The ratio of 3 to 1, in accordance with which the distribution of the dominant and recessive characters results in the first generation, resolves itself therefore in all experiments into the ratio of 2 : 1 : 1 if the dominant character be differentiated according to its significance as a hybrid character or a parental one. Since the members of the first generation spring directly from the seed of the hybrids, it is now clear that the hybrids form seeds having one or other of the two differentiating characters, and of these one-half develop again the hybrid form, while the other half yield plants which remain constant and receive the dominant or recessive characters [respectively] in equal numbers.
The Subsequent Generations [Bred] 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 six generations, 3 and 7 through five, and 4, 5, and 6 through four, 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 fertilisation, 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 assumed, 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 assumed 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 |
| 2n-1 | : | 2 | : | 2n-1 | ||
In the tenth generation, for instance, 2n-1 = 1023. There result, therefore, in each 2,048 plants which arise in this generation 1,023 with the constant dominant character, 1,023 with the recessive character, and only two hybrids.