206 PHYSIOLOGIC GENETICS 



out with laboratory mammals. And, furthermore, the estimation of heritability is 

 not the only interest in a sib analysis. The correlation between full sibs is also of 

 interest, because, when compared with the half-sib correlation, it shows how important 

 nongenetic causes of resemblance between progeny of the same mother are. It would 

 therefore seem desirable to sacrifice some precision in the estimate of heritability in 

 order to have a more convenient design and to obtain the additional information 

 about full sibs. To include full sibs within the half-sib families it is only necessary 

 to measure more than one offspring from each mother. The optimal design is then 

 more complicated and must necessarily be a compromise. 1061 If it is desired to estimate 

 the full-sib and the half-sib correlations with equal precision, and if the full-sib 

 correlation is not augmented by maternal effects, then each male should be mated 

 to three or four females, and between 5 and 10 offspring from each female should be 

 measured. If, however, the full-sib correlation is augmented by maternal effects, 

 then it is better to have more females mated to each male and fewer offspring from 

 each female. 



The computation of the heritability from data obtained in this way needs some 

 explanation. The computation consists of an analysis of variance leading to the 

 estimation of three components of variance, attributable to sires, to dams, and to 

 individuals. The correlations are estimated from these components. Sums of squares 

 are computed in the usual way for the following sources of variation : 



between sires (that is, between half-sib families) ; 



between dams within sires (that is, between full-sib families within half-sib 

 families) ; 



within dams (that is, among individuals within full-sib families). 

 The computation of the three components corresponding to these sources of variation 

 is straightforward if all dams have the same number of offspring and all sires are mated 

 to the same number of dams. 1230 But equality of numbers is seldom achieved and a 

 modification of the procedure is required. The procedure will be described without ex- 

 plaining the reasons for it. A full explanation is given by King and Henderson. 710 The 

 sums of squares are composed of the three components in certain proportions which de- 

 pend on the distribution of numbers within the classes and subclasses. These expected 

 compositions of the sums of squares are given in table 46. It will be seen that each com- 

 ponent appears with a certain coefficient which is some function of the numbers. By 

 computing these coefficients and equating the expected composition to the observed 

 value of each sum of squares, three equations containing three unknowns are obtained. 

 (The sum of squares for the total is entered in the table only for the sake of complete- 

 ness; it is not required.) The coefficient of the within-dam component, W, in each 

 sum of squares is equal to the number of degrees of freedom corresponding to that 

 source of variation. The first step in the solution of the equations is therefore to divide 

 each sum of squares, both expected and observed, by the appropriate degrees of free- 

 dom, and so obtain the expected and observed mean squares. The solution of the 

 equation is then straightforward. 



