considered as ‘reducing divisions.’ I refer to all those cases in which
the longitudinal splitting of the loops is either entirely wanting, or
does not occur until after the loops have left the equator of the
spindle and have moved towards the poles. In both instances the bearing
upon the question would be the same, for only half the number of
primary loops would reach each pole in either case. If therefore the
primary loops are not made up of identical pairs, it follows that the
two daughter-nuclei can only contain half the number of ancestral
germ-plasms which were contained in the mother-nucleus. Whether the
loops divide on their way to the poles or at the poles themselves, no
difference will be brought about in the number of ancestral germ-plasms
which they contain, for this number can neither increase nor diminish.
The _quantity_ of the different ancestral germ-plasms can alone be
increased in this way. I am here referring to observations made by
Carnoy[261] on the cells which form the spermatozoa in various
Arthropods. It must be admitted, however, that these divisions cannot
be regarded as ‘reducing divisions,’ if Flemming’s[262] suggestion be
confirmed, that in all these observations the fact has been overlooked
that the equatorial loops are not primary but secondary, and that they
have arisen from the longitudinal splitting of the nuclear thread
during previous stages of nuclear division. But this point can only be
decided by renewed investigation. Although many excellent results have
been obtained in the subject of karyokinesis, there is still very much
to be learnt before our knowledge is complete; and this is not to be
wondered at when we remember the great difficulties in the way of
observation which are chiefly raised by the minute size of the objects
to be investigated. Flemming’s most recent publications prove that we
are still in the midst of investigation, and that highly interesting
and important processes have hitherto escaped attention. A secure basis
of facts is only very gradually obtained, and there are still many
conflicting opinions upon the details of this process. I should
therefore consider it to be entirely useless, from my point of view, to
enter into a critical examination of everything known about all the
details of karyokinesis. I am quite content to have shown how it may be
imagined that the reduction required by my theory takes place during
nuclear division; and at the same time to have pointed out that there
are already observations which may be interpreted in this sense. But
even if I am mistaken in this interpretation, the theoretical necessity
for a reduction in the number of ancestral germ-plasms, a reduction
repeated in every generation, seems to me to be so securely founded
that the processes by which it is effected _must_ take place, even if
they are not supplied by the facts already ascertained. There must be
two kinds of karyokinesis according to the different physiological
effect of the process. First, a karyokinesis by means of which all the
ancestral germ-plasms are equally distributed in each of the two
daughter-nuclei after having been divided into halves: secondly, a
karyokinesis by means of which each daughter-nucleus receives only half
the number of ancestral germ-plasms possessed by the mother-nucleus.
The former may be called ‘equal division,’ the latter ‘reducing
division.’ Of course these two processes, which differ so greatly in
their effects, must also be characterized by morphological differences,
but we cannot assume that the latter are necessarily visible. Just as,
during the division of the first and second nuclear spindle in the egg
of _Ascaris megalocephala_, karyokinesis takes, upon the whole, the
same morphological course, although we must ascribe different
physiological meanings to the two processes of division,—so it may be
in other cases. The ‘reducing division’ must be always accompanied by a
reduction of the loops to half their original number, or by a
transverse division of the loops (if such division ever occurs);
although reduction can only occur when the loops are not made up of
identical pairs. And it will not always be easy to decide whether this
is the case. On the other hand, the form of karyokinesis in which a
longitudinal splitting of the loops takes place _before_ they separate
to form the daughter-nuclei must always, as far as I can see, be
considered as an ‘equal division.’ In the accompanying figures II and
III, diagrams are given illustrating these two forms of karyokinesis,
but I do not mean to imply that it is impossible to imagine any other
form in which they may occur.
In Figure II a nuclear spindle is seen at _A_, and at its equatorial
zone there are twelve primary loops. The transverse cross-lines and
other markings on the loops indicate that they are composed of
different ancestral germ-plasms. The loops are shaded differently in
order to render the diagram clear. At _B_ six of the loops are seen to
have moved to either pole, so that the figure is a representation of
the ‘reducing division.’ Figure III is a diagrammatic representation of
‘equal division.’ The six loops at the equatorial zone of _A_ are shown
by different cross-lining and shading to be composed of different
ancestral germ-plasms. The loops split longitudinally in a direction
indicated by the longitudinal line upon each of them. In _B_ the halves
of the loops are seen to have moved to the opposite poles of the
spindle, so that there are not only six loops at each pole, but also
all the six combinations of ancestral germ-plasms.
[Illustration: Figs. II, III.]
Perhaps some may be inclined to look upon direct nuclear division as a
‘reducing division,’ but I believe that such a view would be incorrect.
