# Popular Science Monthly/Volume 85/October 1914/Phenomena of Inheritance V

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THE
POPULAR SCIENCE
MONTHLY
OCTOBER, 1914
* PHENOMENA OF INHERITANCE
By Professor EDWIN G. CONKLIN
PRINCETON UNIVERSITY
A. OBSERVATIONS OF INHERITANCE
THE observations of men in all ages have established the fact that in general "like produces like," and that, in spite of many exceptions, children are in their main characteristics like their parents. And yet offspring are never exactly like their parents, and this has led to the saying that "like does not produce like but only somewhat like." What is meant is that there are general resemblances but particular differences between parents and offspring.
Individuals and Their Characters
In considering organic individuals one may think of them as wholes or as composed of parts, as indivisible unities or as constituent characters; either aspect is a true one and yet neither is complete in itself. Formerly in discussions on heredity the individual was regarded in its entirety and when all hereditary resemblances and differences were averaged it was said that one child resembled the father, another child the mother. This method of lumping together and averaging resemblances and differences led to endless confusion. In heredity, no less than in anatomy, it is necessary to deal with the constituents of organisms; in short, the organism must be analyzed and each part studied by itself. Francis Galton was one of the first to bring order out of chaos by dealing with traits or characters singly instead of treating all together. He made careful studies on the inheritance of weight and size in the seeds of sweet peas, and on the inheritance of stature, eye color, intellectual capacity, artistic ability and certain diseases in man. At the same time that Galton was thus laying the foundations for a scientific study of heredity by dealing with characters separately, ​another and even greater student of heredity, Gregor Mendel, was doing the same thing in his experiments with garden peas, but inasmuch as Mendel's work remained practically unknown for many years, Galton has been rightly recognized as the founder of the scientific study of heredity.
Of course, neither Galton nor any one else, who has followed his method of dealing with the characters of organisms singly, ever supposed that such characters could exist independently of other characters and apart from the entire organism. This is such a self-evident fact that it may seem needless to mention it, and yet there have been critics who have believed, or have assumed to believe that modern students of heredity attempt to analyze organisms into independently existing characters, whereas in most cases they have done only what the anatomist does in treating separately the various organs of the body.
Hereditary Resemblances and Differences
The various characters into which an organism may be analyzed show a greater or smaller degree of resemblance to the corresponding characters of its parents. Whenever the differential cause of a character is a germinal one, the character is, by definition, inherited; on the other hand, whenever this differential cause is environmental the character is not inherited. While it is true that inheritance is most clearly recognized in those characters in which offspring resemble their parents, even characters in which they differ from their parents may be inherited, as is plainly seen when, in any character, a child resembles a grandparent or a more distant ancestor more than either parent. Sometimes actually new characters arise in descendants which were not present in ascendants, but which are thereafter inherited. Accordingly inherited characters may be classified as resemblances and differences, though both are determined by germinal organization, or heredity. There is, therefore, no fundamental difference between inherited similarities and dissimilarities. Heredity and variation are not opposing nor contrasting tendencies which make offspring like their parents in one case and unlike them in another; really inherited characters may be like or unlike those of the parents.
On the other hand, many resemblances and differences between parents and offspring are not due to heredity at all, but to environmental conditions. By means of experiment it is possible to distinguish between hereditary and environmental resemblances and differences, but among men where experiments are generally out of the question it is often difficult or impossible to make this distinction.
I. Hereditary Resemblances
1. Racial Characters.—All peculiarities which are characteristic of a race, species, genus, order, class and phylum are of course inherited, ​otherwise there would be no constant characteristics of these groups and no possibility of classifying organisms. The chief characters of every living thing are unalterably fixed by heredity. Men do not gather grapes of thorns nor figs of thistles. Every living thing produces offspring after its own kind. Men, horses, cattle; birds, reptiles, fishes; insects, mollusks, worms; polyps, sponges, microorganisms—all of the million known species of animals and plants differ from one another because of inherited peculiarities—because they have come from different kinds of germ cells.
2. Individual Characters.—Many characters which are peculiar to certain individuals are known to be inherited, and in general use the word inheritance refers to the repetition in successive generations of such individual peculiarities. Among such individual characters are the following:
(a) Morphological Features.—Hereditary resemblances are especially recognizable in the gross and minute anatomy of every organism in the form, structure, location, size, color, etc., of each and every part. The number of such individual peculiarities which are inherited is innumerable and only a few of the more striking—of the greatest and smallest of these can be mentioned.
It is a matter of common knowledge that unusually great or small stature runs in certain families, and Galton developed a formula for determining the approximate stature of children from the known stature of the parents and from the mean stature of the race. However his statistical and mathematical formulas give only general or average results, from which, there are many individual departures and exceptions.
In the same way the color of the skin, the color and form of hair, and the color of eyes are, in general, like those of one or more of the parents or grandparents. We all know that certain facial features such as the shape and size of eyes, nose, mouth and chin are generally characteristic of certain families.
But the inheritance of anatomical features extends to much more minute characters than those just mentioned. In certain families a few hairs in the eyebrows are longer than the others; or there may be patches of parti-colored hair over the scalp; or dimples in the cheek, chin, or other parts of the skin may occur; and these trifling peculiarities are inherited with all the tenacity shown in the transmission of more important characters. Johannsen has found races of beans in which the average weight of individual seeds differed only by.02 to .03 gram, and yet these minute differences in weight were characteristic of each race and were of course inherited. Jennings has found races of paramecium which show hereditary differences of.005 mm. in length (Fig. 46). Nettleship says that the lens of the human eye weighs only about 175 milligrams, or about one three millionth part ​of the body weight, and in hereditary cataract only about one twentieth part of the lens becomes opaque, and yet this minute fraction of the body weight shows the influence of heredity. Even the size, shape and
number of the cells in certain organs, and in given embryonic stages, may be repeated generation after generation; and if our analysis were sufficiently complete we should doubtless find that even the minute parts of cells, such as nuclei, chromosomes and centrosomes, show individual peculiarities which are inherited.
