320 Forms of Reduplication 



These considerations shew that the reduplication hypothesis adequately 

 explains the occurrence of all the ratios hitherto determined. We 

 perceive too how segregation and cell-division may he associated, and 

 that these appear to be carried out symmetrically. In the complete 

 absence of reduplication there is a typical radial symmetry of the 

 segregation apparatus. When reduplication sets in, a bilateral structure 

 is developed, and this may ultimately assume quite a complex form. 

 There seems some reason, moreover, to believe that the development of 

 cells at the two ends of the same axis may be unequal. This would 

 produce a new form of symmetry — -the structure becoming two-ended, 

 enabling one to distinguish not only between different axes, but between 

 the two ends of the same axis. In such a case, with a single pair 

 of allelomorphs A, a, we should get a divergence from the gametic 

 ratio, — 1 : 1 and the normal zygotic ratio, — 1 : 2 : 1. Such divergences 

 are not infrequently met with in the literature of genetics. We may, 

 therefore, ultimately find cases of asymmetrical types of reduplication, 

 such as are represented by the ratios 



The experimental determination of such ratios would of course be 

 difficult. 



Finally let us consider the case of four or more factors A, B, C, D ... 

 with reduplication between A and B, A and C, A and D ... of the form 



M : 1 : 1 : n, m : \ : \ : in, f : \ : \ : p In addition to the derivative 



reduplication between B and C, there will be now reduplications also 

 between B and D and C and D .... 



The gametic series for four factors A, B, C and D would be 



nmpABCD + nviABCd + npABcD + «ABcd 

 -1- mpAhCD + mAbCd + yjAbcD -1- Abed 

 + aBCD -f- jiSiBCd + w^aBcD -|- w;)aBcd 

 + (iabCD + «pabCd -t- )/?;;abcD + nmpa.bcd 



and it can be shewn, by extracting, that the reduplications between B 

 and D and C and D have the form : — 



BD : Bd : bD : bd :: rip + I : n + p : n + p : np + 1, 

 CD : Cd : cD : cd :: mp + I : iii + p : in +p : mp + 1. 



