# A Critique of the Theory of Evolution/III

CHAPTER III
THE FACTORIAL THEORY OF HEREDITY AND THE COMPOSITION OF THE GERM PLASM
* 1. The Cellular Basis of Organic Evolution and Heredity
* 2. The Mechanism of Mendelian Heredity Discovered in the Behavior of the Chromosomes
* 3. The Four Great Linkage Groups of Drosophila Ampelophila
** a. Group I.
** b. Group II.
** c. Group III.
** d. Group IV.
* 4. Localization of Factors in the Chromosomes
** a. The Evidence from Sex Linked Inheritance
** b. The Evidence from Interference
** c. The Evidence from Non-Disjunction
* 5. How Many Genetic Factors are there in the Germ-plasm of a Single Individual?
* 6. Conclusions
The discovery that Mendel made with edible peas concerning heredity has been found to apply everywhere throughout the plant and animal kingdoms—to flowering plants, to insects, snails, crustacea, fishes, amphibians, birds, and mammals (including man).
There must be something that these widely separated groups of plants and animals have in common—some simple mechanism perhaps—to give such definite and orderly series of results. There is, in fact, a mechanism, possessed alike by animals and plants, that fulfills every requirement of Mendel's principles.
The Cellular Basis of Organic Evolution and Heredity
In order to appreciate the full force of the evidence, let me first pass rapidly in review a ​ few familiar, historical facts, that preceded the discovery of the mechanism in question.
Throughout the greater part of the last century, while students of evolution and of heredity were engaged in what I may call the more general, or, shall I say, the grosser aspects of the subject, there existed another group of students who were engaged in working out the minute structure of the material basis of the living organism. They found that organs such as the brain, the heart, the liver, the lungs, the kidneys, etc., are not themselves the units of structure, but that all these organs can be reduced to a simpler unit that repeats itself a ​ thousand-fold in every organ. We call this unit a cell (fig. 45).
The egg is a cell, and the spermatozoon is a cell. The act of fertilization is the union of two cells (fig. 47, upper figure). Simple as the process of fertilization appears to us today, its discovery swept aside a vast amount of mystical speculation concerning the rôle of the male and of the female in the act of procreation.
Within the cell a new microcosm was revealed. Every cell was found to contain a spherical body called the nucleus (fig. 46a). Within the nucleus is a network of fibres, a sap fills the interstices of the network. The network resolves itself into a definite number of threads at each division of the cell (fig. 46 b-e). These threads we call chromosomes. Each species of animals and plants possesses a characteristic number of these threads which have a definite size and sometimes a specific shape and even characteristic granules at different levels. Beyond this point our strongest microscopes fail to penetrate. Observation has reached, for the time being, its limit.
The story is taken up at this point by a new set of students who have worked in an entirely different field. Certain observations and experiments that we have not time to consider ​ now, led a number of biologists to conclude that the chromosomes are the bearers of the hereditary units. If so, there should be many such units carried by each chromosome, for the number of chromosomes is limited while the number of independently inherited characters is large. In Drosophila it has been demonstrated not only that there are exactly as many groups of characters that are inherited together as there are pairs of chromosomes, but even that it is possible to locate one of these groups in a particular chromosome and to state the relative position there of the factors for the characters. If the validity of this evidence is accepted, the study of the cell leads us finally in a mechanical, but not in a chemical sense, to the ultimate units about which the whole process of the transmission of the hereditary factors centers.
But before plunging into this somewhat technical matter (that is difficult only because it is unfamiliar), certain facts which are familiar for the most part should be recalled, because on these turns the whole of the subsequent story.
The thousands of cells that make up the cell-state that we call an animal or plant come from the fertilized egg. An hour or two after fertilization the egg divides into two cells (fig. 47). Then each half divides again. Each ​ quarter next divides. The process continues until a large number of cells is formed and out of these organs mould themselves.
At every division of the cell the chromosomes also divide. Half of these have come from the mother, half from the father. Every cell contains, therefore, the sum total of all the chromosomes, and if these are the bearers of the hereditary qualities, every cell in the body, ​ whatever its function, has a common inheritance.
