Part 3

(4) The offspring as a group average lower in grade than their parents—that is, their mean regresses on 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.

In Table 15 have 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 of all offspring in the corresponding generations we have the following:

TABLE A.

+-----------+-----------------------+------------------------+ |Generation.| Mean of offspring of | Mean of offspring of | | | 3.75 parents. | all parents. | +-----------+-----------------------+------------------------+ | 4 | 2.75 | 2.73 | | 5 | 3.07 | 2.90 | | 6 | 3.22 | 3.11 | | 7 | 3.35 | 3.20 | | 8 | 3.49 | 3.48 | | 9 | 3.50 | 3.54 | | 10 | 3.69 | 3.73 | | 11 | 3.75 | 3.77 | | 12 | 3.83 (35 individuals)| 3.94 (590 individuals)| +-----------+-----------------------+------------------------+

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 now below the average of the race, actually produce offspring of higher grade than themselves, viz, 3.83. It will thus be seen that the regression 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 are above the 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, and vice versa; but that (2) the somatic character of an individual is not a perfect index 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.

MINUS SELECTION SERIES.

This series begins with selected parents ranging in grade from -1.25 to -1.87. Their average, if each pair is weighted in proportion to the number of its offspring, is -1.46. The offspring (Table 16), like the offspring of the original plus selections, regress toward grade 0. They range in grade from +0.25 to -2.00, their mean being -1.00. The total number of offspring recorded in this generation is only 55, this being too small to warrant the calculation of a correlation coefficient.

Generation 2 (Table 17) is somewhat larger, but still too small to make statistical constants based upon it of much consequence. The offspring show substantially the same range of variation as in the previous generation, but with a slightly higher average (-1.07). The coefficient of correlation (-0.03) is negative, but too small to be significant. The record of the next eleven generations will be found summarized in Tables 18 to 28, or in more condensed form in Tables 29 and 30. Generation 13 (Table 28) is still incomplete.

The mean of the parents steadily rises from -1.56 in generation 3 to -2.50 in generation 13. The mean of the offspring rises by like increments from -1.18 in generation 3 to -2.39 in generation 13. There is throughout these generations a positive correlation between parents and offspring. This amounts on the average to 0.137 as compared with 0.193 observed in the plus selection series. The absolute change in amount of pigmentation is no doubt less in the minus selection than in the plus selection series, but if the change were recorded as percentage decrease of pigmentation in one case and percentage increase in the other, the change indicated would probably be as great in one as in the other.

In the minus as in the plus series we observe:

(1) The character of the offspring varies with that of the parents; high-grade parents have high-grade offspring and vice versa.

(2) The variability of the race (as indicated by the standard deviation) undergoes some reduction and the limits of variation, both upper and lower, are displaced in the direction of the selection.

(3) The regression from a new and extreme class of parents is at first large, but decreases as the selection is repeated and finally disappears altogether when the average of the race becomes equal to the particular grade under discussion.

RETURN SELECTION.

The plus and minus selection series already described make it clear that one can, in a race of hooded rats, either increase or decrease the average pigmentation at will, and at the same time secure more advanced stages either of pigmentation or of depigmentation than those previously occurring in the race. The question now arises, are these changes permanent; will these displaced means retain their new position, if the race is left to itself; or will the newly obtained stages vanish as soon as selection is suspended? A presumption that the changes will prove permanent is afforded by the gradual decrease of regression and its final reversal in the case of offspring of a particular grade, upon repeated selection made in the same direction. (See page 12.) But in order to test the matter more directly and thoroughly, the experiment has been repeatedly made of reversing the course of selection, after it had been in progress for several generations, with a view of ascertaining whether the return toward the former condition of the race would be made more speedily and easily than the original departure from it had been.

