MERISTIC PHENOMENA
Twenty years ago in describing the facts of Variation, argument was
necessary to show that these phenomena had a special value in the
sciences of Zoology and Botany. This value is now universally understood
and appreciated. In spite however of the general attention devoted to
the study of Variation, and the accumulation of material bearing on the
problem, no satisfactory or searching classification of the phenomena is
possible. The reason for this failure is that a real classification must
presuppose knowledge of the chemistry and physics of living things which
at present is quite beyond our reach.
It is however becoming probable that if more knowledge of the chemical
and physical structure of organisms is to be attained, the clue will
be found through Genetics, and thus that even in the uncoordinated
accumulation of facts of Variation we are providing the means of
analysis applicable not only to them, but to the problems of normality
also.
The only classification that we can yet institute with any confidence
among the phenomena of Variation is that which distinguishes on the one
hand variations in the processes of division from variations in the
nature of the substances divided.
Variations in the processes of division are most often made apparent by
a change in the number of the parts, and are therefore called _Meristic_
Variations, while the changes in actual composition of material are
spoken of as _Substantive_ Variations. The Meristic Variations form on
the whole a natural and fairly well defined group, but the Substantive
Variations are obviously a heterogeneous assemblage.
Though this distinction does not go very far, it is useful, and in
all probability fundamental. It is of value inasmuch as it brings
into prominence the distinct and peculiar part which the process
of division, or, more generally, repetition of parts, plays in the
constitution of the forms of living things.
That there may be a real independence between the Meristic and the
Substantive phenomena is evident from the fact both that Meristic
changes may occur without Substantive Variation, and that the substances
composing an organism may change without any perceptible alteration
in its meristic structure. When the distinction between these two
classes of phenomena is perceived it will be realised that the study
of genetics has on the one hand a physical, or perhaps more strictly
a mechanical aspect, which relates to the manner in which material is
divided and distributed; and also a chemical aspect, which relates
to the constitution of the materials themselves. Somewhat as the
philosophers of the seventeenth and eighteenth centuries were awaiting
both a chemical and a mechanical discovery which should serve as a
key to the problems of unorganised matter, so have biologists been
awaiting two several clues. In Mendelian analysis we have now, it is
true, something comparable with the clue of chemistry, but there is
still little prospect of penetrating the obscurity which envelops the
mechanical aspect of our phenomena. To make clear the application of
the terms chemical and mechanical to the problem of Genetics the nature
of that problem must be more fully described. In its most concrete form
this problem is expressed in the question, how does a cell divide? If
the organism is unicellular, and the single cell is the whole body,
then the process of heredity is accomplished in the single operation of
cell-division. Similarly in animals and plants whose bodies are made
up of many cells, the whole process of heredity is accomplished in the
cell-divisions by which the germ-cells are formed. When therefore we see
a cell dividing, we are witnessing the process by which the form and the
properties of the daughter-cells are determined.
Now this process has the two aspects which I have called mechanical
and chemical. The term "_Entwicklungsmechanik_" has familiarised us
with the application of the word mechanics to these processes, but on
reflexion it will be seen that this comprehensive term includes two
sorts of events which are sometimes readily distinguishable. There
is the event by which the cell _divides_, and the event by which the
two halves or their descendants are or may be _differentiated_. It
is common knowledge that in some cell-divisions two similar halves,
indistinguishable in appearance, properties, and subsequent fate, may
be produced, while in other divisions daughter-cells with distinct
properties and powers are formed. We cannot imagine but that in the
first case, when the resulting cells are identical, the division is a
mechanical process by which the mother-cell is simply cut in two; while
in order that two differentiated halves may be produced, some event must
have taken place by which a chemical distinction between the two halves
is effected.[1] In any ordinary Mendelian case we have a clear proof
that such a chemical difference may be established between germ-cells.
The facts of colour-inheritance for instance prove that germ-cells,
otherwise identical, may be formed _possessing_ the chromogen-factor
which is necessary to the formation of colour in the flowers, or
_destitute_ of that factor. Similarly the germ-cells may possess the
ferment which, by its action on the chromogenic substance, produces the
colour, or they may be without that ferment. The same line of argument
applied to a great range of cases. Nevertheless, though differences
in chemical properties are often thus constituted by cell-divisions,
and though we are thus able to make a quasi-chemical analysis of the
individual by determining and enumerating these properties, yet it is
evident that the distribution of these factors is not itself a chemical
process. This is proved by the fact that similar divisions may be
effected between halves which are exactly alike, and also by the fact
that the numbers in which the various types of germ-cells are formed
negative any suggestion of valency between them. The recognition of the
unit-factors may lead--indeed must lead--to great advances in chemical
physiology which without that clue would have been impossible, but
in causation the chemical phenomena of heredity must be regarded as
secondary to the physical or mechanical phenomena by which the cells
and their constituents are divided and separated. When therefore we
speak of the _essential_ phenomena of heredity we mean the mechanics
of division, especially, though not, as we shall see, exclusively, of
_cell_-division; and in the relation between the two halves of the
dividing cell we have the problem presented in what seems to be its
simplest form.
In attempting to form some conception of the processes by which bodily
characteristics are transmitted, or--to avoid that confusing metaphor
of "transmission"--how it comes about that the offspring can grow to
resemble its parent, continuity of the germ-substance which in some
animals is a visible phenomenon,[2] gives at least apparent help. An egg
for example on becoming adult develops in certain parts a particular
pigment. The eggs of that adult when they reach the appropriate age
develop the same pigment. We have no clear picture of the mechanism by
which this process is effected, but when we realise that the pigment
results from the interaction of certain substances, and that since
all the eggs are in reality pieces of the same material, it seems,
unless we inquire closely, not unnatural that the several pieces of the
material should exhibit the same colours at the same periods of their
development. The continuity of the material of the germs suggests that
there is a continuity of the materials from which the pigment is formed,
and that thus an actual bit of those substances passes into each egg
ready at the appropriate moment to generate the pigment. The argument
thus outlined applies to all _substantive_ characteristics. In each case
we can imagine, if we will, the appearance of that characteristic as due
to the contribution of its rudiment from the germ tissues.
When we consider more critically it becomes evident that the aid given
by this mental picture is of very doubtful reality, for even if it were
true that any predestined particle actually corresponding with the
pigment-forming materials is definitely passed on from germ to germ,
yet the power of increase which must be attributed to it remains so
incomprehensible that the mystery is hardly at all illuminated.
When however we pass from the substantive to the meristic characters,
the conception that the character depends on the possession by the germ
of a particle of a specific material becomes even less plausible. Hardly
by any effort of imagination can we see any way by which the division
of the vertebral column into _x_ segments or into _y_ segments, or of a
Medusa into 4 segments or into 6, can be determined by the possession
or by the want of a material particle. The distinction must surely be
of a different order. If we are to look for a physical analogy at all
we should rather be led to suppose that these differences in segmental
numbers corresponded with changes in the amplitude or number of dividing
waves than with any change in the substance or material divided.
PHENOMENA OF DIVISION
I have said that in the division of a cell we seem to see the problem in
its simplest form, but it is important to observe that the problem of
division may be presented by the bodies of animals and plants in forms
which are independent of the divisions between cells. The existence of
pattern implies a repetition of parts, and repetition of parts when
developed in a material originally homogeneous can only be created by
division. Cell-division is probably only a special case of a process
similar to that by which the pattern of the skeleton is laid down in
a unicellular body such as that of a Radiolarian or Foraminiferan.
Attempts have lately been made to apply mathematical treatment to
problems of biology. It has sometimes seemed to me that it is in the
geometrical phenomena of life that the most hopeful field for the
introduction of mathematics will be found. If anyone will compare one
of our animal patterns, say that of a zebra's hide, with patterns known
to be of purely mechanical production, he will need no argument to
convince him that there must be an essential similarity between the
processes by which the two kinds of patterns were made and that parts
at least of the analysis applicable to the mechanical patterns are
applicable to the zebra stripes also. Patterns mechanically produced are
of many and very diverse kinds. One of the most familiar examples, and
one presenting some especially striking analogies to organic patterns,
is that provided by the ripples of a mackerel sky, or those made in a
flat sandy beach by the wind or the ebbing tide. With a little search
we can find among the ripple-marks, and in other patterns produced by
simple physical means, the closest parallels to all the phenomena of
striping as we see them in our animals. The forking of the stripes, the
differentiation of two "faces," the deflections round the limbs and
so forth, which in the body we know to be phenomena of division, are
common both to the mechanical and the animal patterns. We cannot tell
what in the zebra corresponds to the wind or the flow of the current,
but we can perceive that in the distribution of the pigments, that
is to say, of the chromogen-substances or of the ferments which act
upon them, a rhythmical disturbance has been set up which has produced
the pattern we see; and I think we are entitled to the inference that
in the formation of patterns in animals and plants mechanical forces
are operating which ought to be, and will prove to be, capable of
mathematical analysis. The comparison between the striping of a living
organism and the sand-ripples will serve us yet a little farther,
for a pattern may either be formed by actual cell-divisions, and
the distribution of differentiation coincidently determined, or--as
visibly in the pigmentation of many animal and plant tissues--the
pattern may be laid down and the pigment (for example) distributed
through a tissue across or independently of the cell-divisions of the
tissue. Our tissues therefore are like a beach composed of sands of
different kinds, and different kinds of sands may show distinct and
interpenetrating ripples. When the essential analogy between these
various classes of phenomena is perceived, no one will be astonished at,
or reluctant to admit, the reality of discontinuity in Variation, and if
we are as far as ever from knowing the actual causation of pattern we
ought not to feel surprised that it may arise suddenly or be suddenly
modified in descent. Biologists have felt it easier to conceive the
evolution of a striped animal like a zebra from a self-coloured type
like a horse (or of the self-coloured from the striped) as a process
involving many intergradational steps; but so far as the _pattern_ is
concerned, the change may have been decided by a single event, just as
the multitudinous and ordered rippling of a beach may be created or
obliterated at one tide.
[Illustration: FIG. 1. Tusk of Indian elephant, showing an abnormal
segmentation.]
This point is well illustrated by the tusk of an Indian elephant which
I lately found in a London sale-room. This tusk is by some unknown
cause, presumably a chronic inflammation, thrown up into thirteen
well-marked ridges which closely simulate a series of segments (Fig. 1).
Whatever the cause the condition shows how easily a normally unsegmented
structure may be converted into a series of repeated parts.
The spread of segmentation through tissues normally unsegmented is very
clearly exemplified in the skates' jaws shown in Fig. 2. The right
side of the upper figure shows the normal arrangement in the species
_Rhinoptera jussieui_, but the structure on the left side is very
different. The probable relations of the several rows of teeth to the
normal rows is indicated by the lettering, but it is evident that by
the appearance of new planes of division constituting separate centers
of growth, the series has been recast. The pattern of the left side is
so definite that had the variation affected the right side also, no
systematist would have hesitated to give the specimen a new specific
name. The other two drawings show similar variations of a less extensive
kind, the nature of which is explained by the lettering of the rows of
teeth.
[Illustration: FIG. 2. Jaws of Skates (_Rhinoptera_) showing meristic
variation. (For a detailed discussion see _Materials for the Study of
Variation_, p. 259.)]
