Chapter II: Part 2

It would be possible to suppose, as the senior author has elsewhere suggested (Castle, 1912), that the Mendelian unit character involved in these experiments is subject to quantitative variation and that such quantitative variations have a tendency to persist from generation to generation. This would account for the effectiveness and permanency of selection when brought to bear upon the variations. It might also form a basis for explaining the increased variability which follows crossing, this being regarded as due to contamination in the heterozygote, but there are certain other observed effects of crossing which it seems impossible to account for on this basis. In particular it is observed that while crossing the minus series makes it _less_ minus as the hypothesis of contamination would demand, crossing the plus series makes it _less plus_, the opposite of what a contamination theory would demand. For we can readily understand, on the basis of contamination, how a +6 gamete being combined with a -2 gamete might change the latter in a plus direction; but if the same +6 gamete is associated with a +4 gamete we should expect it, if it has any influence at all, to make this also more plus, but the observed effect is the opposite; the extracted gametes are _less_ plus in character.

This difficulty is met by an alternative explanation, the main feature of which was first suggested by our colleague, Dr. E. M. East, viz, that although we seem to be dealing with a single unit character as evidenced by the monohybrid ratios obtained, nevertheless the modifications which form a basis for selection are due (in part at least) to agencies transmitted independently of the hooded pattern (not forming a part of the same unit character), and which may be present in Irish as well as in wild rats. By crosses with such rats the supposed modifiers may become associated with the hooded pattern in extracted recessive individuals and so increase its extent. Such increase does actually occur in experiment.

The hypothesis of modifiers independent in transmission of the hooded unit will account for the fact that F₂ is more variable than F₁ when crosses are made, on the familiar principle of recombination of independent factors. It will account for the observed effectiveness of selection on the ground that what selection accomplishes in the plus series is the isolation of homozygous conditions of modifiers at first present only in heterozygous form, and that what it accomplishes in the minus series is the isolation of conditions homozygous for _lack_ of modifiers (or for inhibitors) of pigmentation. This same hypothesis will account also for the observed reduction of variability during the progress of selection, for as soon as any particular modifier attains a homozygous condition in the race it will cease to occasion variability, and as more and more factors become homozygous the variability should accordingly diminish and finally disappear altogether, so far as it is due to internal and heritable causes.

At this point the hypothesis of modifiers encounters serious difficulty, if one holds the prevalent or “genotype” conception as to the nature of Mendelian factors, viz, that they are fixed and unchangeable and not subject to quantitative variation, but only to combination in different ways with other factors. This conception has been presented very clearly by Dr. East (1912). Some objections to this view had previously been stated by Castle (1912) and need not here be repeated.

If we assume that there exists at the outset a definite number of modifiers and that these possess a definite and unchanging power to modify, then it is evident that selection can do nothing but secure homozygous conditions as regards the presence or absence of these modifiers. When such homozygous conditions are secured, selection will cease to modify the race. The experiment has progressed far enough to show that extensive modification through selection is possible without any marked falling off in variability. No indication is observable that selection will become ineffective before an all-black rat is obtained in the plus series and an all-white rat in the minus series. A _nearly_ all-black race of rats has already been secured. We propose to continue the experiments until demonstrative evidence is obtained.

If the fixed-factor idea as regards modifiers of the hooded pattern is rejected, there remain still two possible alternative views regarding them. Either we may consider that the modifiers vary in strength, that is, in power to modify, or we may consider that new modifiers arise from time to time, which selection may either add in homozygous form to the germinal complex or reject altogether from it. If we assume that the modifiers vary in strength, we shall have to grant also the possibility that the character modified, the hooded pattern, may itself vary in strength independently of its modifiers. For evidence see the description of the “mutant” series, page 30. This assumption, I understand, would be unacceptable to those who hold a genotype conception of heredity, though we ourselves can offer no valid objection to it.

If, on the other hand, we admit that new modifiers or inhibitors are from time to time coming into existence spontaneously, and that selection can use these to modify the pattern either in a plus or in a minus direction, then we must admit that selection is an agency of real creative power, able to modify unit characters indefinitely so long as physiological limitations are not reached.

Now it seems to us probable that what we call the unit-character for hooded pattern is itself variable; also that “modifiers” exist—that is, the extent of the hooded pattern is not controlled exclusively by a single localized portion of the germ-cell; otherwise we should be at a loss for an explanation of the peculiar results from crossing plus series hooded rats with those which are still more extensively pigmented; for by such crosses the pigmentation is rendered not _more_ extensive but _less_ so. This result we can explain on the supposition that the selected plus series has accumulated _more_ modifiers of the hooded pattern than the wild race contains, so that a cross tends to reduce the number of modifiers in the extracted hooded individuals. No other explanation at present offers itself for this wholly unexpected but indubitable result. If a different one can be found we are quite ready to discard the hypothetical modifiers as a needless complication, contenting ourselves with the supposition that the unit character for hooded pattern is itself variable, and that for this reason racial change in either plus or minus directions may be secured at will through repeated selection.

We have been led to adopt tentatively an hypothesis that modifying factors exist independent of the single factor for hooded pattern (though both the factor for hooded pattern and its modifiers may, so far as we can see, be quantitatively variable) by another series of observations, which will now be described.

THE “MUTANT” SERIES.

