. Journal of genetics. e form M : 1 : 1 : n, m : \ : \ : in, f : \ : \ : p In addition to the derivative reduplication between B and C, there will be now reduplications alsobetween 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 + and it can be shewn, by extracting, that the reduplications between Band 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 :
. Journal of genetics. e form M : 1 : 1 : n, m : \ : \ : in, f : \ : \ : p In addition to the derivative reduplication between B and C, there will be now reduplications alsobetween 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 + and it can be shewn, by extracting, that the reduplications between Band 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. A. H. Trow 321 This result may be reached more easily by making use of the generalformula on p. 319. For if AB : Ab : aB : ab :: n : 1 : 1 : n, and AD : Ad : aD : ad :: p : 1 : 1 : p, then BD : Bd : bD : bd :: np + 1 : n+p +p: np + 1. Any number of derivative ratios may be ascertained in the same way bythis method. This more complex case may be represented graphically thus:— «mpABCD. m aBcD m^;aBcd nm/j abed According to this scheme of segregation (which however must notbe regarded as the only possible one), each additional factor (or pair ofallelomorphs) Ee, Ff, Gg, etc. will necessitate a further dichotomy ofeach branch. If these additional branches are equally developed it canreadily be shewn that reduplication does not take place. We have theimportant rule that equal dichotomies produce normal segregation;uneipial dichotomies produce reduplications. These two types of behaviourmay occur in any order or at any stage in the phylogeny, but asBateson and Punnett have already stated, they cannot occur simul-taneously. 322 Forms of Beduplieafion There seems to be no reason why the most various types of re-duplication should not occur together in the same plant as the result ofthe same cross. The hypothesis of reduplication seems adequate toexplain the occurrence of any type of ratio. The most suggestive point which emerges from the analysis is
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