At an early stage in the development of the animal certain cells are set apart to form the organs of reproduction. In some animals these cells can be identified early in the cleavage (fig. 48).
The reproductive cells are at first like all the other cells in the body in that they contain a full complement of chromosomes, half paternal and half maternal in origin (fig. 49). They divide as do the other cells of the body for a long time (fig. 49, upper row). At each division each chromosome splits lengthwise and its halves migrate to opposite poles of the spindle (fig. 49 c).
But there comes a time when a new process appears in the germ cells (fig 49 e-h). It is essentially the same in the egg and in the sperm cells. The discovery of this process we owe to the laborious researches of many workers in many countries. The list of their names is long, and I shall not even attempt to repeat it. The chromosomes come together in pairs (fig. 49 a). Each maternal chromosome mates with a paternal chromosome of the same kind. ​
Then follow two rapid divisions (fig. 49 f, g and 50 and 51). At one of the divisions the double chromosomes separate so that each resulting cell comes to contain some maternal and ​ some paternal chromosomes, i.e. one or the other member of each pair. At the other division each chromosome simply splits as in ordinary cell division.
The upshot of the process is that the ripe eggs (fig. 51) and the ripe spermatozoa (fig. ​ 50) come to contain only half the total number of chromosomes.
When the eggs are fertilized the whole number of chromosomes is restored again.
The Mechanism of Mendelian Heredity Discovered in the Behavior of the Chromosomes
If the factors in heredity are carried in the chromosomes and if the chromosomes are definite structures, we should anticipate that there should be as many groups of characters as there are kinds of chromosomes. In only one ​ case has a sufficient number of characters been studied to show whether there is any correspondence between the number of hereditary groups of characters and the number of chromosomes. In the fruit fly, Drosophila ampelophila, we have found about 125 characters that are inherited in a perfectly definite way. On the opposite page is a list of some of them.
It will be observed in this list that the characters are arranged in four groups, Groups I, II, III and IV. Three of these groups are equally large or nearly so; Group IV contains only two characters. The characters are put into these groups because in heredity the members of each group tend to be inherited together, i.e., if two or more enter the cross together they tend to remain together through subsequent generations. On the other hand, any member of one group is inherited entirely independently of any member of the other groups; in the same way as Mendel's yellow-green pair of characters is inherited independently of the round-wrinkled pair.
| Group I Abnormal Bar Bifid Bow Cherry Chrome Cleft Club Depressed Dot Eosin Facet Forked Furrowed Fused Green Jaunty Lemon Lethals, 13 Miniature Notch Reduplicated Ruby Rudimentary Sable Shifted Short Skee Spoon Spot Tan Truncate intensifier Vermilion White Yellow | Group II Antlered Apterous Arc Balloon Black Blistered Comma Confluent Cream II Curved Dachs Extra vein Fringed Jaunty Limited Little crossover Morula Olive Plexus Purple Speck Strap Streak Trefoil Truncate Vestigial | Group III Band Beaded Cream III Deformed Dwarf Ebony Giant Kidney Low crossing over Maroon Peach Pink Rough Safranin Sepia Sooty Spineless Spread Trident Truncate intensifier Whitehead White ocelli | Group IV Bent Eyeless |
​ If the factors for these characters are carried by the chromosomes, then we should expect that those factors that are carried by the same chromosome would be inherited together, provided the chromosomes are definite structures in the cell.
In the chromosome group of Drosophila, (fig. 52) there are four pairs of chromosomes, three of nearly the same size and one much smaller. Not only is there agreement between the number of hereditary groups and the number of the chromosomes, but even the size relations are the same, for there are three great groups of characters and three pairs of large chromosomes, and one small group of characters and one pair of small chromosomes. ​
The Four Great Linkage Groups of Drosophila Ampelophila
The following description of the characters of the wild fly may be useful in connection with the account of the modifications of these characters that appear in the mutants.