In the tenth generation of the plus selection series there appeared two individuals, a male and a female, of considerably higher grade than any previously recorded in this series. They are not included in Table 10 because we have been and still are in doubt as to their exact nature and think it best to give a separate account of them. If entered in Table 10 one would appear as a 5½ individual born of 3⅞ parents (mean grade), the other as a 5¾ individual born of 3¾ parents (mean grade). The nearest individuals in grade to these two produced by the same group of parents are of grade 4½, but some 4⅛ parents of the same generation produced two offspring of grade 5. (See Table 10.) Because of the marked advance in grade of these individuals beyond the ordinary range of variation in the series we called them “mutants,” without wishing then or now to commit ourselves to any particular theory as to their nature or origin. We have used the term and now use it as one of convenience merely. The two “mutant” individuals had the same father and their mothers were sisters. Their pedigree for two generations is as follows:

Mutants. Parents. Grandparents.
{ ♀ 2956, +3¾ } { ♀ 1939, +3¾
♂ 4763, +5½ { ♀ 2957, +3½ } { ♂ 1817, +3¾
{
♀ 5153, +5¾ { { ♀ 1162, +3½
{ ♂ 2963, +4 { ♂ 1810, +3¾

The mutant male was mated with the mutant female and also with other females of the plus series, with the results shown in Table 51. In every case the young fall into two distinct groups, one of which varies about the general mean of the plus series (approximately 3¾), while the other varies about the father’s grade as a mean (approximately 5½).

The mutant female had 16 young, 6 in the lower group, mean 3.87, and 10 in the upper group, mean 5.60. (See Table 51, lowest row.) The other females had in all 114 young almost equally divided between the two groups, 58 in the lower group, mean 3.73, and 56 in the upper group, mean 5.45. This result indicates clearly (what the sequel also confirms) that the male mutant transmitted in half his gametes the high grade of pigmentation which he himself manifested, while in the other half of his gametes he transmitted the ordinary condition of the plus race at that time. In other words his “mutant” character behaved as a dominant unit in relation to the ordinary condition of the plus race.

It is evident that the female mutant was of similar constitution. This being the case, we should expect three-fourths of the offspring of the two mutants to be in the upper group. In reality 10 of their 16 young were of this sort.

The male mutant was mated also with females of the minus series with the results indicated in Table 52. Again, the offspring fall into two distinct groups, a lower and an upper. The lower group should be comparable with the result obtained in F₁ when the plus and minus races are crossed with each other. (Compare Table 50.) Such it proves to be. It includes 35 individuals of mean grade -0.49 and standard deviation 0.77. Series 2 of Table 50 is nearly contemporaneous with this experiment. The F₁ offspring in that series were of mean grade -1 and standard deviation 0.60.

The upper group of offspring (Table 52) result, we may suppose, from a mutant gamete (grade about 5½) united with a narrow series gamete (grade about -2). This group includes 31 individuals varying closely about grade 4½, and with a standard deviation of only 0.31. The lower average grade of this group (4.43) compared with the similar group of Table 51, which had a mean of 5.47, shows the influence of the minus-series gamete upon the heterozygote in lowering its grade by about 1. Whether the plus-series gametes have any effect upon the grade of the heterozygotes recorded in the upper group of Table 51 is not certain, because a _homozygous_ group of mutants has not yet been established. It may be observed, however, that one individual in the upper group of Table 51 was of grade 6 (colored all over), and it is possible that homozygous “mutants,” when obtained, will approximate that grade, as most wild rats do. Further, a comparison of Tables 51 and 53 shows that mutant heterozygotes formed by crosses with the plus series are of slightly _lower_ mean grade than the offspring of the two mutants, among which should occur both homozygous and heterozygous mutants. It seems probable, therefore, that homozygous mutants will be found to be of somewhat higher grade than heterozygous ones.

The question early suggested itself to our minds, will these “mutants” prove to be mutants in the sense of De Vries? Will they prove to be more stable than the modifications ordinarily secured by selection in our experiments? To test this matter, we have raised two additional generations of offspring from the two mutants and have bred a second generation of offspring from each of the four groups of F₁ offspring recorded in Tables 51 and 52, derived from matings with the plus and minus races respectively.

The F₂ descendants of the two original mutants proved very similar to the F₁ descendants. (See Table 53.) They fall as before into two groups, an upper and a lower. The former includes 30 individuals of mean grade 5.52, the latter 2 of mean grade 3.37. As the parents of this generation were taken wholly from the _upper_ group of offspring of generation F₁, and as theoretically that group should contain 2 heterozygous individuals to one which is homozygous for the “mutant” character, it is to be expected that in F₂ more than three-fourths of the offspring will fall in the upper group. For any pair, one member of which is homozygous for the mutant character, should produce only offspring falling in the upper group; and offspring falling in the _lower_ group should be produced only by pairs _both_ members of which are heterozygous.

The upper group in F₂ should contain a larger proportion of homozygous mutants than in F₁, and since the parents of F₃ were chosen from this upper group of F₂ offspring, it is not surprising that the 11 F₃ offspring recorded up to this time all fall in the upper group. The mean of this upper group is remarkably constant through the three generations, and the variability of the group as measured by its standard deviation is also low, namely, 0.19. This indicates that the mutant character is a strongly dominant unit in relation to the ordinary condition of the plus series.

Table 54 shows the character of the F₂ offspring of the original male mutant mated with females of the plus series. The lower group parents, those into which the mutant character did not presumably enter at all, produced 59 offspring recorded in the first part of Table 54. Their mean grade is 3.78 and their standard deviation 0.33. These are very close to the constants of the general plus series, which for generation 10 were 3.73 and 0.36, respectively.