This power to divide is a fundamental attribute of life, and of that
power cell-division is a special example. In regard to almost all the
chief vital phenomena we can say with truth that science has made some
progress. If I mention respiration, metabolism, digestion, each of these
words calls to mind something more than a bare statement that such
acts are performed by an animal or a plant. Each stands for volumes of
successful experiment and research, But the expression cell-division,
the fundamental act which typifies the rest, and on which they all
depend, remains a bare name. We can see with the microscope the outward
symptoms of division, but we have no surmise as to the nature of the
process by which the division is begun or accomplished. I know nothing
which to a man well trained in scientific knowledge and method brings
so vivid a realisation of our ignorance of the nature of life as the
mystery of cell-division. What is a living thing? The best answer in
few words that I know is one which my old teacher, Michael Foster, used
to give in his lectures introductory to biology. "A living thing is a
vortex of chemical and molecular change." This description gives much,
if not all, that is of the essence of life. The living thing is unlike
ordinary matter in the fact that, through it, matter is always passing.
Matter is essential to it; but, provided that the flow in and out is
unimpeded, the life-process can go on so far as we know indefinitely.
Yet the living "vortex" differs from all others in the fact that it
can divide and throw off other "vortices," through which again matter
continually swirls.
We may perhaps take the parallel a stage further. A simple vortex, like
a smoke-ring, if projected in a suitable way will twist and form two
rings. If each loop as it is formed could grow and then twist again to
form more loops, we should have a model representing several of the
essential features of living things.
It is this power of spontaneous division which most sharply
distinguishes the living from the non-living. In the excellent book
dealing with the problems of development, lately published by Mr.
Jenkinson a special emphasis is very properly laid on the distinction
between the processes of division, and those of differentiation. Too
often in discussions of the developmental processes the distinction
is obscured. He regards differentiation as the "central difficulty."
"Growth and division of the nucleus and the cells," he tells us,
are side-issues. This view is quite defensible, but I suspect that
the division _is_ the central difficulty, and that if we could get
a rationale of what is happening in cell-division we should not be
long before we had a clue to the nature of differentiation. It may be
self-deception, but I do not feel it impossible to form some hypothesis
as to the mode of differentiation, but in no mood of freest speculation
are we ever able to form a guess as to the nature of the division. We
see differentiations occurring in the course of chemical action, in
some phenomena of vibration and so forth: but where do we see anything
like the spontaneous division of the living cell? Excite a gold-leaf
electroscope, and the leaves separate, but we know that is because they
were double before. In electrolysis various substances separate out at
the positive and negative poles respectively. Now if in cell-division
the two daughter-cells were always dissimilar--that is to say, if
differentiation always occurred--we could conceive some rough comparison
with such dissociations. But we know the dissimilarity between
daughter-cells is not essential. In the reproduction of unicellular
organisms and many other cases, the products formed at the two poles
are, so far as we can tell, identical. Any assumption to the contrary,
if we were disposed to make it, would involve us in difficulties still
more serious. At any rate, therefore, if differentiation be really the
central difficulty in development, it is division which is the essential
problem of heredity.
Sir George Darwin and Professor Jeans tell us that "gravitational
instability" consequent on the condensation of gases is "the primary
agent at work in the actual evolution of the universe," which has led to
the division of the heavenly bodies. The greatest advance I can conceive
in biology would be the discovery of the nature of the instability which
leads to the continual division of the cell. When I look at a dividing
cell I feel as an astronomer might do if he beheld the formation of a
double star: that an original act of creation is taking place before me.
Enigmatical as the phenomenon seems, I am not without hope that, if it
were studied for its own sake, dissociated from the complications which
obscure it when regarded as a mere incident in development, some hint as
to the nature of division could be found. It is I fear a problem rather
for the physicist than for the biologist. The sentiment may not be a
popular one to utter before an assembly of biologists, but looking at
the truth impersonally I suspect that when at length minds of first rate
analytical power are attracted to biological problems, some advance will
be made of the kind which we are awaiting.
The study of the phenomena of bodily symmetry offers perhaps the
most hopeful point of attack. The essential fact in reproduction is
cell-division, and the essential basis of hereditary resemblance is
the symmetry of cell-division. The phenomena of twinning provide a
convincing demonstration that this is so. By twinning we mean the
production of equivalent structures by division. The process is one
which may affect the whole body of an animal or plant, or certain of
its parts. The term twin as ordinarily used refers to the simultaneous
birth of two individuals. Those who are naturalists know that such twins
are of two kinds, (1) twins that are not more alike than any other
two members of the same family, and (2) twins that are so much alike
that even intimate friends mistake them. These latter twins, except in
imaginative literature, are always of the same sex.
It is scarcely necessary for me to repeat the evidence from which it has
been concluded that without doubt such twins arise by division of the
same fertilised ovum. There is a perfect series of gradations connecting
them with the various forms of double monsters united by homologous
parts. They have been shown several times to be enclosed in the same
chorion, and the proofs of experimental embryology show that in several
animals by the separation of the two first hemispheres of a dividing egg
twins can be produced. Lastly we have recently had the extraordinarily
interesting demonstration of Loeb, to which I may specially refer.
Herbst some years ago found that in sea water, from which all lime salts
had been removed, the segments of the living egg fall apart as they are
formed. Using this method Loeb has shown that a temporary immersion in
lime-free sea water may result in the production of 90 per cent. of
twins. We are therefore safe in regarding the homologous or "identical"
twins as resulting from the divisions of one fertilised egg, while the
non-identical or "fraternal" twins, as they are called, arise by the
fertilisation of two separate ova.[3]
In the resemblance of identical twins we have an extreme case of
hereditary likeness[4] and a proof, if any were needed, that the
cause of individual variation is to be sought in the differentiation
of germ-cells. The resemblance of identical twins depends on two
circumstances, First, since only two germ-cells take part in their
production, difference between the germ cells of the same individual
cannot affect them. Secondly the division of the fertilised ovum,
the process by which they became two instead of one, must have been
a symmetrical division. The structure of twins raises however one
extremely significant difficulty, which as yet we cannot in any way
explain. The resemblance between twins is a phenomenon of symmetry,
like the resemblance between the two sides of a bilaterally symmetrical
body. Not only is the general resemblance readily so interpreted, but
we know also that in double monsters, namely unseparated twins, various
anatomical abnormalities shown by the one half-body are frequently shown
by the other half-also.[5] The two belong to one system of symmetry.