The head and thorax of the wild fly are grayish-yellow, the abdomen is banded with alternate stripes of yellow and black. In the male, (fig. 4 to right), there are three narrow bands and a black tip. In the female there are five black bands (fig. 4 to left). The wings are gray with a surface texture of such a kind that at certain angles they are iridescent. The eyes are a deep, solid, brick-red. The minute hairs that cover the body have a very definite arrangement that is most obvious on the head and thorax. There is a definite number of larger hairs called bristles or chaetae which have a characteristic position and are used for diagnostic purposes in classifying the species. On the foreleg of the male there is a comb-like organ formed by a row of bristles; it is absent in the female. The comb is a secondary sexual character, and it is, so far as known, functionless. ​
Some of the characters of the mutant types are shown in figures 53, 54, 55, 56. The drawing of a single fly is often used here to illustrate more than one character. This is done to economize space, but of course there would be no difficulty in actually bringing together in the same individual any two or more characters belonging to the same group (or to different groups). Without colored figures it is not possible to show many of the most striking differences of these mutant races; at most dark and light coloring can be indicated by the shading of the body, wings, or eyes.
Group I
In the six flies drawn in figure 53 there are shown five different wing characters. The first of these types (a) is called cut, because the ends of the wings look as though they had been cut to a point. The antennae are displaced downward and appressed and their bristle-like aristae are crumpled.
The second figure (b) represents a fly with a notch in the ends of the wings. This character is dominant, but the same factor that ​ produces the notch in the wings is also a recessive lethal factor; because of this latter effect of the character no males of this race exist, and the females of the race are never pure but hybrid. Every female with notch wings bred to a wild male, will produce in equal numbers notch winged daughters and daughters with normal wings. There will be half as many sons as daughters. The explanation of ​ this peculiar result is quite simple. Every notch winged female has one X chromosome that carries the factor for notch and one X chromosome that is "normal". Daughters receiving the former chromosomes are notched because the factor for notch is dominant, but they are not killed since the lethal effect of the notch factor is recessive to the normal allelomorph carried by the other chromosome that the daughters get from their father. This normal factor is recessive for notch but dominant for life. This same figure (b) is used here to show three other sex linked characters. The spines on the thorax are twisted or kinky, which is due to a factor called "forked". The effect is best seen on the thorax, but all spines on the body are similarly modified; even the minute hairs are also affected. Ruby eye color might be here represented—if the eyes in the figure were colored. The lighter color of the body and antennae is intended to indicate that the character tan is also present. The light color of the antennae is the most certain way of identifying tan. The tan flies are interesting because they have lost the positive heliotropism ​ that is so marked a feature in the behavior of D. ampelophila. As this peculiarity of the tan flies is inherited like all the other sex linked characters, it follows that when a tan female is bred to a wild male all the sons inherit the recessive tan color and indifference to light, while the daughters show the dominant sex linked character of their father, i.e., they are "gray", and go to the light. Hence when such a brood is disturbed the females fly to the light, but the males remain behind.
One of the first mutants that appeared in D. ampelophila was called rudimentary on account of the condition of the wings (c). The same mutation has appeared independently several times. In the drawing (c) the dark body color is intended to indicate "sable" and the lighter color of the eyes is intended to indicate eosin. This eye color, which is an allelomorph of white, is also interesting because in the female the color is deeper than in the male. In other cases of sex linked factors the character is the same in the two sexes.
In the fourth figure (d) the third and fourth longitudinal veins of the wing are fused into ​ one vein from the base of the wing to the level of the first cross-vein and in addition converge and meet near their outer ends. The shape of the eye is represented in the figure as different from the normal, due to another factor called "bar". This is a dominant character, the hybrid condition being also narrow, but not so narrow as the pure type. Vermilion eye color might also be here represented—due to a factor that has appeared independently on several occasions.
In the fifth figure (e) the wings are shorter and more pointed than in the wild fly. This character is called miniature. The light color of the drawing may be taken to represent yellow body color, and the light color of the eye white eye color.
