402 W. A. BECKER AND M. A. MARSDEN 



Table 2. Genetic and environmental model of covariances of 

 relatives 



Proportion of variance contributed by each source 



Genetic variance Environmental variance 

 Variance Addi- Domi- Epi Between Within Binomial 

 component tive nance static plots plots variance 



















1 







a 2 = cov„ r „. (covariance tester half sibs) 

 a 2 = cov^.^ (covariance candidate half sibs) 



° 2 TC~ cov f " C0V S(T') " C0V 5rn ( cov f = covariance full sibs) 

 a 2 = environmental variance between plots 



°\ 



1/4 







>1/16 











°\ 



1/4 







>1/16 











° 2 TC 







1/4 



>l/8 











o 2 

 e 















1 







°\ 























° 2 d 



1/2 



3/4 



<3/4 







1 



2 



b 



2 -, = (o 2 q - covf) + o 2 ^ (o 2 q = total genetic variance; o 2 ^ 

 environmental variance within a plot 



The term (o 2 e - = a 2 ^) can be estimated accurately only when m is 

 equal to the actual harmonic mean. For fn = 1, this term is overestimated 

 and, therefore the gain is underestimated depending upon the magnitude 

 of c* d . 



If the actual selection differential is not known but the proportion 

 selected is, then S = i op where i can be obtained from tables (e.g., 

 Becker, 1967) for a given percent selected and op is the phenotypic 

 standard deviation. 



Heritability where candidate trees were selected for general com- 

 bining ability on the basis of their progeny means and these candidates 

 remated together (stage B) was also estimated. The future progeny of a 

 candidate and the candidate's tested offspring were half sibs because 

 they had one parent in common (the candidate) and, therefore, the 

 numerator was the covariance of half sibs. The denominator was the 

 variance of the selection units which in this case were the means of the 

 candidate's progenies. The selection gain was: 



