Stability and adaptability of curled green-leaf lettuce lines using the REML/Blup mixed model

The objective of this work was to estimate the stability and genotypic adaptability of advanced lines and cultivars of curled green-leaf lettuce (Lactuca sativa), in different growing environments and seasons, using the REML/Blup mixed model. Ten genotypes, seven cropping environments, and two growing seasons were studied in 2015. Plant yield traits were evaluated, and data were subjected to the Selegen-REML/Blup software. Genotype stability and adaptability were analyzed using the harmonic mean of genotypic values (HMGV) and the relative performance of genotypic values (RPGV), respectively. The harmonic mean of RPGV (HMRPGV) was used to simultaneously estimate the stability, adaptability, and yield of breeding lines or cultivars. Considering the combined analysis of the two seasons for the set of traits, the lines L₆, L₇, and L₈ were selected as promising ones and recommended for planting. The breeding lines selected for all season exhibit good yield and are considered superior to the commercial cultivars Vanda and Vera.

Index terms:
Lactuca sativa; cropping systems; HMRPGV; mixed models

Authorship

Willame dos Santos Candido

Universidade Federal de Goiás, Regional Jataí, BR 364, Km 195, no 3.800, CEP 75801-615 Jataí, GO, Brazil. E-mail: candidows.melhorista@gmail.comUniversidade Federal de GoiásBrazilJataí, GO, BrazilUniversidade Federal de Goiás, Regional Jataí, BR 364, Km 195, no 3.800, CEP 75801-615 Jataí, GO, Brazil. E-mail: candidows.melhorista@gmail.com

Renato Silva Soares

Universidade Estadual Paulista Júlio de Mesquita Filho, Via de Acesso Prof. Paulo Donato Castellane, s/no, CEP 14884-900 Jaboticabal, SP, Brazil. E-mail: renato_2366@hotmail.com, carol.a.franco@hotmail.com, guilhermedinizzz@hotmail.com, edgarddragde@gmail.com, marcusvmarin@gmail.com, leilatb@fcav.unesp.brUniversidade Estadual PaulistaBrazilJaboticabal, SP, BrazilUniversidade Estadual Paulista Júlio de Mesquita Filho, Via de Acesso Prof. Paulo Donato Castellane, s/no, CEP 14884-900 Jaboticabal, SP, Brazil. E-mail: renato_2366@hotmail.com, carol.a.franco@hotmail.com, guilhermedinizzz@hotmail.com, edgarddragde@gmail.com, marcusvmarin@gmail.com, leilatb@fcav.unesp.br

Carolina Andrade Franco

Guilherme Matos Martins Diniz

Edgard Henrique Costa Silva

Marcus Vinicius Marin

Leila Trevisan Braz

SCIMAGO INSTITUTIONS RANKINGS

Tables | Formulas

Tables (5)
Formulas (1)

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Table 1.
Genotypes and cropping environments used in the experiments carried out in the summer (January-March) and winter (June-August) growing seasons in 2015.

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Table 2.
Estimates of variance components and genetic parameters for volume (V), number of leaves (NL), marketable production (MP), total production (TP), and stem length (SL) of curled green-leaf lettuce (Lactuca sativa), involving ten genotypes, tested in seven cropping environments and two growing seasons, in the municipality of Jaboticabal, in the state of São Paulo, Brazil, in 2015.

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Table 3.
Global joint analysis of deviance (Anadev) on the analysis involving 10 genotypes of curled green-leaf lettuce (Lactuca sativa), tested in seven cropping environments in the summer and winter, for the characters volume (V), number of leaves (NL), marketable production (MP), total production (TP), and stem length (SL) in the municipality of Jaboticabal, in the state of São Paulo, Brazil, 2015.

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Table 4.
Mulamba and Mock indices applied to the genetic values of the characters, for the joint analysis of 10 genotypes of curled green-leaf lettuce (Lactuca sativa) in seven cropping environments and two growing seasons, in the municipality of Jaboticabal, in the state of São Paulo, Brazil, 2015.

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Table 5.
Harmonic mean of genotypic values (HMGV), relative performance of genotypic values (RPGV), and RPGV multiplied by the general mean (GM), harmonic mean of relative performance of genotypic values (HMRPGV) and HMRPGV multiplied by the general mean (GM), for the characters volume, number of leaves, marketable production, total yield, and stem length of 10 curled green-leaf lettuce (Lactuca sativa) genotypes for stability, adaptability, and stability and adaptability, respectively, for seven cropping environments and two growing seasons, in the municipality of Jaboticabal, in the state of São Paulo, Brazil, 2015.

