Being Well-Born: An Introduction to Eugenics

CHAPTER III

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 BrÜnn, 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 BrÜnn. 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.

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.

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 formulÆ in which B indicates the determiner of Black in the germ-cell and W the determiner of White: ? signifies male; ? female.

IN THE ORIGINAL PARENTS

W × B = WB = Blue

IN THE HYBRIDS

? germ- cells	? germ- cells		?		?
			W	×	W	==	WW	==	White
		or	W	×	B	==	WB	==	Blue
		or	B	×	W	==	BW	==	Blue
			B	×	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.

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 F₁ 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:

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 F₁) 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 F₁ for the hybrid progeny of the first cross, the initial letter of the word “filial.” F₂ would indicate the next generation, F₃ 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 formulÆ 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 F₁) 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 F₂ generation 5,474 round and 1,850 wrinkled seed), but independently of the latter. For while in the progeny of the hybrids (Gen. F₁), 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 formulÆ 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 F₁ 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 F₁) 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.

?	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 (F₂) 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; ? 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 F₂ 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 F₂ 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 F₁ 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.

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 F₂ 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 F₂ 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 F₃ generation from isolated and self-fertilized plants of this F₂ 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 F₁ 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 F₂ generation and subsequent generations than in the F₁ 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 F₁ 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 F₁ 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.

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.

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