3 { 1 _Ab_ class may produce either all _Ab_’s,
{ 2 _or_ both _Ab_’s and _ab_’s.
{ 1 _AB_ class may produce either all _AB_’s,
{ 2 _or_ both _AB_’s and _Ab_’s,
9 { 2 _or_ both _AB_’s and _aB_’s,
{ 4 _or_ all four possible classes again, namely,
{ _AB_’s, _Ab_’s, _aB_’s, and _ab_’s,
and the average number of members of each class will approach the ratio
1 : 3 : 3 : 9 as indicated above.
The details of these experiments and of others like them made with
_three_ pairs of differentiating characters are all set out in Mendel’s
memoir.
Professor de Vries has worked at the same problem in some dozen species
belonging to several genera, using pairs of varieties characterised by
a great number of characters: for instance, colour of flowers, stems,
or fruits, hairiness, length of style, and so forth. He states that in
all these cases Mendel’s principles are followed.
The numbers with which Mendel worked, though large, were not large
enough to give really smooth results[10]; but with a few rather
marked exceptions the observations are remarkably consistent, and
the approximation to the numbers demanded by the law is greatest in
those cases where the largest numbers were used. When we consider,
besides, that Tschermak and Correns announce definite confirmation in
the case of _Pisum_, and de Vries adds the evidence of his long series
of observations on other species and orders, there can be no doubt
that Mendel’s law is a substantial reality; though whether some of
the cases that depart most widely from it can be brought within the
terms of the same principle or not, can only be decided by further
experiments.
[10] Professor Weldon (p. 232) takes great exception to this
statement, which he considerately attributes to “some writers.”
After examining the conclusions he obtained by algebraical study of
Mendel’s figures I am disposed to think my statement not very far out.
One may naturally ask, How can these results be brought into harmony
with the facts of hybridisation hitherto known; and, if all this is
true, how is it that others who have carefully studied the phenomena
of hybridisation have not long ago perceived this law? The answer to
this question is given by Mendel at some length, and it is, I think,
satisfactory. He admits from the first that there are undoubtedly cases
of hybrids and cross-breds which maintain themselves pure and do not
break up. Such examples are plainly outside the scope of his law. Next
he points out, what to anyone who has rightly comprehended the nature
of discontinuity in variation is well known, that the variations in
_each_ character must be _separately_ regarded. In most experiments in
crossing, forms are taken which differ from each other in a multitude
of characters--some continuous, others discontinuous, some capable of
blending with their contraries, while others are not. The observer on
attempting to perceive any regularity is confused by the complications
thus introduced. Mendel’s law, as he fairly says, could only appear in
such cases by the use of overwhelming numbers, which are beyond the
possibilities of practical experiment. Lastly, no previous observer had
applied a strict statistical method.
Both these answers should be acceptable to those who have studied the
facts of variation and have appreciated the nature of Species in the
light of those facts. That different species should follow different
laws, and that the same law should not apply to all characters alike,
is exactly what we have every right to expect. It will also be
remembered that the principle is only explicitly declared to apply to
discontinuous characters[11]. As stated also it can only be true where
reciprocal crossings lead to the same result. Moreover, it can only be
tested when there is no sensible diminution in fertility on crossing.
[11] See later.
Upon the appearance of de Vries’ paper announcing the “rediscovery”
and confirmation of Mendel’s law and its extension to a great number
of cases two other observers came forward almost simultaneously and
independently described series of experiments fully confirming Mendel’s
work. Of these papers the first is that of Correns, who repeated
Mendel’s original experiment with Peas having seeds of different
colours. The second is a long and very valuable memoir of Tschermak,
which gives an account of elaborate researches into the results of
crossing a number of varieties of _Pisum sativum_. These experiments
were in many cases carried out on a large scale, and prove the main
fact enuntiated by Mendel beyond any possibility of contradiction.
The more exhaustive of these researches are those of Tschermak on
Peas and Correns on several varieties of Maize. Both these elaborate
investigations have abundantly proved the general applicability of
Mendel’s law to the character of the plants studied, though both
indicate some few exceptions. The details of de Vries’ experiments are
promised in the second volume of his most valuable _Mutationstheorie_.
