458 FRED H. HULL 



In the current sense that any interaction of alleles is dominance, aA > AA 

 is overcomplete dominance, overdominance. In a similar sense all inter- 

 actions of non-alleles are epistasis. Dominance and epistasis differ in dis- 

 tribution on chromosomes, but not necessarily in underlying physiology so 

 far as I can see. Overepistasis would excite no particular comment. 



Dominance and epistasis are no more fundamental properties of genes than 

 is interaction a property of a unit of nitrogen or phosphorus. These fertilizer 

 elements may exhibit an interaction in plant growth if made available to a 

 living plant, or they may seem to act independently. One quantity of nitro- 

 gen may be adequate for the needs of the plant. Adding the same quantity 

 again may produce no further effect. There is an interference or decreasing 

 returns interaction. 



East (1936) has discussed dominance as a decreasing returns or interfer- 

 ence interaction of active alleles Ai and Ai in the homozygote. The amount 

 by which the two together failed to do twice as much as either alone was a the 

 dominance effect — a loss which could not explain heterosis. East then pro- 

 posed that if Ai should develop by successive steps to ^44 (analogous to re- 

 placing successive parts of one bag of nitrogen above with phosphorus until 

 there is one of phosphorus and one of nitrogen) of a different quality, Ai and 

 ^4 might interfere very little or none in ^1^44. The principle as East states it 

 is: "The cumulative action of the non-defective allelomorphs of a given gene 

 approaches the strictly additive as they diverge from each other in function." 



The effect of the phosphorus and nitrogen together is the sum of their 

 separate effects — no interference. Dominance by interference disappears 

 when Ai and ^44 are independent in functions, leaving yl 1^4 superior to either 

 AiAi or .44.44. Now it must be clear that any deviation of AiAi from the 

 mid-point between the two homozygotes must be interpreted as dominance 

 of ^ito .4 4 for the .4 1 functionor dominanceof .44to^4ifor the.44 function or 

 both. If the primary dominance in each case is complete, .4i.4 4 will just equal 

 the sum of .4i.4i and .44.44 in total effect beyond a neutral aa. 



Overdominance may occur when: (1) aa is neutral and aA is nearer to an 

 optimum dose of A than is AA, (2) A' and A are both active for separate 

 supplementary functions and each is dominant to the other for its own 

 function (cf. East, 1936), (3) A' and A are both active for separate primary 

 functions, and the primary functions interact to produce an effect greater 

 than those of either A'A' or AA (Hull, 1945a). 



Pseudo-overdominance may occur when A and B are linked: (1) with no 

 epistasis, aB and Ab combinations simulate the second case above, (2) with 

 positive epistasis aB and Ab simulate the third case. 



If {aB X Ab) is superior to both (ab X AB) and (AB X AB), selection 

 may tend to tighten the repulsion linkage until ab and AB disappear and the 

 paired blocks are hardly distinguishable from alleles with primary over- 

 dominance. 



It is clear enough that the frequency of heterozygotes is greater and of 



