MENDELISM
=New Discoveries in the Field of Heredity.--=Writing in 1899, one of
America's well-known zoologists asserts that, "It is easier to weigh an
invisible planet than to measure the force of heredity in a single grain
of corn." And yet only two or three years later we find another prominent
naturalist saying regarding heredity that, "The experiments which led to
this advance in knowledge are worthy to rank with those that laid the
foundation of the atomic laws of chemistry." Again, "The breeding pen is
to us what the test-tube is to the chemist--an instrument whereby we
examine the nature of our organisms and determine empirically their
genetic properties." Here is a decided contrast of statement and yet both
were justifiable at the time of utterance. For even at the writing of the
first statement the investigations were in progress which, together with
the rediscovery of certain older work, were to transfer our knowledge of
heredity from the realm of speculation to that of experiment and disclose
certain definite principles of genetic transmission.
Through a knowledge of these principles in fact, the shifting of certain
characters is reducible to a series of definitely predictable proportions
and the skilled breeder may proceed to the building up of new and
permanent combinations of desirable characters according to mathematical
ratios and, what is of equal importance, he can secure the elimination of
undesirable qualities. While there are many limitations in the application
of these principles and while new facts and modifications are constantly
being discovered concerning them, nevertheless they represent the first
approximations to definite laws of hereditary transmission that we have
ever been able to make, and the practical fact confronts us that whatever
our theoretical interpretations may be, the principles are so definite
that through their application important improvements of crops and
domesticated animals have already actually been secured and one may
confidently expect still others to follow.
=Mendel.--=The principles involved are called the Mendelian principles
after their discoverer, Gregor Johann Mendel, abbot of a monastery at
Bruenn, Austria. After eight years of patient experimenting in his cloister
garden with plants, chiefly edible peas, he published his results and
conclusions in 1866, in the _Proceedings of the Natural History Society of
Bruenn_. While known to a few botanists of that day, the full importance of
the contribution was not recognized, and in the excitement of the
post-Darwinian controversy, the facts were lost sight of and ultimately
forgotten.
=Rediscovery of Mendelian Principles.--=In 1900 three men, Correns, De
Vries and Tschermak, working independently--in different countries, in
fact--rediscovered the principles and called attention anew to the
long-forgotten work of Mendel which they had come upon in looking over the
older literature on plant breeding. These investigators added other
examples from their own experiments. Since their rediscovery the
principles have been confirmed in essential features and extended by
numerous experimentalists with regard to a wide range of hereditary
characters in both animals and plants.
=Independence of Inheritable Characters.--=It has been found that many
truly heritable characteristics or traits of an individual, whether plant
or animal, are comparatively independent of one another and may be
inherited independently. Where there are contrasted characters in father
and mother, such as white plumage and black plumage in fowls, smooth coat
and wrinkled coat in seed, horns and hornlessness in cattle, long fur and
short fur in rabbits, beard and beardlessness in wheat, albino condition
and normal condition, etc., there is obviously a bringing together of the
determiners of the two traits in the resulting offspring. In the third
generation, however, in the progeny of these offspring, the two distinct
characters may be set apart again, thus showing that in the second
generation while perhaps one only was visible, the factors which determine
both were nevertheless present, and moreover, they were present in a
separable condition.
=Illustration of Mendelism in the Andalusian Fowl.--=Let us take as a
simple example the case of the Andalusian fowl. Although it is not a case
established by Mendel it illustrates certain of the essential conditions
underlying Mendelism in a more obvious way than the cases worked out by
Mendel himself. The so-called blue Andalusian fowl results from a cross of
a color variety of the fowl which is black with one which is white with
black-splashed feathers. The result is the same irrespective of which
parent is black. When bred with their like, whether from the same parents
or different parents, these blue fowls produce three kinds of progeny,
approximately one-fourth of which are black like the one grandparent,
one-fourth white like the other grandparent, and the remaining half, blue
like the parents (Fig. 16). Moreover, the black fowls obtained in this way
will, when interbred, produce only black offspring and the same is true of
the white fowls. To all appearances as far as color is concerned they are
of as pure type as the original grandparents. With the blue fowls,
however, the case is different, for when bred together they will produce
the same three kinds of progeny that their parents produced and in the
same proportions. Again the white and the black are true to type but the
blue will always yield the three classes of offspring and this through
generation after generation.
[Illustration: FIG. 16
Diagram showing the scheme of inheritance in the blue Andalusian fowl.]
These facts may be illustrated graphically as follows where the word
"black" indicates the original black parent, "white" the original white
(black splashed) parent and "blue" the hybrid offspring.
