Selection and recommend of quinoa (Chenopodium quinoa) genotypes based on the yield genotypic adaptability and stability

The present study aimed to select and recommend quinoa genotypes based on the yield genotypic adaptability and stability, by the method of the Harmonic mean of relative performance of genotypic values. Five experiments were conducted during the crop seasons of 2014 and 2015 in two locations in the Western region of Paraná State, Brazil. This study involved the evaluation of the yield of thirteen quinoa genotypes. Initially, the genotypic values (GV) were obtained by employing BLUP/REML methodology for mixed models. After, the values of the harmonic mean for genotypic value (HMGV*MG), the relative performance for genotypic values (RPGV*MG) and the harmonic mean of the relative performance for genotypic values (HMRPGV*MG) were obtained. The genotypes Q1317 and Q2014 were the best indicated for cultivation in the summer crop, with medium yield genotypic stability and adaptability. The genotype Q1318 is recommended for winter crop, presenting high yield genotypic stability and adaptability.

Keywords:
Chenopodium quinoa; genotypic value; BLUP/REML; mixed model

Authorship

Edmar Soares de Vasconcelos ^**Corresponding author: edmar.vasconcelos@unioeste.br

Universidade Estadual do Oeste do Paraná, Departamento de Agronomia, Marechal Cândido Rondon, Paraná, Brazil. edmar.vasconcelos@unioeste.br; mmecher@bol.com.br; mkliemann@nideraseeds.com; mlang@unioeste.brUniversidade Estadual do Oeste do ParanáBrazilMarechal Cândido Rondon, Paraná, Brazil Universidade Estadual do Oeste do Paraná, Departamento de Agronomia, Marechal Cândido Rondon, Paraná, Brazil. edmar.vasconcelos@unioeste.br; mmecher@bol.com.br; mkliemann@nideraseeds.com; mlang@unioeste.br

http://orcid.org/0000-0002-0481-9879

Marcia de Moraes Echer

Marcio André Kliemann

Marcelo Júnior Lang

^*Corresponding author: edmar.vasconcelos@unioeste.br

SCIMAGO INSTITUTIONS RANKINGS

Tables | Formulas

Tables (4)
Formulas (5)

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Table 1:
Environmental descriptions of site, year and crop seasons, as well as the seeding system used

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Table 2:
Results of deviance analyze, components of variance and determination of coefficients for to the joint analysis of the thirteen quinoa genotypes in five environments, in Marechal Cândido Rondon and Entre Rios do Oeste - Paraná, Brazil

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Table 3:
Predicted genotypic values (GV) to the yield trait of thirteen quinoa genotypes evaluated in five environments, for 2014 and 2015 agricultural years, in Marechal Cândido Rondon (MCR) and Entre Rios do Oeste (ERO) - Paraná, Brazil

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Table 4:
Stability of genotypic values (HMGV), adaptability of genotypic values (RPGV*MG), stability and adaptability of genotypic values (HMRPGV*MG) for the yield trait in thirteen quinoa genotypes evaluated in five environments, in 2014/2015 agricultural year, in Marechal Cândido Rondon and Entre Rios do Oeste - Paraná, Brazil

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Table 1: Environmental descriptions of site, year and crop seasons, as well as the seeding system used

Envi-ronment	Municipalities	Latitude	Longitude	Altitude	Year / Crop season	Seeding system
1	Marechal Cândido Rondon	-24.5321	-54.0176	422	2014 / Winter	conventional¹
2	Entre Rios do Oeste	-24.6813	-54.2854	267	2014/15 /Summer	no-tillage²
3	Entre Rios do Oeste	-24.6757	-54.2817	260	2014/15 /Summer	conventional organic³
4	Marechal Cândido Rondon	-24.5316	-54.0176	421	2014/15 /Summer	conventional
5	Entre Rios do Oeste	-24.6810	-54.2823	265	2015 / Winter	no-tillage

¹
- Seeding system with soil tillage and use of chemical fertilizer, herbicides and insecticides when necessary; ²- Seeding system without soil tillage, desiccation of area with herbicide, use of chemical fertilizer, herbicides and insecticides when necessary; ³- Seeding system with soil tillage and use of organic fertilizer, without use of herbicides and insecticides.