How then does it happen that the body of one of a pair of twins does
not show a transposition of viscera? We know that the relation of right
and left implies that the one should be the mirror-image of the other.
Such a relation of images may be maintained even in minute details.
For example if the same pattern of finger-print is given by the fingers
of the two hands, one is the reverse of the other. In double monsters,
namely unseparated twins, there is evidence that an inversion of viscera
does occur with some frequency. Evidence from such cases is not so clear
and simple as might be expected, because as a matter of fact, the heart
and stomach, upon which the asymmetry of the viscera chiefly depend, are
usually common to the two bodies. Duplicity generally affects either
the anterior end alone, or the posterior end alone. The division is
generally _from the heart forwards_, giving two heads and two pairs of
anterior limbs on a common trunk, or _from the heart backwards_, giving
two pairs of posterior limbs with the anterior body common. In either
case, though the bodies may be grouped in a common system of symmetry,
neither can be proved to show definite reversal of the parts. To see
that reversal recourse must be had to more extreme duplications, such as
the famous Siamese Twins. They, as a matter of fact, were an excellent
instance of the proposition that twins are related as mirror-images,
for both of them had eleven pairs of ribs instead of the normal twelve,
and one of them had a partial reversal of viscera.[6] (Küchenmeister,
_Verlagerung_, etc., p. 204.)
If anyone could show how it is that neither of a pair of twins has
transposition of viscera the whole mystery of division would, I expect,
be greatly illuminated.[7] At present we have simply to accept the fact
that twins, by virtue of their detachment from each other, have the
power of resuming the polarity which is proper to any normal individual.
It was nevertheless with great interest that I read Wilder's recent
observation[8] that occasionally in identical twins the finger-print of
one or both the index-fingers may be reversed, showing that there is
after all some truth in the notion that reversal should occur in them.
There is another phenomenon by twinning which, if we could understand
it, might help. I refer to the free-martin, the subject of one of John
Hunter's masterpieces of anatomical description. In horned cattle twin
births are rare, and when twins of opposite sexes are born, the male
is perfect and normal, but the reproductive organs of the female are
deformed and sterile, being known as a free-martin. The same thing
occasionally happens in sheep, suggesting that in sheep also twins may
be formed by the division of one ovum; for it is impossible to suppose
that mere development in juxtaposition can produce a change of this
character. I mention the free-martin because it raises a question of
absorbing interest. It is conceivable that we should interpret it by
reference to the phenomenon of gynandromorphism, seen occasionally in
insects, and also in birds as a great rarity. In the gynandromorph one
side of the body is male, the other female. A bullfinch for instance has
been described with a sharp line of division down the breast between the
red feathers of the cock on one side and the brown feathers of the hen
on the other. (Poll, H., _SB. Ges. Nat. Fr._, Berlin, 1909, p. 338.) In
such cases neither side is sexually perfect. If the halves of such a
gynandromorph came apart, perhaps one would be a free-martin.
The behaviour of homologous twinning in heredity has been little
studied. It does not exist as a normal feature in any animal which
is amenable to experiment, and we cannot positively assert that a
comparable phenomenon exists in plants; for in them--the Orange, for
example--polyembryony may evidently be produced by a parthenogenetic
development of nucellar tissue. It is possible that in Man twinning
is due to a peculiarity of the mother, not of the father. It may and
not rarely does descend from mother to daughter, but whether it can be
passed on through a male generation to a daughter again, there is not
sufficient evidence to show. The facts as far as they go are consistent
with the inference which may be drawn from Loeb's experiment, that the
twinning of a fertilized ovum may be determined not by the germ-cells
which united to form it, but by the environment in which it begins to
develop. The opinion that twinning may descend through the male directly
has been lately expressed by Dr. J. Oliver in the _Eugenics Review_
(1912), on the evidence of cases in which twins had occurred among the
relations of fathers of twins, but I do not know of any comprehensive
collection of evidence bearing on the subject.
Besides twinning of the whole body a comparable duplicity of various
parts of the same body may occur. Such divisions affect especially those
organs which have an axis of bilateral symmetry, such as the thumb, a
cotyledon, a median petal, the frond of a fern or the anal fin of a
fish. From the little yet known it is clear that the genetic analysis
of these conditions must be very difficult, but evidence of any kind
regarding them will be valuable. We want especially to know whether
these divisions are due to the _addition_ of some factor or power which
enables the part to divide, or whether the division results from the
_absence_ of something which in the normal body prevents the part from
dividing. Breeding experiments, so far as they go, suggest that the less
divided state is usually dominant to the more divided.[9] The two-celled
Tomato fruit is dominant to the many-celled type. The Manx Cat's tail,
with its suppression of caudal segmentation is a partial dominant over
the normal tail. The tail of the Fowl in what is called the "Rumpless"
condition is at least superficially comparable with that of the Manx
Cat, and though the evidence is not wholly consistent, Davenport
obtained facts indicating that this suppressed condition of the caudal
vertebrae is an imperfect dominant.[10]
Some evidence may also be derived from other examples of differences
which at first sight appear to be substantive though they are more
probably meristic in ultimate nature. The distinction between the
normal and the "Angora" hair of the Rabbit is a case in point. We can
scarcely doubt that one of the essential differences between these two
types is that in the Angora coat the hair-follicles are more finely
divided than they are in the normal coat, and we know that the normal,
or less-divided condition, is dominant to the Angora, or more finely
divided.