Parental
Generation (P) Black x White Black x White
| |
First Filial | |
Generation (F_{1}) Blue x Blue
|
+------------------------------------------+
| | |
Second Filial Black Blue White
Generation (F_{2}) (25%) (50%) (25%)
| | |
| +-------------------------+ |
| | | | |
Third Filial Black Black Blue White White
Generation (F_{3}) | (25%) (50%) (25%) |
| | | | |
| | +-------------+ | |
| | | | | | |
Fourth Filial Black Black Black Blue White White White
Generation (F_{4}) (25%) (50%) (25%)
=The Cause of the Mendelian Ratio.--=Concerning the cause of this peculiar
ratio of inheritance in crossed forms Mendel suggested a simple
explanation. Animals or plants that can be cross-bred, obviously must be
forms that produce a new individual from the union of two germ-cells, one
of which is provided by each parent. Mendel's idea was that there must be
some process of segregation going on in the developing germ-cells of each
hybrid whereby the factors for the two qualities are set apart in
different cells with the result that half of the germ-cells of a given
individual will contain the determiner of one character and half, the
determiner of the other. That is, a given germ-cell carries a factor for
one or the other of the two alternate characters but not the factors for
both. In a plant, for example, in the male line, half of the pollen grains
would bear germ-cells carrying the determiner of one character and half,
that of the other. Similarly, in the female line, half of the ovules would
contain the determiner of the one character and half, that of the other.
Likewise in animals as regards such pairs of characters there would be two
classes of germ-cells in the male and two in the female. In the case of
the blue Andalusian fowls under discussion this would mean that half of
the mature germ-cells of the male carry the black-producing factor, and
half carry the white-producing factor, and the same is true of the
germ-cells of the female. Thus when two such crossed forms are mated,
there are, by the laws of chance, four possible combinations, namely: (1)
white-determining sperm-cells and white-determining ovum; (2)
white-determining sperm-cells and black-determining ovum; (3)
black-determining sperm-cells and white-determining ovum; and (4)
black-determining sperm-cells and black-determining ovum. Manifestly, the
first combination can only give white offspring; the second, white and
black, gives blue (by such a cross the original blues were established);
likewise, the third, black and white, gives blue; and the fourth
combination can only give black offspring. This matter may be graphically
represented by the following formulae in which B indicates the determiner
of Black in the germ-cell and W the determiner of White: [male] signifies
male; [female] female.
IN THE ORIGINAL PARENTS
W x B = WB = Blue
IN THE HYBRIDS
[male] [female]
germ- germ-
cells cells [male] [female]
W----W W x W = WW = White
\/ W x B = WB = Blue
/\ or B x W = BW = Blue
B----B B x B = BB = Black
Thus of the four possible combinations one only can produce white fowls,
two (WB or BW) can produce blue fowls, and one black fowls. That is, the
ratio is 1:2:1 or the 25, 50 and 25 per cent., respectively, of our
diagram. The black fowls or the white fowls will breed true in subsequent
generations when mated with those of their own color because the
determiner of the alternative character has been permanently eliminated
from their germ-plasm; but the blue fowls will always yield three types of
offspring because they still possess the two classes of germ-cells.
=Verification of the Hypothesis.--=The hypothesis that germ-cells of
crossed forms are of two classes with respect to a given pair of Mendelian
characters is further substantiated by the following facts. If in the case
of the fowls under discussion one of the blue fowls is mated with an
individual of the white variety, half of the progeny will be blue and
half white. For the hybrid has two kinds of germ-cells, black producing,
which we have designated by the letter B, and white producing (or W) in
equal number while the white parent has only one kind, white producing. It
is obvious that if half the germ-cells of the hybrid form are of the type
B then half the progeny will be of the BW type, which is blue, and the
other half will be of the WW type, which is white. In the same way if we
mate a hybrid and a black fowl, half of the progeny will be black and half
will be blue, that is, there could only be WB and BB types.
The fact must not be lost sight of that since the pairings are wholly
determined by the laws of chance the proportions are likely to be only
approximate. It is obvious that the greater the number of individuals, the
nearer the results will approach the expected ratio.
