INTERACTION OF FACTORS
We have now reached a point at which it is possible to formulate a definite
conception of the living organism. A plant or animal is a living entity
whose properties may in large measure be expressed in terms of
unit-characters, and it is the possession of a greater or lesser number of
such unit-characters renders it possible for us to draw sharp distinctions
between one individual and another. These unit-characters are represented
by definite factors in the gamete which in the process of heredity behave
as indivisible entities, and are distributed according to a definite
scheme. The factor for this or that unit-character is either present in the
gamete or it is not present. It must be there in its entirety or completely
absent. Such at any rate is the view to which recent experiment has led us.
But as to the nature of these factors, the conditions under which they
exist in the gamete, and the manner in which they produce their specific
effects in the zygote, we are at present almost completely in the dark.
The case of the fowls' combs opens up the important question of the extent
to which the various factors can {43} influence one another in the zygote.
The rose and the pea factors are separate entities, and each when present
alone produces a perfectly distinct and characteristic effect upon the
single comb, turning it into a rose or a pea as the case may be. But when
both are present in the same zygote their combined effect is to produce the
walnut comb, a comb which is quite distinct from either and in no sense
intermediate between them. The question of the influence of factors upon
one another did not present itself to Mendel because he worked with
characters which affected different parts of the plant. It was unlikely
that the factor which led to the production of colour in the flower would
affect the shape of the pod, or that the height of the plant would be
influenced by the presence or absence of the factor that determined the
shape of the ripe seed. But when several factors can modify the same
structure it is reasonable to suppose that they will influence one another
in the effects which their simultaneous presence has upon the zygote. By
themselves the pea and the rose factors each produce a definite
modification of the single comb, but when both are present in the zygote,
whether as a single or double dose, the modification that results is quite
different to that produced by either when present alone. Thus we are led to
the conception of characters which depend for their manifestation on more
than one factor in the zygote, and in the present chapter we may consider a
few of the {44} phenomena which result from such interaction between
separate and distinct factors.
White x White
|
Red -------------- F_1
|
+----------+
Red White ------- F_2
(9) (7)
One of the most interesting and instructive cases in which the interaction
between separate factors has been demonstrated is a case in the sweet pea.
All white sweet peas breed true to whiteness. And generally speaking the
result of crossing different whites is to produce nothing but whites,
whether in F_1 or in succeeding generations. But there are certain strains
of white sweet peas which when crossed together produce only coloured
flowers. The colour may be different in different cases, though for our
present purpose we may take a case in which the colour is red. When such
reds are allowed to self-fertilise themselves in the normal way and the
seeds sown, the resulting F_2 generation consists of reds and whites, the
former being rather more numerous than the latter in the proportion of
9 : 7. The raising of a further generation from the seeds of these F_2
plants shows that the whites always breed true to whiteness, but that
different reds may behave differently. Some breed true, others give reds
and whites in the ratio 3 : 1, while others, again, give reds and whites in
the ratio 9 : 7. As in the case of the fowls' combs, this case may be
interpreted in terms of the presence and absence of two factors. {45}
White White
AAbb aaBB
/ \ / \
/ \ / \
Ab Ab aB aB gametes of parents
`-------'
Red F_1
AaBb
/ \
/ \
AB AB
Female gametes Ab Ab Male gametes
of F_1 aB aB of F_1
ab ab
Red in the sweet pea results from the interaction of two factors, and
unless these are both present the red colour cannot appear. Each of the
white parents carried one of the two factors whose interaction is necessary
for the production of the red colour, and as a cross between them brings
these two complementary factors together the F_1 plants must all be red. As
this case is of considerable importance for the proper understanding of
much that is to follow, and as it has been completely worked out, we shall
consider it in some detail. Denoting these two colour factors by A and B
respectively we may proceed to follow out the consequences of this cross.
Since all the F_1 plants were red the constitution of the parental whites
must have been AAbb and aaBB respectively, and their gametes consequently
Ab and aB. The constitution of the F_1 plants must, therefore, be AaBb.
Such a plant being heterozygous for two factors produces a series of
gametes of the four kinds AB, Ab, aB, ab, and produces them in equal
numbers (cf. p. 36). To obtain the various types of zygotes which are
produced when such {46} a series of pollen grains meets a similar series of
ovules we may make use of the same "chessboard" system which we have
already adopted in the case of the fowls' combs.
+------+------+------+------+
|AB....|AB....|AB....|AB....|
|AB....|Ab....|aB....|ab....|
|......|......|......|......|
+------+------+------+------+
|Ab....|Ab |Ab....|Ab |
|AB....|Ab |aB....|ab |
|......| |......| |
+------+------+------+------+
|aB....|aB....|aB |aB |
|AB....|Ab....|aB |ab |
|......|......| | |
+------+------+------+------+
|ab....|ab |ab |ab |
|AB....|Ab |aB |ab |
|......| | | |
+------+------+------+------+
FIG. 7.
