THE MUTATED GENE 101 



reached a definite concentration at the level M. For simplicity's 



sake, we assume that the hereditary character in question is 

 the size of something, controlled by the number of cell divisions. 

 For our model we assume that the reaction in question is one that 

 stops further cell division. If the progress of cell division up to 

 this point is determined independently, the size of the organ 

 will be smaller the earlier the curve reaches the level M. If, 

 now, the cell divisions proceed in equal intervals, the hetero- 

 zygote Aa will be exactly intermediate between AA and aa. 

 Let us now suppose that the rate of cell division increases with 

 time as marked on line M. (the numbers indicate succeeding cell 

 divisions) and that the number of cell divisions alone decides the 

 size of the organ. In this case, in the heterozygote, cell division 

 ceases before six divisions have been completed, and therefore 

 the small size (.4.4) appears almost completely dominant. 

 (Stopping after five divisions characterizes A A.) If cell divi- 

 sions proceed faster at first and then slow up (line M 2 ), almost 

 complete dominance of the large size (aa = 11 steps) results. 

 Dominance in this case is then conceived as a function of the 

 following variables: the velocities of reaction controlled by the 

 main gene, the threshold concentration at which this reaction 

 leads to a morphogenetic effect, the type of effect, the numerical 

 system of the independently determined process that is involved. 

 It is clear that this simple model allows for innumerable varia- 

 tions. To mention only one, the reaction A may stop or initiate 

 or slow down or speed up cell division or growth between the 

 divisions. It is clear that this type of model may be easily 

 changed to fit any imaginable gene-controlled process; and of 

 course other variables of a rate type, threshold type, or all-or- 

 none type may be easily added to describe the most different 

 cases. 



Wright (1934d) has used the same type of reasoning but put 

 more emphasis, as Goldschmidt also originally did, on the rate 

 of reaction catalyzed by the genes in question. This means that, 

 though not neglecting the other variables of our model (Fig. 

 23), he emphasized specially the rate relations between the 

 products of dominant, heterozygous, and recessive genes, which 

 in our model have been assumed to be of a simple type. Wright's 

 deductions may therefore be added to that model as a further 

 analysis of one of its variables. Wright starts from the neces- 



