CHAPTER IX
REPULSION AND COUPLING OF FACTORS
Although different factors may act together to produce specific results in the zygote through their interaction, yet in all the cases we have hitherto considered the heredity of each of the different factors is entirely independent. The interaction of the factors affects the characters of the zygote, but makes no difference to the distribution of the separate factors, which is always in strict accordance with the ordinary Mendelian scheme. Each factor in this respect behaves as though the other were not present.
A few cases have been worked out in which the distribution of the different factors to the gametes is affected by their simultaneous presence in the zygote. And the influence which they are able to exert upon one another in such cases is of two kinds. They may repel one another, refusing, as it were, to enter into the same zygote, or they may attract one another, and, becoming linked together, pass into the same gamete, as it were by preference. For the moment we may consider these two sets of phenomena apart.
One of the best illustrations of repulsion between factors occurs in the sweet pea. We have already seen that the loss of the blue or purple factor (B) from the wild bicolor results in the formation of the red bicolor known as Painted Lady (Pl. IV., 7). Further, we have seen that the hooded standard is recessive to the ordinary erect standard. The omission of the factor for the erect standard (E) from the purple bicolor (Pl. II., 5) results in a hooded purple known as Duke of Westminster (Pl. II., 7). And here it should be mentioned that in the corresponding hooded forms the difference in colour between the wings and standard is not nearly so marked as in the forms with the erect standard, but the difference in structure appears to affect the colour, which becomes nearly uniform. This may be readily seen by comparing the picture of the purple bicolor on Plate II. with that of the Duke of Westminster flower.
Now when a Duke of Westminster is mated with a Painted Lady the factor for erect standard (E) is brought in by the red, and that for blue (B) by the Duke, and the offspring are consequently all purple bicolors. Purples so formed are all heterozygous for these two factors, and were the case a simple one, such as those which have already been discussed, we should expect the F2 generation to consist of the four forms: erect purple, hooded purple, erect red, and hooded red in the ratio 9 : 3 : 3 : 1. Such, however, is not the case. The F2 generation
actually consists of only three forms, viz. erect red, erect purple, and hooded purple, and the ratio in which these three forms occur is 1 : 2 : 1. No hooded red has been known to occur in such a family. Moreover further breeding shows that while the erect reds and the hooded purples always breed true, the erect purples in such families never breed true, but always behave like the original F1 plant, giving the three forms again in the ratio 1 : 2 : 1. Yet we know that there is no difficulty in getting purple bicolors to breed true from other families; and we know also that hooded red sweet peas exist in other strains.
On the assumption that there exists a repulsion between the factors for erect standard and blue in a plant which is heterozygous for both, this peculiar case receives a simple explanation. The constitutions of the erect red and the hooded purple are EEbb and eeBB respectively and that of the F1 erect purple is EeBb. Now let us suppose that in such a zygote there exists a repulsion
between E and B, such that when the plant forms gametes these two factors will not go into the same gamete. On this view it can only form two kinds of gametes, viz. Eb and eB, and these, of course, will be formed in equal numbers. Such a plant on self-fertilisation must give the zygotic series EEbb + 2 EeBb + eeBB, i.e. 1 erect red, 2 erect purples, and 1 hooded purple. And because the erect reds and the hooded purples are respectively homozygous for E and B, they must thenceforward breed true. The erect purples, on the other hand, being always formed by the union of a gamete Eb with a gamete eB, are always heterozygous for both of these factors. They can, consequently, never breed true, but must always give erect reds, erect purples, and hooded purples in the ratio 1 : 2 : 1. The experimental facts are readily explained on the assumption of repulsion between the two
factors B and E during the formation of the gametes in a plant which is heterozygous for both.
Other similar cases of factorial repulsion have been demonstrated in the sweet pea, and two of these are also concerned with the two factors with which we have just been dealing. Two distinct varieties of pollen grains occur in this species, viz. the ordinary oblong form and a rather smaller rounded grain. The former is dominant to the latter.[[7]] When a cross is made between a purple with round pollen and a red with long pollen the F1 plant is a long pollened purple. But the F2 generation consists of purples with round pollen, purples with long pollen, and reds with long pollen in the ratio 1 : 2 : 1. No red with round pollen appears in F2 owing to repulsion between the factors for purple (B) and for long pollen (L). Similarly plants produced by crossing a red hooded long with a red round having an erect standard give in F1 long pollened reds with an erect standard, and these in F2 produce the three types, round pollened erect, long pollened erect, and long pollened hooded, in the ratio 1 : 2 : 1. The repulsion here is between the long pollen factor (L) and the factor for the erect standard (E).
