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, iscrossed with one of a white variety, the F1generation 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, andform) 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 thatone 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 F1for the hybrid progeny of the first cross, the initial letter of the word “filial.” F2would indicate the next generation, F3the 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 orgroup 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 ahomozygote(like things united) with reference to that character, while in those in which the determiners are unlike, as Bb, the individual is termed aheterozygote(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 beduplex, 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 hybridoffspring 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 asdelayed 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 atone 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 ofallelomorphs 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, oppositep. 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 F2generation 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 F1generation hybrids respectively are as follows:
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 rand 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.
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, oppositep. 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:
Since roundness (R) and yellowness (Y) are dominant to angularity (r) and greenness (y) in allcombinations 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 F2would 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 samephenotype. 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 samegenotype, 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 tobelieve 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 F2generation 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 F1heterozygote was therefore BbB′b′. The four possible types of gametesfor male and female are BB′, Bb′, bB′, bb′, and the tabulation would be as follows:
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 F2generation gave approximately sixty-three red to one white-grained individual. Here it wasfound 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 F2generation 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 F3generation from isolated and self-fertilized plants of this F2generation.
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 F1generation 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 F2generation and subsequent generations than in the F1generation. 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 F1mulatto would therefore be heterozygous for pigmentation, andsubsequent 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 F1generation. 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 beingof 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 chromosomesbefore 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.
MENDELISM IN MAN
The Mendelian Principles Probably Applicable to Many Characters of Man.—We are really just beginning to make the proper observations and collect the necessary data with reference to the application of Mendelian principles to the traits of man. Yet brief as has been our study we have disclosed much significant evidence which makes it seem highly probable that many of his characters, good and bad, of mind and body are as subservient to these laws as are the traits and features of lower forms. Davenport and Plate record over sixty human characters or defects which are seemingly inherited in Mendelian fashion. Although about fifty of these are pathological or abnormal conditions, this does not mean that such conditions are more prone to follow Mendelian inheritance but merely that being relatively conspicuous or isolated they are easier to follow and tabulate.
Difficult to get Correct Data.—While it must be said that in many cases no simple form of Mendelian tabulation has been unequivocally established, yet the general behavior of the various inheritable traits in question is so obviously related to the conventional Mendelian course that there seems little reason for doubting that they are at bottom the same. Failure to obtain exact proportions may be attributable in partto the probability that what we loosely regard as a character should in reality be analyzed into more elemental components, and above all to the fact that from the very nature of the conditions under which human records must be obtained, there is considerable chance of inaccuracy or error in such accounts. How many human traits follow Mendelian rules remains largely for future investigators to establish.
We are handicapped at the outset in man by the many difficulties of getting correct data from the genealogies on which we must depend, or in fact of getting any genealogy at all, for in this country at least, most families keep imperfect records of births and deaths and many of the institutions for the various kinds of defectives have little in their records that will help us in following out hereditary conditions. Then in matters of disease we meet with the fact that many former diagnoses were erroneous. In yet other cases, and this is particularly true among mental and moral defectives, we are often not sure of the paternity of a given child. Furthermore, one is likely to be misled by the proportions which may occur in the very limited number of children of any given couple.
Still other difficulties exist. Among these is the fact, for example, that in many cases of defect or susceptibility to disease, a given individual in the stock may have the trait in an expressible and transmissible form, yet it never comes to expression because that individual has been fortunate enough to escape the environmental stimulus which would call it forth. Thus one highly susceptible to tuberculosis might escape infection, or persons hovering on the verge of insanitymight never receive the precipitating stimulus which would topple them into actual insanity; yet each would be wrongfully recorded in a genealogy looking to such traits as perfectly normal. Or again if it be a question of intellectual brilliancy as shown by accomplishment in the realm of scholarship, or of worldly affairs, the ones who although possessing them have had no chance to display unusual talents would be tabulated as average whereas in fact they should be recorded as of high rank. That this is particularly likely to happen in the case of women is evident.