It is only approximately true that the nuclear thread is divided into
two halves of equal quantity by direct division, and exact equality
would only happen as it were accidentally; so that we cannot speak of a
perfectly equal distribution of the ancestral germ-plasm in the two
daughter-nuclei. But the ‘reducing division’ must obviously effect an
exactly regular and uniform distribution of the ancestral germ-plasms,
although this does not imply that every ancestral germ-plasm of the
mother-nucleus would be represented in each of the two daughter-nuclei.
But if out of e.g. eight nuclear loops at the equatorial plane, four
pass into one, and the other four into the other daughter-nucleus, each
of the latter will contain an equal number of ancestral germ-plasms,
although different ones. This is indeed part of the foundation of the
theory, for the ‘reducing division’ must remove exactly half of the
original number of ancestral germ-plasms, and precisely the same number
must be replaced at a later period by the sperm-nucleus. This could
hardly be achieved with sufficient precision by direct nuclear division.
I now come to inquire whether the expulsion of the second polar body is
in reality, as I have already maintained, a reduction in the number of
ancestral germ-plasms present in the nucleus of the egg. The view
itself is sufficiently obvious, and it would supply an explanation of
the meaning of the process which is still greatly wanted; but it will
nevertheless be not entirely useless to consider other possible
theories.
It would be quite conceivable to suppose that the youngest egg-cells,
which multiply by division, may undergo one ‘reducing division’ in
addition to the ordinary process. Of course this should occur once
only, for if repeated, the number of ancestral idioplasms in the
nucleus of the germ-cell would undergo a decrease greater than could be
afterwards compensated by the increase due to fertilization. Thus the
number of ancestral germ-plasms would continually decrease in the
course of generations,—a process which would necessarily end with their
complete reduction to a single kind, viz. to the paternal or the
maternal germ-plasm. But the occurrence of such a result is disproved
by the facts of heredity. Although such an early occurrence of the
‘reducing division’ would offer advantages in that nothing would be
lost, for both daughter-nuclei would become eggs, instead of one of
them being lost as a polar body, nevertheless I do not believe that it
really occurs: weighty reasons can be alleged against it.
Above all, the facts of parthenogenesis are against it. If the number
of ancestral germ-plasms received from the parents were reduced to half
in the ovary of the young animal, how then could parthenogenetic
development ever take place? It is true that we cannot at once assert
the impossibility of an early ‘reducing division’ on this account, for
as I have shown above, the power to develope parthenogenetically
depends upon the quantity of germ-plasm contained in the mature egg;
the necessary amount might be produced by growth, quite independently
of the number of different kinds of ancestral germ-plasms which form
its constituents. The size of a heap of grains may depend upon the
number of grains, and not upon the number of different kinds of grains.
But in another respect such a supposition would lead to an unthinkable
conclusion. In the first place, the number of ancestral germ-plasms in
the germ-cells would be diminished by one half in each new generation
arising by the parthenogenetic method; thus after ten generations only
1/1024 of the original number of ancestral germ-plasms would be present.
Now, it might be supposed that the ‘reducing division’ of the young
egg-cells was lost at the time when the parthenogenetic mode of
reproduction was assumed by a species; but this suggestion cannot hold,
because there are certain species in which the same eggs can develope
either sexually or parthenogenetically (e.g. the bee). It seems to me
that such cases distinctly point to the fact that the reduction in the
number of ancestral germ-plasms must take place immediately before the
commencement of embryonic development, or, in other words, at the time
of maturation of the egg. It is only decided at this time whether the
egg of the bee is to develope into an embryo by the parthenogenetic or
the sexual method; such decision being brought about, as was shown
above, by the fact that only one polar body is expelled in the first
case, while two are expelled in the second. But if we are obliged to
assume that reproduction by means of fertilization, necessarily implies
a reduction to one half of the number of ancestral germ-plasms
inherited from the parents,—the further conclusion is obvious, that the
second division of the egg-nucleus and the expulsion of the second
polar body represent such a reduction, and that this second division of
the egg-nucleus is unequal in the sense mentioned above, viz. one half
of the ancestral germ-plasms remains in the egg-nucleus, the original
number being subsequently restored by conjugation with a sperm-nucleus;
while the other half is expelled in the polar body and perishes.
I may add that observations, so far as they have extended to such
minute processes, do indeed prove that the number of loops is reduced
to one half. It has been already mentioned that, according to Carnoy,
such reduction occurs in _Ascaris megalocephala_, but the same author
also describes the process of the formation of polar bodies in a large
number of other _Nematodes_[263], and his descriptions show that the
process occurs in such a way that the number of ancestral germ-plasms
must be reduced by half. Sometimes half the number of primary loops
pass into the nucleus of the polar body, while the other half remains
in the egg. In other cases, as in _Ophiostomum mucronatum_, the primary
nuclear rods divide transversely,—a process which must produce the same
effect. It is true that these observations require confirmation, and
since, with unfavourable objects, the difficulties of observation are
extremely great, there may have been errors of detail; but I do not
think that there is any reason for doubting the accuracy of the
essential point. And this essential point is the fact that the number
of primary loops is divided into half by the formation of the polar
body.
