QUANTITATIVE INHERITANCE 



207 



Table 46 



Estimation of components of variance from a sib analysis with unequal 

 numbers in the families 



Source of variation 



Degrees of freedom 



Expected composition of sums of 

 squares 



Total 



Between sires 

 Between dams 

 (within sires) 

 Within dams 



N - 1 

 m — \ 



N - n 



(N - \)W + (N - KJD + (N - K 2 )S 

 (m - \)W + (K 3 - K X )D + (N - K 2 )S 

 (n - m)W + (N - K 3 )D 



(N - n)W 



S = Component of variance attributable to sires. 

 D = Component of variance attributable to dams. 



W = Component of variance attributable to individuals within full-sib families. 

 N = Total number of offspring. 



n = Total number of dams (full-sib families). 

 m = Number of sires (half-sib families). 

 k d = Number of offspring of any one dam. 

 k s — Number of offspring of any one sire. 



I k\ v _ I k\ r _ V 2 * 2 <*t 



A-i - 



Ko 



*3=2 



TV "* N "° £- k s 



f This means: compute 2 k? d jk s for each sire group and then sum over all sire groups. 



Table 47 



Numerical example of the computation of the coefficients of the components of 

 variance in a sib analysis with unequal numbers in the families 



