Heredity of Blood Type in Man

Chapter III. Numerical Observation on Various Hypotheses of Inheritance of Human Blood Types

Abstract

Generally in a group of individuals who have continuous fertilization from other families, the frequency of the gametes is regulated, as a matter of course, and consequently the frequency of zygotes is regulated throughout many generations, once the proportion of gametes has reached a certain point of equilibrium. But it is evident that so long as the frequency of gametes has not reached a state of equilibrium, changes take place according to the generation. It is appropriate, in my opinion, to consider that the frequency of the blood types in the gametes in the present generation is in a transition stage on the way toward a point of equilibrium.
If my hypothesis is adopted, the frequency of the four kinds of gametes can be calculated by the following formulae. The respective frequency is represented by ab......R, Ab......P, aB......Q, AB......Z.
R=√O
Z=1-√O+a+B+AB+× 2n+2/2n+3
P=1/2{√A+O-√O+1-(√B+O+1-√O+a+B+AB+× 2n+2/2n+3)}
Q=1/2{√B+O-√O+1-(√B+O+1-√O+a+B+AB+× 2n+2/2n+3)}
When the theoretical rate of distribution of the blood type of masses and the actual rate are compared by ealculating the frequency of the gametes after the priciple of each of the hypotheses above-mentioned, it can be seen that the numerical value obtained by my method fits the facts better than that obtained by other hypotheses. Moreover, when the frequency of each hereditary type is calculated from the frequency of the respective gametes, and the anticipated division among the children of the next generation is observed comparatively and statistically, entire agreement between the anticipated division and the actual fact can be found by my hypothesis and not by any other, in the case of coupling when the parents are of the O, A and B types. But in the case of coupling when the parents are of the AB type, 2 pair allelomorphism has, as shown in the following table, a qualitative agreement, but a marked quantitative disparity. If the hypothesis of 3-multiple allelomorphism is adopted, somewhat quantitative approximation can be shown, but the result is quite opposite qualitatively. When my hypothesis is adopted, however, complete harmony is recognized between theory and fact both quantitatively and qualitatively.