ESTIMATION OF AVERAGE DOMINANCE OF GENES 499 



and Af 22 (see Table 30.2) are equal and hence that the two mean squares may 

 be pooled.' Let the pooled mean square be symbolized by M20. Then 



(M20 - M23) / rn estimates aj = (t;^ 



and 



(M23 - M24) / r estimates aj^ 



,, 7T estimates ^ . = a- . 



M20 — M23 2w- 



Experiment III 



Following Tables 30.3 and 30.4 we see that 



(M„ — M,J /2 r estimates a^ = iSw^ 



^ 31 33 m ° 



(Afg, — M33) / r estimates a^^ = jZa^w^ 



so that 



M32— M33 .. . -2 

 ■77 —— estimates a^ 



M31 —M33 



ASSUMPTIONS 



Evaluation of procedures described above should obviously begin with 

 examination of assumptions underlying derivations of mean square expecta- 

 tions listed in Tables 30.1 to 30.3 and genetic interpretations placed on vari- 

 ance components in Table 30.4. Premises involved in the derivation of mean 

 square expectations were as follows: 



1. Random choice of individuals mated for production of ex- 

 perimental progenies. 



2. Random distribution of genotypes relative to variations 

 in environment. 



3. No non-genic maternal effects. 



The first of these can be assured easily in the conduct of the experiment. 



The second is equally easy to assure in so far as environmental variations 



within the experiment are concerned. On the other hand, the environments 



encountered in an experiment conducted within the confines of a single year 



1. By taking an unweighted mean since degrees of freedom will also be equal when 

 m = n. 



