ESTIMATION OF AVERAGE DOMINANCE OF GENES 501 



Save for deviations due to natural selection, the second assumption is as- 

 sured by the fact that the population used is an F2 of a cross of homozygous 

 lines. Moreover, natural selection strong enough to have more than a trivial 

 effect on gene frequencies can only occur if the development of a moderately 

 large proportion of F2 plants is so slow or aberrant as to prevent their effec- 

 tive use as parents. Thus a good stand of usable plants constitutes insurance 

 that this assumption is satisfied. 



Number three is also assured by the origin of the populations. Multiple 

 alleles in an Fo of homozygous lines can result only from mutation, and in the 

 light of present knowledge of mutation rates would be expected very infre- 

 quently. 



On the other hand, complete validity of the fourth assumption is improb- 

 able. Present day geneticists are in general agreement that quantitative char- 

 acters, and particularly physiologically complex ones such as yield, are influ- 

 enced by many genes. If that is so, there may well be linkages among some of 

 the genes affecting any single character. Furthermore, specific linkage rela- 

 tionships in an Fi of homozygous lines must be in either the coupling or repul- 

 sion phase, and equilibrium between the phases cannot occur in the Fo. In 

 fact the approach to equilibrium in later generations is rather slow unless 

 linkage is very loose (see Wright, 1933). 



The effect of linkage is to cause upward bias in estimates of a. Thus 

 Comstock and Robinson (1948) in discussion of Experiments I and II and 

 Robinson et al. (1949) in discussing results obtained using Experiment I in- 

 dicated that values of a larger than one can result either from true overdom- 

 inance or from repulsion linkage of genes that are completely or partially 

 dominant to their alleles. The same conclusion can be inferred from Mather 

 (1949). 



The situation can be summarized in another manner by stating that values 

 of a in excess of unity do not distinguish true overdominance in the action of 

 alleles from what Mangelsdorf has termed pseudo-overdominance or over- 

 dominance at the gamete level. However, in defense of the procedures under 

 discussion, it must be emphasized that knowing one or the other of these two 

 phenomena is at work is an advance over being uncertain as to whether either 

 is operative. On the other hand there is good reason to attempt to distinguish 

 which is responsible if estimates of a by the methods described are much 

 greater than one. One source of such supplementary information is an exten- 

 sion of Experiment III to be considered briefly in the next section. 



The assumption of no epistasis is no more realistic than that of no linkages. 

 It has been pointed out (Comstock and Robinson, 1948) that epistasis prob- 

 ably causes upward bias in the estimates of a, but that the amount of bias 

 may not be large. Subsequent investigation of several simple epistatic models 

 with respect to expected values of estimates of a from Experiments I and II 

 have turned up nothing to change that ])oint of view. It must be emphasized 