(b) Teratological and Pathological Peculiarities are really only unusual or abnormal anatomical characters, but of such interest and importance as to deserve special mention. Many such abnormalities are undoubtedly inherited, among which are the following: polydactylism, in which more than the normal number of digits are present; syndactylism, or a condition of webbed fingers and toes; brachydactylism, in which the fingers are short and stumpy and usually contain less than the normal number of joints; acondroplasy, or short and crooked limbs, such as occur in certain breeds of dogs and sheep and in certain ​human dwarfs; myopia in which the eyeball is elongated; glaucoma or swelling of the eyeball; coloboma, or open suture of the iris; otosclerosis, or thickened tympanic membrane, causing "hardness of hearing"; some forms of deaf-mutism, due to certain defects of the inner ear; and many other characters too numerous to mention here. On the other hand many abnormal or monstrous conditions are due to abnormal environment and are not inherited.
The question of the inheritance of diseases may be briefly considered here. If a disease is due to some defect in the hereditary constitution, it is inherited; otherwise, according to our definition of heredity, it is not. Of course no disease develops without extrinsic causes but when one individual takes a disease while another under the same conditions does not, the differential cause may be an inherited one, or it may be due to differences in the previous conditions of life. There is no doubt that certain diseases run in families and have the appearance of being inherited, but in this case as in many others it is extremely difficult in the absence of experiments to distinguish between effects due to intrinsic causes and those due to extrinsic ones. Where the specific cause of a disease is some microorganism the individual must have been infected at some time or other, almost invariably after birth. In few instances, is the oosperm itself infected, and even when it is this is not, strictly speaking, a case of inheritance, but rather one of early infection. Pearson has found that there is a marked correlation (represented by the number.55 when complete correlation is 1) between the tuberculous parents and tuberculous children, but there is very little evidence that the child is ever infected before birth. What is inherited in this case is probably slight resistance to the tubercle bacillus. There is evidence that almost all adult persons have been infected at one time or another by this bacillus, but it has not developed far in all of them because some have superior powers of resistance. Such greater or smaller resistance, stronger or weaker build, is inherited, and while diminished resistance is not the direct cause of tuberculosis it is a predisposing cause. The same is probably true of many other diseases, the immediate causes of which are extrinsic, while only the more remote, or predisposing causes, are hereditary.
(c) Physiological peculiarities are inherited as well as morphological ones; indeed function and structure are only two aspects of one and the same thing, namely, organization. For all morphological characters there are functional correlatives, for functional characters morphological expressions, and if the one is inherited so is the other. But there are certain characters in which the physiological aspect is more striking than the morphological one. For example, longevity is a physiological character which is undoubtedly dependent upon many causes, but in the case of species which differ greatly in length of life there can be little ​doubt that we are dealing with an inherited character. The great differences in the length of life of an elephant and a mouse, of a parrot and a pigeon, of a cicada and a squash bug, are as surely the result of inherited causes as are the differences in structure between those animals. Within the same species different races or lines show characteristic differences in length of life; in the case of man the average length of life is much greater in some families than in others, and life insurance companies take account of this fact. Even within the same organism certain organs or cells are short-lived, whereas others are long-lived; some cells and organs live only through the early embryonic period, while others live as long as the general organism.
Obesity is another physiological character which may be inherited; the members of certain families grow fat in spite of themselves, while other families remain thin however well fed they may be. Here also many factors enter into the result, but it seems probable that the differentiating factor is a hereditary one. Baldness affects the male members of certain families when they have reached a given age, while in others neither care, dissipation nor age can rob a man of his bushy top. Hemophilia, or excessive bleeding, after an injury, which is due to a deficiency in the clotting power of the blood, is strongly inherited in the male line in certain families. Fecundity and a tendency to bear twins or triplets, left-handedness, a peculiar lack of resistance to certain diseases, and many other physiological peculiarities are probably inherited.
(d) Psychological characters appear to be inherited in the same way that anatomical and physiological traits are; indeed all that has been said regarding the correlation of morphological and physiological characters applies also to psychological ones. No one doubts that particular instincts, aptitudes and capacities are inherited among both animals and men, nor that different races and species differ hereditarily in psychological characteristics. Certain breeds of dogs such as the mastiff, the bull dog, the terrier, the collie, and many others, are characterized by peculiarities of temperament, affection, intelligence and disposition. No one who has much studied the subject can doubt that different human races and families show characteristic differences in these same respects. It is quite futile to argue that exceptional individuals may be found in one race with the mental characteristics of another race; the same could be said of different races of dogs, or of the sizes of different races of beans or of paramecia. The fact is that racial characteristics are not determined by exceptional and extreme individuals but by the average or mean qualities of the race; and measured in this way there is no doubt that certain types of mind and disposition are characteristic of certain families.
There is no longer any question that some kinds of ​feeble-mindedness, epilepsy and insanity are inherited, and that there is often a hereditary basis for nervous and phlegmatic temperaments, for emotional, judicial and calculating dispositions. Nor can it be denied that strength or weakness of will, a tendency to moral obliquity or rectitude, capacity or incapacity for the highest intellectual pursuits, occur frequently in certain families and appear to be inherited. In spite of certain noteworthy exceptions, which may perhaps be due to remarkable variations, statistics collected by Galton show that genius is hereditary; while the work of certain recent investigators, particularly Goddard, Davenport and Weeks, proves that feeble-mindedness and epilepsy are also inherited; and the careful work of Mott and of Rosanoff leaves no room for doubt that certain types of insanity are hereditary. It frequently happens that families in which hereditary insanity occurs also have other members afflicted with epilepsy, hysteria, alcoholism, etc., which would indicate that the thing inherited is an unstable condition of the nervous system which may take various forms under slightly different conditions. Woods has collected data concerning "Heredity in Royalty" which seem to show that very high or low grades of intellect and virtues may be traced through the royal families of Europe for several generations.
