208 PHYSIOLOGIC GENETICS 



Table 48 



Components of variance of litter size in mice, estimated from a sib analysis 

 (Data of J. C. Bowman, unpublished) 



Mean square 

 Source d.f. Expected Observed 



W + 4.16 D + 9.75 S = 17.10 

 W + 3.48 D = 10.79 



W = 2.19 



Components: W = 2.19 



10 79 - 2 19 

 D _ 10.79^2.19 = 247 



s = 17.10 - 2.19 - (4.16 x 2.47) _ g Ag 



S + D + W = 5.14 



Correlation of half sibs = 0.48/5.14 - 0.093 ± 0.064 

 Correlation of full sibs =2.95/5.14 =0.57 ± 0.036 

 Heritability: h 2 = 4 x 0.093 = 0.37 ± 0.258 



The computation of the quantities K x , K 2 , and K 3 , which appear in the co- 

 efficients of the components in the sums of squares, need not be as troublesome as the 

 formulae given at the foot of table 46 might suggest. The computation, which is 

 illustrated numerically in table 47, may be done as follows. Tabulate the sires and the 

 dams to which each sire is mated. Against each dam tabulate the number of its off- 

 spring that were measured (k d ). Add these and tabulate the number of offspring 

 measured from each sire (k s ) . Now square each k d and enter the sum of these squares 

 obtained from each sire group as shown under 2 kd 2 m tne table. This gives every- 

 thing needed for the computation of the three K's ; the computations are shown at the 

 right-hand side of table 47. The coefficients of the components in the sums of squares 

 and mean squares can now be entered, and these are shown at the foot of table 47. 

 An example to show the solution of the equations with real data is given in table 48. 



The sib correlations are obtained from the components of variance as follows : 



S 



Correlation of half sibs = 

 Correlation of full sibs = 



S + D + W 

 S + D 



S + D + W 



The estimate of the heritability is four times the correlation of half sibs. If the 

 component of variance between dams (D) is not greater than the component between 

 sires (S), then there is no evidence that the full-sib correlation has been augmented by 

 nonadditive variance or by nongenetic causes of resemblance. If this is the case, then 

 the full-sib correlation provides the more reliable estimate of the heritability. The 

 heritability is twice the full-sib correlation. 