Yet another similar case is known in which we are concerned with quite different factors. In some sweet peas the axils whence the leaves and flower stalks spring from the main stem are of a deep red colour. In others they are green. The dark pigmented axil is dominant to the light one. Again, in some sweet peas the anthers are sterile, setting no pollen, and this condition is recessive to the ordinary fertile condition. When a sterile plant with a dark axil is crossed by a fertile plant with a light axil, the F1 plants are all fertile with dark axils. But such plants in F2 give fertiles with light axils, fertiles with dark axils, and steriles with dark axils in the ratio 1 : 2 : 1. No light axilled steriles appear from such a cross owing to the repulsion between the factor for dark axil (D) and that for the fertile anther (F).
These four cases have already been found in the sweet pea, and similar phenomena have been met with by Gregory in primulas. To certain seemingly analogous cases in animals where sex is concerned we shall refer later.
Now all of these four cases present a common feature which probably has not escaped the attention of the reader. In all of them the original cross was such as to introduce one of the repelling factors with each of the two parents. If we denote our two factors by A and B, the crosses have always been of the nature AAbb × aaBB. Let us now consider what happens when both of the
factors, which in these cases repel one another, are introduced by one of the parents, and neither by the other parent. And in particular we will take the case in which we are concerned with purple and red flower colour, and with long and round pollen, i.e. with the factors B and L. When a purple long (BBLL) is crossed with a red round (bbll) the F1 (BbLl) is a purple with long pollen, identical in appearance with that produced by crossing the long pollened red with the round pollened purple. But the nature of the F2 generation is in some respects very different. The ratio of purples to reds and of longs to rounds is in each case 3 : 1, as before. But instead of an association between the red and the long pollen characters the reverse is the case. The long pollen character is now associated with purple and the round pollen with red. The association, however, is not quite complete, and the examination of a large quantity of similarly bred material shows that the purple longs are about twelve times as numerous as the purple rounds, while the red rounds are rather more than three times as many as the red longs. Now this peculiar result could be brought about if the gametic series produced by the F1 plant consisted of 7 BL + 1 Bl + 1 bL + 7 bl out of every 16 gametes. Fertilization between two such similar series of 16 gametes would result in 256 plants, of which 177 would be purple longs, 15 purple rounds, 15 red longs, and 49 red rounds—a proportion of the four different kinds very close to
that actually found by experiment. It will be noticed that in the whole family the purples are to the reds as 3 : 1, and the longs are also three times as numerous as the rounds. The peculiarity of the case lies in the distribution of these two characters with regard to one another. In some way or other the factors for blue and for long pollen become linked together in the cell divisions that give rise to the gametes, but the linking is not complete. This holds good for all the four cases in which repulsion between the factors occurs when one of the two factors is introduced by each of the parents. When both of the factors are brought into the cross by the same parent we get coupling between them instead of repulsion. The phenomena of repulsion and coupling between separate factors are intimately related, though hitherto we have not been able to suggest why this should be so.
Nor for the present can we suggest why certain factors should be linked together in the peculiar way that we have reason to suppose that they are during the process of the formation of the gametes. Nevertheless the phenomena are very definite, and it is not unlikely that a further study of them may throw important light on the architecture of the living cell.
