400 W. A. BECKER AND M. A. MARSDEN 



a2 - I 821 - i a 2 . 



P m m 



Table 1 gives the analysis of variance model with the expectations of mean 

 squares assuming candidates and testers random and replications fixed. 

 The variances og and o 2 ^ cannot be separated and therefore o 2 e - j= o 2 rf 

 is one term. 



GENETIC 



Table 2 gives the genetic meaning in terms of covariance of rela- 

 tives of the variance components of table 1 as well as the designation 

 of binomial sampling and environmental variances. 



Estimation of Heritabilities and Prediction of Selection Gain 

 



Heritabilities were obtained by considering them as regression 

 coefficients of future progeny on the test material. The general formula 

 would be 



, 2 _ covariance (test material --future progeny) 

 variance of selection units 



where the test material are the measured individuals and selection units 

 are the units used for selection such as individuals, means of full or 

 half sib families, or means of progeny. For selection on an individual 

 basis (stage C in Fig. 1) the selection gain would be 



cov (dam-daughter) Q cov ( s ire-daughter) 



Aff92 = " ~^) + s ~~ ^ 



_ cov (dam-son) _ cov^ (sire-son) 

 AG *j = o n ~ + b Q 5 , 



** D ° 2 P(D) S ° 2 P{D) 



where the sexes are kept separate both in the progeny, daughters (99) and 

 sons (jy) , and in the parents. The dams (0) are the maternal parents and 

 the sires (S) are the paternal parents, with P = phenotype; S - selectional 

 differential; and AG = selection gain. The covariances of parent -offspring 

 each estimates 1/2 additive genetic variance. However, because pine trees 

 are monoecious the terms and separate equations for daughters and sons 

 must be combined, and 





A, 7 



2 cov (parent-offspring) 



In the design used in these experiments the covariance of parent off- 

 spring was not measured. Twice the covariance of candidates half sibs 

 (2 o 2 c) was substituted for cov (parent-offspring) , giving 



4 o 2 

 AG = S 



°V° 2 r C + F°W°VF°V 



rith W = 1 because individual selection was practiced. 



