Scheme of inheritance in the cross of tall with dwarf pea. Gametes represented by small and zygotes by larger circles.
We may now proceed with the help of the accompanying scheme (Fig. 1) to deduce the results that should flow from Mendel's conception of the nature of the gametes, and to see how far they are in accordance with the facts. Since the original tall plant belonged to a strain which bred true, all the gametes produced by it must bear the tall character. Similarly all the gametes of the original dwarf plant must bear the dwarf character. A cross between these two means the union of
a gamete containing tallness with one bearing dwarfness. Owing to the completely dominant nature of the tall character, such a plant is in appearance indistinguishable from the pure tall, but it differs markedly from it in the nature of the gametes to which it gives rise. When the formation of the gametes occurs, the elements representing dwarfness and tallness segregate from one another, so that half of the gametes produced contain the one, and half contain the other of these two elements. For on hypothesis every gamete must be pure for one or other of these two characters. And this is true for the ovules as well as for the pollen grains. Such hybrid F1 plants, therefore, must produce a series of ovules consisting of those bearing tallness and those bearing dwarfness, and must produce them in equal numbers. And similarly for the pollen grains. We may now calculate what should happen when such a series of pollen grains meets such a series of ovules, i.e. the nature of the generation that should be produced when the hybrid is allowed to fertilise itself. Let us suppose that there are 4x ovules so that 2x are "tall" and 2x are "dwarf." These are brought in contact with a mass of pollen grains of which half are "tall" and half are "dwarf." It is obvious that a "tall" ovule has an equal chance of being fertilised by a "tall" or a "dwarf" pollen grain. Hence of our 2x "tall" ovules, x will be fertilised by "tall" pollen grains and x will be fertilised by "dwarf" pollen grains. The former must give rise to tall
plants, and since the dwarf character has been entirely eliminated from them they must in the future breed true. The latter must also give rise to tall plants, but since they carry also the recessive dwarf character they must when bred from produce both tails and dwarfs. Each of the 2x dwarf ovules, again, has an equal chance of being fertilised by a "tall" or by a "dwarf" pollen grain. Hence x will give rise to tall plants carrying the recessive dwarf character, while x will produce plants from which the tall character has been eliminated, i.e. to pure recessive dwarfs. Consequently from the 4x ovules of the self-fertilised hybrid we ought to obtain 3x tall and x dwarf plants. And of the 3x talls x should breed true to tallness, while the remaining 2x, having been formed like the original hybrid by the union of a "tall" and a "dwarf" gamete, ought to behave like it when bred from and give talls and dwarfs in the ratio 3 : 1. Now this is precisely the result actually obtained by experiment (cf. p. [17]), and the close accord of the experimental results with those deduced on the assumption of the purity of the gametes as enunciated by Mendel affords the strongest of arguments for regarding the nature of the gametes and their relation to the characters of the zygotes in the way that he has done.
It is possible to put the theory to a further test. The explanation of the 3 : 1 ratio of dominants and recessives in the F2 generation is regarded as due to the F1 individuals producing equal numbers of gametes bearing the
dominant and recessive elements respectively. If now the F1 plant be crossed with the pure recessive, we are bringing together a series of gametes consisting of equal numbers of dominants and recessives with a series consisting solely of recessives. We ought from such a cross to obtain equal numbers of dominant and recessive individuals, and further, the dominants so produced ought all to give both dominants and recessives in the ratio 3 : 1 when they themselves are bred from. Both of these expectations were amply confirmed by experiment, and crossing with the recessive is now a recognised way of testing whether a plant or animal bearing a dominant character is a pure dominant, or an impure dominant which is carrying the recessive character. In the former case the offspring will be all of the dominant form, while in the latter they will consist on the average of equal numbers of dominants and recessives.
So far we have been concerned with the results obtained when two individuals differing in a single pair of characters are crossed together and with the interpretation of those results. But Mendel also used plants which differed in more than a single pair of differentiating characters. In such cases he found that each pair of characters followed the same definite rule, but that the inheritance of each pair was absolutely independent of the other. Thus, for example, when a tall plant bearing coloured flowers was crossed with a dwarf plant
bearing white flowers the resulting hybrid was a tall plant with coloured flowers. For coloured flowers are dominant to white, and tallness is dominant to dwarfness. In the succeeding generation there are plants with coloured flowers and plants with white flowers in the proportion of 3 : 1, and at the same time tall plants and dwarf plants in the same proportion. Hence the chances that a tall plant will have coloured flowers are three times as great as its chance of having white flowers. And this is also true for the dwarf plants. As the result of this cross, therefore, we should expect an F2 generation consisting of four classes, viz. coloured talls, white talls, coloured dwarfs, and white dwarfs, and we should further expect these four forms to appear in the ratio of 9 coloured talls, 3 white talls, 3 coloured dwarfs, and 1 white dwarf. For this is the only ratio which satisfies the conditions that the talls should be to the dwarfs as 3 : 1, and at the same time the coloured should be to the whites as 3 : 1. And these are the proportions that Mendel found to obtain actually in his experiments. Put in a more general form, it may be stated that when two individuals are crossed which differ in two pairs of differentiating characters the hybrids (F1) are all of the same form, exhibiting the dominant character of each of the two pairs, while the F2 generation produced by such hybrids consists on the average of 9 showing both dominants, 3 showing one dominant and one recessive,
3 showing the other dominant and the other recessive, and 1 showing both recessive characters. And, as Mendel pointed out, the principle may be extended indefinitely. If, for example, the parents differ in three pair of characters A, B, and C, respectively dominant to a, b, and c, the F1 individuals will be all of the form ABC, while the F2 generation will consists of 27 ABC, 9 ABc, 9 AbC, 9 aBC, 3 Abc, 3 aBc, 3 abC, and 1 abc. When individuals differing in a number of alternative characters are crossed together, the hybrid generation, provided that the original parents were of pure strains, consists of plants of the same form; but when these are bred from a redistribution of the various characters occurs. That redistribution follows the same definite rule for each character, and if the constitution of the original parents be known, the nature of the F2 generation, i.e. the number of possible forms and the proportions in which they occur, can be readily calculated. Moreover, as Mendel showed, we can calculate also the chances of any given form breeding true. To this point, however, we shall return later.