Part 2

The fundamental importance of Mendel’s law of heredity is generally recognized among biologists. It is a working hypothesis whose utility is fully substantiated by abundant results daily increasing in amount. But biologists are not in agreement as to how much this law includes. All perhaps would agree that it implies the existence in the germ-cell of specific determiners essential for the production of particular characteristics in the offspring. Further, no one probably will object to the statement that it implies a dual or duplex condition of the zygote as regards determiners and a simple or simplex condition of the gamete. Thirdly, the fact will be admitted by all that most mendelizing characters are wholly independent of each other in heredity, for which reason we are forced to suppose that their determiners are distinct within the germ-cell.

But beyond these few generalizations great diversity of opinion exists. As regards the very nature and function of the determiners, some consider them unvarying, and explain the observed variation of mendelizing characters in organisms as due to a modifying action of other determiners. At one time even a modifying action of other determiners was denied, and the theory was advanced that the gametes extracted from a mendelian cross are pure as regards the single characters which may have been concerned in that cross. Investigations carried out by Castle have done something to dispel this idea. In particular it was shown (Castle, 1905, 1906; Castle and Forbes, 1906) that in guinea-pigs, polydactylism, long-hair, and rough coat are mendelizing characters which are affected in the degree of their development by crosses—that is, when these characters are “extracted” from crosses the characters are not exactly the same as before; hence the gametes are not “pure.”

The experimental result is not denied, but in order to save the substance of the theory its advocates now suppose that the determiners have not changed, but in consequence of the cross certain modifiers have become associated with them which change their appearance in the organism. The real unchanging thing is now called the “genotype,” its appearance the “phenotype.”

In this genotype theory we are dealing only with a new and more refined aspect of the “theory of pure gametes.” It is not a necessary part of mendelism, not even an original part; but it is very important for us to know whether it is true or not. For if it is true, selection unattended by hybridization is largely a waste of time, as De Vries and Johannsen have maintained, and Jennings and Pearl have reiterated.

The investigation which we are about to describe was started six years ago to test the validity of the theory of pure gametes which was then current. Pure “genes” had not yet been invented. The investigation has been in continuous progress ever since, and while we expect to continue it further, it seems to us desirable that the results already obtained be presented for criticism.

Some conception of the work entailed in the investigation may be gathered from the statement that we have during its progress reared and studied the color pattern of over 25,000 rats. A long and arduous investigation of this kind has been made possible by a series of grants from the Carnegie Institution of Washington made to the senior author, for which he here makes grateful acknowledgment. Thanks are also due to Dean W. C. Sabine, of Harvard University, for encouraging and supporting the work in a variety of ways.

MATERIAL AND METHODS.

In June 1906 Dr. Hansford MacCurdy completed, under the direction of the senior author, a study of the inheritance of color in rats. His studies had shown that the piebald pattern of “hooded” rats behaves as a mendelian recessive character in relation to the uniform or nearly uniform coloration of wild rats, but that the hooded pattern, when extracted from a cross with wild stock, shows a different variability, the pigmentation of the extracted recessives being increased in extent. This result was interpreted as showing the unsoundness of the current doctrine of “purity of the gametes” in mendelian crosses.

Upon the conclusion of Dr. MacCurdy’s experiments, the pedigreed stock which he had used was not entirely discarded. A certain portion of it was utilized for new experiments designed to show whether the “hooded” coat-pattern can be modified by selection unattended by cross-breeding.

Two series of selections were started in October 1907, in one of which animals were chosen as parents which had pigmentation as extensive as possible. This we may call the plus series. In the other series animals were chosen as parents which had pigmentation as restricted as possible. This we may call the minus series.