Correns in regard to Maize and Tschermak in the case of _P. sativum_
have obtained further proof that Mendel’s law holds as well in the case
of varieties differing from each other in _two_ pairs of characters,
one of each pair being dominant, though of course a more complicated
expression is needed in such cases[12].
[12] Tschermak’s investigations were besides directed to a
re-examination of the question of the absence of beneficial
results on cross-fertilising _P. sativum_, a subject already much
investigated by Darwin, and upon this matter also important further
evidence is given in great detail.
That we are in the presence of a new principle of the highest
importance is manifest. To what further conclusions it may lead us
cannot yet be foretold. But both Mendel and the authors who have
followed him lay stress on one conclusion, which will at once suggest
itself to anyone who reflects on the facts. For it will be seen that
the results are such as we might expect if it be imagined that the
cross-bred plant produced pollen grains and egg-cells, each of which
bears only _one_ of the alternative varietal characters and not both.
If this were so, and if on an average the same number of pollen grains
and egg-cells transmit each of the two characters, it is clear that on
a random assortment of pollen grains and egg-cells Mendel’s law would
be obeyed. For 25 per cent. of “dominant” pollen grains would unite
with 25 per cent. “dominant” egg-cells; 25 per cent. “recessive” pollen
grains would similarly unite with 25 per cent. “recessive” egg-cells;
while the remaining 50 per cent. of each kind would unite together.
It is this consideration which leads both Mendel and those who have
followed him to assert that these facts of crossing prove that each
egg-cell and each pollen grain is pure in respect of each character
to which the law applies. It is highly desirable that varieties
differing in the form of their pollen should be made the subject of
these experiments, for it is quite possible that in such a case strong
confirmation of this deduction might be obtained. [Preliminary trials
made with reference to this point have so far given negative results.
Remembering that a pollen grain is not a germ-cell, but only a bearer
of a germ-cell, the hope of seeing pollen grains differentiated
according to the characters they bear is probably remote. Better hopes
may perhaps be entertained in regard to spermatozoa, or possibly female
cells.]
As an objection to the deduction of purity of germ-cells, however, it
is to be noted that though true intermediates did not generally occur,
yet the intensity in which the characters appeared did vary in degree,
and it is not easy to see how the hypothesis of _perfect_ purity in the
reproductive cells can be supported in such cases. Be this, however, as
it may, there is no doubt we are beginning to get new lights of a most
valuable kind on the nature of heredity and the laws which it obeys. It
is to be hoped that these indications will be at once followed up by
independent workers. Enough has been said to show how necessary it is
that the subjects of experiment should be chosen in such a way as to
bring the laws of heredity to a real test. For this purpose the first
essential is that the differentiating characters should be few, and
that all avoidable complications should be got rid of. Each experiment
should be reduced to its simplest possible limits. The results obtained
by Galton, and also the new ones especially described in this paper,
have each been reached by restricting the range of observation to one
character or group of characters, and it is certain that by similar
treatment our knowledge of heredity may be rapidly extended.
* * * * *
To the above popular presentation of the essential facts, made for
an audience not strictly scientific, some addition, however brief,
is called for. First, in regard to the law of Ancestry, spoken of on
p. 5. Those who are acquainted with Pearson’s _Grammar of Science_,
2nd ed. published early in 1900, the same author’s paper in _Proc.
R. S._ vol. 66, 1900, p. 140, or the extensive memoir (pubd. Oct.
1900), on the inheritance of coat-colour in horses and eye-colour in
man (_Phil. Trans._ 195, A, 1900, p. 79), will not need to be told that
the few words I have given above constitute a most imperfect diagram of
the operations of that law as now developed. Until the appearance of
these treatises it was, I believe, generally considered that the law
of Ancestral Heredity was to be taken as applying to phenomena like
these (coat-colour, eye-colour, &c.) where the inheritance is generally
_alternative_, as well as to the phenomena of _blended_ inheritance.
Pearson, in the writings referred to, besides withdrawing other large
categories of phenomena from the scope of its operations, points out
that the law of Ancestral Heredity does not satisfactorily express the
cases of alternative inheritance. He urges, and with reason, that these
classes of phenomena should be separately dealt with.
