ESTIMATION OF AVERAGE DOMINANCE OF GENES 505 



where alj is the variance of contributions from thejth locus to pair means, 



(Txjk is the covariance of contributions from the _;th and ^th loci to pair 

 means, 



alj is the variance of contributions from thej'th locus to pair diflferences, 



crljk is the covariance of contributions from they'th and ^th loci to pair dif- 

 ferences, and 2^ indicates summation over all pairs of loci. 



;, k 



From equations (1) and (2) it is apparent that general expressions for al^ and 

 alti can be written as soon as we know (i) the variance of contributions of 

 any single locus to pair means and differences, and (ii) the covariance of con- 

 tributions of any two loci to pair means and differences. 



With respect to two loci, there will be ten types of variable parent (when 

 classification is by types of gametes giving rise to the parent plant). Table 

 30.6 lists these, together with their frequencies in the population and the 



TABLE 30.6 



FREQUENCIES OF VARIABLE PARENT TYPES AND CONTRI- 

 BUTIONS* OF INDIVID U.\L LOCI TO EXPECTED 

 GENETIC V.-VLUES OF PROGENIES 



* Coded by subtraction of mi + =i (or m -\- zi) where z is the contribution Irom the locus when homozygous 

 for the b allele. 



t On the basis that frequencies in which BiBi, Bibi, biBt, and bibi gametes are produced in the generation 

 preceding that used for variable parents are p, r, s, and t, respectively, p + r -{■ s + t = 1.0. 



t For ease of printing, subscripts to a and « are omitted in rows beyond the first. However, the subscript 

 used in the first row of each column applies throughout the column. 



contributions of the two loci to the expected genetic values of progenies and 

 to pair means and differences. As is evident from genotypes indicated for the 

 homozygous lines, the initial linkage phase assumed is repulsion. The re- 

 quired variances and co variances can be worked out directly from informa- 

 tion in the table. For example, the variance of contributions from the Lst 

 locus to pair means is 



(p-ij^2pr+ r^) (u^ + a^u^) y i -{- (Ip s -{- 2pt -\- 2 r s + 2 rt) a\ul/ 4 



+ (5'^ + 2 5/ + /'^)(aiMi-Mi)V4- (2x,)2 



