5.2 Methods and materials
5.2.5 Statistical analysis of data
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Where: Y is the phenotypic measurement of the trait of interest; μ is the mean; Gj is the effect of the ith TCH or hybrid check; Ej is the effect of the jth environment; Rk is the effect of the kth replication; Bl is the effect of the lth incomplete block; (GE)ij is the interaction terms for genotype and environment; and εijkl is the random error term.
To compute the general and specific combining ability effects of the CMS lines, the hybrid check genotypes were excluded from the analysis and Gi in the above statistical model was partitioned into:
Gi = GCAf + GCAm + SCAfm
Where: GCAf is the general combining ability (GCA) effect of the fth CMS female line (f=1,2..,42); GCAm is the GCA effect of mth male tester line (n=1,2); and SCAfm the specific combining ability (SCA) of the TCH involving tester line m and female line f.
Variance components estimates due to GCA of female lines (σ2GCAf), SCA of TCHs (σ2SCA) and their respective interactions with the environment (σ2GCAfxE and σ2SCAxE) were estimated across trials within each moisture stress level using the mixed model analyses PROC MIXED, Method=TYPE3 procedures in SAS (SAS Institute 2010). All effects in the combining ability model were declared random except μ,and GCAm.
To calculate narrow sense heritability (h2) for each stress level, the estimated variance components associated with GCA and SCA effects were used according to Grieder et al.
(2012) as:
Where: E is the number of environments; T the number of testers; and R the number of replications.
Broad sense heritability (H2) for each stress level was estimated as:
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Where the terms are as for the narrow sense heritability equation.
5.2.5.2 Type A and B genotypic and additive genetic correlations
Phenotypic correlations between traits (rP(x,y)) were determined from TCH means across trials within a stress level or between stress levels (RSE, MSE and NSE). To distinguish between genetic correlations based on H2 and h2, genetic correlation based on H2 is referred to as genotypic correlation and that based on h2 is referred to as additive genetic correlation.
Type A genetic correlations were based on genetic variances across the trials within the same environments (type A). Type A genotypic correlation (rG) between two traits x and y measured on the same genotype within or meaned across the environments were computed according to Holland (2006) as:
Where: rG(x,y) is the Type A genotypic correlations between two traits x and y; Cov(x,y) is the genetic covariance between traits x and y meaned within or across environments;
and σ2G(x) and σ2G(y) are the genetic variances of traits x and y meaned within or across environments.
The type A additive genetic correlation between two traits x and y was calculated based on the covariance model derived by Wu and Matheson (2006) as:
Where: rA(x,y), is the type A additive genetic correlation between the female line GCA effects of trait x and y; CovGCA(x,y) is the covariance between the female line GCA effects for trait x and y meaned for each TCH within or across environments; and σ2GCA(x) and σ2GCA(y) are the variances of the female line GCA effects for trait x and y meaned for each TCH within or across environments.
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Type B genotypic correlation (r’G(x,x*)) between the same trait x and x* measured on the same genotype in different environments was calculated, assuming no environmental covariance between the TCHs means, according to Cooper et al. (1996) as:
Where: r’G(x,x*) is the type B genotypic correlation coefficients between the same trait x and x* measured in different environments; r’P(x,x*) is the phenotypic correlation coefficient between TCH means for the same trait at the different environments pairs; and H2x and H2x* are the broad sense heritabilities of the same trait at the different environments.
Type B additive genetic correlation (r’A (x,x*)), between the same trait measured in different stress levels were calculated, assuming no environmental covariance between the GCA effects, according to Lu et al. (1998) as:
Where: r’A(x,x*) is the type B additive genetic correlation coefficient between the same trait measured in different stress treatments; r’’P(GCAx,GCAx*) is the Pearson correlation coefficient between the GCA effects of same trait in different environments; h2x and h2x*
are narrow sense heritabilities of the same trait in different stress treatments.
5.2.5.3 Indirect response to selection based type A genetic correlation
Indirect response to selection based on secondary traits is synonymous with indirect selection efficiency based on type A rG and rA. Genotypic indirect selection efficiency (ISEG) and additive genetic indirect selection efficiency (ISEA) for selection practiced on secondary traits to improve oil yield in the different stress levels, assuming the same selection intensity, was estimated according to Falconer and Mackay (1996):
, and
Where: H2x and h2x are, respectively the broad and narrow sense heritability of the secondary trait, in this study: SD, HD and SG; H2OY and h2OY are the broad sense and
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narrow sense heritabilities, respectively for oil yield (OY); and all other terms are as previously described.
5.2.5.4 Indirect response to selection based on type B genetic correlations
Type B genotypic (ISE’G) and additive genetic (ISE’A) indirect selection efficiency in the MSE and NSE for the RSE were compared with direct selection in the RSE according to Falconer and Mackay (1996) as:
and
Where: H2x and h2x are the broad and narrow sense heritabilities, respectively of the trait of interest in MSE or NSE; H2x (RSE) and h2x (RSE) are the broad sense and narrow sense heritabilities of the same trait under the RSE target environments, respectively; and all other terms are as previously defined. For indirect selection to be more efficient than direct selection, the square root of heritability in the test environments should be greater than the square root of heritability in the target environments (Falconer and Mackay, 1996).