But even if we could not admit that such a conclusion is securely
founded, it cannot be doubted that the formation of the second polar
body reduces to one half the quantity of the nucleus which would have
become the segmentation-nucleus in the parthenogenetic development of
the egg. This is a simple logical conclusion from the two following
facts: first, parthenogenetic eggs expel only _one_ polar body;
secondly, there are eggs (such as those of the bee) in which it is
absolutely certain that the same half of the nucleus—which is expelled
as the second polar body in the egg requiring fertilization—remains in
the egg when it is to develope parthenogenetically, and acts as half of
the segmentation-nucleus. But this proves that the expelled half of the
nucleus must consist of true germ-plasm, and thus a secure foundation
is laid for the assumption that the formation of the nucleus of the
second polar body must be considered as a ‘reducing division.’
I was long ago convinced that sexual reproduction must be connected
with a reduction in the number of ancestral germ-plasms to one half,
and that such reduction was repeated in each generation. When, in 1885,
I brought forward my theory of the continuity of the germ-plasm, I had
long before that time considered whether the formation and expulsion of
polar bodies must not be interpreted in this sense. But the two
divisions of the egg-nucleus caused me to hesitate. The two divisions
did not seem to admit of such an interpretation, for by it the quantity
of the nucleus is not divided into halves, but into quarters. But a
division of the number of ancestral germ-plasms into quarters would
have caused, as was shown above, a continuous decrease, leading to
their complete disappearance; and such a conclusion is contradicted by
the facts of heredity. For this reason I was led at that time to oppose
Strasburger’s view that the expulsion of the polar bodies means a
reduction of the quantity of nuclear substance by only half. My
objection to such a view was valid when I said that the quantity of
idioplasm contained in the egg-nucleus is not, as a matter of fact,
reduced to one half, but to one quarter, inasmuch as two successive
divisions take place. I may add that I had also considered whether the
two successive divisions might not possess an entirely different
meaning,—whether one of them led to the removal of ovogenetic
nucleoplasm, while the other resulted in a reduction in the number of
ancestral germ-plasms. But at that time there were no ascertained facts
which supported the supposition of such a difference, and I did not
wish to bring forward the idea, even as a suggestion, when there was no
secure foundation for it. The morphological aspects of the formation of
the first and second polar bodies are so extremely similar that such a
supposition might have been considered as a mere effort of the
imagination.
Hensen[264] also rejected the second part of the supposition that
reduction must take place in the number of the hereditary elements of
the egg, and that such reduction is caused by the expulsion of polar
bodies, because he believed it to be incompatible with the fact, which
had just been discovered, that polar bodies are formed by
parthenogenetic eggs. He concludes with these words: ‘If this striking
fact be confirmed, the hypothesis which assumes that the egg must be
divided into half before maturation, is refuted, and there only remains
the rather vague explanation that a process of purification must
precede the development of the embryo.’ Nevertheless Hensen is the only
writer who has hitherto taken into consideration the idea that sexual
reproduction causes a regularly occurring ‘diminution in the hereditary
elements of the egg.’
III. THE FOREGOING CONSIDERATIONS APPLIED TO THE MALE GERM-CELLS.
If the result of the previous considerations be correct, and if the
number of ancestral germ-plasms contained in the nucleus of the
egg-cell destined for fertilization must be reduced by one half, there
can be no doubt that a similar reduction must also take place, at some
time and by some means, in the germ-plasms of the male germ-cells. This
must be so if we are correct in maintaining that the young germ-cells
of a new individual contain the same nuclear substance, the same
germ-plasm, which was contained in the fertilized egg-cell from which
the individual has been developed. The young germ-cells of the
offspring must contain this substance if my theory of the continuity of
the germ-plasm be well founded, for this theory supposes that, during
the development of a fertilized egg, the whole quantity of germ-plasm
does not pass through the various stages of ontogenetic development,
but that a small part remains unchanged, and at a later period forms
the germ-cells of the young organism, after having undergone an
increase in quantity. According to this supposition therefore the
germ-plasm of the parents must be found unchanged in the germ-cells of
the offspring. If this theory were false, if the germ-plasm of the
germ-cells were formed anew by the organism, perhaps from Darwin’s
‘gemmules’ which pour into the germ-cells from all sides, it would be
impossible to understand why it has not been long ago arranged that
each germ-cell should receive only half the number of the ancestral
gemmules present in the body of the parent. Hence the expulsion of the
second polar body—assuming the validity of my interpretation—is an
indirect proof of the soundness of the theory of the continuity of the
germ-plasm, when contrasted with the theory of pangenesis. If
furthermore, a kind of cyclical development of the idioplasm took
place, as supposed by Strasburger, and if its final ontogenetic stage
resulted in the re-appearance of the initial condition of the
germ-plasm, we should fail to understand how any of the ancestral
germ-plasms could be lost during such a course of development.
