Estimation of Breeding Parameters from Phenotypic Data of F4:5 RIL in Ethiopian Malt Barley (Hordeum distichum L.) Breeding Population

Table 3

Parameter estimation and their quantitative genetic expectation assuming an additive model.

Parameters	Genetic expectations	References
Generation means
Mid-parent value	MPVij = (mi + mj)/2	[6]
Cross-mean	C ij = (mi + mj)/2
Genetic variance
Among parents	= ( + )/2 =
Between means of crosses	=
Among lines within crosses	=
Heritability	H^2Cullis = 1 − average standard error from BLUP/	Cullis et al. 2006
Correlation
Phenotypic		[15]
Genotypic
Regression of cross mean on MPV	cij = m + bij(MPij) + eij	[6]
Usefulness of crosses	Uij = Cij + ΔGij = Cij + ihσgij	Schnell & Utz, 1975

m, m_i, and m_j = mean of the RIL population, parent i and j, resp.; MPV_ij = mid-parent value of parent i and j; C_ij = predicted cross-mean;  = variance of additive effects; ,  = genotype variance among crosses and among lines within crosses, resp.; r_p = phenotypic correlation, COV (trait 1, trait 2) = the covariance between the trait values, the denominator is the product of the square root of the phenotypic variance of trait 1 and trait 2;  = genetic correlation, COV (, ) = covariance of the genetic effects and for trait 1 and trait 2, the denominator is the product of the square root of genetic variance of trait 1 and trait 2; b_ij = the slope of regression; ε_ij = error term; U_ij is the usefulness of the cross C_ij,, R_ij = genetic gain, which is a result of segregation variance, heritability (h²) within the cross, and the selection intensity (i).