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



that the matter has not been considered exhaustively, and the possibility 

 remains that in some materials epistasis would be responsible for serious 

 overestimation of a by the methods being discussed. 



The authors' knowledge of the situation may be summarized briefly as 

 follows. It appears possible that with complete dominance the rule, a = 1.0, 

 epistasis might bias estimates upwards by as much as .10 to .25. This cannot 

 be considered serious against the background of an actual estimate of 1.6 as 

 reported for grain yield in corn by Robinson et al. (1949). On the other hand, 

 genetic models can be specified in which the consequences of epistasis would 

 be serious, but to date no such models have been discovered that seem likely 

 to have reality in nature. 



Much investigation of the epistasis problem remains to be done. Theoreti- 

 cal studies of a variety of epistatic models are needed as a basis for under- 

 standing (1) how and to what extent inferences based on expectations de- 

 rived from non-epistatic models may be in error, and (2) how epistasis may 

 be measured and characterized experimentally. Equally important are ex- 

 perimental investigations of the role of epistasis in inheritance of quantita- 

 tive characters of various organisms. The problem in this connection is one 

 of knowing how to obtain critical information. The most familiar approach is 

 that of studying the regression of character measurements on levels of 

 homozygosity as represented at the extremes by inbred lines and Fi's and at 

 intermediate levels by Fa's and various sorts of backcrosses. While this ap- 

 proach has admitted shortcomings, it has not been exploited to the limit of its 

 usefulness. Other possibilities are suggested by Mather (1949). 



EVALUATION OF THE ROLE OF LINKAGE 



It was pointed out above that repulsion linkages are a source of upward 

 bias in estimates of a. In fact if a moderately high number of genes is postu- 

 lated, one finds on careful examination that estimates in excess of one seem 

 inevitable unless dominance at the locus level is considerably less than com- 

 plete. From the point of view of breeding methods it then becomes important 

 to distinguish between true overdominance and pseudo-overdominance. Par- 

 ticularly is this true if the latter is to any important degree a consequence 

 of linkages that are loose enough to allow their effects to be dissipated by 

 recombination in a few generations of random breeding, as opposed to the 

 rather durable associations that appear to be postulated by Anderson (1949). 



If the assumption that frequencies of genes at all segregating loci are one- 

 half were tenable for generations beyond the F2, any of the three experiments 

 would provide a basis for obtaining information on the role of linkage. The 

 procedure would be to compare estimates obtained as described with others 

 obtained when parents were taken from an advanced generation (produced 

 under random mating, not with inbreeding) rather than from the F2. In fact 

 one might systematically repeat the experiment using each successive genera- 



