Biology | Page 6

is to produce
again pure white mice of the composition AGAB. The second union,
AY x CB is to produce mice that appear pure yellow, and have the
formula AYCB. What, now, will be the result of uniting the two forms
thus produced--i.e. AGAB × AYCB? Cuénot's prediction was that they
should yield eight different kinds of mice, of which four should be
white, two yellow, one black and one gray. The actual aggregate result

of such unions, repeatedly performed, compared with the theoretic
expectation, is shown in the foregoing table. As will be seen, the
correspondence, though close, is not absolutely exact, yet is near
enough to prove the validity of the principle on which the prediction
was based, and we may be certain that had a much larger number of
these mice been reared the correspondence would have been still closer.
I have purposely selected a somewhat complicated example, and time
will not admit of a full explanation of the manner in which this
particular result was reached. I will however attempt to give an
indication of the general Mendelian principle by means of which
predictions of this kind are made. This principle appears in its simplest
form in the behavior of two contrasting characters of the same general
type--for instance two colors, such as gray and white in mice. If two
animals, which show respectively two such characters are bred together,
only one of the characters (known as the "dominant") appears in the
offspring, while the other (known as the "recessive") disappears from
view. In the next generation, obtained by breeding these hybrids
together, both characters appear separately and in a definite ratio, there
being in the long run three individuals that show the dominant
character to one that shows the recessive. Thus, in the case of gray and
white mice, the first cross is always gray, while the next generation
includes three grays to one white. This is the fundamental Mendelian
ratio for a single pair of characters; and from it may readily be deduced
the more complicated combinations that appear when two or more pairs
of characters are considered together. Such combinations appear in
definite series, the nature of which may be worked out by a simple
method of binomial expansion. By the use of this principle
astonishingly accurate numerical predictions may be made, even of
rather complex combinations; and furthermore, new combinations may
be, and have been, artificially produced, the number, character and
hereditary capacity of which are known in advance. The fundamental
ratio for a single pair of characters is explained by a very simple
assumption. When a dominant and a recessive character are associated
in a hybrid, the two must undergo in some sense a disjunction or
separation in the formation of the germ-cells of the hybrid. This takes
place in a quite definite way, exactly half the germ-cells in each sex
receiving the potentiality of the dominant character, the other half the

potentiality of the recessive. This is roughly expressed by saying that
the germ-cells are no longer hybrid, like the body in which they arise,
but bear one character or the other; and although in a technical sense
this is probably not precisely accurate, it will sufficiently answer our
purpose. If, now, it be assumed that fertilization takes place
fortuitously--that is that union is equally probable between germ-cells
bearing the same character and those bearing opposite characters,--the
observed numerical ratio in the following generation follows according
to the law of probability. Thus is explained both the fortuitous element
that differentiates these cases from exact chemical combinations, and
the definite numerical relations that appear in the aggregate of
individuals.
Grandparents AG (white) AB (white) AY (white) CB (black) | | | |
+---------+ +-----------+ | | Parents AGAB (white) AYCB (yellow) | |
+----------------------+ | Observed Calculated {AGAY} {ABAY} (White)
81 76 {AGAB} Offspring ---------------{ABAB} { {AGCY} (Yellow)
34 38 {ABCY} { {ABCB (Black) 20 19 {AGCB (Gray) 16 19 ---- ----
151 152
Now, the point that I desire to emphasize is that one or two very simple
mechanistic assumptions give a luminously clear explanation of the
behavior of the hereditary characters according to Mendel's law, and at
one stroke bring order out of the chaos in which facts of this kind at
first sight seem to be. Not less significant is the fact that direct
microscopical investigation is actually revealing in the germ-cells a
physical mechanism that seems adequate to explain the disjunction of
characters on which Mendel's law depends; and this mechanism
probably gives us also at least a key to the long standing riddle of the
determination and heredity of sex. These phenomena are therefore
becoming intelligible from the mechanistic point of view. From any
other they appear as an insoluble enigma. When such progress as this is
being