Diagram to illustrate the nature of the F_2 generation from the two
white sweet peas which give a coloured F_1.
An examination of this figure (Fig. 7) shows that 9 out of the 16 squares
contain both A and B, while 7 contain either A or B alone, or neither. In
other words, on this view of the nature of the two white sweet peas we
should in the F_2 generation look for the appearance of coloured and white
flowers in the ratio 9 : 7. And this, as we have already seen, is what was
actually found by experiment. Further examination of the figure shows that
the coloured plants are not all of the same constitution, but are of four
kinds with respect to their zygotic constitution, viz. AABB, AABb, AaBB,
and AaBb. Since AABB is homozygous for both A and B, all the gametes which
it produces must contain both of these factors, and such a plant must
therefore breed true to the red colour. A plant of the {47} constitution
AABb is homozygous for the factor A, but heterozygous for B. All of its
gametes will contain A, but only one-half of them will contain B, _i.e._ it
produces equal numbers of gametes AB and Ab. Two such series of gametes
coming together must give a generation consisting of x AABB, 2x AABb, and x
AAbb, that is, reds and whites in the ratio 3 : 1. Lastly the red zygotes
of the constitution AaBb have the same constitution as the original red
made from the two whites, and must therefore when bred from give reds and
whites in the ratio 9 : 7. The existence of all these three sorts of reds
was demonstrated by experiment, and the proportions in which they were met
with tallied with the theoretical explanation.
The theory was further tested by an examination into the properties of the
various F_2 whites which come from a coloured plant that has itself been
produced by the mating of two whites. As Fig. 7 shows, these are, in
respect of their constitution, of five different kinds, viz. AAbb, Aabb,
aaBB, aaBb, and aabb. Since none of them produce anything but whites on
self-fertilisation it was found necessary to test their properties in
another way, and the method adopted was that of crossing them together. It
is obvious that when this is done we should expect different results in
different cases. Thus the cross between two whites of the constitution AAbb
and aaBB should give nothing but coloured plants; for these two whites are
of {48} the same constitution as the original two whites from which the
experiment started. On the other hand, the cross between a white of the
constitution aabb and any other white can never give anything but whites.
For no white contains both A and B, or it would not be white, and a plant
of the constitution aabb cannot supply the complementary factor necessary
for the production of colour. Again, two whites of the constitution Aabb
and aaBb when crossed should give both coloured and white flowers, the
latter being three times as numerous as the former. Without going into
further detail it may be stated that the results of a long series of
crosses between the various F_2 whites accorded closely with the
theoretical explanation.
From the evidence afforded by this exhaustive set of experiments it is
impossible to resist the deduction that the appearance of colour in the
sweet pea depends upon the interaction of two factors which are
independently transmitted according to the ordinary scheme of Mendelian
inheritance. What these factors are is still an open question. Recent
evidence of a chemical nature indicates that colour in a flower is due to
the interaction of two definitive substances: (1) a colourless "chromogen,"
or colour basis; and (2) a ferment which behaves as an activator of the
chromogen, and by inducing some process of oxidation, leads to the
formation of a coloured substance. But whether these two bodies exist as
such {49} in the gametes or whether in some other form we have as yet no
means of deciding.
Since the elucidation of the nature of colour in the sweet pea phenomena of
a similar kind have been witnessed in other plants, notably in stocks,
snapdragons, and orchids. Nor is this class of phenomena confined to
plants. In the course of a series of experiments upon the plumage colour of
poultry, indications were obtained that different white breeds did not
always owe their whiteness to the same cause. Crosses were accordingly made
between the white Silky fowl and a pure white strain derived from the white
Dorking. Each of these had been previously shown to behave as a simple
recessive to colour. When the two were crossed only fully coloured birds
resulted. From analogy with the case of the sweet pea it was anticipated
that such F_1 coloured birds when bred together would produce an F_2
generation consisting of coloured and white birds in the ratio 9 : 7, and
when the experiment was made this was actually shown to be the case. With
the growth of knowledge it is probable that further striking parallels of
this nature between the plant and animal worlds will be met with.
Before quitting the subject of these experiments attention may be drawn to
the fact that the 9 : 7 ratio is in reality a 9 : 3 : 3 : 1 ratio in which
the last three terms are indistinguishable owing to the special
circumstances that neither factor can produce a visible effect without {50}
the co-operation of the other. And we may further emphasise the fact that
although the two factors thus interact upon one another they are
nevertheless transmitted quite independently and in accordance with the
ordinary Mendelian scheme.
Agouti x Agouti
|
+---------------+
Agouti x Agouti
|
+---------+---------+
Agouti Black Albino
(9) (3) (4)
One of the earliest sets of experiments demonstrating the interaction of
separate factors was that made by the French zoologist Cuenot on the coat
colours of mice. It was shown that in certain cases agouti, which is the
colour of the ordinary wild grey mouse, behaves as a dominant to the albino
variety, _i.e._ the F_2 generation from such a cross consists of agoutis
and albinos in the ratio 3 : 1. But in other cases the cross between albino
and agouti gave a different result. In the F_1 generation appeared only
agoutis as before, but the F_2 generation consisted of three distinct
types, viz. agoutis, albinos, _and blacks_. Whence the sudden appearance of
the new type? The answer is a simple one. The albino parent was really a
black. But it lacked the factor without which the colour is unable to
develop, and consequently it remained an albino. If we denote this factor
by C, then the constitution of an albino must be cc, while that of a
coloured animal may be CC or Cc, according as to whether it breeds true to
colour or can {51} throw albinos. Agouti was previously known to be a
simple dominant to black, _i.e._ an agouti is a black rabbit plus an
additional greying factor which modifies the black into agouti. This factor
we will denote by G, and we will use B for the black factor. Our original
agouti and albino parents we may therefore regard as in constitution GGCCBB
and ggccBB respectively. Both of the parents are homozygous for black. The
gametes produced by the two parents are GCB, and gcB, and the constitution
of the F_1 animals must be GgCcBB. Being heterozygous for two factors they
will produce four kinds of gametes in equal numbers, viz. GCB, GcB, gCB,
and gcB. The results of the mating of two such similar series of gametes
when the F_1 animals are bred together we may determine by the usual
"chessboard" method (Fig. 8). Out of the 16 squares 9 contain both C and G
in addition to B. Such animals must be agoutis. Three squares contain C but
not G. Such animals must be coloured, but as they do not contain the
modifying agouti factor their colour will be black. The remaining four
squares do not contain C, and in the absence of this colour-developing
factor they must all be albinos. Theory demands that the three classes
agouti, black, and albino should appear in F_2 in the ratio 9 : 3 : 4;
experiment has shown that these are the only classes that appear, and that
the proportions in which they are produced accord closely with the
theoretical expectation. Put briefly, then, the explanation {52} of this
case is that all the animals are black, and that we are dealing with the
presence and absence of two factors, a colour developer (C), and a colour
modifier (G), both acting, as it were, upon a substratum of black. The F_2
generation really consists of the four classes agoutis, blacks, albino
agoutis, and albino blacks in the ratio 9 : 3 : 3 : 1. But since in the
absence of the colour developer C the colour modifier G can produce no
visible result, the last two classes of the ratio are indistinguishable,
and our F_2 generation comes to consist of three classes in the ratio
9 : 3 : 4, instead of four classes in the ratio 9 : 3 : 3 : 1.
+-------+-------+-------+-------+
|GCB....|GCB....|GCB....|GCB....|
|GCB....|GcB....|gCB....|gcB....|
|.......|.......|.......|.......|
|.Agouti|.Agouti|.Agouti|.Agouti|
+-------+-------+-------+-------+
|GcB....|GcB |GcB....|GcB |
|GCB....|GcB |gCB....|gcB |
|.......| |.......| |
|.Agouti| Albino|.Agouti| Albino|
+-------+-------+-------+-------+
|gCB....|gCB....|gCB####|gCB####|
|GCB....|GcB....|gCB####|gcB####|
|.......|.......|#######|#######|
|.Agouti|.Agouti|##BLACK|##BLACK|
+-------+-------+-------+-------+
|gcB....|gcB |gcB####|gcB |
|GCB....|GcB |gCB####|gcB |
|.......| |#######| |
|.Agouti| Albino|##BLACK| Albino|
+-------+-------+-------+-------+
FIG. 8.
Diagram to illustrate the nature of the F_2 generation which may arise
from the mating of agouti with albino in mice or rabbits.
This explanation was further tested by experiments with the albinos. In an
F_2 family of this nature there ought to be three kinds, viz. albinos
homozygous for G (GGccBB), albinos heterozygous for G (GgccBB), and albinos
without G (ggccBB). These albinos are, as it were, like photographic plates
exposed but undeveloped. {53} Their potentialities may be quite different,
although they all look alike, but this can only be tested by treating them
with a colour developer. In the case of the mice and rabbits the
potentiality for which we wish to test is the presence or absence of the
factor G, and in order to develop the colour we must introduce the factor
C. Our developer, therefore, must contain C but not G. In other words, it
must be a homozygous black mouse or rabbit, ggCCBB. Since such an animal is
pure for C it must, when mated with any of the albinos, produce only
coloured offspring. And since it does not contain G the appearance of
agoutis among its offspring must be attributed to the presence of G in the
albino. Tested in this way the F_2 albinos were proved, as was expected, to
be of three kinds: (1) those which gave only agouti, _i.e._ which were
homozygous for G; (2) those which gave agoutis and blacks in approximately
equal numbers, _i.e._ which were heterozygous for G; and (3) those which
gave only blacks, and therefore did not contain G.
Though albinos, whether mice, rabbits, rats, or other animals, breed true
to albinism, and though albinism behaves as a simple recessive to colour,
yet albinos may be of many different sorts. There are in fact just as many
kinds of albinos as there are coloured forms--neither more nor less. And
all these different kinds of albinos may breed together, transmitting the
various colour factors according to the Mendelian scheme of inheritance,
{54} and yet the visible result will be nothing but albinos. Under the mask
of albinism is all the while occurring that segregation of the different
colour factors which would result in all the varieties of coloured forms,
if only the essential factor for colour development were present. But put
in the developer by crossing with a pure coloured form and their variety of
constitution can then at last become manifest.
So far we have dealt with cases in which the production of a character is
dependent upon the interaction of two factors. But it may be that some
characters require the simultaneous presence of a greater number of factors
for their manifestation, and the experiments of Miss Saunders have shown
that there is a character in stocks which is unable to appear except
through the interaction of three distinct factors. Coloured stocks may be
either hoary, with the leaves and stem covered by small hairs, or they may
lack the hairy covering, in which case they are termed glabrous. Hoariness
is dominant to glabrousness; that is to say, there is a definite factor
which can turn the glabrous into a hoary plant when it is present. But in
families where coloured and white stocks occur the white are always
glabrous, while the coloured plants may or may not be hoary. Now colour in
the stock as in the sweet pea has been proved to be dependent upon the
interaction of two separate factors. Hence hoariness depends upon three
separate factors, and a stock cannot be hoary unless {55} it contains the
hoary factor in addition to the two colour factors. It requires the
presence of all these three factors to produce the hoary character, though
how this comes about we have not at present the least idea.
[Illustration: FIG. 9.
Sections of primula flowers. The anthers are shown as black. A, "pin" form
with long style and anthers set low down; B, "thrum" form with short style
and anthers set higher up; C, homostyle form with anthers set low down as
in "pin," but with short style. This form only occurs with the large eye.]
[Illustration: FIG. 10.
Two primula flowers showing the extent of the small and of the large eye.]
A somewhat different and less usual form of interaction between factors may
be illustrated by a case in primulas recently worked out by Bateson and
Gregory. Like the common primrose, the primula exhibits both pin-eyed and
thrum-eyed varieties. In the former the style is long, and the centre of
the eye is formed by the end of the stigma which more or less plugs up the
opening of the corolla (cf. Fig. 9, A); in the latter the style is short
and hidden by the four anthers which spring from higher up in the corolla
and form the centre of the eye (cf. Fig. 9, B). The greater part of the
"eye" is formed by the greenish-yellow patches on each petal just at the
opening {56} of the corolla. In most primulas the eye is small, but there
are some in which it is large and extends as a flush over a considerable
part of the petals (Fig. 10). Experiments showed that these two pairs of
characters behave in simple Mendelian fashion, short style ( = "thrum")
being dominant to long style (= "pin") and small eye dominant to large.
Besides the normal long and short styled forms, there occurs a third form,
which has been termed homostyle. In this form the anthers are placed low
down in the corolla tube as they are in the long-styled form, but the style
remains short instead of reaching up to the corolla opening (Fig. 9, C). In
the course of their experiments Bateson and Gregory crossed a large-eyed
homostyle plant with a small-eyed thrum ( = short style). The F_1 plants
were all short styled with small eyes. {57} On self-fertilisation these
gave an F_2 generation consisting of four types, viz. short styled with
small eyes, short styled with large eyes, _long styled_ with small eyes,
and _homostyled_ with large eyes. The notable feature of this generation is
the appearance of long-styled plants, which, however, occur only in
association with the small eye. The proportions in which these four types
appeared shows that the presence or absence of but two factors is
concerned, and at the same time provides the key to the nature of the
homostyled plants. These are potentially long styled, and the position of
the anthers is that of normal long-styled plants, but owing to some
interaction between the factors the style itself is unable to reach its
full development unless the factor for the small eye is present. For this
reason long-styled plants with the large eye are always of the homostyle
form. What the connecting-link between these apparently unrelated
structures may be we cannot yet picture to ourselves, any more than we can
picture the relation between flower {58} colour and hairiness in stocks. It
is evident, however, that the conception of the interaction of factors,
besides clearing up much that is paradoxical in heredity, promises to
indicate lines of research which may lead to valuable extensions in our
knowledge of the way in which the various parts of the living organism are
related to one another.
Short style } { Homo style
small eye } x { large eye
|
Short style
small eye
|
+-------------+----------+-----------+
Short style Short style Long style Homo style
small eye large eye ("pin") large eye
(9) (3) (3) (1)
* * * * *
{59}