[Illustration: FIG. 3. _I_, _II_, _III_, various degrees of syndactyly
affecting the medius and annularis in the hand; _IV_, syndactyly
affecting the index and medius in the foot. (After Annandale.)]
In the case of the solid-hoofed or "mule-footed" swine, the evidence
shows, as Spillman has lately pointed out,[11] that the condition
behaves as a dominant. The essential feature of this abnormality is
that the digits III and IV are partially united. The union is greatest
peripherally. Sometimes the third phalanges only are joined to form one
bone, but the second and even the first phalanges may also be compounded
together. Here the variation is obviously meristic and consists in a
failure to divide, the normal separation of the median digits of the
foot being suppressed.
[Illustration: FIG. 4. Case of complete syndactyly in the foot. _II_ and
_III_, digit apparently representing the index and medius. _c_^{2} +
_c_^{3}, bone apparently representing the middle and external cuneiform;
_cb_, cuboid; _c_^{1}, internal cuneiform. (After Gruber.)]
Webbing between the digits, in at least some of its manifestations, is
a variation of similar nature. The family recorded by Newsholme[12]
very clearly shows the dominance of this condition. The case is
morphologically of great interest and must undoubtedly have a bearing on
the problems of the mechanics of Division. In discussing the phenomena
of syndactylism I pointed out some years ago that the digits most
frequently united in the human hand are III and IV, while in the foot,
union most frequently takes place between II and III.[13] In Newsholme's
family the union was always between II and III of the foot, except in
the case of one male who had the digits III and IV of the right _hand_
alone webbed together. There can be little doubt that the geometrical
system on which the foot is planned has an axis of symmetry passing
between the digits II and III, while the corresponding axis in the hand
passes between III and IV. Union between such digits may therefore be
regarded as comparable with any non-division or "coalescence" of lateral
structures in a middle line, and when as in these examples such a
condition is shown to be a dominant we cannot avoid the inference that
some concrete factor has the power of suppressing or inhibiting this
division. Figs. 3 and 4 illustrate degrees of union between digits in
the human hand and foot.
It is not in question that various other forms of irregular webbing
and coalescence of digits exist, and respecting the genetic behaviour
of these practically nothing is as yet known. Such a case is described
by Walker,[14] in which the first and second metacarpals of both
feet were fused in mother and daughter, and several more are found
in literature. Contrasted with these phenomena we have the curious
fact that in the Pigeon, Staples-Browne found webbing of the toes a
_recessive_ character. The question thus arises whether this webbing is
of the same nature as that shown to be a dominant in Man, and indeed
whether the phenomenon in pigeons is really meristic at all. There is
some difference perceptible between the two conditions; for in Man
there is not so much a development of a special web-like skin uniting
the digits as a want of proper division between the digits themselves,
and in extreme cases two digits may be represented by a single one. In
the Pigeon I am not aware that a real union of this kind has ever been
observed, and though the web-like skin may extend the whole length of
the digits and be so narrow as to prevent the spread of the toes, it
may, I think, be maintained that the unity of the digits is unimpaired.
For the present the nature of this variation in the pigeon's feet must
be regarded as doubtful, and we should note that if it is actually an
example of a more perfect division being dominant to a less perfect
division, the case is a marked exception to the general rule that
non-division is dominant to division.
Reference must also be made to the phenomenon of fasciation in the stems
of plants. As Mendel showed in the case of _Pisum_ this condition is
often a recessive. The appearances suggest that the difference between a
normal and a fasciated plant consists in the inability of the fasciated
plant to separate its lateral branches. The nature of the condition is
however very obscure and it is equally likely that some multiplication
of the growing point is the essential phenomenon.[15]
Stockard's interesting experiments[16] illustrate this question. He
showed that by treating the embryos of a fish (_Fundulus heteroclitus_)
with a dilute solution of magnesium salts, various cyclopian
monstrosities were frequently produced. These have been called cases
of _fusion_ of the optic vesicles. I would prefer to regard them as
cases of a division suppressed or restricted by the control of the
environment. Conversely, the splendid discovery of Loeb, that an
unfertilised egg will divide and develop parthenogenetically without
fertilisation, as a consequence of exposure to various media, may be
interpreted as suggesting that the action of those media releases
the strains already present in the ovum, though I admit that an
interpretation based on the converse hypothesis, that the medium acts as
a stimulus, is as yet by no means excluded.
In these cases we come nearest to the direct causation or the direct
inhibition of a division, but the meaning of the evidence is still
ambiguous. I incline to compare Loeb's parthenogenesis with the
development (and of course accompanying cell-division) of dormant buds
on stems which have been cut back.
It is interesting to note that sometimes as an abnormality, the
faculty of division gets out of hand and runs a course apparently
uncontrolled. A remarkable instance of this condition is seen in
_Begonia_ "_phyllomaniaca_", which breaks out into buds at any point on
the stem, petioles, or leaves, each bud having, like other buds, the
power of becoming a new plant if removed. We would give much to know the
genetic properties of _B. phyllomaniaca_, and in conjunction with Mr. W.
O. Backhouse I have for some time been experimenting with this plant.
It proved totally sterile. Its own anthers produce no pollen, and all
attempts to fertilise it with other species failed though the pollen of
a great number of forms was tried.
Recently however we have succeeded in making plants which are in every
respect _Begonia phyllomaniaca_, so far as the characters of stems and
leaves are concerned. These plants, of which we have sixteen, were made
by fertilising _B. heracleifolia_ with _B. polyantha_. They are all
beginning to break out in "phyllomania." As yet they have not flowered,
but as they agree in all details with _phyllomaniaca_ there can be
little doubt that the original plant bearing that name was a hybrid
similarly produced. The production of "phyllomania" on a hybrid Begonia
has also been previously recorded by Duchartre.[17] In this case the
cross was made between _B. incarnata_ and _lucida_. The synonymy of
the last species is unfortunately obscure, and I have not succeeded in
repeating the experiment.