The general trend of all recent work on heredity is unmistakable, whether it concerns man or lower animals. The entire organism, consisting of structures and functions, body and mind, develops out of the germ, and the organization of the germ determines all the possibilities of development of the mind no less than of the body, though the actual realization of any possibility is dependent also upon environmental stimuli.
II. Hereditary Differences
There are many limitations or exceptions to the general rule that children resemble their parents. Sometimes these differences are due to new combinations of ancestral characters, sometimes they are actually new characters not present so far as known in any of the ancestors, though even such new characters must arise from new combinations of the elements of old characters, as we shall see later.
1. New Combinations of Characters.—In all cases of sexually produced organisms new combinations of ancestral characters are evident. Usually a child inherits some traits from one parent and other traits from the other parent, so that it is a kind of mosaic of ancestral traits. Such inheritance, bit by bit, of this character from one progenitor and that from another was described by Galton as "particulate" (Fig. 47). On the other hand Galton supposed that in some instances a child might inherit all or nearly all of his traits from one parent; such inheritance he called "alternative" (Fig. 47).
In other cases the traits of the parents appear to blend in the offspring, ​as for example, in the skin color of mulattoes; such cases were called by Galton "blending" inheritance (Fig. 47). Sometimes characters appear in offspring which were "latent" Fig. 47. Diagram of Galton's "Law of Ancestral Inheritance." The whole heritage is represented by the entire rectangle; that derived from each progenitor by the smaller squares; the number of the latter doubles in each ascending generation while its area is halved. After Thompson.) in the parents but were "patent" in one or more of the grandparents; such skipping of a generation, during which a character remains "latent," has long been known as "atavism." At other times characters which were present in distant ancestors, but which have since dropped out of sight, or have remained "latent," reappear in descendants; such cases are known as "reversions."
In still other cases certain characters appear only in the male sex, others only in the female, this being called "sex-limited" inheritance; while in some instances characters are transmitted from fathers through daughters to grandsons or from mothers to sons, all such cases being known as "sex-linked" inheritance.
2. New Characters or Mutations.—But in addition to these permutations in the distribution and combination of ancestral characters new and unexpected characters sometimes develop in the offspring, which were not present, so far as shown, in any of the ascendants, but which, after they have once appeared, are passed on by heredity to descendants. Such inherited variations are usually of two kinds, continuous or slight, and discontinuous or sudden variations. The latter are especially noticeable when variations occur in the normal number of parts, as in four-leaved clover, or six-fingered men, and such numerical variations have been called by Bateson "meristic." However sudden variations may include any marked departure from the normal type, in color, shape, size, chemical compositions, etc. Such sudden variations have long been known to breeders as "sports," and both Darwin and Galton pointed out the fact that such sports have sometimes given rise to new races or breeds, though Darwin was not inclined to assign much importance to them in the general process of evolution. Galton, on the other hand, maintained that variations, or what would now be called "continuous variations," can not be of much significance in the process of evolution, but that the case is quite different with "sports."
More recently the entire biological world has been greatly influenced by the "mutation theory" of de Vries, which has placed a new emphasis upon the importance of sudden variations in the process of evolution. At first de Vries was inclined to emphasize the degree of difference ​between discontinuous and continuous variations, but in later works this distinction is given a minor place as compared with the distinction between inherited and non-inherited variations. Inherited variations, whether large or small, are called by de Vries "mutations," whereas non-inherited variations are known as "fluctuations," the former are caused by changes in germinal constitution, the latter by alterations in environmental conditions; the former represents changes in heredity, the latter changes in development.
3. Mutations and Fluctuations.—This clear cut distinction between mutations and fluctuations marks one of the most important advances ever made in the study of development and evolution. Thousands of fluctuations occur which are purely somatic in character and which do not affect the germ cells, for every single mutation or change in the hereditary constitution; and yet only the latter are of significance in heredity and evolution. This distinction between variations due to environment (fluctuations) and those due to hereditary causes (mutations) was recognized by Weismann and many of his followers, but the actual demonstration on a large scale of the importance of this distinction is due largely to de Vries.
All hereditary variations, whether due to new combinations of old characters or to the appearance of actually new characters, whether small and continuous, or large and discontinuous, have their causes in the organization of the germ cells, just as do inherited resemblances. Heredity is not to be contrasted with variation, nor are hereditary likeness and unlikeness due to conflicting principles; both are the results of germinal organization and both are phenomena of heredity.
4. Every Individual Unique.—As a result of the permutations of ancestral characters, the appearance of mutations, and the fluctuations of organisms due to environmental changes, it happens that in all cases offspring differ more or less from their parents and from one another. No two children of the same family are ever exactly alike (except in the case of identical twins which have come from the same oosperm). Every living being appears on careful examination to be the first and last of its identical kind. This is one of the most remarkable peculiarities of living things. The elements of chemistry are constant, and even the compounds fall into definite categories which have constant characteristics. But the individuals of biology are apparently never twice the same. This may be due to the immense complexity of living units as contrasted with chemical ones, indeed lack of constancy is evident in itself of lack of analysis into real elements or of lack of uniform conditions, but whatever its cause the extraordinary fact remains that every living being appears to be unique.
