“_Voyaging through strange seas of thought alone._”
The only conclusion which most readers could draw from this abstract
and indeed from the article it epitomizes, is that Mendel’s discovery
so far from being of paramount importance, rests on a basis which
Professor Weldon has shown to be insecure, and that an error has come
in through disregard of the law of Ancestral Heredity. On examining the
paper it is perfectly true that Professor Weldon is careful nowhere
directly to question Mendel’s facts or his interpretation of them,
for which indeed in some places he even expresses a mild enthusiasm,
but there is no mistaking the general purpose of the paper. It must
inevitably produce the impression that the importance of the work
has been greatly exaggerated and that supporters of current views on
Ancestry may reassure themselves. That this is Professor Weldon’s own
conclusion in the matter is obvious. After close study of his article
it is evident to me that Professor Weldon’s criticism is baseless and
for the most part irrelevant, and I am strong in the conviction that
the cause which will sustain damage from this debate is not that of
Mendel.
I. THE MENDELIAN PRINCIPLE OF PURITY OF GERM-CELLS AND THE LAWS OF
HEREDITY BASED ON ANCESTRY.
Professor Weldon’s article is entitled “Mendel’s Laws of Alternative
Inheritance in Peas.” This title expresses the scope of Mendel’s work
and discovery none too precisely and even exposes him to distinct
misconception.
To begin with, it says both too little and too much. Mendel did
certainly determine Laws of Inheritance in peas--not precisely the
laws Professor Weldon has been at the pains of drafting, but of that
anon. Having done so, he knew what his discovery was worth. He saw,
and rightly, that he had found a principle which _must_ govern a wide
area of phenomena. He entitles his paper therefore “_Versuche über
Pflanzen-Hybriden_,” or, Experiments in Plant-Hybridisation.
Nor did Mendel start at first with any particular intention respecting
Peas. He tells us himself that he wanted to find the laws of
inheritance in _hybrids_, which he suspected were definite, and that
after casting about for a suitable subject, he found one in peas, for
the reasons he sets out.
In another respect the question of title is much more important. By
the introduction of the word “Alternative” the suggestion is made that
the Mendelian principle applies peculiarly to cases of “alternative”
inheritance. Mendel himself makes no such limitation in his earlier
paper, though perhaps by rather remote implication in the second, to
which the reader should have been referred. On the contrary, he wisely
abstains from prejudicial consideration of unexplored phenomena.
* * * * *
To understand the significance of the word “alternative” as introduced
by Professor Weldon we must go back a little in the history of these
studies. In the year 1897 Galton formally announced the Law of
Ancestral Heredity referred to in the _Introduction_, having previously
“stated it briefly and with hesitation” in _Natural Inheritance_,
p. 134. In 1898 Professor Pearson published his modification and
generalisation of Galton’s Law, introducing a correction of admitted
theoretical importance, though it is not in question that the principle
thus restated is fundamentally not very different from Galton’s[54].
_It is an essential part of the Galton-Pearson Law of Ancestral
Heredity that in calculating the probable structure of each descendant
the structure of each several ancestor must be brought to account._
[54] I greatly regret that I have not a precise understanding of the
basis of the modification proposed by Pearson. His treatment is in
algebraical form and beyond me. Nevertheless I have every confidence
that the arguments are good and the conclusion sound. I trust it may
not be impossible for him to provide the non-mathematical reader with
a paraphrase of his memoir. The arithmetical differences between the
original and the modified law are of course clear.
Professor Weldon now tells us that these two papers of Galton and of
Professor Pearson have “given us an expression for the effects of
_blended_ inheritance which seems likely to prove generally applicable,
though the constants of the equations which express the relation
between divergence from the mean in one generation, and that in
another, may require modification in special cases. Our knowledge of
_particulate_ or mosaic inheritance, and of _alternative_ inheritance,
is however still rudimentary, and there is so much contradiction
between the results obtained by different observers, that the evidence
available is difficult to appreciate.”
But Galton stated (p. 401) in 1897 that his statistical law of heredity
“appears to be universally applicable to bi-sexual descent.” Pearson
in re-formulating the principle in 1898 made no reservation in regard
to “alternative” inheritance. On the contrary he writes (p. 393) that
“if Mr Galton’s law can be firmly established, _it is a complete
solution, at any rate to a first approximation, of the whole problem
of heredity_,” and again (p. 412) that “it is highly probable that
it [this law] is the simple descriptive statement which brings into
a single focus all the complex lines of hereditary influence. If
Darwinian evolution be natural selection combined with _heredity_,
then the single statement which embraces the whole field of heredity
must prove almost as epoch-making as the law of gravitation to the
astronomer[55].”
