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_.
(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: