THE PRESENCE AND ABSENCE THEORY
It was fortunate for the development of biological science that the
rediscovery of Mendel's work found a small group of biologists deeply
interested in the problems of heredity, and themselves engaged in
experimental breeding. To these men the extraordinary significance of the
discovery was at once apparent. From their experiments, undertaken in
ignorance of Mendel's paper, de Vries, Correns, and Tschermak were able to
confirm his results in peas and other plants, while Bateson was the first
to demonstrate their application to animals. Thenceforward the record has
been one of steady progress, and the result of ten years' work has been to
establish more and more firmly the fundamental nature of Mendel's
discovery. The scheme of inheritance, which he was the first to enunciate,
has been found to hold good for such diverse things as height, hairiness,
and flower colour and flower form in plants, the shape of pollen grains,
and the structure of fruits; while among animals the coat colour of
mammals, the form of the feathers and of the comb in poultry, the waltzing
habit of Japanese mice, and eye {30} colour in man are but a few examples
of the diversity of characters which all follow the same law of
transmission. And as time went on many cases which at first seemed to fall
without the scheme have been gradually brought into line in the light of
fuller knowledge. Some of these will be dealt with in the succeeding
chapters of this book. Meanwhile we may concern ourselves with the single
modification of Mendel's original views which has arisen out of more ample
knowledge.
[Illustration: FIG. 2.
A wing feather and a contour feather of an ordinary and a silky fowl. The
peculiar ragged appearance of the silky feathers is due to the absence of
the little hooks or barbules which hold the barbs together. The silky
condition is recessive.]
As we have already seen, Mendel considered that in the gamete there was
either a definite something {31} corresponding to the dominant character or
a definite something corresponding to the recessive character, and that
these somethings whatever they were could not coexist in any single gamete.
For these somethings we shall in future use the term FACTOR. The factor,
then, is what corresponds in the gamete to the UNIT-CHARACTER that appears
in some shape or other in the development of the zygote. Tallness in the
pea is a unit-character, and the gametes in which it is represented are
said to contain the factor for tallness. Beyond their existence in the
gamete and their mode of transmission we make no suggestion as to the
nature of these factors.
[Illustration: FIG. 3.
Two double and an ordinary single primula flower. This form of double is
recessive to the single.]
{32}
[Illustration: FIG. 4.
Fowls' combs. A, pea; B, rose; C, single; D, walnut.]
On Mendel's view there was a factor corresponding to the dominant character
and another factor corresponding to the recessive character of each
alternative pair of unit-characters, and the characters were alternative
because no gamete could carry more than one of the two factors belonging to
the alternative pair. On the other hand, Mendel supposed that it always
carried either one or the other of such a pair. As experimental work
proceeded, {33} it soon became clear that there were cases which could not
be expressed in terms of this conception. The nature of the difficulty and
the way in which it was met will perhaps be best understood by considering
a set of experiments in which it occurred. Many of the different breeds of
poultry are characterised by a particular form of comb, and in certain
cases the inheritance of these has been carefully worked out. It was shown
that the rose comb (Fig. 4, B) with its flattened papillated upper surface
and backwardly projecting pike was dominant in the ordinary way to the
deeply serrated high single comb (Fig. 4, C) which is characteristic of the
Mediterranean races. Experiment also showed that the pea comb (Fig. 4, A),
a form with a low central and two well-developed lateral ridges, such as is
found in Indian game, behaves as a simple dominant to the single comb. The
interesting question arose as to what would happen when the rose and the
pea, two forms each dominant to the same third form, were mated together.
It seemed reasonable to suppose that things which were alternative to the
same thing would be alternative to one another--that either rose or pea
would dominate in the hybrids, and that the F_2 generation would consist of
dominants and recessives in the ratio 3 : 1. The result of the experiment
was, however, very different. The cross rose x pea led to the production of
a comb quite unlike either of them. This, the so-called walnut comb (Fig.
4, D), {34} from its resemblance to the half of a walnut, is a type of comb
which is normally characteristic of the Malay fowl. Moreover, when these
F_1 birds were bred together, a further unlooked-for result was obtained.
As was expected, there appeared in the F_2 generation the three forms
walnut, rose, and pea. But there also appeared a definite proportion of
single-combed birds, and among many hundreds of chickens bred in this way
the proportions in which the four forms walnut, rose, pea, and single
appeared was 9 : 3 : 3 : 1.