DOMINANT AND RECESSIVE
=One Character May Mask the Other.--=In a large number of cases, however,
the actual condition of affairs is not so evident as in the Andalusian
fowl, for instead of being intermediate or different in appearance, the
generation produced by crossing resembles one parent to the exclusion of
the other. Such an overshadowing is spoken of as _dominance_, and the two
characters are termed _dominant_ and _recessive_. Thus when brown
ring-doves and white ring-doves are mated the progeny are all brown, or if
wild gray mice are mated to white mice the progeny are all gray. So black
is dominant to white in rose-comb bantams; brown eyes to blue eyes in man;
beardlessness to beard in wheat, and likewise rough chaff to smooth, and
thick stem to thin; tallness to dwarfness in various plants; normal
condition to the peculiar waltzing condition in the Japanese waltzing
mouse. Numerous other cases might be cited but these are sufficient to
illustrate the condition.
=Segregation in the Next Generation.--=But now the question arises, what
do such crosses as show dominance transmit to the next generation?
Experiments show regarding any given pair of these alternate characters
that they are set apart again in the succeeding generation, returning in a
definite percentage to the respective grandparental types.
[Illustration: FIG. 17
Diagram showing the scheme of inheritance in guinea-pigs when black and
albino forms are crossed.]
=Dominance Illustrated in Guinea-Pigs.--=In guinea-pigs for example (Fig.
17), when an individual (either male or female) of a black variety, is
crossed with one of a white variety, the F_{1} generation are all black
like the black parent. When these are interbred or bred with other blacks
which have had one black and one white parent, only two visible types of
progeny appear, viz., black and white, and these approximately in the
ratio of three to one.
Analysis by further breeding shows, however, that there are in reality
three types, but since dominance is complete the pure extracted dominant
and the mixed dominant-and-recessive type are indistinguishable to our
eye. That is, while the blacks are three times as numerous as the whites,
two out of every three of these blacks are really hybrid and correspond to
the blue fowls of our former example.
The condition is readily comprehended when expressed diagrammatically
thus:
Generation P Black x White Black x White
| |
Generation F_{1} Black (White) x Black (White)
|
+-------------------------------------+
| | |
Generation F_{2} 1 Black 2 Black (White) 1 White
In other words, the germ-cells of the one original parent (Gen. P) would
contain only determiners for black and that of the other parent would
contain only determiners for white. The condition of the individuals
produced by the cross would be represented by the formula B(W). But these
determiners segregate in the germ-cells of the crossed form, whether it be
male or female, into B and W. Hence half the spermatozoa of the male
hybrid (generation F_{1}) would carry the B determiners and half the W
determiners. The same is true of the mature ova of the female hybrid.
Consequently, in mating there are always four equally possible
combinations, viz., BB, B(W), (W)B, and WW. Since B is always dominant
three out of the four matings would yield black individuals, or in other
words the ratio would be 3:1.
The pure blacks when mated together will breed true in subsequent
generations, likewise the whites, but the blacks carrying white as a
recessive will yield when interbred the same ratio of whites and black as
did their hybrid parents (Fig. 17, p. 75).
=Terminology.--=As work in the study of Mendelian inheritance has
progressed and expanded the need of a more precise terminology has become
evident and such is gradually being established. Thus Professor Bateson
has coined the term "allelomorph" (Gk. _one another_, and _form_) to
express more exactly what we have thus far been calling a pair of
alternate or opposite characters. In the blue Andalusian fowls discussed,
the white condition in the one parent is the allelomorph of the black
condition in the other. The term generally means one of the pair of
Mendelian characters themselves as expressed in the individual plants or
animals but when the germinal basis of such phenomena is under discussion,
it is sometimes used to refer to the determiners of such characters. And
by determiner is meant simply the condition which is necessary in the germ
to bring about the occurrence of a definite character. For example, when
we are studying a cross between a red flower and a white flower with
reference to the color factors, the difference between the two plants may
lie in the fact that one produces a red coloring matter and the other
does not. That is, the determiner for red is absent from the white
variety. What the exact relation of color production is to the parts of
the germ-cell we do not know. It could be the function of a single
definite body or the resultant of several cooperating bodies. The latter
is far more likely to be the case. We may suppose that a group of
cooperating substances function to produce red in the red flower but that
in the white flowers one of these bodies is absent or fails to perform its
red-producing function.
It is customary where practicable to refer to the determiner of a
character by the initial letter of the name of the character. The letter
when written as a capital indicates the determiner but when written as a
small letter the absence of the determiner. Thus R may be taken to
represent the determiner for red coloring matter and r its absence. It is
convenient also to have a brief symbol to denote a given generation and
for this purpose Bateson has introduced the symbol F_{1} for the hybrid
progeny of the first cross, the initial letter of the word "filial." F_{2}
would indicate the next generation, F_{3} the third and so on. Likewise P
denotes the original parent generation.
=The Theory of Presence and Absence.--=Many, if not all, allelomorphs
consist of the presence and absence respectively of a given determiner. In
such cases the character represented by the presence of the determiner is
dominant over the character represented by the absence of a determiner.
Thus in the crosses from the wild gray mice and albino mice the progeny
are all gray mice since one parent had the determiner or group of
determiners for grayness and the hybrid offspring must also possess it.
Likewise the presence of black in black guinea-pigs is dominant to its
absence in albino guinea-pigs and the resulting progeny are all black.
However, it has already been mentioned that beardlessness in wheat is
dominant to beard and that the absence of horns in cattle is dominant to
their presence, that is, the progeny of hornless by horned cattle are
without horns except for occasional traces of imperfect horns. Facts like
these would seem at first sight to contradict the assertion just made that
presence is dominant to absence, but it is fairly well established that in
such cases one is not dealing with true absences but with suppressions.
The polled breeds of cattle, for example, are hornless not because of the
absence of determiners for horns but because of the presence of an
additional inhibiting factor which prevents these determiners from
functioning. The horned breeds are without this inhibitor. When horned and
hornless individuals are crossed the presence of the inhibitor from one
line of ancestry is sufficient to suppress the development of horns in the
progeny. A similar explanation would, of course, apply to beardlessness in
wheat.
In writing double-lettered formulae to denote the determiners of characters
in hybrids the condition is represented merely by the capital and small
letter. Thus Rr indicates that red is dominant to its absence.
=Additional Terminology.--=In pure breeds where the determiners are alike
as BB in black or bb in albino guinea-pigs, the individual is said to be a
_homozygote_ (like things united) with reference to that character, while
in those in which the determiners are unlike, as Bb, the individual is
termed a _heterozygote_ (unlike things united) with reference to the
character. Or to use the adjective forms, a pure black guinea-pig is
homozygous for black pigment, an albino guinea-pig is homozygous for
absence of pigment, while a cross between the two is heterozygous for
pigment. Also, where the determiner of a given character is present in
double quantity, that is, from both lines of ancestry, the individual is
said to be _duplex_, where represented in only the single form as in
heterozygous individuals, _simplex_, and where the determiner is absent
entirely, _nulliplex_, with reference to the character in question. Thus
black guinea-pigs of formula BB are duplex with regard to the determiner
for black color, individuals of formula Bb are simplex with reference to
this determiner, and those of formula bb are nulliplex.
A heterozygote in which dominance prevails can be identified with
certainty by breeding to a known recessive and noting the kind of
offspring produced. If the individual was really a heterozygote,
approximately fifty per cent. of the offspring should be of the recessive
type.
=Dominance Not Always Complete.--=As a matter of fact close inspection
shows that in numerous instances dominance is not absolute since traces of
the recessive character may be detectable. For example, in the cross
between smooth and bearded wheat while smoothness is regarded as the
dominant character and beardlessness as the recessive, nevertheless in the
hybrid offspring a slight tendency toward bearding is not infrequently
seen. Or again when horned breeds of cattle are crossed with hornless
ones, a small proportion of such progeny will show traces of imperfect
horns.
In some cases instead of either character dominating the other a form
intermediate between the two parents may result, as we have seen already
in the case of the Andalusian fowl. Thus, certain white-flowered plants
and certain red-flowered plants when crossed produce pink hybrids, and
longheaded and shortheaded wheats when crossed give offspring with heads
of intermediate length. Or again, crosses between white and red cattle may
yield red roans, and between black and white cattle, blue roans.
Thus, while for such pairs of alternative characters as have been studied,
dominance to some considerable degrees at least, seems to be the rule,
still we have gradations down to the intermediate condition, and in some
instances the hybrid with respect to a given character may be unlike
either parent. The things of chief importance in the Mendelian discovery
are the independent, unitary nature of the characters and their
segregation in the offspring of cross-bred forms.
=Modifications of Dominance.--=It should be noted also that there is such
a condition as _delayed dominance_. Davenport found, for example, that
chicks produced by crossing pure white with pure black Leghorn fowls are
speckled black and white, but later in the adult form white becomes
dominant. Likewise conditions of delayed dominance are known in man in
eye-color and notably in color of hair. Some few cases have been recorded
where a character is dominant at one time, recessive at another.
According to Davenport extra toe in fowls may behave in this way.