[Illustration: FIG. 5. Piece of petiole of _Begonia phyllomaniaca_. The
proximal end is to the right of the figure.]
From these facts it seems practically certain that the condition is one
which is due to the meeting of complementary factors. At first sight
we may incline to think that the phyllomania is in some way due to the
sterility. This however cannot be seriously maintained; for not only is
sterility in plants not usually associated with such manifestations, but
we know a Begonia called "Wilhelma" which is exactly _phyllomaniaca_ and
equally sterile, though it has no trace of phyllomania. This plant arose
in the nurseries of MM. P. Bruant of Poitiers, and has generally been
described as a seedling of _phyllomaniaca_, but from the total sterility
of that form this account of its origin must be set aside.
[Illustration: FIG. 6. Two right hind feet of polydactyle cats. _II_
shows the lowest development of the condition yet recorded. The digit,
_d_^{1}, which stands as hallux is fully formed and has three phalanges.
Both it and the digit marked _d_^{2} are formed as _left_ digits. In the
normal hind foot of the cat the hallux is represented by a rudiment only.
_I_ shows a further development of the condition. In this foot there are
_six_ digits. _d_^{1} has two phalanges, but both it and _d_^{2} and
_d_^{3} are shaped as left digits. Thus _d_^{3}, which in the normal
foot would be shaped as a right digit, is transformed so as to look like
a _left_ digit.]
The phenomenon in this case can hardly be regarded as due to the
excitation of dormant buds, for it is apparent on examination that
the new growths are not placed in any fixed geometrical relation to
the original plant. They arise on the petiole, for example, as small
green outgrowths each of which gradually becomes a tiny leaf. The
attitude of these leaves is quite indeterminate, and they may point
in any direction, some having their apices turned peripherally, some
centrally, and others in various oblique or transverse positions (Fig.
5). These little leaves are thus comparable with seedlings, in that
their polarity is not related to, or consequent upon that of the parent
plant. They have in fact that "individuality," which we associate with
germinal reproduction.
There are many curious phenomena seen in the behaviour of parts normally
repeated in bilateral symmetry which may some day guide us towards
an understanding of the mechanics of division. A part like a hand,
which needs the other hand to complete its symmetry, cannot twin by
mere division, yet by proliferation and special modifications on the
radial side of the same limb, even a hand may be twinned. In the well
known polydactyle cats a change of this kind is very common and indeed
almost the rule. When extra digits appear at the inner (tibial) side
of the limb, they are shaped as digits of the other side, and even the
normal digit II (index) is usually converted into the mirror-image
of its normal self. The limb then develops a new symmetry in itself.
Nevertheless it is not easy to interpret these facts as meaning that
there has been some interruption in the control which one side of the
body exercises over the other. The heredity of polydactylism is complex
but there is little doubt that the condition familiar in the Cat is a
dominant. In some human cases also the descent is that of a dominant,
but irregularities are so frequent that no general rule can yet be
perceived. The dominance of such a condition is an exception to the
principle that the less-divided is usually dominant to the more-divided,
a fact which probably should be interpreted as meaning that divisions
are of more than one kind.
Among ordinary somatic divisions, whether of organs, cells, or patterns
of differentiation, the control of symmetry is usually manifested. There
is however one class of somatic differentiations which are exceptionally
interesting from the fact that they may show a complete independence
of such geometrical control. The most familiar examples of these
geometrically uncontrolled Variations are to be seen in bud-sports.
The normal differentiation of the organs of a plant is arranged on
a definite geometrical system, which to those who have never given
special attention to such things before, will often seem surprisingly
precise. The arrangement of the leaves on uninjured, free-growing shoots
can generally be seen to follow a very definite order, just as do the
flowers or the parts of the flowers. If however bud sports occur,
then though the parts included in the sports show all the geometrical
peculiarities proper to the sport-variety, yet the sporting-buds
themselves are not related to each other according to any geometrical
plan.
A very familiar illustration is provided by the distribution of colour
in those Carnations that are not self-coloured. The pigment may, as in
Picotees, be distributed peripherally with great regularity to the edges
of the petals; or, as in Bizarres and Flakes, it may be scattered in
radial sectors which show no geometrical regularity. Now in this case
the pigments are the same in both types of flower, and the chemical
factors concerned in their production must surely be the same. The
difference must lie in the mechanical processes of distribution of
the pigment. In the Picotee we see the orderly differentiation which
we associate with normality; in the Bizarre we see the disorderly
differentiation characteristic of bud-sports. The distribution of colour
in this case lies outside the scheme of symmetry of the plant.
Such a distribution is characteristic of bud-sports, and of certain
other differentiations in both plants and animals, which I cannot on
this occasion discuss. Now reflexion will show that these facts have
an intimate bearing on the mechanical problems of heredity. For first
in the bud-sports we are witnessing the distribution of factors which
distinguish genetic varieties. We do not know the physical nature of
those factors, but if we must give them a name, I suppose we should call
them "ferments" exactly as Boyle did in 1666. He is discussing how it
comes about that a bud, budded on a stock, becomes a branch bearing the
fruit of its special kind. He notes that though the bud inserted be "not
so big oftentimes as a Pea," yet "whether by the help of some peculiar
kind of Strainer or by the Operation of some powerful Ferment lodged in
it, or by both these, or some other cause," the sap is "so far changed
as to constitute a Fruit quite otherwise qualify'd."[18] We can add
nothing to his speculation, and we believe still that by a differential
distribution of "ferments" the sports are produced. All the factors are
together present in the normal parts; some are left out in the sport. In
an analogous case however, that of a variegated _Pelargonium_ which has
green and also albino shoots, Baur proved that the shoots pure in colour
are also pure in their posterity. There can be no doubt that the sports
of Carnations, Azaleas, Chrysanthemums, etc., would behave in the same
way.
The well-known Azaleas Perle de Ledeburg, President Kerchove,
and _Vervaeana_ are familiar illustrations. Perle de Ledeburg is
predominantly white, but it has red streaks in some of its flowers. It
not very rarely gives off a self-red sport. This is evidently due to
the development of a bud in a red-bearing area of the stem. The red in
this plant is not under "geometrical control." Many plants have white
flowers with no markings, but if the red markings are geometrically
ordered differentiations, no self-coloured sports are formed. The case
of _Vervaeana_ is a good illustration of this proposition. It has white
flowers with red markings arranged in an orderly manner on the lower
parts of the petals, especially on the dorsal petals. This is one of the
Azaleas most liable to have red sports, and at first sight it might seem
that the sport represented the red of the central marks. Examination
however of a good many flowers shows that irregular red streaks like
those of Perle de Ledeburg occur, about as commonly as in that variety.
_Vervaeana_ in fact is Perle de Ledeburg with _definite_ red markings
added, and its red sports obviously are those branches the germs of
which came in a patch of the stem bearing these red elements. That this
is the true account is rendered quite obvious by the fact that the red
of the sport is a colour somewhat different from that of the definite
marks, and that these marks are still present on the red ground of the
sporting flowers.
It will be understood that these remarks apply to those cases in which
the production of sports is habitual or frequent, and I imagine in
all such examples it will be found that there are indications of
irregularity in the distribution of the differentiations such as to
justify the view that they are not under that geometrical control which
governs the normal differentiation of the parts. The question next
arises whether these considerations apply also to the production of a
bud-sport as a rare exception, but by the nature of the case it is not
possible to say positively whether the appearance of an exceptional
sport is due to the unsuspected presence of a pre-existing fragment of
material having a special constitution, or to the origin, _de novo_, of
such a material. For instance one of the garden forms of _Pelargonium_
known as _altum_ is liable perhaps once in some hundreds of flowers to
have one or two magenta petals. The normal colour is a brilliant red;
and as we may be fairly sure that this red is recessive to magenta the
interpretation would be quite different according as the appearance of
the magenta is regarded as due to the presence of small areas endowed
with magentaness, or to the spontaneous generation of the factor for
that pigment. Either interpretation is possible on the facts, but the
view that the whole plant has in it scarce mosaic particles of magenta
seems on the whole more consistent with present knowledge.
In _Pelargonium altum_ the enzyme causing the magenta colours must
be distributed in very small areas, but a case in which the magenta
is similarly arranged in a much coarser patchwork may be seen in the
_Pelargonium_ "Don Juan," which often bears whole trusses or branches of
red flowers upon plants having the normal dominant magenta trusses. In
most cases there is little doubt that though the magenta flowered parts
can "sport" to red, the red parts could not produce the magenta flowers.
The asymmetrical, or to speak more precisely, the disorderly, mingling
of the colours in the somatic parts is thus an indication of a similarly
disorderly mixing of the factors for those colours in the germ-tissues,
so that some of the gametes bear enough of the colour-factors to make a
self-coloured plant, while others bear so little that the plant to which
they give rise is a patchwork. If this view is correct we may extend it
so far as to consider whether the fineness or coarseness of the mixture
visible in the flowers or leaves may not give an indication of the
degree to which the factors are subdivided among the germ-cells. We know
very little about the genetic properties of striped varieties. In both
_Antirrhinum_ and _Mirabilis_ it has been found that the striped may
occasionally and irregularly throw self-coloured plants, and therefore
the striping cannot be regarded simply as a recessive character. On the
other hand in _Primula Sinensis_ there are well-known flaked varieties
which ordinarily at least breed true. Whether these ever throw selfs I
do not know, but if they do it must be quite exceptionally. The power
of these flaked plants to breed true is, I suspect, connected with the
fact that in their flowers the coloured and white parts are _intimately_
mixed, this intimate mixture thus being an indication of a similarly
intimate mixture in the germ-cells. It would be important to ascertain
whether self-fertilised seed from the occasional flowers in which the
colour has run together to join a large patch gives more self-coloured
plants than the intimately flaked flowers do.
The next fact may eventually prove of great importance. We have seen
that in bud-sports the differentiation is of the same nature as
that between pure types, and also that in the sporting plant this
differentiation is distributed without any reference to the plant's
axis, or any other consideration of symmetry. Now among the germ-cells
of a Mendelian hybrid exactly such characters are being distributed
allelomorphically, and there again we have strong evidence for believing
that the distribution obeys no pattern. For example, we can in the case
of seeds still _in situ_ perceive how the characters were distributed
among the germ-cells, and there is certainly no obvious pattern
connecting them, nor can we suppose that there is an actual pattern
obscured.
Of this one illustration is especially curious. Individual plants of
the same species are, as regards the decussations of their leaves and
in other respects, _either rights or lefts_. The fact is not emphasized
in modern botany and is in some danger of being forgotten. When, as
in the flowers of Arum, some _Gladioli_, _Exacum_, _St. Paulia_, or
the fruits of _Loasa_, rights and lefts occur on the same stem,
they come off alternately. But if, as in the seedlings of Barley the
twist of the first leaf be examined, it will be seen to be either a
right-or left-handed screw. An ear of barley, say a two-row barley,
is a definitely symmetrical structure. The seeds stand in their
envelopes back to back in definite positions. Each has its organs
placed in perfectly definite places. _If these seeds were buds_ their
differentiations would be grouped into a common plan. One might expect
that the differentiations of these embryos would still fall into the
pattern; but they do not, and so far as I have tested them, any one
may be a right or a left, just as each may carry any of the Mendelian
allelomorphs possessed by the parent plant, without reference to the
differentiation of any other seed. The fertilisation may be responsible,
but our experience of the allelomorphic characters suggest that the
irregularity is in the egg-cells themselves.[19]
_Germ cells thus differ from somatic cells in the fact that their
differentiations are outside the geometrical order which governs
the differentiation of the somatic cells._ I can think of possible
exceptions, but I have confidence that the rule is true and I regard it
as of great significance.
