506 R. E. COMSTOCK AND H. F. ROBINSON 



and the covariance of contributions to pair means from the 1st and 2d 



loci is 



p~{jii-\-aiUi) iu2 + a2U2) / ^-\-2p r (7<i + ai«i) (02^2) /4 + . . . 



... + /- (ajWi — Ml) (a2M2 — U2) /4 — (IfXi) (2x2) . 



The algebraic reductions are tedious, particularly for the covariances, and 

 will not be written out. However, the final expressions, for both the repulsion 

 and coupling phase, are listed in Table 30.7. 



TABLE 30.7 



VARIANCES AND COVARIANCES OF SINGLE 



LOCUS CONTRIBUTIONS TO PAIR 



MEANS AND DIFFERENCES 



Note now that if the frequencies of Bi and B^ (in the population from which 

 the variable parents are taken) are symbolized as qy and q2, then 



p+ r = qi 5+/ = 1 - 9i 



P+ s = qo r + / = 1 - (/2 



(7'~.= lq.{l- q.)u'~ 



crj. = 2^.(1 - q.)ahC-. 

 Substituting in equations (1) and (2), we have 



and 



In general 

 and 





A = 



(3) 



and 



2,U, 



0-2 = 1 0-2 = 'V 0.(1 - o.) a-Ji'.-\-2y^ {pt- rs) ..a.u.a, 



> i.k 



T 



4-2^ {rs -pt) ^^a.u.a 



(4) 



k'^k 



l,k 