Rose x Pea
|
+----+----+
Walnut x Walnut
|
+--------+---+---+--------+
Walnut Rose Pea Single
(9) (3) (3) (1)
Now this, as Mendel showed, is the ratio found in an F_2 generation when
the original parents differ in two pairs of alternative characters, and
from the proportions in which the different forms of comb occur we must
infer that the walnut contains both dominants, the rose and the pea one
dominant each, while the single is pure for both recessive characters. This
accorded with subsequent breeding experiments, for the singles bred
perfectly true as soon as they had once made their appearance. So far the
case is clear. The difficulty comes when we attempt to define these two
pairs of characters. How are we to express the fact that while single
behaves as a simple recessive to either pure rose, or to pure pea, it can
yet appear in F_2 from a cross {35} between these two pure forms, though
neither of them should, on Mendel's view, contain the single? An
explanation which covers the facts in a simple way is that which has been
termed the "Presence and Absence" theory. On this theory the dominant
character of an alternative pair owes its dominance to the presence of a
factor which is absent in the recessive. The tall pea is tall owing to the
presence in it of the factor for tallness, but in the absence of this
factor the pea remains a dwarf. All peas are dwarf, but the tall is a dwarf
plus a factor which turns it into a tall. Instead of the characters of an
alternative pair being due to two separate factors, we now regard them as
the expression of the only two possible states of a single factor, viz. its
presence or its absence. The conception will probably become clearer if we
follow its application in detail to the case of the fowl's combs. In this
case we are concerned with the transmission of the two factors, rose (R)
and pea (P), the presence of each of which is alternative to its absence.
The rose-combed bird contains the factor for rose but not that for pea, and
the pea-combed bird contains the factor for pea but not that for rose. When
both factors are present in a bird, as in the hybrid made by crossing rose
with pea, the result is a walnut. For convenience of argument we may denote
the presence of a given factor by a capital letter and its absence by the
corresponding small letter. The use of the small letter is merely a
symbolic way of intimating {36} that a particular factor is absent in a
gamete or zygote. Represented thus the zygotic constitution of a pure
rose-combed bird is RRpp; for it has been formed by the union of two
gametes both of which contained R but not P. Similarly we may denote the
pure pea-combed bird as rrPP. On crossing the rose with the pea union
occurs between a gamete Rp and a gamete rP, resulting in the formation of a
heterozygote of the constitution RrPp. The use of the small letters here
informs us that such a zygote contains only a single dose of each of the
factors R and P, although, of course, it is possible for a zygote, if made
in a suitable way, to have a double dose of any factor. Now when such a
bird comes to form gametes a separation takes place between the part of the
zygotic cell containing R and the part which does not contain it (r). Half
of its gametes, therefore, will contain R and the other half will be
without it (r). Similarly half of its gametes will contain P and the other
half will be without it (p). It is obvious that the chances of R being
distributed to a gamete with or without P are equal. Hence the gametes
containing R will be of two sorts, RP and Rp, and these will be produced in
equal numbers. Similarly the gametes without R will also be of two sorts,
rP and rp, and these, again, will be produced in equal numbers. Each of the
hybrid walnut-combed birds, therefore, gives rise to a series consisting of
equal numbers of gametes of the four different types RP, Rp, rP, and rp;
and the breeding {37} together of such F_1 birds means the bringing
together of two such series of gametes. When this happens an ovum of any
one of the four types has an equal chance of being fertilised by a
spermatozoon of any one of the four types. A convenient and simple method
of demonstrating what happens under such circumstances is the method
sometimes termed the "chessboard" method. For two series each consisting of
four different types of gamete we require a square divided up into 16
parts. The four terms of the gametic series are first written horizontally
across the four sets of four squares, so that the series is repeated four
times. It is then written vertically four times, care being taken to keep
to the same order. In this simple mechanical way all the possible
combinations are represented and in their proper proportions.
+-------+-------+-------+-------+
|RP |RP |RP |RP |
|RP |Rp |rP |rp |
| | | | |
| Walnut| Walnut| Walnut| Walnut|
+-------+-------+-------+-------+
|Rp |Rp |Rp |Rp |
|RP |Rp |rP |rp |
| | | | |
| Walnut| Rose| Walnut| Rose|
+-------+-------+-------+-------+
|rP |rP |rP |rP |
|RP |Rp |rP |rp |
| | | | |
| Walnut| Walnut| Pea| Pea|
+-------+-------+-------+-------+
|rp |rp |rp |rp |
|RP |Rp |rP |rp |
| | | | |
| Walnut| Rose| Pea| Single|
+-------+-------+-------+-------+
FIG. 5.