Whichever view, the latter or the theory of the continuity of the
germ-plasm, be correct, in either case the male germ-cells of the young
animal must contain the same germ-plasm as that which existed in the
fertilized maternal egg, that is to say, they must contain all the
ancestral germ-plasms of the father and the mother. Here therefore a
reduction must occur, for otherwise the number of ancestral germ-plasms
would be increased by one half at every fertilization. The egg-cell
would furnish 1/2, but the sperm-cell 2/2 of the total quantity of
germ-plasm present in the germ-cells of the parents. But there is no
reason for believing that the reduction of germ-plasm in the sperm-cell
must proceed in precisely the same way as in the egg-cell, viz. by the
expulsion of a polar body. On the contrary, the processes of
spermatogenesis are so remarkably different from those of ovogenesis
that we may expect to find that reduction is also brought about in a
different manner.
The egg-cell does not expel the superfluous ancestral germ-plasms until
the end of its development, and in a form which induces the destruction
of the separated portion. This is certainly remarkable, for germ-plasm
is a most important substance, and although it seems to be wasted in
the production of enormous quantities of sperm- and egg-cells, such
waste is only apparent, and is in reality the means which renders the
species capable of existence. It may perhaps be possible to prove that
in this case also the waste is only apparent. Such proof would be
forthcoming if it could be shown that the means by which reduction is
brought about in eggs is advantageous, and therefore also, _ceteris
paribus_, necessary. We see that everywhere, as far as our observation
extends, the useful is also the actual, unless indeed it is impossible
of attainment or can only be attained by the aid of processes which are
injurious to the species. And if it be asked why germ-plasm is wasted
in the maturation of egg-cells, the following may perhaps be a
satisfactory answer.
Let us suppose that the necessary reduction of the germ-plasm does not
take place by the separation of the second polar body, but that it
happens during the first division of the first primitive-germ-cell
which is found in the embryo, so that the two first egg-cells resulting
from this division would already contain only half the number of
ancestral germ-plasms from the father and the mother, contained in the
fertilized egg-cell. In this case the main object, the reduction of the
ancestral germ-plasms, would be gained by a single division, and all
the succeeding nuclear divisions, causing the multiplication of these
two first germ-cells, might take place by the ordinary form of nuclear
division, viz. ‘equal division.’ But perhaps nature not only cares for
this one main object alone, but also secures certain secondary
advantages at the same time. In the case which we have supposed the
egg-cells of the mature ovary would only contain two different
combinations of germ-plasm, which we may call combinations _A_ and _B_.
Even if millions of egg-cells were formed, every one of them would
contain either _A_ or _B_, and hence (at least as far as the female
pronucleus is concerned) only two kinds of individuals could arise from
such eggs—viz. offspring _A’_ and _B’_. All the offspring _A’_ would be
as similar to one another as identical twins, and the same would be
true of offspring _B’_.
But if the 100th instead of the 1st embryonic germ-cell entered upon
the ‘reducing division,’ a hundred cells would undergo this division at
the same time, and thus two hundred different combinations of ancestral
germ-plasm would arise, and two hundred different kinds of germ-cells
would be found in the mature ovary. A still greater number of different
combinations of hereditary tendencies would arise if the ‘reducing
division’ occurred still later; but undoubtedly the diversity in the
composition of the germ-plasm must be greatest of all when the
‘reducing division’ does not take place during the period in which the
germ-cells undergo multiplication, but at the end of the entire course
of ovarian development, and separately in each full-grown mature egg
ready for embryonic development. In such a case there will be as many
different combinations of ancestral germ-plasms as there are eggs, for,
as I have shown above, it is hardly conceivable that such a complex
body as the nuclear substance of the egg-cell—composed of innumerable
different units—would ever divide twice in precisely the same manner.
Every egg will therefore contain a somewhat different combination of
hereditary tendencies, and thus the offspring which arise from the
different germ-cells of the same mother can never be identical. Hence
by the late occurrence of the ‘reducing division’ the greatest possible
variability in the offspring is secured.
If my interpretation of the second polar body be accepted, it is
obvious that the late occurrence of the ‘reducing division’ is proved.
At the same time we receive an explanation of the advantage gained by
the postponement of the reduction of the germ-plasm until the end of
the ovarian development of the egg; because the greatest possible
number of individual variations in the offspring are produced in this
way.
If I am not mistaken, this argument lends additional support to the
idea which I have previously propounded,—that the most important duty
of sexual reproduction is to preserve and continually call forth
individual variability, the foundation upon which the transformation of
species is built[265].