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Table 1. Genotypes and cropping environments used in the experiments carried out in the summer (January-March) and winter (June-August) growing seasons in 2015.

Genotype⁽¹⁾	Cropping environment⁽²⁾
L₁	Open field without cover
L₂	Cover with millet (Pennisetum americanum L.) straw
L₃	Low tunnel with 50% shade coverage
L₄	White mulching film coverage
L₅	Black mulching covering for 15 days
L₆	White agrotextile blanket (15 days)
L₇	White agrotextile blanket covering in the total cycle
L₈
Vanda
Vera

⁽¹⁾Identification of curled green-leaf lettuce lines: L₁ (line 1) to L₈ (line 8), and the controls Vanda and Vera (commercial cultivars of lettuce).

Table 2. Estimates of variance components and genetic parameters for volume (V), number of leaves (NL), marketable production (MP), total production (TP), and stem length (SL) of curled green-leaf lettuce (Lactuca sativa), involving ten genotypes, tested in seven cropping environments and two growing seasons, in the municipality of Jaboticabal, in the state of São Paulo, Brazil, in 2015.

Parameter	Character
Parameter	Volume	Number of leaves	Marketable production	Total production	Stem length
Vg	3.332x10⁶	0.937	1.748	3.054	0.405
Vgs	1.510x10⁶	0.762	174.345	209.992	0.037
Vge	0.859x10⁶	0.202	39.037	44.199	0.003
Vges	0.167x10⁶	0.841	121.990	191.128	0.091
Vr	9.334x10⁶	4.369	1,650.055	2,112.427	0.285
Vph	15.203x10⁶	7.112	1,987.176	2,560.799	0.820
h²	0.219±0.057	0.132±0.044	0.001±0.004	0.001±0.004	0.494±0.085
c²gs	0.099	0.107	0.088	0.082	0.045
c²ge	0.057	0.028	0.019	0.017	0.004
c²ges	0.011	0.118	0.061	0.075	0.111
rge	0.795	0.822	0.043	0.065	0.992
rgs	0.688	0.552	0.009	0.014	0.917
rge_s	0.849	0.894	0.819	0.828	0.993
rga_e	0.735	0.599	0.189	0.184	0.918
rge_ms	0.829	0.896	0.793	0.822	0.993
rgs_me	0.697	0.588	0.124	0.149	0.919
rges	0.568	0.342	0.005	0.007	0.757
General mean	19,105.859	22.589	226.857	261.837	4.434

Vg, genotypic variance; Vgs, variance of the genotype x season interactions; Vge, variance of genotype x environment interactions; Vges, variance of the genotype x environment x season interactions; Vr, residual variance; Vph, individual phenotypic variance; h², heritability in the broad sense; c²gs, coefficient of determination of the effects of genotype x season interactions; c²ge, coefficient of determination of the effects of genotype x environment interactions; c²ges, coefficient of determination of the effects of genotype x environment x season interactions; rge, genotypic correlation across environments, valid for any season; rgs, genotypic correlation across the seasons, valid for any environment; rgl_s, genotypic correlation across environments, at a given season; rgs_e, genotypic correlation through the season, in a given environment; rge_ms, genotypic correlation across environments, for the mean of all seasons; rgs_me, genotypic correlation across the seasons, for the average of all environments; rges, genotypic correlation across environments and seasons.

Table 3. Global joint analysis of deviance (Anadev) on the analysis involving 10 genotypes of curled green-leaf lettuce (Lactuca sativa), tested in seven cropping environments in the summer and winter, for the characters volume (V), number of leaves (NL), marketable production (MP), total production (TP), and stem length (SL) in the municipality of Jaboticabal, in the state of São Paulo, Brazil, 2015.

Effect	Volume		Number of leaves		Marketable production		Total production		Stem length
Effect	Deviance	LRT	Deviance	LRT	Deviance	LRT	Deviance	LRT	Deviance	LRT
Genotype	8,546.7*	4.61*	1,451.5^ns	2.25^ns	4,298.2^ns	0.00^ns	4,422.7^ns	0.00^ns	157.3**	12.81**
Genotype x environment	8,546.2*	4.12*	1,449.7^ns	0.45^ns	4,298.4^ns	0.22^ns	4,422.9^ns	0.16^ns	144.6^ns	0.02^ns
Genotype x season	8,557.3**	15.21*	1,458.4**	9.13**	4,308.8**	10.61**	4,430.8**	8.09**	149.1*	4.61*
Genotype x environment x season	8,542.2^ns	0.09^ns	1,457.6**	8.27**	4,299.8^ns	1.65^ns	4,425.1^ns	2.42^ns	167.5**	22.97**
Complete model	8,542.1	-	1,449.3	-	4,298.2	-	4,422.7	-	144.5	-
General mean	19,105.9	-	22.6	-	226.9	-	4,422.7	-	4.4	-

**and*Significant at 1 and 5% of probability, respectively, by the likelihood ratio test (LRT) mixed models. ^nsNonsignificant.