The old riddle, what is an individual, finds at least a partial solution
in the reply that an individual is a group of parts differentiated in a
geometrically interdependent order. With the germ-cell a new geometrical
order, with independent polarity is almost if not quite always, begun,
and with this geometrical independence the power of rejuvenescence may
possibly be associated.
The problems thus raised are unsolved, but they do not look insoluble.
The solution may be nearer than we have thought. In a study of the
geometry of differentiation, germinal and somatic, there is a way
of watching and perhaps analyzing what may be distinguished as the
mechanical phenomena of heredity. If any one could in the cases of
the Picotee and the Bizarre Carnation, respectively, detect the real
distinction between the two types of distribution, he would make a
most notable advance. Any one acquainted with mechanical devices can
construct a model which will reproduce some of these distinctions more
or less faithfully. The point I would not lose sight of is that the
analogy with such models must for a long way be a true and valuable
guide. I trust that some one with the right intellectual equipment will
endeavor to follow this guide; and I am sanguine enough to think that a
comprehensive study of the geometrical phenomena of differentiation will
suggest to a penetrative mind that critical experiment which may one day
reveal the meaning of spontaneous division, the mystery through which
lies the road, perhaps the most hopeful, to a knowledge of the nature of
life.
FOOTNOTES:
[1] In saying this we make no assumption as to the particular
cell-division at which differentiation occurs. This may be one of the
maturation-divisions, or it may perhaps be much earlier.
[2] From the recent discoveries of Erwin Baur we are led to surmise
that in the flowering plants the sub-epidermal layer, or some of its
elements, may legitimately be regarded as a similar germ-substance,
continuous in Weismann's sense.
[3] These fraternal twins, which show no special resemblance to each
other, are like the multiple births of other animals, and there is no
disposition for them to be of the same sex. In the sheep, for example,
statistics show that the frequency of pairs of twins, male and female,
is approximately double that of the frequency of pairs, both male or
both female, as it should be if the sex-distribution were fortuitous.
For instance Bernadin (_La Bergerie de Rambouillet_, 1890, p. 100)
gives the following figures for twin-lambs in Merinos: both male, 87;
both female, 83; sexes mixed, 187. The 9-banded Armadillo (_Dasypus
novemcinctus_), in which the young born in one litter are said to be
always of one sex, is the only known exception in Vertebrates, and
is presumably a genuine case of normal polyembryony (see especially,
Rosner, _Bull. Ac. Soc. Cracovie_, 1901, p. 443, and Newman and
Patterson, _Biol. Bull._, XVII, 1909, p. 181), and an important paper
lately published by H. H. Newman and J. T. Patterson, _Jour. Morph._,
1911, XXII, p. 855.
[4] A good collection of evidence as to disease in homologous twins was
lately published by E. A. Cockayne, _Brit. Jour. Child. Diseases_, Nov.,
1911.
[5] Cp. Windle, B. C. A., _Jour. Anal. Phys._, XXVI, p. 295.
[6] Mr. E. Nettleship tells me that in the course of collecting
pedigrees of families containing colour-blind members he has discovered
two cases (shortly to be published) of pairs of twins, which on account
of their very close resemblances must be deemed homologous, one of each
pair being colour-blind and the other normal. Such a distinction between
closely similar twins is most curious and unexpected.
[7] Another paradoxical phenomenon of the same nature occurs in the
Narwhal The males normally have the _left_ tusk alone developed, the
corresponding right tusk remaining as an undeveloped rudiment in its
socket. The left tusk is a left-handed screw. Occasionally the right
tusk is also developed and grows to the same length as that of the
left side, but in such specimens the right tusk is also a left-hand
screw like the tusk of the other side, instead of being reversed as we
should certainly have expected. It need scarcely be remarked that in the
case of the horns of antelopes, and in other examples of spiral organs
arranged in pairs, that of one side of the body is the mirror image of
that on the other side. The Narwhal's tusks in being both twisted in the
same direction are thus highly anomalous, and are comparable with pairs
of twins.
[8] Wilder, H. H., _Amer. Jour. Anat._, 1904, III, p. 452.
[9] Polydactylism which is often a dominant and the web-foot of Pigeons
which is recessive should be remembered as possible exceptions (see p.
49).
[10] Davenport inclined at first to regard rumplessness as a recessive,
but in his latest publication on the subject he definitely concludes
that it is an imperfect dominant. This conclusion accords well with
evidence quoted by Darwin (_An. and Plts._, II, ed. 2, p. 4) that
rumpless fowls may throw tailed offspring. (_Amer. Nat._, 1910, XLIV, p.
134.)
[11] Spillman, W. J., _Amer. Breeders Mag._, 1910, I, p. 178.
[12] Newsholme, _Lancet_, December 10, 1910, p. 1690.
[13] _Materials for the Study of Variation_, 1894, p. 358.
[14] Walker, G., _Johns Hopkins Hospital Bulletin_, XII, 1901, p. 129.
[15] Cp. R. H. Compton, _New Phytologist_, 1911, p. 249.
[16] _Arch. f. Entwickelungsmech._, 1907, XXIII, p. 249.
[17] Bull. Soc. Bot. de France, xxxiv, 1887, p. 182.
[18] R. Boyle, _The Origine of Formes and Qualities_, Oxford, 1666.
[19] Remarkable experiments on this question have lately been carried
out by R. H. Compton (_Camb. Phil. Soc._, XV, 1910, p. 495), showing
that in a certain Barley, "Plumage Corn," the average ratio of left to
right is about 1.5. A fuller paper has since been published by Compton,
_Jour. Genetics_, 1912, II, I, p. 53.