Multivariate diallel analysis by factor analysis for establish mega-traits

NARDINO, MAICON; BARROS, WILLIAN S.; OLIVOTO, TIAGO; CRUZ, COSME DAMIÃO; SILVA, FABYANO F. E; PELEGRIN, ALAN J. DE; SOUZA, VELCI Q. DE; CARVALHO, IVAN R.; SZARESKI, VINICIUS J.; OLIVEIRA, ANTONIO C. DE; MAIA, LUCIANO C. DA; KONFLANZ, VALMOR A.

doi:10.1590/0001-3765202020180874

person MAICON NARDINO

schoolDepartamento de Agronomia, Universidade Federal de Viçosa, Avenida Peter Henry Rolfs, s/n, 36570-900 Viçosa, MG, Brazil

0000-0002-4177-4921

person WILLIAN S. BARROS

schoolDepartamento de Matemática e Estatística, Universidade Federal de Pelotas, Campus Universitário Capão do Leão, s/n, 96010-900 Pelotas, RS, Brazil

0000-0003-1057-6006

person TIAGO OLIVOTO

schoolDepartamento de Fitotecnia, Universidade Federal de Santa Maria, Avenida Roraima, 1000, 97105-340 Santa Maria, RS, Brazil

0000-0002-0241-9636

person COSME DAMIÃO CRUZ

schoolDepartamento de Biologia Geral, Universidade Federal de Viçosa, Avenida Peter Henry Rolfs, s/n, 36570-000 Viçosa, MG, Brazil

0000-0003-3513-3391

person FABYANO F. E SILVA

schoolDepartamento de Zootecnia, Universidade Federal de Viçosa, Avenida Peter Henry Rolfs, s/n, 36570-000 Viçosa, MG, Brazil

0000-0001-9536-1113

person ALAN J. DE PELEGRIN

schoolDepartamento de Fitotecnia, Universidade Federal de Pelotas, Campus Universitário Capão do Leão, s/n, 96001-970 Pelotas, RS, Brazil

0000-0002-0847-2075

person VELCI Q. DE SOUZA

schoolUniversidade Federal do Pampa, Campus São Gabriel, Av. Antonio Trilha, 1847, Vila Camita, 96400-100 São Gabriel, RS, Brazil

0000-0002-6890-6015

person IVAN R. CARVALHO

schoolUniversidade Regional do Noroeste do Estado do Rio Grande do Sul, Rua do Comércio, 3000, 98700–000 Ijuí, RS, Brazil

0000-0001-7947-4900

person VINICIUS J. SZARESKI

schoolDepartamento de Fitotecnia, Universidade Federal de Pelotas, Campus Universitário Capão do Leão, s/n, 96001-970 Pelotas, RS, Brazil

0000-0002-8906-6510

person ANTONIO C. DE OLIVEIRA

schoolDepartamento de Fitotecnia, Universidade Federal de Pelotas, Campus Universitário Capão do Leão, s/n, 96001-970 Pelotas, RS, Brazil

0000-0001-8835-8071

person LUCIANO C. DA MAIA

schoolDepartamento de Fitotecnia, Universidade Federal de Pelotas, Campus Universitário Capão do Leão, s/n, 96001-970 Pelotas, RS, Brazil

0000-0002-4371-261X

person VALMOR A. KONFLANZ

schoolPesquisador Melhorista de Plantas, Rua Aimoré, 991, Centro, 85508-212 Pato Branco, PR, Brazil

0000-0001-6868-3387

Correspondence to: Maicon Nardino E-mail: nardino@ufv.br

AUTHOR CONTRIBUTIONS

Maicon Nardino: responsible for the production planning of the new analysis methodology, execution of crossings in the field, writing and statistical analysis of the article. Alan J. de Pelegrin, Vinicius J. Szareski and Ivan R. Carvalho: responsible for the evaluation of corn hybrids in the three locations in the field and in the laboratory. Tiago Olivoto: responsible for correcting the article, helping in the elaboration of the figures of the combinatorial capacities and map with the location of the experiments. Luciano Carlos da Maia, Antonio C. de Oliveira, Velci Q. de Souza: responsible for the laboratories used in the evaluation of the experiments, financing of materials used in the evaluation and corrections of the article. Willian S. Barros, Cosme Damião Cruz, Fabyano F. e Silva: responsible for planning the new diallel analysis methodology and correcting the article. Valmor A. Konflanz: researcher responsible for the maize lines used in the diallel crossing, with relevant assistance in carrying out the field research.

Departamento de Agronomia, Universidade Federal de Viçosa, Avenida Peter Henry Rolfs, s/n, 36570-900 Viçosa, MG, Brazil

Departamento de Matemática e Estatística, Universidade Federal de Pelotas, Campus Universitário Capão do Leão, s/n, 96010-900 Pelotas, RS, Brazil

Departamento de Fitotecnia, Universidade Federal de Santa Maria, Avenida Roraima, 1000, 97105-340 Santa Maria, RS, Brazil

Departamento de Biologia Geral, Universidade Federal de Viçosa, Avenida Peter Henry Rolfs, s/n, 36570-000 Viçosa, MG, Brazil

Departamento de Zootecnia, Universidade Federal de Viçosa, Avenida Peter Henry Rolfs, s/n, 36570-000 Viçosa, MG, Brazil

Departamento de Fitotecnia, Universidade Federal de Pelotas, Campus Universitário Capão do Leão, s/n, 96001-970 Pelotas, RS, Brazil