During the academic year 1906-7, the experiments were in immediate charge of Mr. W. G. Vinal; during 1907-8 the plus series was in charge of Mr. H. S. Rand, while the minus series was in charge of Mr. F. C. Bradford. Throughout this time the experiments were closely supervised by the senior author, who assisted in the “grading” of every litter of young. In October 1908 the junior author began his association in the experiments, which has continued up to the present time. Throughout these five years he has looked after the details of the experiments almost continuously, but both authors have in most cases taken part together in the grading of the young, and in no case has the grading been done except under the immediate supervision of one or the other of the authors. This fact is stated to show that the personal element in the grading has been kept as constant as possible. In the tabulation of results and computation of statistical constants, the authors have worked together. This statement of results is written by the senior author.

During the year 1906-7 the young rats were graded by the method used by MacCurdy and Castle (1907) that is, the back-stripe was measured and a calculation made of the percentage of the dorsal surface posterior to the hood which was pigmented. But on account of the irregular outline of the back-stripe in many individuals the method of measurement was found to be at best a rough one, as well as extremely laborious. Accordingly in the summer of 1907 a set of arbitrary grades was adopted, which is shown at the top of Plate 1. Each young rat was classed in that grade which it most nearly approached in amount of pigmentation. Skins of rats graded from -3¼ to +4¾ are shown in the middle and lower rows of Plate 1. The grading was done when the rats were about three or four weeks old, at which time selected individuals were reserved as the parents for a later generation, the remainder being discarded. This method has been followed ever since its adoption and the data thus obtained are summarized in the tables, which cover the breeding operations of a little more than six years, 1907-1913.

The grouping of the young in a series of generations is only approximately accurate, for practical considerations have often led us to mate together animals which belonged to different generations of offspring. When, for example, an animal of generation 2 was mated with one of generation 4, the question would arise: To what generation do the offspring belong? In deciding this question we simply added one to the mean of the generations to which the respective parents belonged. In the foregoing case this would be (2 + 4)/2 + 1 = 4.

In case one parent belonged to generation 2 and the other to generation 3, a fractional result would be obtained, thus (2 + 3)/2 + 1 = 3½. In making up the summaries of the generations as given in the tables, offspring like the foregoing, of generation 3½, were divided equally between generations 3 and 4, alternate litters of young as recorded in the ledger being assigned to each. Offspring belonging to generations 2¾ and 3¼ were tabulated in generation 3; those belonging to generations 3¾ and 4¼ were tabulated in generation 4, etc. While, therefore, the generations as tabulated overlap, it is clear that they include groups of offspring of selected parents each the result of one additional selection over the preceding group.

The early generations include too few individuals to be of much statistical value, but where the number of offspring rises to 500 or over, the statistical constants acquire undoubted value. The data have been given in the form of correlation tables which will repay careful study. In the tables a single entry has been made for each individual offspring in that row which corresponds with the mean grade of its two parents. Thus, if one parent were of grade 2 and the other of grade 2½, the offspring would be entered in the row 2¼ along with the offspring of parents both of grade 2¼. Offspring of parents whose mean grade fell between the rows given in the tables were divided equally between the adjacent rows, alternate litters being assigned to each. Thus, if the mean grade of the parents were 2⅟₁₆, alternate litters of offspring would be entered in row 2 and in row 2⅛.

PLUS SELECTION SERIES.

This series begins with pairs ranging in average grade from +1.87 to +3. From these parents were obtained 150 young, which range in grade from +1 to +3, as is shown in Table 1. It will be observed that the lower-grade parents have on the average lower-grade offspring than the higher-grade parents. But in no case is the average grade of the offspring as great as that of their parents. Thus 1.87 parents had 1.82 offspring (average grade); 2.00 parents had 1.76 offspring; 2.25 parents had 1.87 offspring; and so on to 3.00 parents, which had 2.35 offspring. There is a falling back in grade or “regression” of the offspring as compared with their parents, which increases in amount as the grade of the parents becomes higher. (See column “Regression” in Table 1.) The parents of this first generation were chosen because of their high grade. They were all probably in grade above the general average of the population from which they were selected. In the case of those which deviate most from the general average the regression is greatest, as we should expect.