There seems to be no reason to doubt that all the extraordinary
​differences which organisms show, as well as all of their resemblances, are due to differences or resemblances in the hereditary and environmental factors which have been operative in their development. But in view of this universal variability of organisms it is not surprising that inheritance has seemed capricious and uncertain—"a sort of maze in which science loses itself."
B. STATISTICAL STUDY OF INHERITANCE
Francis Galton was one of the first who attempted to reduce the mass of conflicting observations on heredity and variation to some system and to establish certain principles as a result of statistical study. He was the real founder of the scientific study of inheritance, he created characters singly and he introduced quantitative measures. Galton's researches, which were published in several volumes, consisted chiefly in a study of certain families with regard to several selected traits, viz., genius or marked intellectual capacity, artistic faculty, stature, eye color and disease. As a result of his very extensive studies two main principles appeared to be established:
1. The Law of Ancestral Inheritance which he stated as follows:
Fig. 48. Scheme to Illustrate Galton's "Law of Filial Regression" as Shown in the Stature of Parents and Children. The mean height of all parents is shown by the dotted line between 68 and 69 inches. The circles through which the diagonal line runs represent the heights of graded groups of parents and the arrow heads indicate the average heights of their children. The offspring of undersized parents are taller and of oversized parents are shorter than their respective parents. (From Walter.)
​The average contribution of each ancestor was thus stated definitely, the contribution diminishing with the remoteness of the ancestor. This Law of Ancestral Inheritance is represented graphically in the accompanying diagram (Fig. 48). Pearson has somewhat modified the figures given by Galton, holding that in horses and dogs the parents contribute 1/2%, the grandparents 1/3%, the great grandparents 2/9%, etc.
Theoretically the number of ancestors doubles in each ascending generation; there are two parents, four grandparents, eight great-grand-parents, etc. If this continued to be true indefinitely the number of ancestors in any ascending generation would be (2)$^n$, in which n represents the number of generations. There have been about 57 generations since the beginning of the Christian Era, and if this rule held true indefinitely each of us would have had at the time of the birth of Christ a number of ancestors represented by (2)$^{57}$ or about 120 quadrillions—a number far greater than the entire human population of the globe at that time. As a matter of fact, owing to the intermarriage of cousins of various degrees the actual number of ancestors is much smaller than the theoretical number. For example, Plate says that the present Emperor of Germany had only 162 ancestors in the 10th ascending generation, instead of 512, the theoretical number. Nevertheless this calculation will serve to show how widespread our ancestral lines are, and how nearly related are all people of the same race.
Davenport concludes that no people of English descent are more distantly related than 30th cousins, while most people are much more closely related than that. If we allow three generations to a century, and calculate that the degree of cousinship is determined by the number of generations less two, since first cousins appear only in the third generation, the first being that of the parents and the second that of the sons and daughters, we find that 30th cousins at the present time would have had a common ancestor about one thousand years ago or approximately at the time of William the Conqueror. As a matter of fact most persons of the same race are much more closely related than this, and certainly we need not go back to Adam nor even to Shem, Ham and Japhet, to find our common ancestor.
2. The second principle which Galton deduced from his statistical studies is known as the Law of Filial Regression, or what might be called the tendency to mediocrity. He found that on the average extreme peculiarities of parents were less extreme in children. "The stature of adult offspring must, on the whole, be more mediocre than the stature of their parents, that is to say more near to the mean or mid of the general population"; and again, "the more bountifully a parent is gifted by nature, the more rare will be his good fortune if he begets a son who is as richly endowed as himself." This so-called law of filial regression is represented graphically in Fig. 49 in which the actual ​stature of individual parents is shown by the oblique line, the stature of children by the dotted curve, and the mean stature of the race in the horizontal dotted line.
One of the chief aims and results of statistical study is to eliminate individual peculiarities and to obtain general and average results.
Fig. 49. Diagram to Illustrate Three Kinds of Inheritance Described by Galton. (After Walter.)
Such work may be of great importance in the study of heredity, especially where questions of the occurrence or distribution of particular phenomena are concerned; but the causes of heredity are individual and physiological, and averages are of less value in finding the causes of such phenomena than is the intensive study of individual cases.
By observation alone it is usually impossible to distinguish between inherited and environmental resemblances and differences, and yet this distinction is essential to any study of inheritance. If all sorts of likenesses and unlikenesses are lumped together, whether inherited or not, our study of inheritance can only end in confusion. The value of statistics depends upon a proper classification of the things measured and enumerated, and if things which are not commensurable are grouped together the results may be quite misleading and worthless. Unfortunately Galton and Pearson, as well as some of their followers, have not carefully distinguished between hereditary and environmental characters. ​Furthermore much of their material was drawn from a general population in which were many different families and lines not closely related genetically. Consequently their statistical studies are of little value in discovering the physiological principles or laws of heredity. Jennings (1910) well says,
In the case of man we have few certain tests to determine whether the differential cause of any character is hereditary or environmental, but in the case of animals and plants, where experiments may be performed on a large scale it is possible to make such tests by (1) experiments in which environment is kept as uniform as possible while the hereditary factors differ, and (2) experiments in which, in a series of cases, the hereditary factors are fairly constant while the environment differs. In this way the differential cause or causes of any character may be located in heredity, in environment, or in both.
The observational and statistical study of inheritance helped to outline the problem but did little to solve it. Certain phenomena of hereditary resemblances between ascendants and descendants were made intelligible, but there were many peculiar and apparently irregular or lawless phenomena which could not be predicted before they occurred nor explained afterwards. For example when Darwin crossed different breeds of domestic pigeons, no one of which had a trace of blue in its plumage, he sometimes obtained offspring with more or less of the blue color and markings of the wild rock pigeon from which domestic pigeons are presumably descended. He described many cases of dogs, cattle and swine, as well as many cultivated plants, in which offspring resembled distant ancestors and differed from nearer ones; such cases had long been known and were spoken of as "reversion." He observed many cases in which certain characters of one parent prevailed over corresponding characters of the other parent in the offspring, this being known as "prepotency"; but there was no satisfactory explanation of these curious phenomena. They did not come under either of Galton's laws, and their occurrence was apparently so irregular that every such case seemed to be a law unto itself.
C. EXPERIMENTAL STUDY OF INHERITANCE
I. Mendelism
The year 1900 marks the beginning of a new era in the study of inheritance. In the spring of that year three botanists, de Vries, Correns and Tschermak, discovered independently an important principle of ​heredity and at the same time brought to light a long neglected and forgotten work on "Experiments in Plant Hybridization" by Gregor Mendel, in which this same principle was set forth in detail. This principle is now generally known as "Mendel's Law." Mendel, who was a monk and later abbot of the Königskloster, an Augustinian monastery in Brünn, Austria, published the results of his experiments on hybridization in the Proceedings of the Natural History Society of Brünn in 1866. The paper attracted but little attention at the time although it contained some of the most important discoveries regarding inheritance which had ever been made, and it remained buried and practically unknown for thirty-five years. Plant hybridization had been studied extensively before Mendel began his work, but he carried on his observations of the hybrids and of their progeny for a longer time and with greater analytical ability than any previous investigator had done. The methods and results of his work are so well known through the writings of Bateson, Punnett and many others, that it is unnecessary to dwell at length upon them here. In brief Mendel's method consisted in crossing two forms having distinct characters, and then in counting the number of offspring in successive generations showing one or the other of these characters.
During the eight years preceding the publication of his paper in 1866 Mendel hybridized some twenty-two varieties of garden peas. This group of plants was chosen because the different varieties could be cross-fertilized or self-fertilized and were easily protected from the influence of foreign pollen; because the hybrids and their offspring remained fertile through successive generations; and because the different varieties are distinguished by constant differentiating characters. Mendel devoted his attention to seven of these characters, which he followed through several generations of hybrids, viz.,
(1) Differences in the form of the ripe seeds, whether round or wrinkled. (2) Differences in the color of the food material within the seeds, whether pale yellow, orange or green. (3) Differences in the color of the seed coats (and in some cases of the flowers also), whether white, gray, gray brown, leather brown, with or without violet spots. (4) Differences in the form of the ripe pods, whether simply inflated or constricted between the seeds. (5) Differences in the color of the unripe pods whether light to dark green, or vividly yellow. (6) Differences in the positions of the flowers, whether axial, that is distributed along the stem, or terminal, that is bunched at the top of the stem. (7) Differences in the length of the stem, whether tall or short.
​1. Results of Crossing Individuals with one Contrasting Character.—Having determined that these characters were constant for certain varieties or species Mendel then proceeded to cross one variety with another, by carefully removing the unripe stamens, with their pollen, from the flowers of one variety and dusting upon the stigma of such flowers the pollen of a different variety. In this way he crossed varieties
Fig. 50. Diagram Showing the Results of Crossing Yellow-seeded (Lighter Colored) and Green-seeded (Darker Colored) Peas. From Morgan after Thompson.)
of peas which differed from each other in some one of the characters mentioned above, and then studied the offspring of several successive generations with respect to this character.
In every case he discovered that the plants that developed from such a cross showed only one of the two contrasting characters of the parent plants, i. e., all were round-seeded, yellow seeded, tall, etc., although one of the parents had wrinkled seeds, green seeds, or short stem, etc.
​These hybrids when self-fertilized gave rise to a second filial generation of individuals some of which showed the dominant character and others the recessive, the relative numbers of the two being approximately three to one. Thus the hybrids produced by crossing yellow-seeded and green-seeded peas yielded when self-fertilized 6,022 yellow seeds and 2,001 green seeds, or almost exactly three yellow to one green (Fig. 50). The hybrids produced by crossing round and wrinkled seeded varieties yielded in the second filial generation 5,474 round and 1,850 wrinkled seeds, or approximately three round to one wrinkled (Fig. 53). The hybrids from a tall and short stemmed cross produced in the second filial generation 787 long stemmed and 277 short stemmed, or again approximately three tall to one short. And in every other case Mendel found that the ratio of dominants to recessives in the second filial generation was approximately three to one. These recessives derived from hybrid parents are pure and are known as "extracted" recessives; when self-fertilized they produce recessives indefinitely. One third of the dominants are also pure homozygotes, or "extracted" dominants, and when self-fertilized produce pure dominants indefinitely. On the other hand, two thirds of the dominants are heterozygotes and when self-fertilized give rise in the next generation to pure dominants, mixed dominant-recessives and pure recessives in the proportion of 1 : 2 : 1. These general results are summarized in the accompanying diagram (Fig. 51)
Fig. 51. Diagram Showing Results of Mendelian Splitting Where the Parents are Pure Dominants and Pure Recessives (Homozygotes). All pure dominants are represented by black circles, all pure recessives by white ones, while mixed dominant-recessives (heterozygotes) are represented by circles half white and half black. Successive generations are marked F$_1$ F$_{2,}$ F$_{3,}$ etc.
in which dominant characters are indicated by the letter D, recessive characters by R, and mixed dominant-recessives, with the recessive character unexpressed, by D (R); while DD or RR indicate extracted dominants or recessives, that is, pure dominants or recessives which have ​separated out from mixed dominant-recessives, D (R). The parental generation is indicated by the letter P, and the successive filial generations by F$_1$, F$_2$, F$_3$, etc.