[55] I have searched Professor Pearson’s paper in vain for any
considerable reservation regarding or modification of this general
statement. Professor Pearson enuntiates the law as “only correct
on certain limiting hypotheses,” but he declares that of these the
most important is “the absence of reproductive selection, i.e. the
negligible correlation of fertility with the inherited character, and
the absence of sexual selection.” The case of in-and-in breeding is
also reserved.
As I read there comes into my mind that other fine passage where
Professor Pearson warns us
“There is an insatiable desire in the human breast to resume in some
short formula, some brief statement, the facts of human experience.
It leads the savage to ‘account’ for all natural phenomena by
deifying the wind and the stream and the tree. It leads civilized
man, on the other hand, to express his emotional experience in works
of art, and his physical and mental experience in the formulae or
so-called laws of science[56].”
[56] K. Pearson, _Grammar of Science_, 2nd ed. 1900, p. 36.
No naturalist who had read Galton’s paper and had tried to apply it to
the facts he knew could fail to see that here was a definite advance.
We could all perceive phenomena that were in accord with it and there
was no reasonable doubt that closer study would prove that accord to
be close. It was indeed an occasion for enthusiasm, though no one
acquainted with the facts of experimental breeding could consider the
suggestion of universal application for an instant.
But two years have gone by, and in 1900 Pearson writes[57] that the
values obtained from the Law of Ancestral Heredity
[57] _Grammar of Science_, 2nd ed. 1900, p. 480.
“seem to fit the observed facts fairly well in the case of _blended_
inheritance. In other words we have a certain amount of evidence in
favour of the conclusion: _That whenever the sexes are equipotent,
blend their characters and mate pangamously, all characters will be
inherited at the same rate_,”
or, again in other words, that the Law of Ancestral Heredity after
the glorious launch in 1898 has been home for a complete refit. The
top-hamper is cut down and the vessel altogether more manageable;
indeed she looks trimmed for most weathers. Each of the qualifications
now introduced wards off whole classes of dangers. Later on (pp. 487–8)
Pearson recites a further list of cases regarded as exceptional. “All
characters will be inherited at the same rate” might indeed almost be
taken to cover the results in Mendelian cases, though the mode by which
those results are arrived at is of course wholly different.
Clearly we cannot speak of the Law of Gravitation now. Our Tycho Brahe
and our Kepler, with the yet more distant Newton, are appropriately
named as yet to come[58].
[58] _Phil. Trans._ 1900, vol. 195, A, p. 121.
But the truth is that even in 1898 such a comparison was scarcely
happy. Not to mention moderns, these high hopes had been finally
disposed of by the work of the experimental breeders such as Kölreuter,
Knight, Herbert, Gärtner, Wichura, Godron, Naudin, and many more. To
have treated as non-existent the work of this group of naturalists,
who alone have attempted to solve the problems of heredity and
species--Evolution, as we should now say--by the only sound
method--_experimental breeding_--to leave out of consideration almost
the whole block of evidence collected in _Animals and Plants_--Darwin’s
finest legacy as I venture to declare--was unfortunate on the part of
any exponent of Heredity, and in the writings of a professed naturalist
would have been unpardonable. But even as modified in 1900 the Law
of Ancestral Heredity is heavily over-sparred, and any experimental
breeder could have increased Pearson’s list of unconformable cases by
as many again.
But to return to Professor Weldon. He now repeats that the Law of
Ancestral Heredity seems likely to prove generally applicable to
_blended_ inheritance, but that the case of _alternative_ inheritance
is for the present reserved. We should feel more confidence in
Professor Weldon’s exposition if he had here reminded us that the
special case which fitted Galton’s Law so well that it emboldened
him to announce that principle as apparently “universally applicable
to bi-sexual descent” was one of _alternative_ inheritance--namely
the coat-colour of Basset-hounds. Such a fact is, to say the least,
ominous. Pearson, in speaking (1900) of this famous case of Galton’s,
says that these phenomena of alternative inheritance must be treated
separately (from those of blended inheritance)[59], and for them he
deduces a proposed “_law of reversion_,” based of course on ancestry.
He writes, “In both cases we may speak of a law of ancestral heredity,
but the first predicts the probable character of the individual
produced by a given ancestry, while the second tells us the
percentages of the total offspring which on the average revert to each
ancestral type[60].”
[59] “If this be done, we shall, I venture to think, keep not only
our minds, but our points for observation, clearer; and further, the
failure of Mr Galton’s statement in the one case will not in the
least affect its validity in the other.” Pearson (32), p. 143.
[60] _Grammar of Science_, 1900, p. 494. See also Pearson, _Proc.
Roy. Soc._ 1900, LXVI. pp. 142–3.
With the distinctions between the original Law of Ancestral Heredity,
the modified form of the same law, and the Law of Reversion, important
as all these considerations are, we are not at present concerned.
For the Mendelian principle of heredity asserts a proposition
absolutely at variance with all the laws of ancestral heredity, however
formulated. In those cases to which it applies strictly, this principle
declares that the cross-breeding of parents _need_ not diminish
the purity of their germ-cells or consequently the purity of their
offspring. When in such cases individuals bearing opposite characters,
_A_ and _B_, are crossed, the germ-cells of the resulting cross-bred,
_AB_, are each to be bearers either of character A or of character _B_,
not both.
Consequently when the cross-breds breed either together or with the
pure forms, individuals will result of the forms _AA_, _AB_, _BA_,
_BB_[61]. Of these the forms _AA_ and _BB_, formed by the union of
similar germs, are stated to be as pure as if they had had no cross in
their pedigree, and henceforth their offspring will be no more likely
to depart from the _A_ type or the _B_ type respectively, than those of
any other originally pure specimens of these types.
[61] On an average of cases, in equal numbers, as Mendel found.
Consequently in such examples it is _not_ the fact that each ancestor
must be brought to account as the Galton-Pearson Law asserts, and we
are clearly dealing with a physiological phenomenon not contemplated by
that Law at all.
Every case therefore which obeys the Mendelian principle is in direct
contradiction to the proposition to which Professor Weldon’s school is
committed, and it is natural that he should be disposed to consider
the Mendelian principle as applying especially to “alternative”
inheritance, while the law of Galton and Pearson is to include the
phenomenon of blended inheritance. The latter, he tells us, is “the
most usual case,” a view which, if supported by evidence, might not be
without value.
It is difficult to blame those who on first acquaintance concluded
Mendel’s principle can have no strict application save to alternative
inheritance. Whatever blame there is in this I share with Professor
Weldon and those whom he follows. Mendel’s own cases were almost all
alternative; also the fact of dominance is very dazzling at first. But
that was two years ago, and when one begins to see clearly again, it
does not look so certain that the real essence of Mendel’s discovery,
the purity of germ-cells in respect of certain characters, may not
apply also to some phenomena of blended inheritance. The analysis of
this possibility would take us to too great length, but I commend to
those who are more familiar with statistical method, the consideration
of this question: whether dominance being absent, indefinite, or
suppressed, the phenomena of heritages completely blended in the
zygote, may not be produced by gametes presenting Mendelian purity of
characters. A brief discussion of this possibility is given in the
Introduction, p. 31.
Very careful inquiry would be needed before such a possibility could
be negatived. For example, we know that the Laws based on Ancestry
can apply to _alternative_ inheritance; witness the case of the
Basset-hounds. Here there is no simple Mendelian dominance; but are we
sure there is no purity of germ-cells? The new conception goes a long
way and it may well reach to such facts as these.
But for the present we will assume that Mendel’s principle applies only
to _certain phenomena of alternative inheritance_, which is as far as
our warrant yet runs.
No close student of the recent history of evolutionary thought needs
to be told what the attitude of Professor Weldon and his followers
has been towards these same disquieting and unwelcome phenomena of
alternative inheritance and discontinuity in variation. Holding at
first each such fact for suspect, then treating them as rare and
negligible occurrences, he and his followers have of late come slowly
to accede to the facts of discontinuity a bare and grudging recognition
in their scheme of evolution[62].
[62] Read in this connexion Pearson, K., _Grammar of Science_, 2nd
ed. 1900, pp. 390–2.
Professor Weldon even now opens his essay with the statement--or
perhaps reminiscence--that “it is perfectly possible and indeed
probable that the difference between these forms of inheritance
[blended, mosaic, and alternative] is only one of degree.” This may
be true; but reasoning favourable to this proposition could equally
be used to prove the difference between mechanical mixture and
chemical combination to be a difference of degree.
Therefore on the announcement of that discovery which once and for all
ratifies and consolidates the conception of discontinuous variation,
and goes far to define that of alternative inheritance, giving a finite
body to what before was vague and tentative, it is small wonder if
Professor Weldon is disposed to criticism rather than to cordiality.
* * * * *
We have now seen what is the essence of Mendel’s discovery based on a
series of experiments of unequalled simplicity which Professor Weldon
does not venture to dispute.