Hayman’s diallel analysis of traits related to the production and quality of papaya fruit

Cardoso, Deisy Lúcia; Vivas, Marcelo; Amaral Junior, Antonio Teixeira do; Pereira, Messias Gonzaga

doi:10.1590/1678-4499.0114

Universidade Anhanguera (UNIDERP), Unidade Agrárias, Avenida Alexandre Herculano, 1400, 79037280 Campo Grande (MS), Brasil.

Universidade Estadual do Norte Fluminense Darcy Ribeiro (UENF), Centro de Ciências e Tecnologias Agropecuárias (CCTA), Laboratório de Melhoramento Genético Vegetal (LMGV), Av. Alberto Lamego, 2000, 28013-602 Campos dos Goytacazes (RJ), Brasil.

Figures (1)
Tables (5)

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Figure 1
Regressions of

{\hat{W}}_{r}

on

{\hat{V}}_{r}

, for the number of marketable fruit (a), fruit firmness (b) and total soluble solids (c); parents: 1 = ‘Maradol’; 2 = ‘JS12-N’; 3 = ‘JS12-4’; 4 = ‘Sekati’; 5 = ‘Waimanalo’; 6 = ‘Golden’; 7 = SS72-12’; and, 8 = São Mateus’.

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Table 1
Sufficiency test of the additive-dominant model based on the analysis of variance of values of

{\hat{W}}_{r}

–

{\hat{V}}_{r}

and on linear regression analysis of

{\hat{W}}_{r}

, as a function of

{\hat{V}}_{r}

, according to Hayman’s method (Hayman, 1954aHayman, B. I. (1954a). The analysis of variance of diallel tables. Biometrics, 10, 235-244. http://dx.doi.org/10.2307/3001877.
http://dx.doi.org/10.2307/3001877... , bHayman, B. I. (1954b). The theory and analysis of diallel crosses. Genetics, 39, 789-809. PMid:17247520.)

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Table 2
Estimates of genetic and non-genetic parameters for the number of commercial fruit (NCF), fruit firmness (FF) and total soluble solids (TSS), according to Hayman’s method (Hayman, 1954aHayman, B. I. (1954a). The analysis of variance of diallel tables. Biometrics, 10, 235-244. http://dx.doi.org/10.2307/3001877.
http://dx.doi.org/10.2307/3001877... , bHayman, B. I. (1954b). The theory and analysis of diallel crosses. Genetics, 39, 789-809. PMid:17247520.)

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Table 3
Estimates of genetic and non-genetic parameters for the number of commercial fruit (NCF), fruit firmness (FF) and total soluble solids (TSS), according to Hayman’s method (Hayman, 1954aHayman, B. I. (1954a). The analysis of variance of diallel tables. Biometrics, 10, 235-244. http://dx.doi.org/10.2307/3001877.
http://dx.doi.org/10.2307/3001877... , bHayman, B. I. (1954b). The theory and analysis of diallel crosses. Genetics, 39, 789-809. PMid:17247520.)

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Table 4
Estimates of the correlations between the mean values of the parents (

{\bar{Y}}_{r r}

) and the sum of the covariance between means of the parents and averages of the r-th row (

{\hat{W}}_{r}

), and the variance between the averages of the r-th row (

{\hat{V}}_{r}

), expected values of the coordinates

{\hat{W}}_{R}; {\hat{V}}_{R}

and

{\hat{W}}_{D}; {\hat{V}}_{D}

and value predicted for the parents with maximum concentration of dominant (

{\hat{Y}}_{D}

) and recessive (

{\hat{Y}}_{R}

)alleles obtained for number of commercial fruit (NCF), fruit firmness (FF) and total soluble solids (TSS), according to Hayman’s method (Hayman, 1954aHayman, B. I. (1954a). The analysis of variance of diallel tables. Biometrics, 10, 235-244. http://dx.doi.org/10.2307/3001877.
http://dx.doi.org/10.2307/3001877... , bHayman, B. I. (1954b). The theory and analysis of diallel crosses. Genetics, 39, 789-809. PMid:17247520.)