In the case of the peas studied by Mendel the hybrids of the F$_1$ generation show only the dominant character, the contrasted recessive character being present but not expressed. However in certain cases it has been found that the hybrids differ from either parent and in successive generations split up into both parental types and into the hybrid type; thus Correns found that when a white flowered variety of Mirabilis, the four o'clock, was crossed with a red flowered variety all of the hybrids in the F$_1$ generation had pink flowers and from those in the F$_2$ generation there came white-flowered, pink-flowered and red-flowered forms in the proportion of 1 white:2 pink:1 red, as shown in Fig. 56. This is a better illustration of Mendel's principle of splitting than is offered by the peas, since in this case the mixed dominant-recessives D(R) are always distinguishable from the pure dominants DD.
In the F$_2$ generation and in all subsequent ones the pure dominants, and the pure recessives always breed true when self-fertilized, whereas the mixed dominant-recessives continue to split up in each successive generation into pure dominants, mixed dominant-recessives and pure recessives in the proportion 1:2:1. The result of this is that the relative number of dominants and recessives increases in successive generations, whereas the relative number of mixed dominant-recessives decreases, and in a few generations a hybrid race will revert in large part to its parental types if continued hybridization is prevented. On the other hand there is no tendency for the relative number of dominants to increase and of recessives to decrease in successive generations; an equal number of pure dominants and pure recessives is produced in each generation.
With remarkable insight Mendel recognized that the real explanation of the splitting of pure recessives and pure dominants from hybrid parents must be found in the composition of the male and female sex cells. Since such extracted dominants and recessives breed true, just as pure species do, it must be that their germ cells are pure. In the cross between pure races of white and red-flowered Mirabilis the germ cells which unite in fertilization must be pure with respect to white and red, though the individual which develops from this cross is a pink hybrid. But the fact that one quarter of the progeny of this hybrid are pure white, and another quarter pure red, and that these thereafter breed true, proves that the hybrid produces germ cells which are pure with respect to red and white. Furthermore the fact that one half the progeny of this hybrid are themselves hybrid may be explained by assuming that they were produced by the union of germ cells carrying pure white and pure red, as in the first cross in the parental generation.
​Mendel therefore concluded that individual germ cells are always pure with respect to any pair of contrasting characters, even though those germ cells have come from hybrids in which the contrasting characters are mixed. A single germ cell can carry the factors, or causes, for red or white flowers, for green seeds or yellow seeds, for tall stem or short stem, etc., but not for both pairs of these contrasting characters. The hybrids formed by crossing white and red four o'clocks carry the factors for both white and red, but the individual germ cells formed by such a hybrid carry the factors for white or red, but not for both; these factors segregate or separate in the formation of the germ cells so that one half of all the germ cells formed carry the factor for white and the other half that for red.
This is the most important part of Mendel's Law—the central doctrine from which all other of his conclusions radiate. It explains not only the segregation of dominant and recessive characters from a hybrid in which both are present, but also the relative numbers of pure dominants, pure recessives, and mixed dominant-recessives in each generation. For if all germ cells are pure with respect to any particular character the hybrid offspring of any two parents with contrasting characters will produce in equal numbers two classes of germ cells, one bearing the
Fig. 52. Diagram of Mendelian Inheritance, in Which the Individual is Represented by the Large Circle, the Germ Cells by the Small Ones, Dominants Being Shaded and Recessives White. a, Pure dominant x pure recessive = all dominant-recessives, b, Dominant-recessive x dominant-recessive = 1 pure dominant: 2 dominant-recessives: 1 pure recessive, c. Dominant-recessive x pure dominant = 2 pure dominant: 2 dominant-recessive, d, Dominant-recessive x pure recessive = 2 dominant-recessive: 2 pure recessive.
dominant and the other the recessive factor, and the chance combination of these two classes of male and female gametes will yield on the average one union of dominant with dominant, two unions of dominant with recessive and one union of recessive with recessive, thus producing the typical Mendelian ratio, 1DD : 2D(R) : 1RR, as shown in the accompanying diagram (Fig. 52, A, B).
Other Mendelian Ratios
When a pure dominant is crossed with a mixed dominant-recessive all the offspring show the dominant character, though one half are pure dominant and the other half dominant-recessives. Thus if a pure round-seeded variety of pea is crossed with a hybrid between a round and a wrinkled seeded one, all the progeny are round-seeded, though one half of them carry the factor for wrinkled seed; this may be graphically represented as follows:
In subsequent generations the progeny of the pure round (RR) breed true and produce only round-seeded peas, whereas the progeny of the hybrid round and wrinkled (RW) split up into pure round, hybrid round and wrinkled, and pure wrinkled in the regular Mendelian ratio of 1RR : 2R(W) : 1WW (Fig. 52, C).
When a pure recessive is crossed with a mixed dominant-recessive another typical ratio results. Thus if a wrinkled-seeded variety of pea is crossed with a hybrid between a round and wrinkled seeded one, round-seeded and wrinkled-seeded peas are produced in the proportion, of 1 : 1. This is due to the fact that the hybrid produces two kinds of germ cells, the pure-bred but one, and the possible combinations of these are as follows:
This ratio of 1 : 1 is approximately the ratio of the two sexes in many animals and plants, and there is good reason to believe that sex is a Mendelian character of this sort, in which one plant is heterozygous for sex and the other homozygous.
2. Results of Crossings where there is more than one Contrasting Character.—It rarely happens that two individuals differ in a single character only; more frequently they differ in many characters and this leads to a great increase in the number of types of offspring in the F$_2$ generation. But however many pairs of contrasting characters the parents may show each pair may be considered by itself as if it were the only contrasting pair, and when this is done all the offspring may be classified according to the regular Mendelian formula given above.