* * * * *
The whole issue as regards the various possibilities of heredity now
recognized will be made clearer by a very brief exposition of the
several conceptions involved.
If an organism producing germ-cells of a given constitution, uniform in
respect of the characters they bear, breeds with another organism[13]
bearing _precisely similar_ germ-cells, the offspring resulting will,
if the conditions are identical, be uniform.
[13] For simplicity the case of self-fertilisation is omitted from
this consideration.
In practice such a phenomenon is seen in _pure_-breeding. It is true
that we know no case in nature where all the germ-cells are thus
identical, and where no variation takes place beyond what we can
attribute to conditions, but we know many cases where such a result
is approached, and very many where all the essential features which we
regard as constituting the characters of the breed are reproduced with
approximate certainty in every member of the pure-bred race, which thus
closely approach to uniformity.
But if two germ-cells of dissimilar constitution unite in
fertilisation, what offspring are we to expect[14]? First let us
premise that the answer to this question is known experimentally to
differ for many organisms and for many classes of characters, and may
almost certainly be in part determined by external circumstances. But
omitting the last qualification, certain principles are now clearly
detected, though what principle will apply in any given case can only
be determined by direct experiment made with that case.
[14] In all the cases discussed it is assumed that the gametes are
similar except in regard to the “heritage” they bear, and that no
_original_ variation is taking place. The case of mosaics is also
left wholly out of account (see later).
This is the phenomenon of _cross_-breeding. As generally used, this
term means the union of members of dissimilar varieties, or species:
though when dissimilar gametes[15] produced by two individuals
of the same variety unite in fertilisation, we have essentially
_cross_-breeding in respect of the character or characters in which
those gametes differ. We will suppose, as before, that these two
gametes bearing properties unlike in respect of a given character, are
borne by different individuals.
[15] The term “gamete” is now generally used as the equivalent of
“germ-cell,” whether male or female, and the term “zygote” is here
used for brevity to denote the organism resulting from fertilisation.
In the simplest case, suppose a gamete from an individual presenting
any character in intensity _A_ unite in fertilisation with another
from an individual presenting the same character in intensity _a_. For
brevity’s sake we may call the parent individuals _A_ and _a_, and the
resulting zygote _Aa_. What will the structure of _Aa_ be in regard to
the character we are considering?
Up to Mendel no one proposed to answer this question in any other way
than by reference to the intensity of the character in the progenitors,
and _primarily_ in the parents, _A_ and _a_, in whose bodies the
gametes had been developed. It was well known that such a reference
gave a very poor indication of what _Aa_ would be. Both _A_ and _a_
may come from a population consisting of individuals manifesting the
same character in various intensities. In the pedigree of either _A_
or _a_ these various intensities may have occurred few or many times.
Common experience leads us to expect the probability in regard to _Aa_
to be influenced by this history. The next step is that which Galton
took. He extended the reference beyond the immediate parents of _Aa_,
to its grandparents, great-grandparents, and so on, and in the cases he
studied he found that from a knowledge of the intensity in which the
given character was manifested in each progenitor, even for some few
generations back, a fairly accurate prediction could be made, not as to
the character of any individual _Aa_, but as to the average character
of _Aa_’s of similar parentage, in general.
But suppose that instead of individuals presenting one character in
differing intensities, two individuals breed together distinguished by
characters which we know to be mutually exclusive, such as _A_ and _B_.
Here again we may speak of the individuals producing the gametes as _A_
and _B_, and the resulting zygote as _AB_. What will _AB_ be like? The
population here again may consist of many like _A_ and like _B_. These
two forms may have been breeding together indiscriminately, and there
may have been many or few of either type in the pedigree of either _A_
or _B_.
Here again Galton applied his method with remarkable success. Referring
to the progenitors of _A_ and _B_, determining how many of each type
there were in the direct pedigree of _A_ and of _B_, he arrived at the
same formula as before, with the simple difference that instead of
expressing the probable average intensity of one character in several
individuals, the prediction is given in terms of the probable number of
_A_’s and _B_’s that would result on an average when particular _A_’s
and _B_’s of known pedigree breed together.