Table 4. Mulamba and Mock indices applied to the genetic values of the characters, for the joint analysis of 10 genotypes of curled green-leaf lettuce (Lactuca sativa) in seven cropping environments and two growing seasons, in the municipality of Jaboticabal, in the state of São Paulo, Brazil, 2015.

Genotype	Genetic values
Genotype	Plant volume (cm³ per plant)	Number of leaves	Marketable production (g per plant)	Total production (g per plant)	Stem length (cm)	Rank
L₁	20,541.99 (2)	22.13 (9)	226.73 (4)	261.78 (4)	5.02 (9)	28
L₂	20,483.06 (3)	22.34 (6)	226.69 (5)	261.75 (5)	4.84 (8)	27
L₃	21,674.07 (1)	22.25 (8)	226.93 (3)	262.19 (3)	5.32 (10)	25
L₄	19,423.58 (5)	22.35 (5)	226.51 (8)	261.41 (8)	4.32 (4)	30
L₅	16,194.14 (10)	22.27 (7)	226.62 (7)	261.04 (10)	3.04 (1)	35
L₆	19,817.59 (4)	23.35 (3)	228.17 (1)	263.37 (1)	4.47 (6)	15
L₇	18,898.56 (6)	23.77 (1)	226.69 (6)	261.65 (6)	4.21 (3)	22
L₈	18,878.08 (7)	23.57 (2)	227.33 (2)	262.35 (2)	4.13 (2)	15
Vanda	17,489.92 (9)	22.74 (4)	226.46 (9)	261.54 (7)	4.47 (5)	34
Vera	17,657.59 (8)	21.13 (10)	226.44 (10)	261.30 (9)	4.52 (7)	44
General mean	19,105.86	22.59	226.86	261.84	4.43

Bold values indicate the genotypes selected by the index in the environment.

Table 5. Harmonic mean of genotypic values (HMGV), relative performance of genotypic values (RPGV), and RPGV multiplied by the general mean (GM), harmonic mean of relative performance of genotypic values (HMRPGV) and HMRPGV multiplied by the general mean (GM), for the characters volume, number of leaves, marketable production, total yield, and stem length of 10 curled green-leaf lettuce (Lactuca sativa) genotypes for stability, adaptability, and stability and adaptability, respectively, for seven cropping environments and two growing seasons, in the municipality of Jaboticabal, in the state of São Paulo, Brazil, 2015.

