ESTIMATION OF AVERAGE DOMINANCE OF GENES 509 



Substituting these and the numerical values of the a's and 7<'s, we find 



Locus Linkage 



Pair Phase (pt — rs)UiUk (pt — rs)aiUiakUk {rs — pt)aiUjakUk 



1 and 2 Repulsion -.2 .0720 



3 and 4 Coupling .3 .1920 



5 and 6 Coupling . 4 . 3200 



5 and 7 Repulsion -.15 .0960 



6 and 7 Repulsion -.40 .3200 



.05 .5120 .4880 



With these three sums and the values found above for \'^q{\ — q)u- and 

 2^(1 — q)a~u^ we compute 



ct2 = 2.00+ ( -.05) = 1.95 



and 



Thus, while 



(T^^^^ = 2.57 + 2 (.5 12) +2 (.488) =4.5 7 



., ^ Sa^^ ^ ^^7_ ^ 

 '^' 2m2 2(2.0) 



the experiment would estimate 



flnj_ ^ _Jj^i_ =11- 

 2(t2 2 (1.95) • ' ■ 



Put differently, the estimate of a^ provided by Experiment III would in this 

 case have positive bias in the amount 1.17 — .64 = .53. 



The foregoing example is given only to clarify the meaning of the formulae, 

 not to suggest the amount of bias that may actually be present in practice. 

 The actual bias with any specific material would depend on the amount of 

 linkage and the relative prevalence of coupling and repulsion phases. How- 

 ever, the bias can only be positive and may range from a negligible to a large 

 amount depending on the prevalence of repulsion linkage. While such bias 

 detracts from the described estimate as a criterion of average dominance at 

 the locus level, it is worth emphasizing that it represents a pseudo-overdomi- 

 nance effect which if persistent (due to closeness of linkages responsible) has 

 much the same significance for short-run breeding practice as true overdomi- 

 nance. If the bias declines fairly rapidly as opportunity is provided for re- 

 combination, Experiment III offers a means of measuring that decline and 

 thereby gaining an idea of the extent to which apparent dominance stems 

 from linkage relationships that are loose enough to allow a near approach to 

 equilibrium of linkage phases within a moderate number of generations. 



AMOUNT OF DATA REQUIRED 



An exhaustive consideration of this problem would require more space 

 than can be devoted to it here. Detailed discussion will therefore be limited 

 to one specific question. Let P symbolize the probability of an estimate of a 