In the last figure (f) the wings are represented as pads, essentially in the same condition that they are in when the fly emerges from the pupa case. Not all the flies of this stock have the wings in this condition; some have fully expanded wings that appear normal in all respects. Nevertheless, about the same percentage of offspring show the pads irrespective of ​ whether the parents had pads or expanded wings.
The flies of this stock show, however, another character, which is a product of the same factor, and which is constant, i.e., repeated in all individuals. The two bristles on the sides of the thorax are constantly absent in this race. The lighter color of the eye in the figure may be taken to indicate buff—a faint yellowish color. The factor for this eye color is another allelomorph of white.
There are many other interesting characters that belong to the first group, such as abnormal abdomen, short legs, duplication of the legs, etc. In fact, any part of the body may be affected by a sex-linked factor.
Group II
In the first figure (a) of figure 54 that contains members of Group II the wings are almost entirely absent or "vestigial". This condition arose at a single step and breeds true, although it appears to be influenced to some extent by temperature, also by modifiers that sometimes appear in the stock. Purple ​ eye color belongs in Group II; it resembles the color of the eye of the wild fly but is darker and more translucent.
In the second figure (b) the wing is again long and narrow and sometimes bent back on itself, as shown here. In several respects the wing resembles strap (d) but seems to be due ​ to another factor, called antler, insufficiently studied as yet.
In the third figure (c) the wings turn up at the end. This is brought about by the presence of the factor called jaunty.
In the fourth figure the wings are long and narrow and several of the veins are unrepresented. This character, "strap", is very variable and has not yet been thoroughly studied. On the thorax there is a deep black mark called trefoil. Even in the wild fly there is a three pronged mark on the thorax present in many individuals. Trefoil is a further development and modification of this mark and is due to a special factor.
In the fifth figure (e) the wings are arched. The factor is called arc. The dark color of the body, and especially of the wings, indicates the factor for black.
The sixth figure (f) shows the wings "curved" downwards. In addition there is present a minute black speck at the base of each wing, due to another factor called speck.
In the seventh figure (g) the wing is truncate. Its end is obliquely squared instead of ​ rounded; it may be longer than the body, or shorter when other modifying factors are present. The mutation that produces this type of wing is of not infrequent occurrence. It has been shown by Muller and Altenburg that there are at least two factors that modify this character—the chief factor is present in the second chromosome; alone it produces the truncate wing in only a certain percentage of cases, but when the modifiers are also present about ninety percent of the individuals may show the truncate condition of the wing. But the presence of these factors makes the stock very infertile, so that it is difficult to maintain.
In the eighth figure (h) the legs are shortened owing to the absence of a segment of the tarsus. The stock is called dachs—a nickname given to it because the short legs suggested the dachshund.
Group III
In figure 55, (a), a mutant type called bithorax is shown. The old metathorax is replaced by another mesothorax thrust in between the normal mesothorax and the abdomen. It ​ carries a pair of wings that do not completely unfold. On this new mesothorax the characteristic arrangement of the bristles is shown. Thus at a single step a typical region of the body has doubled. The character is recessive.
The size of the adult fly of D. ampelophila varies greatly according to the amount of nourishment obtained by the larva. After the fly emerges its size remains nearly constant, as in many insects. Two races have, ​ however, been separated by Bridges that are different in size as a result of a genetic factor. The first of these, called dwarf, is represented by figure 55, (b).
The race is minute, although of course its size is variable, depending on food and other conditions. The same figure shows the presence of another factor, "sooty", that makes the fly very dark. Maroon eye color might be here represented, due to still another factor.
In the third figure (c) the other mutation in size is shown. It is called "giant". The flies are twice the size of wild flies. An eye color, called peach, might here be represented. It is an allelomorph of pink.
In the fourth figure (d) the mutant called dichaete is shown. It is characterized by the absence of two of the bristles on the thorax. Other bristles may also be absent, but not so constantly as the two just mentioned. Another effect of the same factor is the spread-out condition of the wings. The very dark eye color in this figure may be taken to indicate the presence of another factor, "sepia", which causes the eyes to assume a brown color that ​ becomes black with age. Most of the other mutations in eye color that have occurred tend to give a lighter color: this one, which is also recessive, makes the eye darker.
