5.3 Data analysis
• b × site partitioned into:
• site × b1, site × b2 and site*b3
• c = maternal effects
• d = reciprocal effects other than maternal effects 5.3.1 The adequacy of additive–dominance model
The adequacy of the additive–dominance model was tested through Wr- Vr analysis of variance, regression analysis and t2 test (uniformity of Wr, Vr) as described by Singh and Chaudhary (1995), and Dabholkar (1999). The model was considered adequate when the analysis of Wr-Vr was found not to be significant indicating the absence of epistasis.
If epistasis was present Wr-Vr varied between arrays. Additionally, the model was considered adequate when the regression coefficient significantly deviated from zero and not from unity. Furthermore, significant value of the t2-test indicated the inadequacy of the model. If dominance is present the Wr +Vr values must change from array to array.
5.3.2 Estimation of genetic variance components
The genetic components of variation (Table 5.3) were estimated following the procedure given by Hayman (1954a, b).
5.3.3 Graphical analysis
The graphic representation of the covariance (Wr) of all the offspring’s in each parental arrays with the non-recurring parents and the variance (Vr) of all components of the rth array was done. By plotting Wr/Vr (covariance/variance) graph, the information about the presence of dominant and recessive genes in the parental genotypes was evaluated.
The distribution of dominant and recessive genes among parents was determined by order of array points along the regression line. Parents with preponderance of dominant genes were located near the origin while those with array points located very far away from the origin possessed more recessive genes. Parents with array point located at the middle of the regression line had equal frequencies of dominant and recessive genes.
For the average level of dominance, over-dominance was indicated when the intercept was negative, complete dominance when regression line passed through the origin and partial dominance when the slope of regression line intercepted Wr-axis above the origin.
In the absence of epistasis, Wr is linked to Vr by regression line of a unit slope (Singh and Chaudhary, 1995).
Table 5.3: Components of genetic variation and genetic parameters Serial Components
1 D= additive
2 H1=variation due to dominance effects of genes
3 H2= variation due to dominant effect of genes correlated for gene distribution
4 F= Relative frequency of dominant and recessive alleles- it determines the relative frequency of dominant and recessive genes in the parental population. F is positive when dominant genes are more than recessive genes
5 h2 = overall dominance effect of heterozygous loci 6 E= environmental variance
7 √H1/D= Average degree of dominance
8 H2/4H1 = proportion of genes with positive and negative effects in the parents. If the ratio is equal to 0.25 it indicates symmetrical distribution of the positive and negative genes.
9 √4DH1 + F) / (√4DH1- F= proportion of dominant and recessive genes in the parents. If the ratio is 1, then the dominant and recessive genes in parents are equal in proportion. The ratio > 1 indicates more dominant genes and when the ratio < 1 it indicates more recessive genes.
10 Heritability (narrow- sense) was estimated based on Verhalen and Murray (1969) formula as cited by (Singh and Chaudhary, 1995). F2 heritability= 1/4D/(1/4D+1/16H1-1/8F+E)
11 Correlation coefficient between the parental order of dominance (Wr + Vr) for each array and mean of common parent of array (Yr).
12 r2 = prediction of measurements of completely dominant and recessive parents
5.3.2 Generation mean analysis
The data collected was subjected to combined analysis of variance using the general linear model procedure (PROC GLM) in SAS version 9.3 (SAS Institute, 2011) to determine whether there were significant differences. The model used was,
Yijk = µ + Gi + Ej + G × E + rk (E) + eijk
Where Yijk= spot blotch disease score of ith generation in jth environment of kth replication, µ= overall mean, gi= generation mean, Ej= jth environment, G × E=
generation × environment interaction, rk= kth replication within E environment and eijk=
residual factor.
Mean separation between generations was done in SAS version 9.3 (SAS Institute, 2011) using least significance difference (LSD) procedure for pair wise comparison (P≤
0.05) as suggested by Kang (1994).
Data was submitted to generation mean analysis (GMA) using the methodology proposed by Mather and Jinks (1971) following the significant analysis of variance. The GMA was performed using PROC GLM and PROC REG procedures in accordance with SAS macros described by Kang (1994). The genetic model used was;
Y = m + a + d + 2aa + 2ad +2dd Where;
• and are the coefficients for a and d, respectively
• Y = generation mean
• m = mean of the F2 generation as the base population and intercept value
• a = additive effects
• d = dominance effects
• aa = additive x additive gene interaction effects
• ad = additive x dominance gene interaction effects
• dd = dominance x dominance gene interaction effects
A stepwise linear regression was used to estimate the additive and dominant parameters. The regression analysis was carried out using PRO REG macros in SAS developed by Kang (1994). The regression analysis was weighted based on the inverse of the variance of means and matrix parameter (Checa et al., 2006). To establish the parameters that were acceptable within the model, R2 and F-test (goodness of- fit) were used (Ceballos et al., 1998). The F-test was calculated using the formula below (Checa et al., 2006):
Fc = (SSq general model) - (SSq reduced model) /difference in df
SSq residual from the general model / df residual from the general model Where SSq = sums of squares, df = degrees of freedom, Fc = F calculated
To determine the importance of additive, dominance and epistatic effects, the model’s parameters were tested sequentially one at a time starting with additive effects and then
in combination with other parameters of the model (Ceballos et al., 1998). The importance of the gene effect estimates was based on the ratio between the sums of squares and the total sums of square after entering the different elements in the model.
Significance of the genetic estimates was also determined by dividing the estimated parameter values with their standard errors, if the value exceeded 1.96 then it was considered significant (Singh and Chaudhary, 1995).
Variance components (additive, dominance and environment) were estimated as described by Mather and Jinks (1982) using the equation below,
• A = (2σ2F2) – σ2BCP1+ σ2BCP2
• D= σ2G (F2) - σ2A (F2)
• E = 1/4 (σ2P1 + σ2P2 + (2σ2F1)
Where: A = Additive genetic variance, D = Dominance variance and E = Environmental component of variance
Where: σ2P1 = variance of parent 1; σ2P2 = variance of parent 2; σ2F1 = variance of F1;
σ2F2 = variance of F2 generation; σ2BCP1 = variance of backcross to parent 1; σ2BCP2
= variance of backcross to parent 2.
Narrow sense heritability (h2) was estimated as follows;(Warner, 1952).
h2= [σ2F2 – (σ2BCP1 + σ2BCP2) /2] / σ2F2.
Where, σ2F2 = variance of F2 generation, σ2BCP1 = variance of backcross to parent 1;
σ2BCP2 = variance of backcross to parent 2.
The coefficient of dominance (F) was calculated by the formula: (Mather and Jinks, 1982),
F = σ2BCP2 – σ2BCP1