SPECIFIC AND GENERAL COMBINING ABILITY 361 



ances effected by inbreeding are automatically taken into account. If selec- 

 tion is intense, the samj^le mean may considerably overestimate the i)o[)ula- 

 tion mean appropriate for subtraction from the records. The safest procedure 

 is to regard ^t as unknown and to estimate it by the procedure described 

 earlier (equations 3, 4, 5) . It is also of interest to note that joint estimation by 

 this method of such factors as environmental trends and age effects automati- 

 cally eliminates biases in the estimates resulting from use of selected data. 



SELECTION FOR GENERAL COMBINING ABILITY 

 IN TOPCROSS TESTS 



When it comes to estimation of the general combining abilities of inbred 

 lines or of the values of specific crosses, apparently no application has been 

 made of the selection index method. This failure may have been due to diffi- 

 culty in obtaining the estimates of the needed variances and covariances, 

 failure to see that the method was applicable, or the opinion that since inbred 

 lines can be carefully tested more efficient but complex methods of appraisal 

 are not worth the extra computational labor. We propose to show here how 

 the methods can be applied to such selection problems, to indicate some situ- 

 ations in which it may result in considerably more efficiency in selection than 

 the use of the straight means of the lines or crosses as the criteria of selection, 

 and to present some approximate solutions which are relatively easy to 

 compute. 



Let us consider first one of the most simple tests of lines, the topcross test. 

 In this test a random sample of individuals from each of several lines is mated 

 to a tester population, and measurements are taken on the resulting progeny. 

 If only one trait is considered important, the lines are usually rated according 

 to the means of their topcross progeny. This method of ranking is as good as 

 any, provided either that the same number of progeny is obtained for each 

 line or that the sampling errors of the line means are negligible. Seldom, at 

 least in large animal tests, would either of these conditions hold. Accidents 

 usually preclude attainment of equal numbers, and sampling errors are usual- 

 ly large. If sequential testing is done, numbers would always be unequal. By 

 sequential testing we mean here that lines are given a preliminary test, and a 

 certain fraction of those performing worst are discarded. Then the remaining 

 lines, accompanied perhaps by some new lines, are given another test, and so 

 on through any number of cycles desired. The lines surviving several such 

 tests would obviously have larger numbers of progeny than the new lines, and 

 it would be a very inefficient procedure to disregard the results of prior tests 

 on the older lines when choosing between them and the newer, less well- 

 tested lines. 



The way in which the lines should be ranked on the basis of all information 

 is analogous to choosing between individuals with different numbers of rec- 

 ords. In the latter case both repeatability of single records and the number of 