In the fifth figure (e) the color of the darkest fly is due to a factor called ebony, which is an allelomorph of sooty.
In the sixth figure (f) the wings are beaded, i.e., the margin is defective at intervals, giving a beaded-like outline to the wings. This condition is very variable and much affected by other factors that influence the shape of the wings. The lighter eye color of the drawing may be taken to represent pink.
In the seventh figure (g) the wings are curled up over the back. This is a recessive character.
Group IV
Only two mutants have been obtained that do not belong to any of the preceding groups; these are put together in Group IV. It has been shown that they are linked to each other and the linkage is so close that it has thus far been impossible to obtain the dominant recessive. ​ One of these mutants, called "eyeless" (fig. 56, a, a$^1$), is variable—the eyes are often entirely absent or represented by one or more groups of ommatidia. The outline of the original eye, so to speak, is strongly marked out and its area might be called a rudimentary organ, if such a statement has any meaning here.
The other figure (b) represents "bent", so called from the shape of the wings. This ​ mutant is likewise very variable, often indistinguishable from the wild type, yet when well developed strikingly different from any other mutant.
This brief account of a few of the mutant races that can be most easily represented by uncolored figures will serve to show how all parts of the body may change, some of the changes being so slight that they would be overlooked except by an expert, others so great that in the character affected the flies depart far from the original species.
It is important to note that mutations in the first chromosome are not limited to any part of the body nor do they affect more frequently a particular part. The same statement holds equally for all of the other chromosomes. In fact, since each factor may affect visibly several parts of the body at the same time there are no grounds for expecting any special relation between a given chromosome and special regions of the body. It can not too insistently be urged that when we say a character is the product of a particular factor we mean no more than that it is the most conspicuous effect of the factor. ​
If, then, as these and other results to be described point to the chromosomes as the bearers of the Mendelian factors, and if, as will be shown presently, these factors have a definite location in the chromosomes it is clear that the location of the factors in the chromosomes bears no spatial relation to the location of the parts of the body to each other.
Localization of Factors in the Chromosomes
The Evidence from Sex Linked Inheritance
When we follow the history of pairs of chromosomes we find that their distribution in successive generations is paralleled by the inheritance of Mendelian characters. This is best shown in the sex chromosomes (fig. 57). In the female there are two of these chromosomes that we call the X chromosomes; in the male there are also two but one differs from those of the female in its shape, and in the fact that it carries none of the normal allelomorphs of the mutant factors. It is called the Y chromosome.
The course followed by the sex chromosomes and that by the characters in the case of sex ​ linked inheritance are shown in the next diagram of Drosophila illustrating a cross between a white eyed male and a red eyed female.
​ The first of these represents a cross between a white eyed male and a red eyed female (fig. 58, top row). The X chromosome in the male is represented by an open bar, the Y chromosome is bent. In the female the two X chromosomes are black. Each egg of such a female will contain one "black" X after the polar bodies have been thrown off. In the male there will be two classes of sperm—the female-producing, carrying the (open) X, and the male-producing, carrying the Y chromosome. Any egg fertilized by an X bearing sperm will produce a female that will have red eyes because the X (black) chromosome it gets from the mother carries the dominant factor for red. Any egg fertilized by a Y-bearing sperm will produce a male that will also have red eyes because he gets his (black) X chromosome from his mother.
When, then, these two F$_1$ flies (second row) are inbred the following combinations are expected. Each egg will contain a black X (red eye producing) or a white X (white eye producing) after the polar bodies have been extruded. The male will produce two kinds of sperms, of which the female producing will contain a black X (red eye producing). Since any egg may by chance be fertilized by any sperm there will result the four classes of individuals shown on the bottom row of the diagram. All the females will have red eyes, because irrespective of the two kinds of eggs involved all the female-producing sperm carry a black X. Half of the males have red eyes because half of the eggs have had each a red-producing X chromosome. The other half of the males have white eyes, because the other half of the eggs had each a white-producing X chromosome. Other evidence has shown that the Y chromosome of the male is indifferent, so far as these Mendelian factors are concerned.