The second division of Table 54 shows the character of the young produced by the F₁ parents of the upper group (Table 51). Such parents are supposed to have received a “mutant” gamete from their father, grade about 5.50, and a plus-series gamete from their mother, grade about 3.75. If they produce gametes of these same two sorts, their offspring should also fall into two corresponding groups; in fact they do. There are 11 offspring of mean grade 3.86 and 79 offspring of mean grade 5.50. As in the previous generation, the two groups do not approach each other in grade. The mean and standard deviation of the lower group of offspring are similar to those of the plus race. The mean of the upper group is about the same as that of their parents (upper group of offspring, Table 51), namely, 5.50, as compared with 5.45; their standard deviation is somewhat lower, namely, 0.15, as compared with 0.23. This result indicates that the “mutant” character and the hooded character of the plus series segregate from each other in a simple way without modifying each other appreciably. It seems possible that they contain the _same modifiers_ (if modifiers are present) and differ merely by the main unit which we called the hooded character in the early part of this paper. Each contains a different condition of that main unit. Consequently there is no increase of variability in F₂ when these two conditions are intercrossed. This we should expect to happen, if they differed by more than a single factor.

A very different result is obtained from the cross between the mutant and narrow races. Although F₁ from that cross was quite variable (see Table 52), F₂ is still more variable (see Table 55). The lower group F₁ individuals, which resembled F₁ between the plus and minus races, produced 61 young (first division of Table 55), which resemble F₂ between the plus and minus races. They range in grade from -2 to +3¼, mean +0.58, standard deviation 1.17. In the two series of crosses between the plus and minus races (Table 50) the means were +0.24 and +0.72, respectively, and the standard deviations 1.01 and 0.87. This indicates, as did the cross with the plus series, that the “lower group” gametes produced by the original mutant male did not differ materially from gametes produced by the ordinary plus race from which the mutant sprang.

The second division of Table 55 shows the character of the F₂ young produced by the upper group of F₁ offspring recorded in Table 52. It consists of two groups, a lower and an upper. The lower represents the extracted minus race, the upper represents the extracted dominants or mutants, whether homozygous or heterozygous. The former group has an average of +0.75 and a standard deviation of 1.03, which values are close to the corresponding constants of Series 2, Table 50, the latest of the plus-minus crosses, in which the mean was +0.72 and the standard deviation 0.87.

The upper group offspring of Table 55, second division, the homozygous and heterozygous mutants, number 68; they have a mean grade of 4.77 as compared with 4.43 in F₁, which consisted exclusively of heterozygotes. This shows the extracted homozygotes to be of higher grade than the heterozygotes. The highest grade mutant among the 31 F₁ young, all of which were heterozygotes, was of grade 5, but among the 68 F₂ young are 16 of higher grade than 5. We expect one-third of these 68 individuals to be homozygotes. Now all of the F₂ mutants from the cross of mutant with plus race (Table 54) were of grade 5 or higher, only 2 in 79 being as low as 5, and 13 of the 79 being of grade 5¾, a grade not attained at all in F₂ from the mutant-minus cross (Table 55). This result shows us that the cross with the minus race does affect permanently the mutant character, lowering its grade even in homozygous mutants extracted from the cross. It also increases the variability of the mutants, for the standard deviation of the mutant group in Table 55 is 0.44, whereas in Table 54 (mutant-plus F₂), in a like number of individuals, it was 0.15, or only about one-third as great.

That the variability of the mutants is unaffected by a cross with the plus race, but that it is increased by a cross with the minus race, and that, further, the mean of the mutants is affected little or none by a cross with the plus race, but that it is lowered by a cross with the minus race—these several facts are all conformable with the hypothesis that _the change in variability due either to crossing or to selection results from modifying factors_ which, as they are independent of the main factor concerned, are probably transmitted in a different part or component of the germ-cell than that factor. For if the mutant and the plus race are alike as regards the modifiers, but differ only in the main factor, then no change in variability should result from intercrossing them, but only alternative conditions as regards the main factor. This is the observed result. But if the mutant and the minus race differ not only in the main factor, but also in modifiers which are independent of it, then, when they are crossed, we may expect that through independent segregation of main factor and modifiers the extracted minus race will be raised in grade, while the extracted mutants are lowered, and both will become more variable. This also is the observed result.

One objection may be offered to this interpretation, namely, that the increased variability is not delayed until F₂, but is already in evidence to some extent in F₁. The same thing was observable in the crosses of the plus and minus series (Table 50). From that table, Series 1, it will be observed that when the plus and minus races had standard deviations of 0.49 and 0.50, respectively, their F₁ offspring had a standard deviation of 0.71, an increase by nearly one-half; F₂ showed a further increase to 1.01. In series 2, Table 50, the uncrossed races (generation 10) had standard deviations of 0.36 and 0.24; their F₁ offspring had a standard deviation of practically twice this, namely 0.60; F₂ showed a further increase to 0.87.

At the time of the mutant-minus race crosses, the minus race (generation 10) had a standard deviation of 0.24, the plus race of 0.36. F₁ (lower group) had a standard deviation of 0.77, and F₂ of 1.17. F₁ mutants (upper group) had a standard deviation of 0.31 which rose in F₂ to 0.44. These various facts will perhaps be better grasped if presented in tabular form:

TABLE C.

