364 C R. HENDERSON 



tal factors well enough, further simplification is possible. Let Wi be the cor- 

 rected mean of the progeny of zth line. Then 



p = 7^ 



Hi e 



This result is a straightforward application of the principles of the selection 

 index. 



It must be quite apparent that efficient appraisals of the general combin- 

 ing abilities of lines depend on knowledge of the variances and covariances of 

 general combining abilities and of the variance of error. It hardly seems like- 

 ly that estimates of the line variances and covariances can be obtained with 

 accuracy comparable to estimates of additive genetic variances and covari- 

 ances with respect to individuals. The latter estimates are based on studies of 

 heritability and on the known facts of the hereditary mechanism. In the case 

 of inbred lines, however, the sample of different lines tested is usually so 

 small as to make the estimates of al less reliable than we should like. A way 

 around this difficulty in the case of traits for which heritability is well known 

 is to compute the expected variances and covariances based on knowledge of 

 (tI in the original population from which the lines were formed, the inbreeding 

 of the different lines, and the relationships between pairs of lines. It seems 

 likely that such estimates would be more reliable when the number of lines 

 is small than would estimates arising from the actual line tests. We cannot 

 be any more precise regarding this point until methods are developed for 

 placing confidence limits on estimates of variances and covariances arising 

 from non-orthogonal data. 



SELECTION FOR GENERAL COMBINING ABILITY, MATERNAL ABILITY, 

 AND SPECIFIC ABILITY IN LINE CROSS TESTS 



If we wish to estimate the general combining ability of lines relative to the 

 population from which the lines themselves can reasonably be regarded as a 

 random sample, line crosses give, for fixed size of testing facilities, more accu- 

 rate estimates than do topcrosses. The reason for this is that we obtain from 

 each cross estimates of the general combining abilities of two or more lines. 

 Also, line crosses enable one to estimate differences in maternal abilities un- 

 confounded with differences in general combining abilities and to appraise the 

 values of specific crosses. In those species for which hand mating is the cus- 

 tomary procedure, little more labor is required for line cross than for topcross 

 tests. The estimation of line and line cross characteristics from line cross data 

 is no different in principle from what we have already described with respect 

 to estimation of additive genetic values of individuals or general combining 

 abilities of lines. As before, we wish to obtain unbiased and most efficient esti- 

 mates of certain genetic values. For the sake of simplicity of presentation we 



