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. {89}
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 F_2 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 F_2 generation {90} 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 F_1
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.
Painted Lady x Duke of Westminster
(erect red) | (hooded purple)
|
Purple Invincible
(erect purple)
|
+-------------+-----------------+
| | |
Painted Purple Invincible Duke of
Lady Westminster
(1) (2) (1)
EEbb eeBB Parents
/\ /\
/ \ / \
/ \ / \
Eb Eb eB eB gametes
\------------/
EeBb F_2
____/ \____
/ \
Fem. gametes of F_1 Eb ---> EEbb <--- Eb Male gametes of F_1
Eb ---> EeBb <--- eB
eB ---> EeBb <--- Eb
eB ---> eeBB <--- eB
\----/
F_2 generation
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
F_1 erect purple is EeBb. Now let us suppose that in such a zygote there
exists a repulsion {91} 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 {92} 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 F_1
plant is a long pollened purple. But the F_2 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 F_2 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 F_1 long pollened reds with an erect
standard, and these in F_2 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).
{93}
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 F_1 plants are all fertile with dark axils. But such plants in
F_2 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 x aaBB. Let us now consider what happens when both
of the {94} 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 F_1 (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 F_2 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 F_1 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 {95} 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 {96} 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
+ 7 BBLl + 7 BbLL + BbLl
+ BbLl
+ 49 BbLl
\---------------------------------/
177 purple, long
+ BBll + 7 Bbll + bbLL + 7 bbLl + 49 bbll
+ 7 Bbll + 7 bbLl
\-------------/ \-----------/ \-----/
15 purple, 15 red, 49 red,
round long 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 {97} 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 F_2 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, {98} 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 | Distribution of | No. of | |
|Gametes|Factors in Gametic| Zygotes | Form of F_2 Generation. |
| in | Series |produced.| |
|series.| | | |
+-------+------------------+---------+---------------------------------+
| | 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) | 4n^2 |3n^2-(2n-1) 2n-1 2n-1 n^2-(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 3n^2 - (2n - 1) show
both of the dominant characters and n^2 - (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 n^2 its
value becomes less and less. The larger n becomes the more negligible is
its value relatively to n^2. If, therefore, the coupling were very close,
the series 3n^2 - (2n - 1) : (2n - 1) : (2n - 1) : n^2 - (2n - 1) would
approximate more and more to the series 3n^2 : n^2, _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.
* * * * *
{99}