​But when two or more contrasting characters of the parents are followed to the F$_2$ generation many permutations of these characters occur thus giving rise to a larger number of types of individuals than when a single pair of characters is concerned. When there is only one pair of contrasting characters there are usually but two types of offspring apparent in the F$_2$ generation, viz., dominants and recessives in the ratio of 3 : 1 (Fig. 53); where there are two pairs of contrasting
Fig. 53. Monohybrid Diagram Showing Results of Crossing Round (R) Seeded with Wrinkled (W) Seeded Peas. Large circles represent zygotes, small ones, or single letters, gametes. In F$_1$ all individuals are round but contain round and wrinkled gametes. In F$_2$ the ♂ gametes are placed above the square, the ♀ ones to the left, and the possible combinations of ♂ and ♀ gametes are shown in the small squares, the relative numbers of different types being 1 RR : 2 R(W) : 1 WW. Fig. 54. Dihybrid Diagram Showing Results of Crossing Peas Having Yellow-round (YR) Seeds with Others Having Green-wrinkled (GR) Ones. Four types of germ cells are formed by such a hybrid, viz., YR, YW, GR, GW, and the 16 possible combinations (genotypes) of these ♂ and ♀ gametes are shown in the small squares. Since recessive characters do not appear when mated with dominant ones these 16 genotypes produce 4 phenotypes in the following relative numbers: 9YR : 3YW : 3GR : 1GW. There is 1 pure dominant (upper left corner), 1 pure recessive (lower right corner), 4 homozygotes in diagonal line between these corners and 12 heterozygotes.
characters in the parents there are four types of offspring in the F$_2$ generation in the ratio of (3 : 1)$^2$ = 9 : 3 : 3 : 1; when there are three pairs of contrasting characters in the parents there are eight types of offspring apparent in the F$_2$ generation in the proportions of (3 : 1)$^3$ = 27 : 9 : 9 : 9 : 3 : 3 : 3 : 1, etc. Thus when Mendel crossed a variety of peas bearing round and yellow seeds with another variety having wrinkled and green seeds all the offspring of the F$_1$ generation bore round and yellow seeds, round being dominant to wrinkled, and yellow to green. ​But the plants raised from these seeds, when self-fertilized, yielded seeds of four types, round and yellow (RY), wrinkled and yellow (WY), round and green (RG), and wrinkled and green (WG) in the proportion of 9:3:3:1 as shown in figure 54.
In this case also this ratio may be explained by assuming that the germ cells (ovules and pollen) are pure with respect to each of the contrasting characters, round-wrinkled, yellow-green, and therefore any combination of these may occur in a germ cell except the combinations RW and YG. Accordingly there are four possible kinds of germ cells as follows: ${\begin{matrix}Y&&&G\\\mid &\diagdown &\diagup &\mid \\\mid &\diagup &\diagdown &\mid \\R&&&W\end{matrix}}$ i.e., YR, YW, GR, GW. Each one of these four kinds of pollen may fertilize each one of the same four kinds of ovules giving rise to sixteen combinations, no two of which are alike, as shown in Fig. 54. The dominant characters are in this case round and yellow, and only when one of these is absent can its contrasting character, wrinkled or green, develop. Accordingly the sixteen possible combinations yield seeds of four different appearances and in the following proportions: 9RY:3RG:3WY:1WG. Only one individual in each of these four classes is pure (homozygous) and continues to breed true in successive generations; in Fig. 54 these are found in the diagonal from the upper left to the lower right corner. All other individuals are heterozygous and show Mendelian splitting in the next generation.
When parents differ in three contrasting characters a much larger number of combinations are possible in the F$_2$ generation. Thus if a pea with round (R) and yellow (Y) seeds, and with tall (T) stem is crossed with one having wrinkled (W) and green (G) seeds, and dwarf (D) stem all the progeny of the F$_1$ generation have round and yellow seeds and tall stem, R, Y and T being dominant to W, G and D. But in the F$_2$ generation there are sixty-four possible combinations (genotypes) of these six characters; but since a recessive character does not develop if its contrasting dominant character is present there are only eight types which come to expression (phenotypes) and in the following numbers: 27RYT:9RYD:9RGT:3RGD:9WYT:3WYD:3WGT:1WGD. Of these sixty-four genotypes only eight are homozygous and breed true (those lying in the diagonal between upper left and lower right corners in Fig. 55), while only one is pure dominant and one pure recessive (in the upper left and lower right corners of Fig. 55).
When the parents differ in one character only, the offspring formed by their crossing are called monohybrids, when there are two contrasting characters in the parents the offspring are dihybrids, when three, trihybrids, and when the parents differ in more than three characters the offspring are called polyhybrids. There are certainly few cases in which parents actually differ in only a single character, but since each contrasting character may be dealt with separately, as if it were the only ​one, and since the number of types of offspring increases greatly when more than one or two characters are considered at the same time, it is customary to deal simultaneously with only one or two characters of hybrids, even though the parents may have differed in many characters.
Fig. 55. Trihybrid Diagram Showing Results of Crossing Peas Having round-yellow seeds and tall stem (RYT) with peas having wrinkled green-seeds and Dwarf Stem (WGD). Eight types of germ cells result from such a hybrid, as shown in the ♂ gametes above the square and the ♀ ones to the left of it, and the possible combinations (genotypes) of these ♂ and ♀ gametes are shown in the 64 small squares of which only 1 is pure dominant (upper left corner), 1 pure recessive (lower right corner) and 8 homozygotes (in diagonal line between these corners). The relative numbers of the different phenotypes are 27 RYT : 9 RYD : 9 RGT : 9 WYT : 3 RGD : 3 WYD : 3 WGT : 1 WGD.
3. Inheritance Formulæ.—Mendel represented the hereditary constitution of the plants used in his experiments by letters employed as symbols, dominant characters being represented by capitals and recessives by small letters. The seven contrasting characters of his peas could be represented as follows:
* Seeds, round (A), or wrinkled (a); yellow (B); or green (b); with gray seed coats (C), or white seed coats (c).