The reciprocal experiment is illustrated in figure 59. A white eyed female is mated to a red eyed male (top row). All the mature eggs of such a female contain one white-producing X chromosome represented by the open bar in the diagram. The red eyed male contains female-producing X-bearing sperm that carry the factor for red eye color, and male-producing Y chromosomes. Any egg fertilized by an X-bearing sperm will become a red eyed female because the X chromosome that comes from the father carries the dominant factor for red eye color. Any egg fertilized by a Y-bearing sperm will become a male with white eyes because the only X chromosome that the male contains comes from his mother and is white producing. ​
When these two F$_1$ flies are inbred (middle row) the following combinations are expected. Half the eggs will contain each a white producing X chromosome and half red producing. The female-producing sperms will each contain a white X and the male-producing sperms will each contain an indifferent Y chromosome. Chance meetings of egg and sperm will give the four F$_2$ classes (bottom row). These consist of white eyed and red eyed females and white eyed and red eyed males. The ratio here is 1:1 and not three to one (3:1) as in other Mendelian cases. But Mendel's law of segregation is not transgressed, as the preceding analysis has shown; for, the chromosomes have followed strictly the course laid down on Mendel's principle for the distribution of factors. The peculiar result in this case is due to the fact that the F$_1$ male gets his single factor for eye color from his mother only and it is linked to or contained in a body (the X chromosome) that is involved in producing the females, while the mate of this body—the Y chromosome—is indifferent with regard to these factors, yet active as a mate to X in synapsis. ​
In man there are several characters that show exactly this same kind of inheritance. Color blindness, or at least certain kinds of color blindness, appear to follow the same scheme. A color blind father transmits through his daughters his peculiarity to half of his grandsons, but to none of his grand-daughters (fig. 38A). The result is the same as in the case of the white eyed male of Drosophila. Color blind women are rather unusual, which is expected from the method of inheritance of this character, but in the few known cases where such color blind women have married normal husbands the sons have inherited the peculiarity from the mother (fig. 38B). Here again the result is the same as for the similar combination in Drosophila. ​
In man the sex formula appears to be XX for the female and XO for the male (fig. 60), and since the relation is essentially the same as that in Drosophila the chromosome explanation is the same. According to von Winiwarter there are 48 chromosomes in the female and 47 in the male (fig. 61). After the extrusion of the polar bodies there are 24 chromosomes in the egg. In the male at one of the two maturation ​ divisions the X chromosome passes to one pole undivided (fig. 61, C). In consequence there are two classes of sperms in man; female producing containing 24 chromosomes, and male producing containing 23 chromosomes. If the factor for color blindness is carried by the X chromosome its inheritance in man works out on the same chromosome scheme and in the same way as does white eye color (or any other sex linked character) in the fly, for the O sperm in man is equivalent to the Y sperm in the fly.
In these cases we have been dealing with a single pair of characters. Let us now take a case where two pairs of sex linked characters enter the cross at the same time, and preferably a case where the two recessives enter the cross from the same parent.
If a female with white eyes and yellow wings is crossed to a wild male with red eyes and gray wings (fig. 62), the sons are yellow and have white eyes and the daughters are gray and have red eyes. If two F$_1$ flies are mated they will produce the following classes. ​
| Yellow White | Gray Red | Yellow Red | Gray White |
| $\underbrace {\qquad \qquad \quad }$ 99.% | $\underbrace {\qquad \qquad \quad }$ 99.% | $\underbrace {\qquad \qquad \quad }$ 1.% | $\underbrace {\qquad \qquad \quad }$ 1.% |
Not only have the two grandparental combinations reappeared, but in addition two new combinations, viz., grey white and yellow red. The two original combinations far exceed in numbers the new or exchange combinations. If we follow the history of the X chromosomes we discover that the larger classes of grandchildren appear in accord with the way in which the X chromosomes are transmitted from one generation to the next.