APPENDIX TO CHAPTER IX
As it is possible that some readers may care, in spite of its complexity, to enter rather more fully into the peculiar phenomenon
of the coupling of characters, I have brought together some further data in this Appendix. In the case we have already considered, where the factors for blue colour and long pollen are concerned, we have been led to suppose that the gametes produced by the heterozygous plant are of the nature 7 BL : 1 Bl : 1 bL : 7 bl. Such a series of ovules fertilised by a similar series of pollen grains will give a generation of the following composition:—
| 49 BBLL | + 7 BBLl | + 7 BbLL | + 49 | BbLl | + BBll | + 7 Bbll | + bbLL | + 7 bbLl | + 49 bbll |
| + 7 BBLl | + 7 BbLL | + | BbLl | + 7 Bbll | + 7 bbLl | ||||
| + | BbLl | ||||||||
| + 49 | BbLl | ||||||||
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|
|
| ||||||
| 177 purple, long | 15 purple, round | 15 red, long | 49 red, round | ||||||
and as this theoretical result fits closely with the actual figures obtained by experiment we have reason for supposing that the heterozygous plant produces a series of gametes in which the factors are coupled in this way. The intensity of the coupling, however, varies in different cases. Where we are dealing with another, viz. fertility (F) and the dark axil (D), the experimental numbers accord with the view that the gametic series is here 15 FD : 1 Fd : 1 fD : 15 fd. The coupling is in this instance more intense. In the case of the erect standard (E) and blueness (B) the coupling is even more intense, and the experimental evidence available at present points to the gametic series here being 63 Eb : 1 EB : 1 eB : 63 eb. There is evidence also for supposing that the intensity of the coupling may vary in different families for the same pair of factors. The coupling between blue and long pollen is generally on the 7 : 1 : 1 : 7
basis, but in some cases it may be on the 15 : 1 : 1 : 15 basis. But though the intensity of the coupling may vary it varies in an orderly way. If A and B are the two factors concerned, the results obtained in F2 are explicable on the assumption that the ratio of the four sorts of gametes produced is a term of the series—
| 3 AB + | Ab + | aB + | 3 | ab |
| 7 AB + | Ab + | aB + | 7 | ab |
| 15 AB + | Ab + | aB + | 15 | ab, etc., etc. |
In such a series the number of gametes containing A is equal to the number lacking A, and the same is true for B. Consequently the number of zygotes formed containing A is three times as great as the number of zygotes which do not contain A; and similarly for B. The proportion of dominants to recessives in each case is 3 : 1. It is only in the distribution of the characters with relation to one another that these cases differ from a simple Mendelian case.
As the study of these series presents another feature of some interest, we may consider it in a little more detail. In the accompanying table are set out the results produced by these different series of gametes. The series marked by an asterisk have already been demonstrated experimentally. The first term in the series,
in which all the four kinds of gametes are produced in equal numbers is, of course, that of a simple Mendelian case where no coupling occurs.
| No. of Gametes in series. | Distribution of Factors in Gametic Series | No. of Zygotes produced. | Form of F2 Generation. | |||
| AB. Ab. aB. ab. | AB. | Ab. | aB. | ab. | ||
| 4 | 1 : 1 : 1 : 1 | 16 | 9 | 3 | 3 | 1 |
| 8 | 3 : 1 : 1 : 3 | 64 | 49 | 7 | 7 | 9 |
| 16 | 7 : 1 : 1 : 7 | 256 | 177 | 15 | 15 | 49* |
| 32 | 15 : 1 : 1 : 15 | 1024 | 737 | 31 | 31 | 225* |
| 64 | 31 : 1 : 1 : 31 | 4096 | 3009 | 63 | 63 | 961 |
| 128 | 63 : 1 : 1 : 63 | 16384 | 12161 | 127 | 127 | 3969* |
| 2n | (n-1) : 1 : 1 : (n-1) | 4n2 | 3n2-(2n-1) | (2n-1) | (2n-1) | n2-(2n-1) |
Now, as the table shows, it is possible to express the gametic series by a general formula (n + 1) AB + Ab + aB + (n - 1) ab, where 2n is the total number of the gametes in the series. A plant producing such a series of gametes gives rise to a family of zygotes in which 3n2 - (2n - 1) show both of the dominant characters and n2 - (2n - 1) show both of the recessive characters, while the number of the two classes which each show one of the two dominants is (2n - 1). When in such a series the coupling becomes closer the value of n increases, but in comparison with n2 its value becomes less and less. The larger n becomes the more negligible is its value relatively to n2. If, therefore, the coupling were very close, the series 3n2 - (2n - 1) : (2n - 1) : (2n - 1) : n2 - (2n - 1) would approximate more and more to the series 3n2 : n2, i.e. to a simple 3 : 1 ratio. Though the point is probably of more theoretical than practical interest, it is not impossible that some of the cases which have hitherto been regarded as following a simple 3 : 1 ratio will turn out on further analysis to belong to this more complicated scheme.