Genotype	HMGV	RPGV	RPGV*GM	HMRPGV	HMRPGV*GM
	Volume
L₁	19,708.19 (2)	1.08	20,547.49 (2)	1.08	20,543.37 (2)
L₂	19,603.34 (3)	1.07	20,478.76 (3)	1.07	20,467.78 (3)
L₃	20,942.69 (1)	1.14	21,779.56 (1)	1.14	21,752.81 (1)
L₄	18,687.42 (5)	1.02	19,459.27 (5)	1.02	19,445.31 (5)
L₅	15,312.04 (10)	0.84	16,076.29 (10)	0.84	16,056.71 (10)
L₆	18,925.22 (4)	1.04	19,775.97 (4)	1.03	19,772.59 (4)
L₇	18,147.80 (6)	0.99	18,913.89 (6)	0.99	18,911.39 (6)
L₈	18,029.39 (7)	0.98	18,838.79 (7)	0.98	18,823.38 (7)
Vanda	16,795.35 (9)	0.92	17,511.23 (9)	0.91	17,665.98 (9)
Vera	16,957.84 (8)	0.93	17,677.35 (8)	0.92	17,665.98 (8)
	Number of leaves
L₁	21.86 (9)	0.98	22.13 (9)	0.98	22.13 (9)
L₂	22.06 (6)	0.99	22.33 (6)	0.99	22.34 (6)
L₃	21.96 (8)	0.98	22.25 (8)	0.98	22.24 (8)
L₄	22.08 (5)	0.99	22.35 (5)	0.99	22.35 (5)
L₅	22.01 (7)	0.99	22.28 (7)	0.99	22.27 (7)
L₆	23.09 (3)	1.03	23.36 (3)	1.03	23.36 (3)
L₇	23.49 (1)	1.05	23.78 (1)	1.05	23.78 (1)
L₈	23.30 (2)	1.04	23.58 (2)	1.04	23.57 (2)
Vanda	22.43 (4)	1.01	22.72 (4)	1.01	22.72 (4)
Vera	20.83 (10)	0.93	21.11 (10)	0.93	21.11 (10)
	Marketable production
L₁	206.71 (6)	0.99 (6)	226.60 (6)	0.99 (6)	226.58 (6)
L₂	207.67 (2)	1.00 (3)	227.07 (3)	1.00 (3)	227.05 (3)
L₃	206.42 (9)	0.99 (7)	226.56 (7)	0.99 (7)	226.54 (7)
L₄	206.20 (10)	0.99 (10)	226.36 (10)	0.99 (10)	226.33 (10)
L₅	206.44 (8)	0.99 (9)	226.45 (9)	0.99 (9)	226.43 (9)
L₆	208.17 (1)	1.01 (1)	228.19 (1)	1.01 (1)	228.17 (1)
L₇	206.97 (5)	0.99 (4)	226.74 (4)	0.99 (4)	226.74 (4)
L₈	207.43 (3)	1.00 (2)	227.46 (2)	1.00 (2)	227.42 (2)
Vanda	206.64 (7)	0.99 (8)	226.46 (8)	0.99 (8)	226.44 (8)
Vera	207.16 (4)	0.99 (5)	226.68 (5)	0.99 (5)	226.67 (5)
	Total production
L₁	241.26 (6)	0.99 (6)	261.66 (6)	0.99 (6)	261.64 (6)
L₂	242.19 (2)	1.00 (3)	262.13 (3)	1.00 (3)	262.11 (3)
L₃	241.13 (7)	0.99 (4)	261.79 (4)	0.99 (4)	261.77 (4)
L₄	240.63 (9)	0.99 (9)	261.25 (9)	0.99 (9)	261.23 (9)
L₅	240.49 (10)	0.99 (10)	260.89 (10)	0.99 (10)	260.89 (10)
L₆	243.04 (1)	1.01 (1)	263.46 (1)	1.01 (1)	263.44 (1)
L₇	241.43 (5)	0.99 (5)	261.69 (5)	0.99 (5)	261.69 (5)
L₈	242.13 (3)	1.00 (2)	262.53 (2)	1.00 (2)	262.51 (2)
Vanda	241.03 (9)	0.99 (8)	261.43 (8)	0.99 (8)	261.42 (8)
Vera	241.48 (4)	0.99 (7)	261.52 (7)	0.99 (7)	261.50 (7)
	Stem length
L₁	4.98 (2)	1.13	5.03 (2)	1.13	5.03 (2)
L₂	4.79 (3)	1.09	4.84 (3)	1.09	4.84 (3)
L₃	5.28 (1)	1.20	5.32 (1)	1.20	5.32 (1)
L₄	4.27 (7)	0.97	4.31 (7)	0.97	4.31 (7)
L₅	2.98 (10)	0.68	3.03 (10)	0.68	3.02 (10)
L₆	4.43 (5)	1.01	4.47 (5)	1.01	4.48 (5)
L₇	4.16 (8)	0.95	4.21 (8)	0.95	4.21 (8)
L₈	4.08 (9)	0.93	4.13 (9)	0.93	4.13 (9)
Vanda	4.42 (6)	1.01	4.47 (6)	1.01	4.47 (6)
Vera	4.48 (4)	1.02	4.52 (4)	1.02	4.52 (4)

Bold values indicate the genotypes selected for stability and adaptability parameters.

HMGV = \frac{1}{\sum_{i = 1}^{1} \frac{1}{G V_{j}}}, RPGV = \frac{1}{l} (\frac{\sum G V_{j}}{M_{j}}), and H M R P G V = \frac{1}{\sum_{l = 1}^{1} \frac{1}{R P G V_{j}}}

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Stability and adaptability of curled green-leaf lettuce lines using the REML/Blup mixed model

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Mensagem

[TFN1] ⁽¹⁾Identification of curled green-leaf lettuce lines: L₁ (line 1) to L₈ (line 8), and the controls Vanda and Vera (commercial cultivars of lettuce).