The smaller classes of grandchildren, the exchange combinations or cross-overs, as we call them, can be explained by the assumption that at some stage in their history an interchange of parts has taken place between the chromosomes. This is indicated in the diagrams.
The most important fact brought out by the experiment is that the factors that went in together tend to stick together. It makes no difference in what combination the members of ​ the two pairs of characters enter, they tend to remain in that combination.
If one admits that the sex chromosomes carry these factors for the sex-linked characters—and the evidence is certainly very strong in favor of this view—it follows necessarily from these facts that at some time in their history there has been an interchange between the two sex chromosomes in the female.
There are several stages in the conjugation of the chromosomes at which such an interchange between the members of a pair might occur. There is further a small amount of direct evidence, unfortunately very meagre at present, showing that an interchange does actually occur.
At the ripening period of the germ cell the members of each pair of chromosomes come together (fig. 49, e). In several forms they have been described as meeting at one end and then progressively coming to lie side by side as shown in fig. 63, e, f, g, h, i. At the end of the process they appear to have completely united along their length (fig. 63, j, k, l). It is always a maternal and a paternal ​ chromosome that meet in this way and always two of the same kind. It has been observed that as the members of a pair come together they occasionally twist around each other (fig. 63, g, l, and 64, and 65). In consequence a part of one chromosome comes to be now on one side and now on the other side of its mate.
When the chromosomes separate at the next division of the germ cell the part on one side passes to one pole, the part on the other to the opposite pole, (figs. 64 and 65). Whenever the chromosomes do not untwist at this time there must result an interchange of pieces where they were crossed over each other.
Janssens has found at the time of separation ​ evidence in favor of the view that some such interchange probably takes place.
We find this same process of interchange of characters taking place in each of the other three groups of Drosophila. An example will show this for the Group II.
If a black vestigial male is crossed to a gray long-winged female (fig. 66) the offspring are gray long. If an F$_1$ female is back-crossed to a black vestigial male the following kinds of flies are produced:
| Black vestigial | Gray long | Black long | Gray vestigial |
| $\underbrace {\qquad \qquad \quad }$ 83% | $\underbrace {\qquad \qquad \quad }$ 83% | $\underbrace {\qquad \qquad \quad }$ 17% | $\underbrace {\qquad \qquad \quad }$ 17% |
The combinations that entered are more common in the F$_2$ generations than the cross-over classes, showing that there is linkage of the factors that entered together.
Another curious fact is brought out if instead of back-crossing the F$_1$ female we back-cross the F$_1$ male to a black vestigial female. Their offspring are now of only two kinds, black vestigial and gray long. This means that in the male there is no crossing-over or interchange of pieces. This relation holds not only for the Group II but for all the other groups as well.
Why interchange takes place in the female of Drosophila and not in the male we do not know at present. We might surmise that when in the male the members of a pair come together they do not twist around each other, hence no crossing-over results.
Crossing-over took place between white and yellow only once in a hundred times. Other characters show different values, but the same value under the same conditions is obtained from the same pair of characters. ​
If we assume that the nearer together the factors lie in the chromosome the less likely is a twist to occur between them, and conversely the farther apart they lie the more likely is a twist to occur between them, we can understand how the linkage is different for different pairs of factors.
On this basis we have made out chromosomal maps for each chromosome (fig. 67). The diagram indicates those loci that have been most accurately placed.
The Evidence from Interference
There is a considerable body of information that we have obtained that corroborates the location of the factors in the chromosome. This evidence is too technical to take up in any detail, but there is one result that is so important that I must attempt to explain it. If, as I assume, crossing over is brought about by twisting of the chromosomes, and if owing to the material of the chromosomes there is a most frequent distance of internode, then, when crossing over between nodes takes place at same level at a-b in figure 68, the region on ​ each side of that point, a to A and b to B, should be protected, so to speak, from further crossing over. This in fact we have found to be the case. No other explanation so far proposed will account for this extraordinary relation.