Universidade Federal do Pampa, Campus São Gabriel, Av. Antonio Trilha, 1847, Vila Camita, 96400-100 São Gabriel, RS, Brazil

Universidade Regional do Noroeste do Estado do Rio Grande do Sul, Rua do Comércio, 3000, 98700–000 Ijuí, RS, Brazil

Pesquisador Melhorista de Plantas, Rua Aimoré, 991, Centro, 85508-212 Pato Branco, PR, Brazil

Code	Trait	Units/Scale	Assessment methodology
EH	Ear height	cm	Measured from ground surface to the ear node
PH	Plant height	cm	Measured from ground surface to the insertion of the flag leaf
EH/PH	Ear height/Plant height ratio	cm	Ratio between ear height and plant height
ARS	Aggressiveness of the root system	notes	We used notes from 7 to 10. Data was transformed by using PROC OPSCORE in SAS 9.2
FLD	Flag leaf distance	cm	Distance from the flag leaf insertion to the first branch of the tassel
DLN	Distance from the last node	cm	Measured from the last node to the first branch of the tassel
TL	Tassel length	cm	Measured from flag leaf to the end of the tassel
NBT	Number of branches in the tassel	nยบ	Average number of branches from three tassels per plot
EM	Ear mass	kg	Mass from all ears of the plot, with straw
NKE	Number of kernels per ear	nยบ	Average value from thee ears each plot
KD	Kernel depth	mm	Average values, assessed by measurement of length of 30 kernels from three ears each plot
FKM	Fifty-kernel mass	g	Average values from 8 replicates from 50 kernels each plot
GYP	Grain yield per plot	kg	The kernel mass each plot was adjusted to 13% moisture and a covariance considering 42 plants per plot was used (Cruz, 2013)
GYH	Grain yield per hectare	mg ha^-1	The average mass from 42 plants were extrapolated to 60.000 plants

Source		Sum of Squares
Source	DF	MT-1†	MT-2‡	MT-3§
Crossing (C)	89	239397.21**	42028.74^ns	143778.15^ns
GCA¶	9	157047.22*	20741.66^ns	78184.74^ns
SCA#	35	56607.03**	11338.95^ns	26664.28^ns
RSCA††	45	25742.96^ns	9948.13^ns	38929.13^ns
Environment(E)	2	16392050.19	5750285.80	42654548.85
C×E	178	189394.55**	102461.84**	322381.44**
CGC×E	18	101628.24**	55329.92**	161833.34**
SCA×E	70	33958.52**	19208.64**	93806.70**
RSCA ×E	90	53807.79**	27923.28**	66741.40**
Error	534	126401.47	75537.74	217566.54
	E	Quadratic terms
${\hat{ϕ}}_{CGC}$	1	511.01	18.13	71.32
	2	25.7	127.67	100.79
	3	47.27	21.44	358.02
${\hat{ϕ}}_{CEC}$	1	252.47	5.67	77.85
	2	21.62	67.38	13.88
	3	38.81	1.67	278.21
${\hat{ϕ}}_{CGC} / {\hat{ϕ}}_{CEC}$	1	2.02	3.2	0.92
	2	1.18	1.89	7.26
	3	1.22	12.83	1.29
${\hat{ϕ}}_{RECÍPROCO}$	1	145.98	8.53	62.36
	2	5.76	59.33	-15.47
	3	24.53	1.68	140.77

GCA	MT-1†			MT-2‡			MT-3§
GCA	FW¶	PB#	CN††	FW	PB	CN	FW	PB	CN
1	-5.97	-3.36	-0.99	3.19	8.93	5.7	-4.56	-2.19	0.51
2	47.58	21.26	40.93	-6.17	-6.14	0.72	1.89	9.26	13.18
3	24.63	1.65	16.89	-4.53	14.08	5.36	-3.88	0.27	5.52
4	-31.42	-12.21	-25.06	10.28	5.73	3.19	0.44	-8.12	-7.36
5	-18.58	-6.3	-11.99	14.3	-4.08	-2.89	9.75	-2.67	1.27
6	9.87	-2.24	16.77	-13.72	-0.39	-10.15	0.24	8.43	6.76
7	-13.3	-12.75	-5.28	-8.54	8.29	-2.82	-5.08	-0.27	-0.12
8	-12.68	-0.82	-8.25	0.04	5.9	2.42	-1.61	0.27	-3.78
9	2.99	4.88	-9.18	5.37	-5.49	-0.49	0.77	-1.42	-8.09
10	-3.11	9.89	-13.85	-0.23	-26.83	-1.04	2.04	-3.57	-7.88

[tfnII] *and ** significant at the 0.05 and 0.01 probability level, respectively; ^ns, nonsignificant at the 0.05 probability level.

† MT-1, mega-trait 1, plant stature-related traits.

‡ MT-2, mega-trait 2, tassel size-related traits.

§ MT-٣, mega-trait ٣, grain yield-related traits.

¶ GCA, general combining ability.

# SCA, specific combining ability.

†† RSCA, reciprocal specific combining ability.

${\hat{ϕ}}_{CGC}$ , estimate quadratic component associated GCA.

${\hat{ϕ}}_{CEC}$ , estimate quadratic component associated SCA.

${\hat{ϕ}}_{CGC} / {\hat{ϕ}}_{CEC}$ , ratio between estimate quadratic components associated GCA and SCA.

${\hat{ϕ}}_{RECÍPROCO}$ , estimate quadratic component associated RSCA.

Multivariate diallel analysis by factor analysis for establish mega-traits

Abstract