Heredity, race, and society.

  • Dunn, L. C. (Leslie Clarence), 1893-1974.
Date:
1947
Catalogue details

Licence: Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)

Credit: Heredity, race, and society. Source: Wellcome Collection.

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    that the proportions of a pair of genes will remain constant regardless of what the proportion is. Suppose, for example, that the original pool consisted of 90 per cent T and 10 per cent t sex cells. If % 0 of the sex cells have T and y i0 have t, then when we draw them out two at a time, each T will have nine chances of meeting a T and one chance of meeting a t; each t will also have nine chances of meeting a T to one chance of meeting a t. Therefore 81 per cent (9 times 9) of all combina tions, thence of all people arising from such fertilized eggs, will have two T genes; 18 per cent (9 times 1 taken twice) wijl have a T and a t, and one per cent (one times one) will have two t genes. The generation arising from such random mating will therefore consist of: If each of these contributes two genes to the poo! from which the genes of the next generation will be drawn, the pure tasters will contribute 162 T sex cells, the hybrid tasters 18 T and 18 t sex cells, and the non- tasters 2 t sex cells. The totals are 180 T and 20 t or a ratio of 90 per cent T to 10 per cent t. Since this is the same as the original proportion, the second and all following generations will continue to have 99 per cent of tasters and 1 per cent of non-tasters. The proportions of the genes will remain constant indefinitely regardless of what their original propor tions may be. For those who are not afraid of first year algebra, here is the proof of this statement. Suppose that a fraction q of the sex- cells of the original settlers carry the gene T, and a fraction (l-q) the gene t. The first generation of islanders will, then, consist of: q 2 TT -j- 2q (l-q) Tt -{- (l-q) 2 tt — 1. The pool of sex cells of the next generation will contain q 2 -\- q (l-q) = q cells with T, and q (l-q) -f- (1-q) 2 = (l-q) cells with t. Obvi ously, the relative frequencies of T and t remain con stant. Using the proportions of tasters and non-tasters in the United States 70 per cent to 30 per cent, we can 81 per cent 18 per cent 1 per cent tt tasters non-tasters