What advantage, may be asked, is there in obtaining numerical data of this kind? It is this:—whenever a new character appears we need only determine in which of the four groups it lies and its distance from two members within that group. With this information we can predict with a high degree of probability what results it will give with any other member of any group. Thus we can do on paper what would require many months of labor by making the actual experiment. In a word we can predict what will happen in a situation where prediction is impossible without this numerical information. ​
The Evidence from Non-Disjunction
In the course of the work on Drosophila exceptions appeared in one strain where certain individuals did not conform to the scheme of sex linked inheritance. For a moment the hypothesis seemed to fail, but a careful examination led to the suspicion that in this strain something had happened to the sex chromosomes. It was seen that if in some way the X chromosomes failed to disjoin in certain eggs, the exceptions could be explained. The analysis led to the suggestion that if the Y chromosome had got into the female line the results would be accounted for, since its presence there would be expected to cause this peculiar non-disjunction of the X chromosomes.
That this was the explanation was shown when the material was examined. The females that gave these results were found by Bridges to have two X's and a Y chromosome.
The normal chromosome group of the female is shown in figure 52 and the chromosome group of one of the exceptional females is shown in figure 69. In a female of this kind ​ there are three sex chromosomes X X Y which are homologous in the sense that in normal individuals the two present are mates and separate at the reduction division. If in the X X Y individual X and X conjugate and separate at reduction and the unmated Y is free to move to either pole of the spindle, two kinds of mature eggs will result, viz., X and XY. If, on the other hand, X and Y conjugate and separate at reduction and the remaining X is free to go to either pole, four kinds of eggs will result—XY—X—XX—Y. As a total result four kinds of eggs are expected: viz. many XY and X eggs and a few XX and Y eggs.
These four kinds of eggs may be fertilized either by female-producing sperms or ​ male-producing sperms, as indicated in the diagram (fig. 70).
If such an XXY female carried white bearing Xs (open X in the figures), and the male ​ carried a red bearing X (black X in the figures) it will be seen that there should result an exceptional class of sons that are red, and an exceptional class of daughters that are white. Tests of these exceptions show that they behave subsequently in heredity as their composition requires. Other tests may also be made of the other classes of offspring. Bridges has shown that they fulfill all the requirements predicted. Thus a result that seemed in contradiction with the chromosome hypothesis has turned out to give a brilliant confirmation of that theory both genetically and cytologically.
How Many Genetic Factors are there in the Germ-plasm of a Single Individual
In passing I invite your attention to a speculation based on our maps of the chromosomes—a speculation which I must insist does not pretend to be more than a guess but has at least the interest of being the first guess that we have ever been in position to make as to how many factors go towards the makeup of the germ plasm. ​
We have found practically no factors less than .04 of a unit apart. If our map includes the entire length of the chromosomes and if we assume factors are uniformly distributed along the chromosome at distances equal to the shortest distance yet observed, viz. .04, then we can calculate roughly how many hereditary factors there are in Drosophila. The calculation gives about 7500 factors. The reader should be cautioned against accepting the above assumptions as strictly true, for crossing-over values are known to differ according to different environmental conditions (as shown by Bridges for age), and to differ even in different parts of the chromosome as a result of the presence of specific genetic factors (as shown by Sturtevant). Since all the chromosomes except the X chromosomes are double we must double our estimate to give the total number of factors, but the half number is the number of the different kinds of factors of Drosophila. ​
Conclusions
I have passed in review a long series of researches as to the nature of the hereditary material. We have in consequence of this work arrived within sight of a result that seemed a few years ago far beyond our reach. The mechanism of heredity has, I think, been discovered—discovered not by a flash of intuition but as the result of patient and careful study of the evidence itself.
With the discovery of this mechanism I venture the opinion that the problem of heredity has been solved. We know how the factors carried by the parents are sorted out to the germ cells. The explanation does not pretend to state how factors arise or how they influence the development of the embryo. But these have never been an integral part of the doctrine of heredity. The problems which they present must be worked out in their own field. So, I repeat, the mechanism of the chromosomes offers a satisfactory solution of the traditional problem of heredity.