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



and location do not constitute a random sample of the environments that 

 occur within the wider limits of time and space for which we would like ex- 

 perimental findings to apply. The consequence of this is that, if interaction of 

 genotype with environment is a source of variation, each mean square arising 

 from variation among progenies will contain some variance from such inter- 

 action. Thus, to have been rigorously correct, the expectations of all mean 

 squares between progenies should have included terms recognizing contribu- 

 tions from this source. Separate estimation of the genetic and interaction 

 components of mean squares between progenies could not be effected with 

 data collected in a single year and location. If the ratio of these two sorts of 

 variance is constant for the several mean squares, and there is no obvious 

 reason why it should vary, the presence of interaction variance does not bias 

 the estimates of a^ since numerator and denominator are affected propor- 

 tionately. Nevertheless this constitutes a possible weakness of the methods 

 but one which, if important, can be corrected by replication of all progenies 

 over years and locations. 



There are many characters and organisms for which it appears safe to 

 assume maternal affects are absent or of no consequence. This assumption 

 must be viewed with some suspicion when dealing with seedling characters 

 of plants or any character for which there is any hint that cytoplasmic in- 

 heritance may be operating, and it is definitely not tenable for pre-maturity 

 characters of mammals. Maternal effects do not contribute to the pertinent 

 mean squares in the variance analysis of Experiment III and only to M22 in 

 that of Experiment II. Thus these two experiments are useful in the presence 

 of maternal effects, though if II is used 2«^ must be estimated from M21 

 instead of jointly from Mi\ and M^i- 



Assumptions involved in deriving the genetic interpretations of variance 

 components are as follows: 



1. Regular diploid behavior at meiosis. 



2. Population gene frequencies of one-half at all loci where 

 there is segregation (not necessary for Experiment III). 



3. No multiple allelism. 



4. No correlation of genotypes at separate loci. This implies 

 no linkage among genes affecting the character studied or that, 

 if linkages exist, the distribution of genotypes is at equilibrium 

 with respect to coupling and repulsion phases. 



5. No epistasis, i.e., the effect of variation in genotype at any 

 single locus is not modiiied by genes at other loci. 



In accord with the first of these, usefulness of the procedures described is 

 limited to studies with diploids or amphidiploids in which multivalent meiotic 

 associations are entirely absent or are absent in meiotic divisions giving rise 

 to fertile gametes. 