A Generalized Presence-Absence Formula for Man.—In man as in lower forms some characters or traits are due presumably to the presence of determiners or to their absence. Likewise, dominance and recessiveness are as much in evidence, for in tracing back pedigrees of various traits we find the same forms of tabulation that obtain for these conditions in plants and lower animals hold good. For typical cases in man let us use a generalized presence-absence formula and the arbitrary symbol A for the presence of the determiner of the character (double in the individual, single in the germ) and a for its absence. Thus AA represents a condition in which similar determiners have been derived from both parents and the individual isduplexas regards the character in question; each mature germ-cell will have the determiner. Aa represents a condition in which the individual has received the determiner from only one parent and is thereforesimplexwith regard to the character; half of the gametes of such an individual will have the determiner and half will lack it. Lastly, aa represents totalabsence of the determiner. Such an individual isnulliplex. He or she will not have the determiner represented in any of the gametes, and can not, of course, transmit a trait represented by the determiner.
It is evident that six kinds of gametic matings are possible among individuals representing these various formulæ. These matings are as follows:
Indications of Incomplete Dominance.—While in cases of strict Mendelian dominance it is not possibleto distinguish directly the simplex from the duplex condition, as a matter of fact the individual of simplex constitution sometimes has the character represented in the single determiner less perfectly developed than in the corresponding character of duplex origin. In studying defects in man due to the absence of a determiner, where theoretically presence of the determiner (normality) is dominant over its absence in individuals of simplex constitution, one finds it recorded with increasing frequency that such individuals are more or less “intermediate” or are “tainted” with the defect; thus showing that the defect though obscured is not wholly in abeyance. Thus individuals carrying epilepsy or feeble-mindedness which are regarded as recessive traits, while not showing specific feeble-mindedness or epilepsy, may nevertheless apparently show a neuropathic taint in the form of migraine, alcoholism or other lapse from normality. The condition is seemingly more akin in some cases to that found in the offspring of certain red flowers crossbred with white flowers, which though red do not show the same intensity of color as the original red parent. Just as here the single determiner or single “dose” of redness is insufficient to produce the intensity of color that appears when the offspring receive two determiners for red, one from each parent, so in man a single determiner for normality of a specific character is inadequate in some cases to make the individual wholly normal. Or possibly some cases are more of the type of those in which the character in question, for instance the red color of some wheats and corn, may be produced by any one of two or three determiners, the intensity ofthe characters (red color, e. g.) depending on whether one, two or three determiners are present.
Why After the First Generation Only Half the Children May Show the Dominant Character.—If the trait is a simple dominant one it is clear that it will appear in each generation and always spring from an affected individual. By referring back to our tabulation of possible matings on page 100 where the dominant character is represented by the letter A, this can be seen at a glance. If the trait is present in the duplex condition in one parent and absent from the other, then formula 3 applies; all children will show the trait, but in the simplex form (Aa). If the trait is present in the simplex form in one parent and absent in the other, formula 2 applies. Fifty per cent. of the children will have the character in the simplex form (Aa) which means also an even chance of transmitting it to their offspring; fifty per cent. will not inherit it and will be incapable, furthermore, of transmitting it, since they have become nulliplex (aa). In human genealogies if an individual having an unusual trait which is inherited as a dominant marries a normal person and half of the offspring show the trait (and this is common), this means that the parent manifesting the trait had it represented only in the simplex condition, otherwise all of the children would have shown it. Even though the original ancestor who first developed the condition or structure may have had it in a duplex form, it would after the first mating, if this were with an individual lacking the trait, be represented only in the simplex form (see formula 5) and could never become duplex again unless twoindividuals both having the character married, and then only in twenty-five per cent. of the offspring (see formula 3). If the trait is a defect all the children showing it, even though marrying normal (nulliplex) individuals, will pass it on again to half their children, but those who do not show it may ordinarily marry with impunity since its non-expression in their make-up means, as far as we know at present, that their germ-plasm has been purged of the defect and that they are therefore nulliplex with reference to it.
Eye-Color in Man.—Of normal characters in man which follow the Mendelian formula perhaps eye-color is the best established. Brown or black eye-color is due to amelaninpigment absent from the blue or gray eye. That is, a brown eye is practically a blue eye plus an additional layer of pigment on the outer surface of the iris. The different shades of brown and the black are due to the relative abundance of this pigment. Gray color and the shades of blue seem to be a modification of an original dark blue, due to structural differences in the fibrous tissues of the iris.
In inheritance brown or black is dominant to blue or gray, or in other words thepresenceandabsenceof a pigment P constitutes a pair of allelomorphs. Hence two brown-eyed parents, if P is duplex in both (or duplex in one and simplex in the other) can have only brown-eyed children. Thus,