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 inTable 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” inTable 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 andvice 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 onpage 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 verylow 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, Tables6 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 toTable 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 precedinggenerations 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 andvice versa.
(4) The offspring as a group average lower in grade than their parents—that is, their meanregresseson that of the selected parents, but because of the higher mode about which variation occurs in each generation certain of the offspring are of higher grade than their parents. Thus an elevation of the grade of the parents in the next generation is made possible.
(5) With the selection of more extreme parents, the absolute regression of the offspring has not increased, but on the contrary has slightly diminished—that is, the advance made by the parents is retained by their offspring.
InTable 15have been brought together for comparison the means of the several horizontal rows of Tables 1 to 13. By examining the vertical columns of Table 15 the mean grade of the offspring of parents of a particular grade in any generation may be compared at a glance with that of parents of the same grade in any other generation. By running the eye down the columns, it will be observed that the mean grade of the offspring tends to increase upon repeated selection. Thus parents of grade 3.75 appear first in generation 4, the grade of their offspring being 2.75; the offspring of such parents in subsequent generations grade in order, 3.07, 3.22, 3.35, 3.49, 3.50, 3.69, 3.75, and 3.83 (twelfth generation not complete). The difference between parents and offspring in this series grows less and less and finally disappears altogether. If the grade of 3.75 parents in this series is compared with the grade ofalloffspring in the corresponding generations we have the following:
In generation 4 the 3.75 parents represented the most advanced individuals of the series, a whole grade in advance of the general average of the race. Their offspring showed a correspondingly large regression. The general average of the race steadily advanced in later generations until in generation 11 it equaled that of the 3.75 parents; then the regression vanished. In the following generation, 12 (which is still incomplete, but in which the average of the offspring thus far is 3.94), the 3.75 group of parents, which are nowbelowthe average of the race,actually produce offspring of higher grade than themselves, viz, 3.83. It will thus be seen that theregression is uniformly toward the mean of the race and changes its direction when that mean changes its position with reference to a particular grade of parents. This conclusion is supported by other columns of Table 15, but is best illustrated by this particular case because here the selection has extended over a greater number of generations than elsewhere in the series.
If one examines the horizontal rows of Table 15, he finds in general that numbers increase toward the right. Exceptions are commonest toward the ends of the rows where fewest individuals are represented. This increase means that, within any generation, as the grade of the parents rises, that of their offspring rises also. Since in general the selected parents areabovethe general average of the race for the time being, regression is naturally downward in nearly all cases.
From what precedes we may conclude (1) that in this series of rats the somatic character (appearance) of an individual is in general a true indication of its germinal character, since the higher the grade of the parents the higher the grade of the offspring, andvice versa; but that (2) the somatic character of an individual is not aperfectindex of its germinal character, since the offspring of aberrant individuals are less aberrant than themselves,i. e., the offspring regress toward the mean of the race; yet that (3) by selection of plus variations we can displace, in a plus direction, not only the mean of the race, but also the upper and lower limits of its variation, the total amount of variability (standard deviation) being thereby only slightly decreased.