Diagram to illustrate the nature of the F_2 generation from the cross
of rose comb x pea comb.
Fig. 5 shows the result of applying this method to our series RP, Rp, rP,
rp, and the 16 squares represent the different kinds of zygotes formed and
the proportions in which they occur. As {38} the figure shows, 9 zygotes
contain both R and P, having a double or a single dose of either or both of
these factors. Such birds must be all walnut combed. Three out of the 16
zygotes contain R but not P, and these must be rose-combed birds. Three,
again, contain P but not R and must be pea-combed birds. Finally one out of
the 16 contains neither R nor P. It cannot be rose--it cannot be pea. It
must, therefore, be something else. As a matter of fact it is single. Why
it should be single and not something else follows from what we already
know about the behaviour of these various forms of comb. For rose is
dominant to single; therefore on the Presence and Absence theory a rose is
a single plus a factor which turns the single into a rose. If we could
remove the "rose" factor from a rose-combed bird the underlying single
would come into view. Similarly a pea comb is a single plus a factor which
turns the single into a pea, and a walnut is a single which possesses two
additional modifying factors. Singleness, in fact, underlies all these
combs, and if we write their zygotic constitution in full we must denote a
walnut as RRPPSS, a rose as RRppSS, a pea as rrPPSS, and a single as
rrppSS. The crossing of rose with pea results in a reshuffling of the
factors concerned, and in accordance with the principle of segregation some
zygotes are formed in which neither of the modifying factors R and P are
present, and the single character can then become manifest. {39}
The Presence and Absence theory is to-day generally accepted by students of
these matters. Not only does it afford a simple explanation of the
remarkable fact that in all cases of Mendelian inheritance we should be
able to express our unit-characters in terms of alternative pairs, but, as
we shall have occasion to refer to later, it suggests a clue as to the
course by which the various domesticated varieties of plants and animals
have arisen from their wild prototypes.
[Illustration: FIG. 6.
Fowls' combs. A and B, F_1 hen from rose x Breda; C, an F_1 cock from the
cross of single x Breda; D, head of Breda cock.]
Before leaving this topic we may draw attention to some experiments which
offer a pretty confirmation of the view that the rose comb is a single to
which a modifying factor for roseness has been added. It was argued that if
we could find a type of comb in which the factor for singleness was absent,
then on crossing such a comb with a rose we ought, if singleness really
underlies rose, to obtain some single combs in F_2 from such a cross. Such
a comb we had the good fortune to find in the Breda fowl, a breed largely
used in Holland. This fowl is usually spoken of as combless, for the place
of the comb is taken by a covering of short bristlelike feathers (Fig. 6,
D). In reality it possesses the vestige of a comb in the form of two minute
lateral knobs of comb tissue. Characteristic also of this breed is the high
development of the horny nostrils, a feature probably correlated with the
almost complete absence of comb. The first step in the experiment was to
prove the absence of the factor for singleness in the Breda. {40} On
crossing Breda with single the F_1 birds exhibit a large comb of the form
of a double single comb in which the two portions are united anteriorly,
but diverge from one another towards the back of the head (Fig. 6, C). The
Breda contains an element of duplicity which is dominant to the simplicity
of the ordinary single comb. But it cannot contain the factor for the
single comb, because as soon as that is put into it by crossing with a
single the comb {41} assumes a large size, and is totally distinct in
appearance from its almost complete absence in the pure Breda. Now when the
Breda is crossed with the rose duplicity is dominant to simplicity, and
rose is dominant to lack of comb, and the F_1 generation consists of birds
possessing duplex rose combs (Fig. 6, A and B). On breeding such birds
together we obtain a generation consisting of Bredas, duplex roses, roses,
duplex singles, and singles. From our previous experiment we know that the
singles could not have come from the Breda, since a Breda comb to which the
factor for single has been added no longer remains a Breda. Therefore it
must have come from the rose, thus confirming our view that the rose is in
reality a single comb which contains in addition a dominant modifying
factor (R) whose presence turns it into a rose. We shall take it,
therefore, that there is good experimental evidence for the Presence and
Absence theory, and we shall express in terms of it the various cases which
come up for discussion in succeeding chapters.
Rose x Breda
|
+---------+---------+
| |
Duplex x Duplex
Rose | Rose
+-------+------+-------+-------+
| | | | |
Duplex Rose Duplex Single Breda
Rose Single (Duplex
and Simplex)
* * * * *
{42}