Table 2: Results of deviance analyze, components of variance and determination of coefficients for to the joint analysis of the thirteen quinoa genotypes in five environments, in Marechal Cândido Rondon and Entre Rios do Oeste - Paraná, Brazil

Effect	Deviance¹	LRT (χ²)²	Component of Variance	Coeficient of determination
Genotypes	2077.03	0.01^NS	156.6970^NS	0.0026^NS
Genotypes x Environments	2121.81	44.79**	30995.4645⁺	0.5080⁺
Residue	-	-	25533.9046	0.4185
Complete Model	2077.02	-	61017.3124	1.0000
Block/Environments	2085.34	F = 8.32**	4331.2463^NS	0.0710^NS

¹
- Deviance of the adjusted model without the corresponding effects; ²- Likelihood Ratio for models with and without the respective effect. * and ** Significant by the chi-square test at 5% (3.84) and 1% (6.63), respectively. ⁺- Significant by the t test (p ≤ 0.05).

Table 3: Predicted genotypic values (GV) to the yield trait of thirteen quinoa genotypes evaluated in five environments, for 2014 and 2015 agricultural years, in Marechal Cândido Rondon (MCR) and Entre Rios do Oeste (ERO) - Paraná, Brazil

Location	Genotype	Summer Crop	Winter Crop	Organic Summer Crop¹
Location	Genotype	GV⁴	GV⁴	GV⁴
ERO²	Q2014	1833.73 b	-	182.91 b
	Q1301	1592.14 c	301.62 c	111.45 c
	Q1302	1476.06 d	342.36 b	169.41 b
	Q1303	1596.95 c	-	165.95 b
	Q1304	1553.89 c	202.65 e	225.83 a
	Q1306	1709.18 c	201.45 e	158.52 b
	Q1310	1688.30 c	310.35 c	195.8 a
	Q1317	1988.02 a	249.09 d	139.13 b
	Q1318	1504.09 c	466.34 a	149.05 b
	Q1320	1804.33 b	429.79 a	174.7 b
	Q1321	1968.61 a	-	161.14 b
	Q1324	1408.38 d	202.56 e	153.07 b
	Q1331	1272.62 e	245.56 d	98.35 c
MCR³	Q2014	1957.87 a	164.13 e	-
	Q1301	1810.73 b	284.85 c	-
	Q1302	1217.65 d	161.05 e	-
	Q1303	1691.81 b	266.35 c	-
	Q1304	1634.38 b	450.44 a	-
	Q1306	2027.13 a	227.94 d	-
	Q1310	1408.13 c	337.95 b	-
	Q1317	1518.40 b	354.74 b	-
	Q1318	1720.29 b	333.35 b	-
	Q1320	1772.15 b	191.18 e	-
	Q1321	1420.53 c	213.13 d	-
	Q1324	1566.94 b	486.98 a	-
	Q1331	1650.3 b	367.65 b	-

¹
- The Organic Crop was in the year 2015; ² - The summer crop was in the crop year of 2014/2015 and the winter crop was in the year 2015; ³ - The summer crop was in the crop year of 2014/2015 and the winter crop was in the year 2014; and ⁴- Genetic values followed by the same letter belong to the same group by the Tocher test.

Table 4: Stability of genotypic values (HMGV), adaptability of genotypic values (RPGVMG), stability and adaptability of genotypic values (HMRPGVMG) for the yield trait in thirteen quinoa genotypes evaluated in five environments, in 2014/2015 agricultural year, in Marechal Cândido Rondon and Entre Rios do Oeste - Paraná, Brazil

Genotypes	HMGV	RPGV*MG	HMRPGV*MG
Q2014	317.056 c	808.505 c	732.610 d
Q1301	294.479 d	767.804 e	748.933 d
Q1302	302.452 d	711.085 f	661.653 e
Q1303	363.716 b	795.338 d	792.915 c
Q1304	389.466 a	898.510 a	826.805 b
Q1306	298.724 d	762.017 e	728.604 d
Q1310	397.113 a	856.586 b	844.262 b
Q1317	329.317 c	815.386 c	795.337 c
Q1318	381.697 a	904.916 a	870.070 a
Q1320	347.226 c	867.519 b	809.989 c
Q1321	330.315 c	765.182 e	739.101 d
Q1324	336.210 c	824.182 c	758.278 d
Q1331	272.452 e	722.080 f	682.017 e

¹
- HMGV, RPGV*MG and HMRPGV*MG values followed by the same letter belong to the same group by Tocher test.

y = X_{r} + Z_{g} + W_{b} + T_{g a} + e

{G V}_{i j} = {\hat{μ}}_{j} + {\hat{g}}_{i} + {\hat{g e}}_{i j}

{H M G V}_{i} = \frac{1}{\sum_{j = 1}^{l} \frac{1}{{G V}_{i j}}}

{R P G V}_{i} * M G = \frac{1}{l} (\frac{\sum_{j = 1}^{l} {V G}_{i j}}{M_{j}}) * M G

{H M R P G V}_{i} * M G = \frac{1}{\sum_{j = 1}^{l} \frac{1}{{R P G V}_{i j}}} * M G

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