SPECIFIC AND GENERAL COMBINING ABILITY 369 



Sires: £ f Y) -'-') = ;/.. (m" + ^D + S — (<t"' + <t2 + a^) +5^2, 



where 5 denotes number of different lines used as the male line. 



n-.. 

 'I 



where d is the number of different lines used as the female line. 

 Crosses: e( V -^^-^^■'■•^-') = «•• (m^ + 2a^ + a'-') 



C<T- 



where c denotes the number of different crosses (regarding reciprocals as one 

 cross) 



Correction Factor: -E (^-— ) = "••M"+ ^ (;/, -f ».,) Vp/M.. 



2 



e 



The above sums of squares and expectations are quite easy to compute and 

 once this is done all one needs to do is to subtract the correction factor and 

 its expectation from the other sums of squares and expectations and solve the 

 resulting set of four equations for a\, cr^,, a,, and af. 



FURTHER RESEARCH NEEDED 

 If maximum progress through selection for general and specific combining 

 ability is to be attained, much additional research is needed. From a statisti- 

 cal standpoint we need to know if an index based on minimization of E{6—dY 

 comes close to maximizing progress through selection by truncation when the 

 distributions are not the multivariate normal. If such an index does not do 

 so, we need to know what practicable index or indexes will. Further, if 

 nothing is known of the variances and covariances needed in construction of 

 indexes or if there are available only estimates with large sampling errors, we 

 need to know if the index based on the assumption that the estimate is the 

 true value is best from the standpoint of maximizing genetic progress. Final- 

 ly, much more work is needed on the problem of estimating variance and co- 

 variance components and placing confidence limits on such estimates. 



