2 9 1,611 342 4 14 0.500 0.284 0.397 DHTC–2a 20,000 2 0.50 6,216 = 7 9 888 293 2 13 0.479 0.271 0.271 S1TC-DHTC–2c 10,000 2 0.71 267 = 3 9 89 686 9 10 0.683 0.321 0.566 S1TC-DHTC–2c 20,000 2 0.71 775 = 5 9 155 735 11 14 0.778 0.265 0.566 S1TC-DHTC–2c 40,000 2 0.71 852 = 4 9 213 2,388 10 12 0.829 0.242 0.559 S1TC-DHTC–2c 20,000 1 0.71 1,115 = 5 9 223 868 9 10 0.924 0.152 0.599 S1TC-DHTC–2c 20,000 3 0.71 477 = 3 9 159 896 13 14 0.570 0.321 0.610 S1TC-DHTC–2c 20,000 2 0.50 737 = 11 9 67 820 11 13 0.648 0.316 0.552 Nj = optimum number of test candidates in stage j, Lj = optimum number of test locations in stage j, SD = the standard deviation, and H = the average coefficient of coancestry among the selected DH lines 0.8 0.7 0.6 0.5 ^ Probability P(0.1%) 3.6 3.4 3.2 0.4 3.0 2.8 b and Fig. 1 Selection gain (D G) the probability of selecting b superior genotypes ( Pð0:1%Þ) as a function of the number of crosses in the first stage (N1C ) for selection strategies 1 (open square), 2a (open circle), 2b (open triangle), and 2c (open diamond) in breeding scheme DHTC (solid symbols) and S1TC-DHTC (hollow symbols) 3.8 DHTC–2a: number of crosses 9 DH lines within crosses; S1TC-DHTC–2c: number of crosses 9 S1 families within crosses ^ Selection gain ∆G a 2 5 10 15 20 30 Number of crosses at first stage N1C 40 2 5 10 15 20 30 40 Number of crosses at first stage N1C 123
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