* Pods, green (D), or yellow (d); inflated (E), or constricted (e).
* Habit, tall (F), or dwarf (f).
* Flowers, axial (G), or terminal (g).
​It is possible for one plant to have all of these dominant characters or all of the recessive ones, or part of one kind and part of the other. The inheritance formula of a plant having all seven of the dominant characters is ABCDEFG; of one having all of the recessive characters abcdefg. When two such plants are crossed the inheritance formula of the hybrid is AaBbCcDdEeFfGg, and since the dominant and recessive characters (or rather determiners of characters) represented by these seven pairs of letters separate in the formation of the gametes, and since each separate determiner may be associated with either member of the other six pairs, the number of possible combinations of these determiners in the gametes is (2)$^7$ or 128. That is, in this case 128 kinds of germ cells may be produced, each having a different inheritance formula; and since each of these 128 kinds of male germ cells may unite with any one of the 128 kinds of female germ cells, the number of possible combinations is (128)$^2$ or 16,384, which represents the number of combinations of these characters which are possible in the F$_2$ generation. Every one of these more than sixteen thousand genotypes may be represented by various combinations of the letters ABCDEFG and abcdefg.
When many characters are concerned it is difficult to remember what each letter stands for, and consequently it is customary in such cases to designate characters by the initial letter in the name of that character. By this form of short hand one can show in a graphic way the possible segregations and combinations of hereditary units in gametes and zygotes through successive generations, and as a result many modern works on Mendelian inheritance look like pages of algebraic formulæ.
Some progress has been made, as was pointed out in the last lecture, in identifying certain structures of the germ cells with certain hereditary units, but quite irrespective of what these units may be and where they may be located it is possible, by means of the Mendelian theory of segregation of units in the germ cells and of chance combinations of these in fertilization to predict the number of genotypes and phenotypes which may be expected as the result of a given cross.
4. Presence and Absence Hypothesis.—Mendel spoke of the presence of contrasting or differentiating characters in the plants which he crossed, such as round or wrinkled seeds, tall or short stems, etc. Many other writers regard these contrasting characters as positive and negative expression of a single character, and consequently they speak of the presence or absence of single characters; thus round seeds are due to the presence of a factor for roundness (A) while wrinkled seeds are characterized by the absence of that factor (a). Round seeds are wrinkled seeds plus the factor for roundness. Most of the phenomena of Mendelian inheritance are more simply stated in terms of presence or absence of single characters than in terms of contrasting characters.
​When both gametes carry similar positive factors the zygote has a "double dose" of such factors and is said to be duplex; when only one of the gametes carries such a factor the zygote has a "single dose" and is simplex, when neither gamete carries a positive factor or factors, the zygote receives only negative factors and is said to be nulliplex. Thus the union of gametes AB (♀) and AB (♂) yields zygote AABB, which is duplex in constitution; gametes Ab (♀) and aB (♂) yield zygote AaBb, which is simplex; gametes ab (♀) and ab (♂) yield zygote aabb, which is nulliplex.
In some instances a character comes to full expression only when it is derived from both parents, that is, when it is duplex; if derived from one parent only, that is, if simplex, it is diluted in appearance and is intermediate between the two parents. For example, when white
Fig. 56. Results of Crossing White-flowered and Red-flowered Races of Mirabilis Jalapa (Four O'clocks), giving a pink hybrid in F$_1$, which when inbred gives in F$_2$ 1 white, 2 pink, 1 red. (From Morgan, after Correns.)
flowered four o'clocks which are nulliplex are crossed with red-flowered ones which are duplex the progeny, which are simplex, bear pink flowers; in this case red flowers are produced only when the factor for red is derived from both parents, pink flowers when it is derived from one parent, white flowers when it is derived from neither parent (Fig. 56).
5. Summary of Mendelian Principles.—Since the rediscovery in 1900 of Mendel's work many investigators have carried out similar experiments on many species of animals and plants and have greatly extended our knowledge of the principles of inheritance discovered by Mendel, but in the main Mendel's conclusions have been confirmed ​again and again, so that there is no doubt that they constitute an important rule of inheritance among all organisms.
In brief the "Mendelian Law of Alternative Inheritance" or of hereditary "splitting" consists of the following principles:
(a) The principle of unit characters.—The total heritage of an organism may be analyzed into a number of characters which are inherited as a whole and are not further divisible; these are the so-called "unit characters" (de Vries).
(b) The principle of dominance.—When contrasting unit characters are present in the parents they do not as a rule blend in the offspring, but one is dominant and usually appears fully developed, while the other is recessive and temporarily drops out of sight.
(c) The principle of segregation.—Every individual germ cell is "pure" with respect to any given unit character, even though it come from an "impure" or hybrid parent. In the germ cells of hybrids there is a separation of the determiners of contrasting characters so that different kinds of germ cells are produced, each of which is pure with regard to any given unit character. This is the principle of segregation of unit characters, or of the "purity" of the germ cells. Every sexually produced individual is a double being—double in every cell—one half having been derived from the male and the other half from the female sex cell. This double being, or zygote, again becomes single in the formation of the germ cells only once more to become double when the germ cells unite in fertilization.
(To be concluded)
* ↑ Third of the Norman W. Harris Lectures for 1914 at Northwestern University on "Heredity and Environment in the Development of Men," to be published by the Princeton University Press.
* ↑ "Hereditary Genius," Prefatory Chapter.
* ↑ Bateson introduced the term homozygote for pure bred individuals resulting from the union of gametes which are hereditarily similar, and heterozygote for hybrids resulting from the union of hereditarily dissimilar gametes. The gametes formed from a homozygote are all of the same hereditary type, those formed from a heterozygote are of two or more different types.