Gregor Mendel - The Subsequent Generations From the Hybrids lyrics

7. The Subsequent Generations From the Hybrids The proportions in which the descendants of the hybrids develop and split up in the first and second generations presumably hold good for all subsequent progeny. Experiments 1 and 2 have already been carried through 6 generations; 3 and 7 through 5; and 4, 5, and 6 through 4; these experiments being continued from the third generation with a small number of plants, and no departure from the rule has been perceptible. The offspring of the hybrids separated in each generation in the ratio of 2:1:1 into hybrids and constant forms. If A be taken as denoting one of the two constant characters, for instance the dominant, a the recessive, and Aa the hybrid form in which both are conjoined, the expression A + 2Aa + a shows the terms in the series for the progeny of the hybrids of two differentiating characters. The observation made by Gärtner, Kölreuter, and others, that hybrids are inclined to revert to the parental forms, is also confirmed by the experiments described. It is seen that the number of the hybrids which arise from one fertilization, as compared with the number of forms which become constant, and their progeny from generation to generation, is continually diminishing, but that nevertheless they could not entirely disappear. If an average equality of fertility in all plants in all generations be a**umed, and if, furthermore, each hybrid forms seed of which one-half yields hybrids again, while the other half is constant to both characters in equal proportions, the ratio of numbers for the offspring in each generation is seen by the following summary, in which A and a denote again the two parental characters, and Aa the hybrid forms. For brevity's sake it may be a**umed that each plant in each generation furnishes only 4 seeds. Ratios Generation A Aa a A : Aa : a ---------------------------------------------------- 1 1 2 1 1 : 2 : 1 2 6 4 6 3 : 2 : 3 3 28 8 28 7 : 2 : 7 4 120 16 120 15 : 2 : 15 5 496 32 496 31 : 2 : 31 n n n 2 - 1 : 2 : 2 - 1 In the tenth generation, for instance, 2^n - 1 = 1023. There result, therefore, in each 2048 plants which arise in this generation 1023 with the constant dominant character, 1023 with the recessive character, and only two hybrids.