This phenomenon of regression, which is a very general one in cases of selection, was first observed by Galton in selecting sweet-peas of varying size from a mixed population. Later Johannsen, who repeated the experiment with beans, found that by pedigree culture he was able to break the mixed population up into pure lines within which, considered singly, no regression occurred. We shall need later to return to this subject and consider whether pure lines free from regression exist or can be produced as regards the hooded pattern of rats.

Returning to the examination of Table 1, since the high-grade parents produce higher-grade offspring than do the low-grade parents, it is evident that we might hope by further selection either to isolate a pure line of high-grade rats which would be free from regression and therefore stable, or else to advance the grade of the offspring still higher, even though regression persists. As a measure of the extent to which high-grade parents have high-grade offspring and vice versa, in each generation, we may employ the well-known correlation coefficient. This for Table 1 is 0.30.

The second generation in the plus series (Table 2) includes the offspring of parents which appear as offspring of the higher grades in Table 1, together with a few individuals which appear in Table 2 both as offspring and as parents of other offspring, by reason of their having been mated with generation 1 individuals and so having produced generation 1½ offspring, as explained on page 8. To obtain larger numbers of offspring, several new pairs were added to the experiment in this generation, which do not appear in Table 1 either as offspring or as parents, but which were derived from the same general stock as the parents of generation 1. Their inclusion here accounts for the very low range of the offspring in Table 2, which extends from -1.00 to +3.75. The parents’ range (means of pairs) extends from 2.00 to 3.12. The grand average of the parents is 2.52, that of the offspring is 1.92. The correlation between grade of parents and grade of offspring is 0.32.

From this point on in the series no new stock was added and each generation of offspring furnished the parents for the following generation, except for the slight overlapping of generations when parents of different generations were mated with each other, as has already been explained.

In generation 3, Table 3, the parents ranged from 2.12 to 3.37 in grade, the offspring from 0.75 to 4.00. The mean of the parents was 2.73, that of the offspring 2.51. The degree of correlation between parents and offspring is expressed by the coefficient 0.33 (a perfect correlation would give 1.00).

In generation 4, Table 4, the selection of parents became considerably more rigid; most of the parental pairs were of grade 3 or higher, their average being 3.09. The average grade of the offspring was 2.73, their range extending from 0.75 to 3.75. The correlation in this generation fell very low, to 0.07, not because of a lessened regression but rather because of a very high regression on the part of the offspring of high-grade parents.

In generation 5, Table 5, the grade of the selected parents ranged from 2.75 to 4.12, its mean being 3.33. The offspring, showing the usual regression, ranged from 0.75 to 4.25, their mean grade being 2.90. The correlation between parents and offspring in this generation was 0.16. The number of individuals comprising this generation of offspring was 610.

It is scarcely necessary to discuss separately the correlation table for each of the next eight generations, Tables 6 to 13. The number of offspring rises to a maximum (1,408) in generation 8, Table 8; then declines to less than 200 in generation 13. But as this generation and the preceding one are still being produced, it is probable that the number recorded will be considerably increased before the generation is complete. The means of parents and offspring and the other statistical constants for the several generations can be most easily compared by reference to Table 14. Leaving out of consideration the exceptional generation, 2, the following will be observed:

(1) The mean of the selected parents has steadily advanced throughout the series, as has also that of their offspring.

(2) The variability (standard deviation) of the parents as a group has decreased somewhat as increase in numbers made a more rigid selection possible; that of the offspring has undergone a similar change.

(3) The correlation between parents and offspring has not materially changed. The average of the correlation coefficients for the entire series is 0.194, for the last three generations it is 0.175, for the three preceding generations it is 0.141, for the three which precede those it is 0.185, while for the first four generations it is 0.253. In every case the correlation is positive—that is, the higher-grade parents have higher-grade offspring and vice versa.