=Mendel's Own Work.--=Mendel[2] himself worked out his principles on seven
pairs of characters which he found in common culinary peas. Placing the
dominant characters first, these may be enumerated as follows: (1) Tall by
dwarf; (2) green pod (unripe) by yellow; (3) pod inflated by pod
constricted between the individual peas; (4) flowers arranged along the
axis of the plant by flowers bunched together at the top; (5) seed skin
colored by seed skin white; (6) cotyledons yellow by cotyledons green; (7)
seed rounded by seed wrinkled.
He found that each pair of characters followed the same law as any other
pair when more than one pair of the characters occurred in the same
plants, but that each pair behaved independently of the other. The meaning
of this is that we may get various combinations of characters not
associated in the original pure stocks, the number of such combinations
depending on the number of pairs of allelomorphs there are.
DIHYBRIDS
=Getting New Combinations of Characters.--=Since this principle is well
illustrated in peas, let us take two pairs of their characters, viz.,
greenness and yellowness (of the cotyledons) and roundness and angularity
to see exactly what happens when two pairs of allelomorphs are involved.
When a specific kind of yellow pea is crossed with a particular kind of
green pea the offspring are always yellow (Fig. 18, opposite p. 84). When
these hybrids (generation F_{1}) are self-fertilized there is the usual
Mendelian segregation; one-fourth the resulting offspring will be green,
one-fourth pure yellow, and one-half, although yellow in appearance, will
be of the mixed type. The exact numbers found by Mendel were 6,022 yellow
seeds to 2,001 green seeds. Now of the original peas (generation P) the
yellow ones are round and the green ones angular (really wrinkled).
Choosing this roundness and angularity respectively as a pair of
characters they are found to follow the same law that the colors follow
(Mendel obtained in the F_{2} generation 5,474 round and 1,850 wrinkled
seed), but independently of the latter. For while in the progeny of the
hybrids (Gen. F_{1}), twenty-five per cent. will be round and of pure type
as regards roundness, twenty-five per cent. angular, and fifty per cent.
round but containing hidden factors of angularity (i. e., roundness is
dominant), the roundness and the yellowness, or the angularity and the
greenness will not always go together as they did in the original
grandparental strains, but there will be in addition some new types of
round green peas and some of angular yellow ones. That is, the factors of
color and of shape have been inherited independently of one another, so
that instead of the two original kinds of peas, four have been produced,
viz., (1) round-yellow (one of the original types); (2) round-green (new
type); (3) angular-yellow (new type); and (4) angular-green (one of the
original types). Furthermore, these will be found to stand in the ratio of
9:3:3:1 respectively.
=Segregations of the Determiners.--=How these combinations come about in
this definite proportion is easily understood if the matter is expressed
in terms of determiners and the possible matings tabulated (Fig. 18). If
we represent the yellow determiner by Y and the green determiner by y, and
likewise the determiners of roundness and angularity by R and r
respectively, then the formulae for the determiners of these two pairs of
characters in the body cells (that is, in the unreduced condition) of the
pure forms and of the F_{1} generation hybrids respectively are as
follows:
In pure round yellow peas RR YY
In pure angular green peas rr yy
In the hybrid Rr Yy
But now in the segregation of these determiners in the germ-cells of the
hybrids (generation F_{1}) the pair of determiners Rr and the pair Yy
operate entirely independently of one another. Their only compulsion is
that each pair be separated into the single determiners, R and r in the
one case and Y and y in the other. So in the separating division which
brings about this divorcement R separates from r irrespective of whether
it is accompanying Y or y into the resulting daughter cell. Thus in some
cases R and Y would pass into one germ-cell, in others R and y, in others
r and Y, and in still others r and y, depending entirely upon the
chance relations of the respective pairs to the plane of division. That
is, the segregation is equally likely to be RY/ry giving gametes RY and
ry, or Ry/rY giving gametes Ry and rY.
[Illustration:
\[Female]
[Male]\ RY Ry rY ry
+-------+--------+--------+--------+
RY | RRYY | RRYy | RRYY | RrYy |
+-------+--------+--------+--------+
Ry | RRYy | RRyy | RrYy | Rryy |
+-------+--------+--------+--------+
rY | RrYY | RrYy | rrYY | rrYy |
+-------+--------+--------+--------+
ry | RrYy | Rryy | rrYy | rryy |
+-------+--------+--------+--------+
(1) 1 RRYY (4) 2 RrYY (7) 1 rrYY
(2) 2 RRYy (5) 4 RrYy (8) 2 rrYy
(3) 1 RRyy (6) 2 Rryy (9) 1 rrYy
9:3:3:1
FIG. 18
Diagram showing the possible combinations arising in the second filial
generation (F_{2}) following a cross between yellow, round (YYRR) and
green, angular or wrinkled (yyrr) peas. Y, presence of factor for yellow;
y, absence of such a factor; R, presence of factor for smoothness or
roundness; r, absence of such a factor; [male] male; [female] female.]
