equalizing or neutralizing of individual differences which it effects.
Quetelet and Galton have attempted to show that intercrossing leads to
a mean which then remains constant. Haycraft supposes that a species
can only remain constant if its individuals are being continually
intercrossed, and that otherwise they would diverge and take different
forms, because the 'protoplasm' has within itself the tendency to
continual variation. The transformation of species is effected by
means of this variation tendency, and the persistency and constancy
of species which are already adapted to the conditions of their life
are secured by the constant intercrossing of the individuals, and the
consequent neutralization of individual peculiarities.
Although the cases already mentioned in which great constancy of
species is associated with purely parthenogenetic reproduction do
not tell in favour of the accuracy of the view just stated, yet
the fundamental idea, that amphigony is an essential factor in the
maintenance and even in the evolution of species, is undoubtedly sound.
We should certainly find neither genera nor species in Nature if
amphigony did not exist; but we cannot simply suppose that amphigony
and variation are, so to speak, antipodal forces, the former of which
secures the constancy of the species, the latter its transformation.
In my opinion, at all events, there is no such thing as a 'tendency'
of the protoplasm to vary, although there is a constant fluctuation of
the characters--dependent on the imperfect equality of the external
influences, especially of nutrition. This certainly results, as far
as it takes place within the germ-plasm, in a continual upward and
downward variation of the hereditary tendencies, and it would lead to
increasing dissimilarity of the individuals were it not that amphigony
is continually equalizing the differences by a constantly repeated
mingling of individuals. Quetelet and Galton have shown that the
tendency of this mingling is towards the establishment of a mean; the
characters of Man, such as bodily size, fluctuate about a mean, which
at the same time shows the maximum of frequency; and the frequency
curve of the various bodily sizes assumes a perfectly symmetrical
form, so that the average size is the most frequent, and deviations
from it upwards or downwards occur more rarely in proportion to the
amount of deviation, the largest and the smallest sizes occurring least
frequently.
Thus an equalizing of variations by means of amphimixis really exists,
and the question we have to ask is, How does it come about? The case
is assuredly not the same as that in which equal quantities of red
and white wine are mixed to make a so-called 'Schiller.' This is
proved even by the fact that the mixture may turn out quite different
even when the wines--the two parents--are alike: for the children
of a pair are often dissimilar. And while the 'Schiller' cannot be
separated again into red wine and white, this happens often in sexual
reproduction, and sometimes to such an extent that the grandchild
exactly resembles one or other of the grand-parents, as is most clearly
proved in the case of plant-hybrids.
There is thus a deep-seated difference, depending on the fact that
what is mingled in amphigony is not simple but composite, not a
simple uniform developmental tendency associated with a simple and
definite substance, but a combination of several or many developmental
tendencies, associated with several equivalent but different material
units. These units are the ids or ancestral plasms, and we have seen
how they are not only halved by reducing division, but are also
arranged in new combinations in amphimixis.
These ids differ very little within the same germ-plasm; in species
which have long been established the majority probably only differ
in correspondence to the individual differences of the fully-formed
organisms, but they are only absolutely alike in the case of two
ids which have been formed by the division of a mother-id. Let us
disregard this for the moment, and assume that all the ids of a
germ-plasm are different: the germ-plasm of a father, _A_, will be
composed of ids _A_ 1-100, that of the mother, _B_, of the ids _B_
1-100. But in each mature germ-cell of these two parents only fifty
ids are contained, and if we assume that the mingling of the ids is
controlled solely by chance, then in the various germ-cells _A_ × _B_
the most diverse combinations of ids may be contained; for instance,
_A_ 1, 3, 5, 7, 9, 11, ...to 99, or _A_ 1-10 and 20-30, and 40-50,
and so on, and similarly in the germ-cells _B_. If all germ-cells
produced by _A_ and by _B_ attained to development, or even if all the
ova succeeded, the thousand or hundred thousand children of this pair
would necessarily exhibit every possible mingling of their characters,
and each in the same number according to the rules of probability
calculations. But it is well known _that this does not happen_; of
the thousands of human ova, for instance, which come to maturity in
the course of the life of a female individual more than ten rarely
develop, and more than thirty never, and these are determined solely
by chance and quite independently of the mixture of ids which they
contain. It is thus purely a matter of chance which of the complexes
of primary constituents contained in the germ-plasm of an individual
are transmitted to descendants, and it is also purely a matter of
chance which combination of ids comes to be developed. Therefore we may
say that no regular neutralizing of contrasts, either in the primary
constituents of the parents or as regards the differences in their
characters, can occur. In one case there is a blended inheritance;
in another the child takes after the father or after the mother; in a
third, and this probably occurs most frequently, the child resembles
the father in some characters and the mother in others.
But how then does Galton's curve of frequency of variations come about?
Why does the mean of any character occur by far the most frequently,
and why does the frequency of a variation diminish regularly in
proportion to its approximation to either extreme? To this it is
answered: Because the process of mingling through amphigony goes on
through numerous generations, and thus an elimination of chance, and
the establishment of an average, must be brought about.
But this does not quite suffice to explain matters, for experience
shows that asymmetrical frequency-curves of variations also occur, even
in species with sexual reproduction. As De Vries has recently shown,
there are also 'half-Galton curves,' that is, curves which suddenly
break off at their highest point. We must conclude from this that the
frequency of the different variations depends not only on their degree,
but also on the greater or less facility with which they arise from the
constitution of the species.
This consideration can be readily elucidated with the help of
Ammon's exposition, and especially of his graphic representation
of the 'playground of variations.' If we think of the indifferent
variations occurring in any character of a species as arranged in
a series ascending from the smallest to the largest, this line may
be regarded as the abscissal-axis, and from it ordinates may be
drawn which express the frequency of the variation in question by
the differences in their length. If the tips of these ordinates
be united, we have the curve of frequency (Fig. 120, _A_), which
according to Galton ought to be symmetrical, and in most cases really
is so. Ammon calls the space between the smallest and the largest
variations the 'variation-playground,' that is, the playground within
which all variations are equally advantageous to the species. This
is not co-extensive with the variation-area, for there may be more
marked deviations below the beginning or above the upper end of the
variation-playground, but these, being disadvantageous, fall under
the shears of personal selection. The variation-playground may also
be called the area of indulgence of variation, because the variations
falling within it are spared from the eliminating activity of
selection, or the variation-area of survivors, because on an average
only those survive whose variations do not overstep the limits of this
area.
[Illustration: FIG. 120. _A_, symmetrical, and _B_, asymmetrical
curve of frequency; after Ammon. _U_, minimal, _O_, maximal limit of
individual variation. _U-O_, the 'variation-playground.' _M_, the mean
of variation. _H_, the greatest frequency or mode of variation.]
This implies that variations below _U_ (the lower limit of the area
of exemption) and above _O_ (the upper limit) can occur, but do not
survive and leave descendants, and we can therefore easily understand
why characters, of which different degrees arise with equal ease from
the constitution of the species, must gradually develop a symmetrical
curve of frequency because of the constant crossing. Obviously
those individuals which stand just upon the borders of admissible
variation will, other conditions being equal, leave behind them
fewer descendants than those which approximate to the middle of the
area of exemption; for as the characters concerned can vary in the
offspring in both directions, there will always be at the lower end
some of the descendants of a pair which will fall below the limits of
exemption, and at the upper end some which will rise above it. This
will happen even when pairing takes place between parents at the middle
or at the other end of the abscissa, for there are always cases of
the preponderance of one parent in heredity. A higher percentage of
the descendants of individuals on the borderline will therefore be
eliminated, and their frequency _must therefore be less_. Even if at
the beginning of the series of observations a condition obtained in
which all the ordinates of the area of exemption were equally high,
those nearest the boundaries would of necessity very soon become lower,
and this in proportion to their distance from the boundary, and the
frequency-curve, which at first would be a straight line (according
to our assumption, which of course does not tally with natural
conditions), would become a symmetrical curve, highest in the middle
and falling equally at either side.
Ammon has worked out the hypotheses on which the curve of frequency
would become asymmetrical. Firstly, when the fertility is greater
towards the upper or lower limit of the area of exemption; secondly,
when germinal selection forces the variation in a particular direction,
upwards or downwards; and thirdly, 'when natural selection intervenes
diversely at the upper or lower limit.' Of these three possibilities
the first two must be acknowledged as quite probable, but the third,
it seems to me, could only cause a temporary asymmetry of the curve,
lasting, that is, only until a state of equilibrium has again been
reached; but that may in certain conditions take a long time.
Asymmetrical curves of frequency (Fig. 120, _B_) therefore arise, for
instance, when the intra-germinal conditions (the 'constitution of the
species') more easily and therefore more frequently produce extreme
variations. In this case the area of exemption can only extend on one
side, and must remain in this state. In _Caltha palustris_, the marsh
marigold, we may find, according to De Vries, among a hundred flowers,
those with five, six, seven, and eight petals, in the following
proportions:--
Petals 5 6 7 8
Number of flowers 72 21 6 1
and thus there is an asymmetrical curve of frequency. But if we take
the whole area of variation as the area of exemption, that is, if we
assume that it is indifferent for the species whether the flowers
have five, six, seven, or eight petals, the preponderance of the
five-petalled flowers may have its reason in the fact that it is much
easier for five than six or more petals to be produced because of the
internal structure of the whole plant.
In this case the maximum of frequency lies at the lower limit of
variation, but it may also lie at the upper. Thus, according to De
Vries, the blossoms of _Weigelia_ vary, in regard to the number of
their petal-tips, in the following manner. Six-tipped corollas were not
found, and among 1,145 flowers there were the following proportions:--
Tips of the corolla 3 4 5
Number of flowers 61 196 888
It is thus clear that amphimixis is an essential factor in the fixing
of forms, but that it certainly does not of itself determine these, and
that it is not always the average of the variations that is the most
frequent, but that the form of the curve of frequency is determined by
other factors also, namely, by germinal and personal selection and by
the directive control which these exert on variations.
The equalizing effect of amphigony may perhaps be expressed
thus: In the case of every new adaptation there is at first a
large area of variation, but this gradually decreases owing to
a continual restriction on the part of natural selection, until
ultimately--when the highest degree of constancy of the character or
species has been attained--it only extends very little beyond the
'adaptation-playground' or the 'area of exemption.'
One of the effects of amphimixis is thus to bring about an increasing
restriction of the area of variation, or, as we usually say, a
constancy of the facies of a given form, a condensation into a species.
How far this result is necessary or useful, and therefore how far
it may be regarded as accounting for the persistence of amphimixis,
we shall discuss in the chapter on the formation of species. My own
view is that even the fact that new adaptations are rendered possible
through amphimixis and amphigony, the mode of reproduction associated
with it, affords in itself a sufficient reason why amphimixis should
have been retained when once it had been introduced.
LECTURE XXIX
THE GENERAL SIGNIFICANCE OF AMPHIMIXIS (_continued_)
Association of amphimixis with reproduction--Origin of amphimixis--Its
lowest forms--Amphimixis in Coccidia--Chromosomes in unicellular
organisms--_Coccidium proprium_--'Amœba-nests' as a preliminary
stage to amphimixis--Plastogamy of the Myxomycetes--Result: a
strengthening of the power of adaptation--Strengthening of the power
of assimilation--Use of complete amphimixis--Proof of its constant
efficacy to be found in the rudimentary organs of Man--Allogamy--Means
taken to prevent the mingling of nearly related forms--Amphimixis is
not a 'formative' stimulus--Attraction of the germ-cells--Effects of
inbreeding compared with those of parthenogenesis--Nathusius's case of
injurious inbreeding--Hindrances to fertilization in the crossing of
species--Probable reason for the injurious effect of inbreeding.
We have endeavoured to understand why amphimixis should have been
established among the processes of life, and we have now to turn to the
question when and how, that is, in what form, it was first introduced.
But first I should like to refer for a little to the association of
amphimixis with reproduction, which we find in all multicellular
organisms, and among the higher types so unexceptionally that, until
not very long ago, amphimixis and reproduction were looked on as
one and the same thing, and all multiplication was believed to be
associated with 'fertilization.' We have seen that this is not the
case, that on the other hand the two processes are quite distinct,
and may be called contrasts rather than equivalents, for reproduction
always means an increase in the number of individuals, while amphimixis
implies--originally at least--their diminution by a half.
Accordingly we found that, in unicellular organisms, amphimixis
is not associated with reproduction, but interpolated between the
divisions, and not even in such a manner that amphimixis precedes every
multiplication by division, but so that the conjugation of two animals
occurs only from time to time, after numerous divisions, sometimes
hundreds, have occurred. It is obvious that this must be so, since, if
amphimixis occurred regularly between every two divisions, no increase
in the number of individuals would be brought about, at least if the
fusion of the two conjugating individuals were complete.
Why, then, is there such an intimate, and in the case of the higher
types, such an indissoluble, association between reproduction and
amphimixis that 'fertilization' appears to be a _sine qua non_ of
reproduction, and not very long ago seemed to us to be the 'quickening
of the ovum,' the 'burning spark' which causes the powder-barrel to
explode?
The reason of this is not difficult to discover; it lies in the
structure of multicellular animals, and in their differentiation
according to the principle of division of labour, for since only
particular cells are capable of reproduction, that is, of giving
rise to the whole, it is in these necessarily that the process of
amphimixis has to occur if its significance lies in its effects on the
succeeding generations. It is true that in the lowest multicellular
organisms, such as the species of _Volvox_, there are, in addition
to the sex-cells, other reproductive cells quite similar to the ova,
whose development into a new colony takes place without amphimixis,
but the higher we ascend in the animal and plant series the rarer are
these 'asexual' germ-cells or 'spores,' and in the highest animal types
they are entirely absent and reproduction occurs only by means of the
'sex-cells.'
I am inclined to look for the cause of this striking phenomenon mainly
in the fact that, if amphimixis had to be retained, this was effected
with increasingly great difficulty the more highly and complexly
differentiated the organisms became, and that more complicated
adaptations were therefore necessary in order that the union of the
two germ-cells might be rendered possible at all. There is first of
all the separation into two kinds of sex-cells, whose far-reaching
differentiations and precise adaptations to the most minute conditions
we have already discussed; then follow the innumerable adaptations
to bring about the meeting of the sex-cells, the arrangements for
copulation, and, finally, the instincts which draw the two sexes
together, the means of attraction which are employed, whether
decorative colours or attractive shapes, stimulating odours or musical
notes, in short, all the diverse and intricate arrangements, which
seem to be more subtly elaborated the higher the organism stands upon
the ladder of life. When we call to mind that sexual differentiations
finally go so far that they dominate the whole organism, alike in
its external appearance and in its internal nature, its feelings,
inclinations, instincts, its will and ability, as well as its structure
down to the finest nerve-elements, we can understand that a mode of
reproduction which demands such a composite disposition of details,
involving a moulding of the whole organism, so to speak, from birth
till death, must of necessity remain the only one, and that there
was no room for the persistence of any essentially different mode
of reproduction with quite different adaptations. Or, to speak
metaphorically, the power of adaptation which is innate in the organism
so exhausted itself in the establishment of this marvellous amphimixis
adjustment that the possibility of any other was totally excluded.
It is true that it is only among the Vertebrates that we find
'the reproductive apparatus' so highly developed, but even among
Molluscs and Arthropods 'sexual' reproduction, that is, reproduction
associated with amphimixis, is the prevailing mode. In these, indeed,
parthenogenesis does occasionally occur, that is to say, sexually
differentiated female germ-cells are, by means of some slight
variations in the maturation of the egg, rendered capable of developing
without previous amphimixis, but this happens only in quite special
cases as an adaptation to quite special circumstances, and can only
be regarded as a temporary cessation of the association between
reproduction and amphimixis. In some cases it is a moiety of the ova
adapted for amphimixis which develop parthenogenetically, as it is the
same sexually differentiated animals, true females, which produce both
sorts, and this is often true to some extent when the differentiation
in the direction of parthenogenesis has advanced further, and the
ova have been separated into those requiring fertilization and those
which are parthenogenetic (e.g. the winter and the summer eggs of the
Daphnidæ). Parthenogenesis is not asexual but unisexual reproduction,
a mode of multiplication which shows us that even in highly
differentiated animals the apparently indissoluble association between
reproduction and amphimixis can be dissolved if circumstances require
it.
But if amphimixis had to be retained in the higher animal forms--and we
have seen reasons why this must be--it could only be effected by means
of unicellular germs, for amphimixis is in essence a fusion of nuclei,
and this is the reason why 'vegetative' reproduction, so-called,
becomes less and less prominent in animals at least, and above the
level of the Arthropods disappears almost entirely.
Let us now return to the question we asked at the beginning--When
and in what form was amphimixis first introduced into the world of
organisms? The best way to answer this is by observation. We must turn
to the lowest forms which now exhibit it, and see whether it occurs
in them in a simpler form, so that we may draw conclusions as to its
origin and its primitive significance, for it would be possible, _a
priori_, that this was something different from what it is now in
the relatively higher organisms, and that a change of function has
gradually come about.
Assuredly the whole intricate complex of adaptations which is now
exhibited on the conjugation of the two sex-cells in animals and
plants, the differentiation of two kinds of 'sexually' antagonistic
cells, with all their special adaptations, the reduction of the
chromosomes, the institution of the karyo-kinetic apparatus, together
with the centrospheres and so on, cannot possibly have arisen all at
once by fortuitous variation, but can only have arisen gradually,
step by step, and as the result of 'innumerable external and internal
influences.' But why should not these arrangements, nowadays so
complex, have had a simple beginning? Why might not this beginning have
been the simple union of the protoplasmic bodies of two non-nucleated
Monera; followed, after the origin of nuclear substances, by the union
of these, and, finally, after the differentiation of a nucleus with
a definite number of chromosomes, with a dividing apparatus, with a
membrane, and so on, by complete amphimixis as we now know it? And how
many transition stages may not be added to fill up the gaps between
these three main stages?