210 PHYSIOLOGIC GENETICS 



data of table 48. The computation is divided into five steps in the table and it needs 

 little further explanation. The observed mean squares are denoted by A, B, and C, 

 and the coefficients of the variance components in the mean squares by a, b, and c, as 

 listed in section I of the table, which represents the analysis of variance as already 

 explained and exemplified in table 48. Next (section II), the sampling variances of 

 the observed mean squares are computed; these are twice the square of the mean square, 

 divided by the corresponding degrees of freedom. Under III the values of the co- 

 efficients (a, b, and c) of the components are listed and three quantities denoted by 

 x, y, and T are computed for later use. The sib correlations, denoted here by 

 P and R, will have already been obtained from the analysis of variance. Now the 

 sampling variances of the two correlation coefficients (half sibs and full sibs) can be 

 computed fairly simply from the formulae given in section IV. Finally (V), the 

 standard errors of the correlation coefficients are the square roots of their variances. 

 Since the half-sib correlation must be multiplied by four to give an estimate of the 

 heritability, the standard error of the correlation must also be multiplied by four to 

 give the standard error of the heritability. If the heritability is estimated from the 

 full-sib correlation (which, however, is not justified in the data presented), its 

 standard error is twice the standard error of the full-sib correlation. 



The heritability estimated from the data of table 48 has a very large standard 

 error. The poor precision of this experiment was due partly to its design. There 

 were 2.6 females per male and 3.7 offspring per female. It would have been better, 

 in view of the high full-sib correlation, to have had more females per male and fewer 

 offspring per female. 



SELECTION 



Artificial selection, as a method in quantitative genetics, may be used for the 

 utilitarian purpose of producing a strain with a higher, or lower, mean expression of a 

 character ; or, alternatively, as a means of investigating the genetics of the character. 

 In both cases the interest centers on the connection between the heritability of the 

 character and the response to selection. The response to be expected can be predicted 

 from a knowledge of the heritability ; or, alternatively, the response observed can be 

 used for the estimation of the heritability. However, the words "in principle" should 

 be added to both these statements because experiments with laboratory animals have 

 shown that there is a complication, not yet fully understood, which interferes with the 

 simple theoretical relationship between heritability and response. This complication 

 will be mentioned later; meanwhile it will be ignored. 



In principle, the response expected (R) is equal to the product of the heritability 

 (A 2 ) and the selection differential (S) : 



R = h 2 S, 