=Four Kinds of Gametes in Each Sex Means Sixteen Possible
Combinations.--=There are, therefore, with reference to the two pairs of
characters under consideration, four kinds of gametes (or mature
germ-cells) produced in equal numbers in each hybrid, viz., RY, Ry, rY,
and ry. That is, in the first type roundness and yellowness are
associated, in the second roundness and greenness, in the third angularity
(lack of roundness) and yellowness, and in the fourth angularity and
greenness.
But since both males and females have these four kinds of gametes, when
they are mated there will be sixteen possible combinations. These may be
tabulated as in Fig. 18, opposite p. 84.
=The 9:3:3:1 Ratio.--=While there are sixteen possible and equally
probable combinations, these will give only nine distinct kinds because
some of the matings are alike. The numbers of the various kinds of matings
are as follows:
(1) 1 RRYY (4) 2 RrYY (7) 1 rrYY
(2) 2 RRYy (5) 4 RrYy (8) 2 rrYy
(3) 1 RRyy (6) 2 Rryy (9) 1 rrYy
Since roundness (R) and yellowness (Y) are dominant to angularity (r) and
greenness (y) in all combinations containing R or Y, the alternative
determiners r or y would be obscured, with the result that individuals
having certain of the combinations would look alike to our eye. For
example, the individuals represented by numbers 1, 2, 4 and 5, since they
contain dominant R and Y, would all appear round and yellow, although in
reality No. 1 would be the only one of pure type (both elements
homozygous) and hence the only one that would breed true in subsequent
generations. The two individuals represented in No. 2 would breed true as
regards shape (RR) but not color (Yy). Just the reverse is true of No. 4
since shape is heterozygous (Rr) and color homozygous (YY). The four
individuals represented in No. 5 are heterozygous with regard to both
elements. Thus nine individuals (1 plus 2 plus 2 plus 4 = 9) represented
in Nos. 1, 2, 4 and 5 would be round and yellow, three individuals (Nos. 3
and 6) would be round and green, three (Nos. 7 and 8) would be angular and
yellow, and only one (No. 9) would be angular and green. That is to say,
the four classes discernible to the eye in generation F_{2} would be
present in the ratio of 9:3:3:1.
=Phenotype and Genotype.--=Forms such as those represented in Nos. 1, 2, 4
and 5 which to the eye appear to be alike, regardless of their germinal
constitution, are said to be of the same _phenotype_. Those of the same
hereditary constitution, as the two individuals represented in No. 8, or
the four individuals in No. 5, are said to be of the same _genotype_, that
is, they are of identical gametic constitution.
As we have seen, it is from the genotypical not the phenotypical
constitution that an offspring is derived and what a given form will bring
forth depends then on its genotype.
=Crosses With More Than Two Pairs of Characters.--=In crosses in which
more than two pairs of contrasted characters are involved the underlying
principles are in no way different, only with each pair of additional
characters there is, of course, a greater number of possible combinations.
Thus with three pairs of characters there will be eight different classes
of gametes in each sex and consequently sixty-four possible combinations
in mating, giving eight different phenotypes in the proportion of
27:9:9:9:3:3:3:1. The largest class manifests the three dominant
characters; the smallest class, the three recessives; the three classes in
the proportion of 9 each exhibit two dominant and one recessive
characters; and those in the proportion of 3 each display two recessive
and one dominant characters.
THE QUESTION OF BLENDED INHERITANCE
We come now to certain types of inheritance in which there seems to be a
true fusion or blend of the contributions from the two parents, the
intermediate condition apparently persisting in subsequent generations
without segregation. Numerous cases of blended inheritance have been cited
in earlier literature of heredity, but as our knowledge of genetics has
progressed many experimental breeders have come to believe that the
blends in such cases are apparent rather than real and that the phenomena
can be best explained on a non-blending unit-character basis, just as we
would explain ordinary Mendelian phenomena.
=Nilsson-Ehle's Discoveries.--=To get their point of view we may review
certain experiments on wheat made by Nilsson-Ehle, together with their
Mendelian interpretation. Nilsson-Ehle found that a certain brown-chaffed
wheat when crossed with a white-chaffed strain yielded a brown-chaffed
hybrid, apparently in accordance with the simple principle of Mendelian
dominance. But these heterozygous brown-chaffed individuals did not in
turn give the expected ratio of 3:1 in the F_{2} generation but a ratio of
15 brown to 1 white, and furthermore the browns were not all of the same
degree of brownness. To be exact, from fifteen different crosses of the
strains he obtained 1,410 brown-chaffed and 94 white-chaffed plants.
