=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 _h.o.m.ozygote_ (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 h.o.m.ozygous for black pigment, an albino guinea-pig is h.o.m.ozygous 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 quant.i.ty, 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 a.s.sociated 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 ill.u.s.trated 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 pa.s.s 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.
[Ill.u.s.tration:
[Female]
[Male] RY Ry rY ry +-------+--------+--------+--------+ RYRRYYRRYyRRYYRrYy+-------+--------+--------+--------+ RyRRYyRRyyRrYyRryy+-------+--------+--------+--------+ rYRrYYRrYyrrYYrrYy+-------+--------+--------+--------+ ryRrYyRryyrrYyrryy+-------+--------+--------+--------+
(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 s.e.x 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 a.s.sociated, 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 h.o.m.ozygous) 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 h.o.m.ozygous (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 cla.s.ses 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 const.i.tution, are said to be of the same _phenotype_. Those of the same hereditary const.i.tution, 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 const.i.tution.
As we have seen, it is from the genotypical not the phenotypical const.i.tution 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 cla.s.ses of gametes in each s.e.x 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 cla.s.s manifests the three dominant characters; the smallest cla.s.s, the three recessives; the three cla.s.ses 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.
[Ill.u.s.tration: FIG. 19
Diagram ill.u.s.trating 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 c.u.mulative 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 a.n.a.lyzable 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 quant.i.tatively 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.