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Table 5
Values of the sum of the covariance between averages of parents and averages of the r-th row (

{\hat{W}}_{r}

), and the variance between the averages of the r-th row (

{\hat{V}}_{r}

); and averages of the number of commercial fruit (NCF), fruit firmness (FF) and total soluble solids (TSS), according to Hayman’s method (1954a,b)

Trait	Anova $({\hat{W}}_{i} - {\hat{V}}_{i})$	Regression W_i=¼(D-H₁)+bV_i
Trait	MS (Lines)	$\hat{b}$ ± Variance	t(H₀:b=1)	t(H₀:b^’=0)
Number of fruit	683.8213NS	1.030±0.006	0.381NS	–1.569NS
Fruit yield	101361.4735**	0.358±0.015	–5.296**	1.779NS
Fruit firmness	43.5694NS	1.004±0.010	0.036NS	–1.556NS
Total soluble solids	0.0750NS	0.842±0.033	–0.869NS	–1.924NS
Pulp thickness	2.1147NS	0.951±0.032	–0.275NS	–2.413^* * and ** significant at 5 and 1% significant level, respectively (Tests F and/or t).

Parameters⁽1⁾	Parameter values
Parameters⁽1⁾	NCF	FF	TSS
$\sqrt{{\hat{H}}_{1} / \hat{D}}$	0.4740	0.6573	0.7045
${\hat{H}}_{2} / 4 {\hat{H}}_{1}$	0.1161	0.1340	0.2657
${\hat{K}}_{D} / {\hat{K}}_{R}$	3.6931	1.6617	1.0807
${\hat{h}}^{2} / {\hat{H}}_{2}$	–0.0226	0.9216	2.2430
${\hat{h}}^{2}_{R}$	0.7461	0.5892	0.5184
${\hat{h}}^{2}_{A}$	0.8135	0.6673	0.6679

Components⁽1⁾	Values of the components ± standard deviation
Components⁽1⁾	NCF	FF	TSS
$\hat{ε}$	49.044±10.45	26.60±2.58	0.46±0.09
$\hat{D}$	681.160±31.34	107.84±7.74	1.57±0.25
${\hat{H}}_{1}$	153.044±72.05	46.59±17.78	0.78±0.59
${\hat{H}}_{2}$	71.066±62.69	24.96±15.47	0.83±0.51
${\hat{h}}^{2}$	–1.608±42.04	23.00±10.38	1.85±0.34
$\hat{F}$	370.556±74.06	35.24±18.28	0.08±0.61
$\hat{D} - {\hat{H}}_{1}$	528.116±61.87	61.25±15.27	0.80±0.51

Parameter	Parameter estimates
Parameter	NCF	FF	TSS
	0.5311	0.6401	–0.5848
${\hat{W}}_{R}; {\hat{V}}_{R}$	578.7546; 458.7166	130.3461; 126.3729	2.2727; 2.5483
${\hat{W}}_{D}; {\hat{V}}_{D}$	130.1612; 23.2016	3.6079; 0.0968	0.1339; 0.0088
${\hat{Y}}_{R}$ Limit	96.4948	113.5169	3.4698
${\hat{Y}}_{D}$ Limit	18.9223	48.3580	13.3359

Genotypes	NCF		FF		STT
Genotypes	${\hat{W}}_{r}$ + ${\hat{V}}_{r}$	AVERAGE	${\hat{W}}_{r}$ + ${\hat{V}}_{r}$	AVERAGE	${\hat{W}}_{r}$ + ${\hat{V}}_{r}$	AVERAGE
‘Maradol’	232.23	21.56	101.28	58.88	2.09	7.93
‘JS 12-N’	259.06	37.83	138.41	94.71	1.86	10.63
‘JS 12-4’	339.43	28.43	82.15	76.71	1.45	10.23
‘Sekati’	381.51	25.66	118.97	70.41	2.08	8.83
‘Waimanalo’	552.56	13.37	93.35	67.89	1.44	10.78
‘Golden’	336.21	62.23	87.12	71.93	1.11	10.88
‘Sunrise Solo 72/12’	706.22	93.44	75.60	69.25	1.72	12.02
‘São Mateus’	373.35	40.28	48.69	61.46	1.39	10.10

[TFN100] ^NS
non-significant.

[TFN200] ^*
and ** significant at 5 and 1% significant level, respectively (Tests F and/or t).

Brasil

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Hayman’s diallel analysis of traits related to the production and quality of papaya fruit

Abstract