+-------------------------------------+-------------------+------+------+ | |Standard deviation | | | | | of races crossed, | S. D.| S. D.| | | same generation. | F₁ | F₂ | +-------------------------------------+---------+---------+------+------+ |Plus-minus cross, series 1 (Table 50)| 0.49 | 0.50 | 0.71 | 1.01 | |Plus-minus cross, series 2 (Table 50)| .36 | .24 | .60 | .87 | |Mutant-minus cross, lower group | .25 | .24 | .77 | 1.17 | |Mutant-minus cross, upper group | .19 | .24 | .31 | .44 | |Mutant-plus cross, lower group | .25 | .36 | .24 | .35 | |Mutant-plus cross, upper group | .19 | .36 | .23 | .15 | +-------------------------------------+---------+---------+------+------+

The mutant-plus cross, it will be observed, shows no increase of variability either in F₁ or in F₂, but crosses involving the minus race show increase of variability both in F₁ and in F₂. Interpreted on a Mendelian basis, this means that the mutant and plus races on the one hand and the minus race on the other hand differ by more than a single factor. If they differed by only a single factor, then crosses between them should bring no increase of variability, either in F₁ or in F₂. This appears to be true as regards the mutant and plus races when crossed with each other. But if the races crossed differ by more than one factor, and if, further, neither parent is homozygous as regards the factors in which they differ, then we may expect an increase in variability both in F₁ and in F₂. This is exactly what we observe when the minus race is crossed with either the plus race or its derivative, the mutant race.

If we suppose that the plus race and the minus race differ from each other by certain “modifiers,” we can not suppose that the plus and the mutant races differ by these same modifiers. They differ in some other _single_ respect; perhaps that in which they differ is the _main_ hooded factor. Are we, then, to suppose that the plus and the minus races _do not_ differ as regards this same main factor? This can not be stated, but we see no reason for considering them identical as regards that factor. It appears that the mutant race arose from the plus race by a single large plus variation, which seems to have its determiner in some single component of the germ-cell. But the fact that this change came as a large quantitative variation does not show that small variations are impossible in that same cell component. It seems to us quite improbable that the plus mutation could have arisen in the minus selection series. We believe that the repeated selection which was practised had something to do with inducing this change in the plus direction. If one can increase at will the “modifiers” which make the pigmentation more extensive, it does not seem strange that after a time a readjustment should occur within the cell which should incorporate modifiers in that part of the cell which is responsible for the unit-character behavior of the hooded pattern. This would amount to a quantitative change in the unit-character for hooded pigmentation.

BIBLIOGRAPHY.

CASTLE, W. E.

1905. Heredity of coat characters in guinea-pigs and rabbits.
Carn. Inst. Wash. Pub. 23.

1906. The origin of a polydactylous race of guinea-pigs. Carn.
Inst. Wash. Pub. 49.

1912. The inconstancy of unit-characters. American Naturalist,
vol. 46, pp. 352-362.

CASTLE, W. E., and ALEXANDER FORBES.

1906. Heredity of hair-length in guinea-pigs and its bearing on
the theory of pure gametes. Carn. Inst. Wash. Pub. 49.

DE VRIES, H.

1901-1903. Die Mutationstheorie. Veit & Co., Leipzig.

EAST, E. M.

1912. The mendelian notation as a description of physiological
facts. American Naturalist, vol. 46, pp. 633-655.

JENNINGS, H. S.

1909. Heredity and variation in the simplest organisms.
American Naturalist, vol. 43, pp. 321-337.

1910. Experimental evidence on the effectiveness of selection.
American Naturalist, vol. 44, pp. 136-145.

JOHANNSEN, W.

1909. Elemente der exakten Erblichkeitslehre. G. Fischer, Jena.

MACCURDY, H., and W. E. CASTLE.

1907. Selection and cross-breeding in relation to the inheritance
of coat-pigments and coat-patterns in rats and guinea-pigs.
Carn. Inst. Wash. Pub. 70.

PEARL, R.

1913. Genetics and breeding. Science, n. s., vol. 37, pp. 539-546.

TABLES.

TABLE 1.—_Classification of the first generation of offspring in the plus selection series. At the head of each column is indicated the grade of the individuals recorded in that column. The figures in the body of the table indicate the numbers of offspring of the several grades indicated._

+--------+--------------------------+-------+------+-----------+ | Grade | Grade of offspring. | | | | | of +--+--+--+--+--+--+--+--+--+Totals.|Means.|Regression.| |parents.|+1|1¼|1½|1¾| 2|2¼|2½|2¾| 3| | | | +--------+--+--+--+--+--+--+--+--+--+-------+------+-----------+ | 1⅞ | 1| 1| 1| 1| 1| | 1| 1| | 7 | 1.82 | .05 | | 2 | 4| 1| 3| 1| 4| 1| 4| | | 18 | 1.76 | .24 | | 2⅛ | | | | | | | | | | | | | | 2¼ | 3| 1| 3| 1| 6| 2| 2| 2| | 20 | 1.87 | .38 | | 2⅜ | | | | | | | | | | | | | | 2½ | 5| | 3| 1|13| 1| 8| 5| 1| 37 | 2.06 | .44 | | 2⅝ | | | | | | 1| 1| 2| 1| 5 | 2.15 | .47 | | 2¾ | 7| | 3| 2|17| 1|12| | 9| 51 | 2.12 | .63 | | 2⅞ | | | | | | | | | | | | | | 3 | | | | 2| 3| 1| 3| | 3| 12 | 2.35 | .65 | | +--+--+--+--+--+--+--+--+--+-------+------+-----------+ |Totals | | | | | | | | | | | | | | or | | | | | | | | | | | | | |means, | | | | | | | | | | | | | | 2.51|20| 3|13| 8|44| 7|31|10| 4| 150 | 2.05 | .46 | +--------+--+--+--+--+--+--+--+--+--+-------+------+-----------+

TABLE 2.—_Classification of offspring in generation 2, plus selection series._

+--------+-----------------------------------------------------------+ | Grade | Grade of offspring. | | of +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ |parents.|-1|-¾|-½|-¼| 0|+¼| ½| ¾| 1|1¼|1½|1¾| 2|2¼|2½|2¾| 3|3¼|3½|3¾| +--------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | 2 | | | 1| | 1| | | 4| 2| 5| 7| 3| 7| 8| 2| 3| 2| 1| | | | 2⅛ | 1| | 1| | 2| 1| 3| 5|12| 8| 5| 5| 8| 2| 1| 2| | | | | | 2¼ | | | | | | | | | | 1| 1| 3| 1| 1| | 1| | | | | | 2⅜ | | | | | | | | | 1| 1| 4| 9| 7| 8| 8| 6| 1| | | | | 2½ | | | | | | | | 4|22|16|19|11|21|13| 7|10| 9| 1| | | | 2⅝ | | | | | 1| | 2| | 3| 1| | 6| 5| 7| 9| 6| 3| 1| | | | 2¾ | | | | 1| | | | 3| 4| 2| 6| 5| 9| 6| 9| 6| 1| | | | | 2⅞ | | | | | | | | | | 1| | 1| 3| 5| 3| 9| 1| | | | | 3 | | | | | | | | | 1| 2| 3| 2|14| 7| 4| 5|11| 6| 3| 1| | 3½ | | | | | | | | | | | | | 2| | 1| | 2| | | | | +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ |Totals | | | | | | | | | | | | | | | | | | | | | | or | | | | | | | | | | | | | | | | | | | | | |means, | | | | | | | | | | | | | | | | | | | | | | 2.52| 1| -| 2| 1| 4| 1| 5|16|45|37|45|45|77|57|44|48|30| 9| 3| 1| +--------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+

+--------+-------+------+-----------+ | Grade | | | | | of |Totals.|Means.|Regression.| |parents.| | | | +--------+-------+------+-----------+ | 2 | 46 | 1.70 | .30 | | 2⅛ | 56 | 1.28 | .82 | | 2¼ | 8 | 1.87 | .38 | | 2⅜ | 45 | 1.92 | .45 | | 2½ | 133 | 1.80 | .70 | | 2⅝ | 44 | 2.11 | .51 | | 2¾ | 52 | 1.92 | .83 | | 2⅞ | 23 | 2.41 | .46 | | 3 | 59 | 2.47 | .53 | | 3½ | 5 | 2.50 | .62 | | +-------+------+-----------+ |Totals | | | | | or | | | | |means, | | | | | 2.52| 471 | 1.92 | .60 | +--------+-------+------+-----------+

TABLE 3.—_Classification of offspring in generation 3, plus selection series._

+--------+-----------------------------------------+---------------------+ | Grade | Grade of offspring. |Totals. | | of +--+--+--+--+--+--+--+--+--+--+--+--+--+--+ Means. | |parents.| ¾| 1|1¼|1½|1¾| 2|2¼|2½|2¾| 3|3¼|3½|3¾| 4| Regression.| +--------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+-----+------+--------+ | 2⅛ | | | 1| 1| 5| 6| 4| 1| 3| | | | | | 21 | 2.06 | .06 | | 2¼ | | | | | | | | | | | | | | | | | | | 2⅜ | | | | | 5| 5| 1| 4| 2| | | | | | 17 | 2.15 | .22 | | 2½ | 1| 2| 1| 2| 5| 5|10|10| 9| 7| 2| | | | 54 | 2.32 | .18 | | 2⅝ | | | 2| 1| 3| 9| 4| 5|15|18| 3| 1| 2| 1| 64 | 2.64 | -.02 | | 2¾ | | | | 2| 1| 7|10| 7| 7| 7| 1| 1| | | 43 | 2.46 | .29 | | 2⅞ | | | 1| | | 7| 3| 7| 9|10| 9| 1| | | 47 | 2.70 | .17 | | 3 | | | | 2| 1|12|14|11|17|11| 3| | | | 71 | 2.49 | .51 | | 3⅛ | | | | | | | | | 2| 5| 1| 2| | | 10 | 3.07 | .05 | | 3¼ | | | | | | | | | 1| 2| | 1| 2| | 6 | 3.17 | .08 | | 3⅜ | | | | | | | | 2| 1| 3| 2| | | | 8 | 2.91 | .46 | | +--+--+--+--+--+--+--+--+--+--+--+--+--+--+-----+------+--------+ |Totals | | | | | | | | | | | | | | | | | | | or | | | | | | | | | | | | | | | | | | |means, | | | | | | | | | | | | | | | | | | | 2.73| 1| 2| 5| 8|20|51|46|47|66|63|21| 6| 4| 1| 341 | 2.51 | .22 | +--------+--+--+--+--+--+--+--+--+--+--+--+--+--+--+-----+------+--------+

TABLE 4.—_Classification of offspring, generation 4, plus selection series._

+--------+---------------------------------------+-----------------------+ | Grade | Grade of offspring. |Totals. | | of +--+--+--+--+--+--+--+--+--+---+--+--+--+ Means. | |parents.| ¾| 1|1¼|1½|1¾| 2|2¼|2½|2¾| 3 |3¼|3½|3¾| Regression.| +--------+--+--+--+--+--+--+--+--+--+---+--+--+--+-----+------+----------+ | 2½ | | | | | 2| | 2| | 4| 3| | | | 11 | 2.55 | .05 | | 2⅝ | | | | | | | | | | | | | | | | | | 2¾ | | | | | | 3| 3| 2| 3| 4| 3| | | 18 | 2.65 | .10 | | 2⅞ | | 1| | | | | 3| 3| 7| 15| 4| 3| 2| 37 | 2.97 | .10 | | 3 | | 1| | 1| 7|12|25|19|35| 29| 9| 4| 1| 143 | 2.60 | .40 | | 3⅛ | | | 1| | 2|11|14|21|28| 30|11| 2| 2| 122 | 2.69 | .43 | | 3¼ | | | | 1| | 1| 6| 8|13| 17| 9| 8| 1| 64 | 2.89 | .36 | | 3⅜ | | | | | 1| | 6| 2| 3| 9| 2| | | 23 | 2.70 | .67 | | 3½ | | | | | | 3| 1| | 2| 3| 6| 2| 3| 20 | 3.02 | .48 | | 3⅝ | | | | | | | | | | | | | | | | | | 3¾ | | | | | | | | 3| 1| 1| 1| | | 6 | 2.75 | 1.00 | | +--+--+--+--+--+--+--+--+--+---+--+--+--+-----+------+----------+ |Totals | | | | | | | | | | | | | | | | | | or | | | | | | | | | | | | | | | | | |means, | | | | | | | | | | | | | | | | | | 3.09| 1| 1| 1| 2|12|30|60|58|96|110|45|19| 9| 444 | 2.73 | .36 | +--------+--+--+--+--+--+--+--+--+--+---+--+--+--+-----+------+----------+

TABLE 5.—_Classification of generation 5, plus selection series._

+--------+-----------------------------------------------+ | Grade | Grade of offspring. | | of +--+--+--+--+--+--+--+--+---+---+---+--+--+--+--+ |parents.| ¾| 1|1¼|1½|1¾| 2|2¼|2½| 2¾| 3 | 3¼|3½|3¾| 4|4¼| +--------+--+--+--+--+--+--+--+--+---+---+---+--+--+--+--+ | 2¾ | | | | | | 1| | | 2| 4| 4| 1| | | | | 2⅞ | | | | | | | 4| 4| 4| 2| 3| 2| 2| | | | 3 | | | | | | | 1| 5| 3| 2| 3| 1| | | | | 3⅛ | | 1| 1| 1| 1| 8| 9|14| 20| 29| 18| 8| 3| 1| | | 3¼ | 1| 1| 1| | 4|12| 6|14| 24| 39| 27| 7| | 1| 1| | 3⅜ | | | | 1| 1| 5|14|11| 25| 36| 28|15| 7| 2| | | 3½ | | | | | | 6| 5|10| 14| 16| 8| 8| 3| | | | 3⅝ | | | | | | 3| 3| 5| 7| 16| 12|11| 4| 3| | | 3¾ | | | | | | | | 2| 2| 4| 3| 2| 1| | | | 3⅞ | | | | | | | 1| 1| | 1| | 1| 2| 2| | | 4 | | | | | | | 1| | | 1| 1| 1| 2| 1| | | 4⅛ | | | | | | 1| | | | 1| | | | 1| | | +--+--+--+--+--+--+--+--+---+---+---+--+--+--+--+ |Totals | | | | | | | | | | | | | | | | | or | | | | | | | | | | | | | | | | |means, | | | | | | | | | | | | | | | | | 3.33| 1| 2| 2| 2| 6|35|44|66|101|151|107|57|24|11| 1| +--------+--+--+--+--+--+--+--+--+---+---+---+--+--+--+--+

+--------+-------+------+-----------+ | Grade | | | | | of |Totals.|Means.|Regression.| |parents.| | | | +--------+-------+------+-----------+ | 2¾ | 12 | 3.00 | -.25 | | 2⅞ | 21 | 2.87 | 0 | | 3 | 15 | 2.81 | .19 | | 3⅛ | 114 | 2.81 | .31 | | 3¼ | 138 | 2.81 | .44 | | 3⅜ | 145 | 2.94 | .43 | | 3½ | 69 | 2.86 | .64 | | 3⅝ | 64 | 3.08 | .54 | | 3¾ | 14 | 3.07 | .68 | | 3⅞ | 8 | 3.35 | .52 | | 4 | 7 | 3.36 | .64 | | 4⅛ | 3 | 3.00 | 1.12 | | +-------+------+-----------+ |Totals | | | | | or | | | | |means, | | | | | 3.33| 610 | 2.90 | .43 | +--------+-------+------+-----------+

TABLE 6.—_Classification of generation 6, plus selection series._

+--------+------------------------------------------+--------------------+ | Grade | Grade of offspring. |Totals. | | of +--+--+--+--+--+---+---+---+---+--+--+--+--+ Means. | |parents.|1½|1¾| 2|2¼|2½| 2¾| 3 | 3¼| 3½|3¾| 4|4¼|4½| Regression.| +--------+--+--+--+--+--+---+---+---+---+--+--+--+--+-----+------+-------+ | 3 | | | | | | 1| | | | 1| | | | 2 | | | | 3⅛ | | 3| 4| 1| 1| 4| 7| 5| 3| | | | | 28 | 2.84 | .28 | | 3¼ | 1| | 3| 3| 8| 26| 31| 31| 24|15| 1| | | 143 | 3.10 | .15 | | 3⅜ | 1| | 5| 6|13| 20| 28| 30| 14| 5| | | | 123 | 2.96 | .41 | | 3½ | | 1| 9| 4|15| 29| 49| 41| 43|17| 4| | | 212 | 3.10 | .40 | | 3⅝ | | | 4| 8|11| 24| 34| 36| 37|21| 5| | 1| 181 | 3.16 | .46 | | 3¾ | 1| 1| 2| 1| 3| 4| 18| 13| 20|13| 2| | | 78 | 3.22 | .53 | | 3⅞ | | | 4| 1| 3| 5| 14| 15| 20|14| 4| | | 80 | 3.26 | .61 | | 4 | | | 1| | | | 2| 1| 5| 4| 1| | | 14 | 3.41 | .59 | | +--+--+--+--+--+---+---+---+---+--+--+--+--+-----+------+-------+ |Totals | | | | | | | | | | | | | | | | | | or | | | | | | | | | | | | | | | | | |means, | | | | | | | | | | | | | | | | | | 3.52| 3| 5|32|24|54|113|183|172|166|90|17| | 1| 861 | 3.11 | .41 | +--------+--+--+--+--+--+---+---+---+---+--+--+--+--+-----+------+-------+

TABLE 7.—_Classification of generation 7, plus selection series._

+--------+----------------------------------------------+ | Grade | Grade of offspring. | | of +--+--+--+--+--+---+---+---+---+---+--+--+--+--+ |parents.|1½|1¾| 2|2¼|2½| 2¾| 3 | 3¼| 3½| 3¾| 4|4¼|4½|4¾| +--------+--+--+--+--+--+---+---+---+---+---+--+--+--+--+ | 3⅛ | | | 2| 2| 4| 5| 7| 4| 3| 1| | | | | | 3¼ | 1| | 6|11| 7| 11| 30| 19| 22| 23| 1| | | | | 3⅜ | 1| 2|10|18|17| 21| 27| 18| 21| 20| 4| 1| | | | 3½ | | | 6| 9| 9| 21| 31| 28| 35| 34| 3| 1| | | | 3⅝ | | | 7|11|13| 26| 47| 53| 75| 49| 7| 1| | | | 3¾ | | | 2| 3| 3| 16| 28| 25| 58| 42| 4| 3| | | | 3⅞ | | | 2| 1| 2| 4| 10| 12| 23| 21| 6| 6| 2| 1| | 4 | | | | | 1| 1| 3| | 2| 4| 3| | | 1| | 4⅛ | | | | | | | | | 1| 1| 1| | | | | +--+--+--+--+--+---+---+---+---+---+--+--+--+--+ |Totals | | | | | | | | | | | | | | | | or | | | | | | | | | | | | | | | |means, | | | | | | | | | | | | | | | | 3.56| 2| 2|35|55|56|105|183|159|240|195|29|12| 2| 2| +--------+--+--+--+--+--+---+---+---+---+---+--+--+--+--+

+--------+-------+------+-----------+ | Grade | | | | | of |Totals.|Means.|Regression.| |parents.| | | | +--------+-------+------+-----------+ | 3⅛ | 28 | 2.87 | .25 | | 3¼ | 131 | 3.09 | .16 | | 3⅜ | 160 | 2.97 | .40 | | 3½ | 177 | 3.18 | .32 | | 3⅝ | 289 | 3.23 | .39 | | 3¾ | 184 | 3.35 | .40 | | 3⅞ | 90 | 3.49 | .38 | | 4 | 15 | 3.53 | .47 | | 4⅛ | 3 | 3.75 | .50 | | +-------+------+-----------+ |Totals | | | | | or | | | | |means, | | | | | 3.56| 1077 | 3.20 | .36 | +--------+-------+------+-----------+

TABLE 8.—_Classification of generation 8, plus series._

+--------+---------------------------------------+-----------------------+ | Grade | Grade of offspring. |Totals. | | of +--+--+--+--+---+---+---+---+--+--+--+--+ Means. | |parents.|1¾| 2|2¼|2½| 2¾| 3 | 3¼| 3½|3¾| 4|4¼|4½| Regression.| +--------+--+--+--+--+---+---+---+---+--+--+--+--+------+------+---------+ | 3¼ | | | | | | 2| | 2| | | | | 4 | 3.25 | 0 | | 3⅜ | | | | | | | | | | | | | | | | | 3½ | | | | 1| 4| 6| 9| 18| 17| 2| 2| | 59 | 3.46 | .04 | | 3⅝ | 1| 2| 9|13|30| 69| 44|144|149|22| 1| | 484 | 3.50 | .12 | | 3¾ | | 2| 1| 9|12| 55| 39|152|173|23| 2| | 469 | 3.49 | .26 | | 3⅞ | | 1| 2| | 4| 23| 18| 98| 69|19| 2| 1| 238 | 3.53 | .34 | | 4 | | | 1| 2| 3| 10| 6| 34| 6| 1| 1| | 64 | 3.31 | .69 | | 4⅛ | | | | | 2| 5| 2| 14| 13|14|10| | 60 | 3.72 | .40 | | 4¼ | | | | | | | 1| 7| 11| 2| 1| | 22 | 3.69 | .56 | | 4⅜ | | | | | | | | | 2| 5| 1| | 8 | 3.96 | .41 | | +--+--+--+--+--+---+---+---+---+--+--+--+------+------+---------+ |Totals | | | | | | | | | | | | | | | | | or | | | | | | | | | | | | | | | | |means, | | | | | | | | | | | | | | | | | 3.75| 1| 5|13|25|55|170|119|469|440|88|20| 1| 1408 | 3.48 | .27 | +--------+--+--+--+--+--+---+---+---+---+--+--+--+------+------+---------+

