General hæmatology : with special reference to the child in health and disease / by W.M. Feldman.

  • Feldman, W. M. (William Moses), 1879-1939.
Date:
1933
Catalogue details

Licence: In copyright

Credit: General hæmatology : with special reference to the child in health and disease / by W.M. Feldman. Source: Wellcome Collection.

    101/114 (page 87)
    • p = V7O -f A — r, = VO -f A —(1 — p — q), since p + q + r = 1. Whence, q = 1 — V O + A ]_ Similarly, p = 1 — VO ) ^See Further, from O = r2, we get r = V O. The formulae also enable us to compute the theo¬ retical frequencies of the two other groups, if those of Group O and either of Group A or of Group B are known. Thus, using the figures on p. 69, for Groups O and A, viz., 0-45 and 0-40 respectively, we get r = v7 0-45 = 0-67. But q = 1 — ^O + A = 1 — V0-85 = 1—0-92 = 0-08. But p = 1 — (q + r), p = 1 — (0-08 + 0-67) = 0-25. Hence frequency of Group B which = q2 + 2qr = 0-0064 -f 2 x 0-08 x 0-67 = 0-11, i.e., 11 per cent., which agrees well with the 10 per cent, given in the table on p. 69. Also AB = 2pq = 2 X 0-25 X 0-8 = 0-4, i.e., 4 per cent., which agrees equally well with the 5 per cent, given in the table. Indeed, the figures in the table only represent the actual observed values in round numbers. In actual fact the observed frequencies found from an examination of 20,000 cases are : Group O = 45 per cent, Group A = 41 per cent ., Group B = 10 per cent., Group AB = 4 per cent. Hence, these formulae, in addition to enabling us to calculate group frequencies, afford the strongest possible evidence not only of the hereditability of the group factors, but also of the particular manner in which they are transmitted. Indeed, von Dungern and Hirszfeld first suggested that the number of trans¬ missible group factors were not three (viz., A, B, and O), but two (viz., A and B), which were dominant to the characters a and b. On the basis of such an hypothesis we get the following calculation :— If p and q are the respective frequencies of the factors A and B, and r and s those of a and b, then