This apparent anomaly in segregation was easily explained, however, when
it was finally figured out that there were really two independent
determiners for brown color, either of which alone could produce a brown
individual, but when combined produced individuals of correspondingly
deeper shades of brown. In such a case then Nilsson-Ehle discovered that
he was dealing merely with a Mendelian dihybrid where two different
determiners B and B' and their respective absences b and b' are involved.
The original brown wheat had both B and B' and the original white b and
b'. The formula for the F_{1} heterozygote was therefore BbB'b'. The four
possible types of gametes for male and female are BB', Bb', bB', bb', and
the tabulation would be as follows:
+-----------------------------------
| BB' | Bb' | bB' | bb'
-----+--------+--------+--------+--------
BB' | BBB'B' | BBB'b' | BbB'B' | BbB'b'
-----+--------+--------+--------+--------
Bb' | BBB'b' | Bb'Bb' | BbB'b' | Bbb'b'
-----+--------+--------+--------+--------
bB' | BbB'B' | BbB'b' | bbB'B' | bbB'b'
-----+--------+--------+--------+--------
bb' | BbB'b' | Bbb'b' | bbB'b' | bbb'b'
-----------------------------------------
It will be observed that there are more brown determiners in some
combinations than others. For instance one of the sixteen contains four
such determiners, viz., B, B', B, B', four contain three determiners, six
contain two, four contain only one, and one contains none. Thus all but
one of the sixteen contain at least one determiner and will therefore be
brown in color but the depth of color will depend on the number of brown
determiners in a given individual. This is more graphically represented in
Fig. 19, p. 90. The largest number of similar individuals, six in all,
contain two determiners each and represent an intermediate "blend" between
the original brown-chaffed and white-chaffed strains. The deeper and the
lighter browns due to more or fewer determinants in an individual would if
one did not know the units in this case look like the fluctuations around
this average which we might expect in a blend.
[Illustration: FIG. 19
Diagram illustrating the proportionate distribution of determiners where
either of two different determiners produces the same character, the
degree of expression of the character depending on the number of the
determiners present. The numerals indicate the number of brown determiners
present in an individual.]
Nilsson-Ehle found another significant case in wheat where one particular
red-grained strain of Swedish wheat when crossed with white-grained
strains produced red-grained offspring, but when these were interbred the
F_{2} generation gave approximately sixty-three red to one white-grained
individual. Here it was found that in the original red wheat there are
three separate determiners which act independently of one another in
heredity, any one of which would make red color; and that they together
with their absences simply follow the Mendelian laws for a trihybrid.
=Such Cases Easily Mistaken for True Blends.--=If we should tabulate the
possible combinations as we did the dihybrid we should see that we would
get individuals having varying numbers of red determiners. Only one of the
sixty-four possible combinations would be without a factor for red. Of the
sixty-four, one would have six determiners for red, six would have five,
fifteen would have four, twenty would have three, fifteen would have two,
six would have one, and one would have none. Since here every additional
red factor means deeper redness in the individual there would be varying
degrees of redness in the F_{2} generation with those having three
determiners, the largest group, standing apparently intermediate. Not
knowing the factors involved we might easily mistake such a case for a
true blend with fluctuations about an average intermediate form.
Nilsson-Ehle finally proved his interpretation by rearing an F_{3}
generation from isolated and self-fertilized plants of this F_{2}
generation.
This same principle of cumulative determiners has also been established in
America by East with field corn.
As the number of duplicate determiners increases it can be readily seen
that the number of apparent blends of different degrees of intermediacy
between the two extremes would rapidly increase.
=Skin-Color in Man.--=In man, the skin-color of the hybrids between
negroes and whites is often cited as a case of blended inheritance in
contradistinction to Mendelian inheritance. The skin-color of the mulatto
of the F_{1} generation is intermediate between that of the white and
black parent. This same degree of intermediacy is commonly supposed to
persist in subsequent generations, but as a matter of fact, careful
investigation has shown that while mulattoes rarely produce pure white or
pure black children, there is considerably greater range in the shades of
color in the F_{2} generation and subsequent generations than in the F_{1}
generation. This is exactly what one would expect of a Mendelian character
in which several cooperating factors were involved. Indeed, Davenport who
has made extensive studies[3] on the inheritance of skin-color in man has
come to the conclusion that the case is really one of Mendelian
inheritance in which several factors for skin-color are concerned. Even
the skin of a white man is pigmented in some degree under normal
conditions. Davenport has shown in the skin of both whites and blacks that
there is a mixture of black, yellow and red pigments. He concludes that
"there are two double factors (AABB) for black pigmentation in the
full-blooded negro of the west coast of Africa and these are separably
inheritable." Since these factors are lacking in white persons the
intermediate color of an F_{1} mulatto would therefore be heterozygous for
pigmentation, and subsequent generations, following the laws for
segregation where a number of factors are concerned, would show different
degrees of color because of the varying combinations of factors.