The first experiment of this sort was a return selection from generation 6 (and 6½) of the minus selection series. The parents of generation 6 (Table 21) averaged -1.86 in grade; the average grade of their offspring was -1.56, a regression of 0.30. The range of the offspring extended from 0 to -2.50. Some low-grade offspring were chosen for a return selection series (Table 31). The mean grade of the selected pairs ranged from -0.37 to -0.87, their mean being -0.60. These parents produced 118 offspring, whose average grade was -1.28, a regression of 0.68 in a direction contrary to that of the regression in the minus selection series. The large amount of the regression might seem to imply that it was even more difficult to return toward the former state of the race (in the neighborhood of 0) than it had been to depart from it, but this can not be insisted on, because the number of individuals under observation is not sufficiently large. To test the reality and permanency of the reversed regression, the selection was repeated five additional times, altogether six successive return selections being made with the idea of undoing what had been effected by six original selections in an opposite direction. The result of the second successive return selection is shown in Table 32. The parents here were of grade -0.50 and they produced 19 offspring of the average grade -0.95, a regression of 0.45 away from 0 as before.

Table 33 shows the result of the third return selection. Individuals entered in Table 32 as offspring appear here as parents. Only those pairs which were of mean grade, -0.25 or -0.37, should really be regarded as a third return selection. They gave offspring with mean grades of -0.63 and -0.86 respectively, which show regression of 0.38 and 0.49 away from 0.

But Table 33 shows also the character of young produced by -1.12 and -1.25 parents in this same third return-selection generation, i. e., by unselected parents of the generation in question. Their young also regress away from 0—that is, in the direction of the original selection. The -1.12 parents produced -1.61 offspring, a regression of 0.49, while the -1.25 parents produced -1.35 offspring, a regression of 0.10. For Table 33 as a whole the regression away from 0 averages 0.31.

A fourth generation in the return-selection series is summarized in Table 34. The parents are of mean grade -0.63; their 50 offspring are of mean grade -1.17, a regression amounting to 0.54 away from 0 and in the direction of the six generations of original selection.

Table 35 contains the results of the fifth generation of the series. The parents are here of mean grade -0.65. The number of offspring is very small (13), but they nevertheless show the reversed regression which characterized the four preceding generations. Their mean was -0.75, a regression of 0.10 away from 0.

A sixth and final generation in this return-selection experiment is summarized in Table 36. It includes 36 offspring of mean grade -0.39, the mean of the parents being -0.26, a regression of 0.13 away from 0. It will be seen, therefore, that the effect of the six original selections had not been entirely overcome by an equal number of return selections. The reason for this is obvious. Much smaller numbers are concerned in the return selections than in the original minus selections. The return selections are accordingly less efficient. Nevertheless, after the sixth return selection we find that 1 in 6 of the offspring have plus grades and their average is lower (that is, less minus) than the offspring in the minus series after a single generation of selection. (Cf. Tables 16 and 36.)

The amount and persistency of the reversed regression in this series show clearly that return selection is not easier or more rapid than the original modification of the race by selection, but that selection in either a plus or minus direction has cumulative and permanent effects.

Further support for this conclusion is furnished by return selections (one each) made from the seventh generation, from the eighth generation, and from the eleventh generation of the minus selection series. (See Tables 37, 38, and 39.) Generation 7 (Table 22) was produced by parents of average grade -2.01. Their offspring were of average grade -1.73, a regression (toward 0) amounting to 0.28. Certain pairs of these offspring of grade -0.75 and -0.87 (mean -0.78) constitute the return selection from generation 7 (Table 37). They had 33 offspring of average grade -1.15, a regression away from 0 amounting to 0.37.

Generation 8 of the minus-selection series (Table 23) was produced by parents of mean grade -2.05. Their offspring were of mean grade -1.80, a regression (toward 0) of 0.25. Certain pairs of these offspring of grades -0.50, -0.62, and -1.00 (mean -0.72), when chosen as parents, produced 41 young of mean grade -1.51, a regression away from 0 amounting to 0.79. (See Table 38.)

Generation 11 of the minus series (Table 26) was produced by parents of mean grade -2.30. The offspring were of mean grade -2.15, a regression of 0.15 toward 0. A pair of the offspring of mean grade -1.62 (Table 39) produced 16 young of mean grade -1.95, a regression of 0.32 away from 0. This result shows that the selected race had now passed the point represented by the grade of the parents (-1.62) and the offspring regressed toward a racial mean as advanced as the most extreme individuals obtained previous to selection.