=Some Investigators Would Question the Existence of Real Blends.--=Still
other reputed blends such as ear length in rabbits and the like have been
shown to be analyzable into Mendelian behavior if one will but postulate
numerous or multiple factors. Just how far we are justified in so
accounting for blends has not yet been established. Some of our most
careful experimentalists in heredity still believe that real blends exist,
particularly where the character is quantitatively expressed--that is, as
more or less of a given size or amount--while others would maintain that
all alleged blends will probably be found to be resolvable into factors
which follow Mendelian rule. It must be left for future investigations to
demonstrate which school is correct.
THE PLACE OF THE MENDELIAN FACTORS IN THE GERM-CELLS
=Parallel Between the Behavior of Mendelian Factors and Chromosomes.--=The
question arises as to whether there is any evidence from the study of
germ-cells themselves to bear out the Mendelian conception of separation
of contrasted characters in the gametes of the F_{1} generation. In the
discussion of the maturation of germ-cells (Chap. II) it has already been
seen that the chromosomes of the germ-cells are in all probability
arranged in homologous pairs, one member being of maternal and the other
of paternal origin, and that furthermore they are closely associated with
the phenomena of heredity. And since in maturation there is an actual
segregation of the chromosomes into two sets, half going to one cell and
half to its mate, a physical basis adequate to the necessities of the case
is really at hand. It will be recalled that the individuals of a pair
separate in such a way at the reduction division that the paternal member
goes to one cell and the maternal member to the other, although each pair
seemingly acts independently of the others with the result that any mature
germ-cell may contain chromosomes from each of the original parents but
never the two chromosomes which earlier made up a pair. The close parallel
between the behavior of chromosomes and the behavior of Mendelian factors,
although the two sets of phenomena were discovered wholly independently of
each other, is obvious. If we suppose that each chromosome bears the
determiner of a Mendelian character and that chromosomes bearing
allelomorphic characters make up the various pairs which are seen in the
early germ-cells of an individual before reduction occurs, then the
segregation of the individuals of an allelomorphic pair into different
gametes must result in consequence of the passing of the corresponding
chromosomes into separate gametes. Fig. 20, p. 95, from Professor Wilson
represents equally well the segregations of pairs of chromosomes or pairs
of Mendelian characters.
[Illustration: FIG. 20
Diagram showing union of factors from the two separate parents in
fertilization and their segregation in the formation of germ-cells (after
Wilson). With four pairs of factors (_Aa_, _Bb_, _Cc_, _Dd_), sixteen
types of gametes are possible, as shown in the series of small circles at
the right. The same diagram equally well represents the pairings and
segregations of chromosomes.]
=A Single Chromosome not Restricted to Carrying a Single Determiner.--=It
has been objected that there may be more pairs of independently heritable
allelomorphic characters than there are pairs of chromosomes. It is true
that there are more pairs of characters than pairs of chromosomes but
there is no reason for supposing that a given chromosome is restricted to
carrying a single unit-determiner. On the contrary it probably carries
several or many. Some workers have pointed out that certain units might be
interchanged during the pairing of chromosomes before the reduction
division, others that inasmuch as the chromosomes become diffuse and
granulated during the intervals between divisions it is not improbable
that the individual units may become separated from their original system
during such times and that it is a matter of chance into which of the
homologous chromosomes, A or a, they enter with the re-establishment of
the chromosomes. On the other hand, cases are known where two or more
separate characters are permanently associated in inheritance, that is, if
they enter a crossed form together they come out together in the
grandchildren as if they were carried in the same unit-body in the
germ-cell. The only observable unit-bodies that fulfil the necessities of
such cases are the chromosomes. This tendency of characters to exist in
groups which are inherited independently of one another is coming more and
more into evidence as we penetrate farther into the intricacies of
inheritance, and it is exactly what we would expect on the supposition
that each chromosome carries the determiners of a number of characters
instead of a single one.