TABLE 9.—_Classification of generation 9, plus series._

+--------+----------------------------------------+----------------------+ | Grade | Grade of offspring. |Totals. | | of +--+--+--+--+--+---+---+---+---+---+--+--+ Means. | |parents.|1¾| 2|2¼|2½|2¾| 3 | 3¼| 3½| 3¾| 4 |4¼|4½| Regression.| +--------+--+--+--+--+--+---+---+---+---+---+--+--+-----+------+---------+ | 3½ | | | | 1| | | 1| 1| 1| | | | 4| 3.25 | .25 | | 3⅝ | | 1| 1| 6|12| 28| 26| 96| 63| 10| 1| | 244| 3.43 | .19 | | 3¾ | 1| 2| 4| 7|19| 45| 50|224|212| 25| 2| | 591| 3.50 | .25 | | 3⅞ | | | | 2| 5| 25| 32|105|177| 64| 8| 6| 424| 3.65 | .22 | | 4 | | | | 1| 2| 5| | 14| 15| 7| | 1| 45| 3.57 | .43 | | 4⅛ | | | | | | 2| | | 4| 1| | | 7| 3.57 | .55 | | 4¼ | | | | | | | 1| | 1| 2| | | 4| 3.75 | .50 | | 4⅜ | | | | | | | | 3| | | | | 3| 3.50 | .87 | | +--+--+--+--+--+---+---+---+---+---+--+--+-----+------+---------+ |Totals | | | | | | | | | | | | | | | | | or | | | | | | | | | | | | | | | | |means, | | | | | | | | | | | | | | | | | 3.78| 1| 3| 5|17|38|105|110|443|473|109|11| 7| 1322| 3.54 | .24 | +--------+--+--+--+--+--+---+---+---+---+---+--+--+-----+------+---------+

TABLE 10.—_Classification of generation 10, plus series._

+--------+-----------------------------------+-------+------+-----------+ | Grade | Grade of offspring. | | | | | of +--+--+--+--+--+---+---+---+--+--+--+Totals.|Means.|Regression.| |parents.|2¼|2½|2¾| 3|3¼| 3½| 3¾| 4 |4¼|4½| 5| | | | +--------+--+--+--+--+--+---+---+---+--+--+--+-------+------+-----------+ | 3¾ | | 1| 1| 9|13| 63|117| 44| 8| 1| | 257 | 3.69 | .06 | | 3⅞ | 1| | 3| 3|16| 95|142| 62|20| 5| | 347 | 3.72 | .15 | | 4 | | | | | 4| 26| 61| 20| 7| 2| | 120 | 3.76 | .24 | | 4⅛ | | | | | | 11| 17| 7| 6| 1| 2| 44 | 3.87 | .25 | | 4¼ | | | | | | 1| 4| 2| 1| | | 8 | 3.84 | .41 | | +--+--+--+--+--+---+---+---+--+--+--+-------+------+-----------+ |Totals | | | | | | | | | | | | | | | | or | | | | | | | | | | | | | | | |means, | | | | | | | | | | | | | | | | 3.88| 1| 1| 4|12|33|196|341|135|42| 9| 2| 776 | 3.73 | .15 | +--------+--+--+--+--+--+---+---+---+--+--+--+-------+------+-----------+

TABLE 11.—_Classification of generation 11, plus series._

+--------+--------------------------------+-------+------+-----------+ | Grade | Grade of offspring. | | | | | of +--+--+--+---+---+---+--+--+--+--+Totals.|Means.|Regression.| |parents.|2¾| 3|3¼| 3½| 3¾| 4 |4¼|4½|4¾| 5| | | | +--------+--+--+--+---+---+---+--+--+--+--+-------+------+-----------+ | 3¾ | | | | 2| 7| 2| | | | | 11 | 3.75 | 0 | | 3⅞ | 2| 7|17| 87|162| 41|11| 3| 3| | 333 | 3.70 | .17 | | 4 | | 3| 2| 25| 87| 65|24| 6| 1| 1| 214 | 3.87 | .13 | | 4⅛ | | 3| 3| 16| 49| 27| 8| 2| 2| | 110 | 3.81 | .31 | | 4¼ | | | | 2| 13| 5| 3| 1| 1| | 25 | 3.91 | .34 | | 4⅜ | | | | | 1| 3| | | | | 4 | 3.94 | .43 | | +--+--+--+---+---+---+--+--+--+--+-------+------+-----------+ |Totals | | | | | | | | | | | | | | | or | | | | | | | | | | | | | | |means, | | | | | | | | | | | | | | | 3.97| 2|13|22|132|319|143|46|12| 7| 1| 697 | 3.78 | .19 | +--------+--+--+--+---+---+---+--+--+--+--+-------+------+-----------+

TABLE 12.—_Classification of generation 12, plus series._

+--------+----------------------------------+-------+------+-----------+ | Grade | Grade of offspring. | | | | | of +--+--+--+--+---+---+--+--+--+--+--+Totals.|Means.|Regression.| |parents.|2½| 3|3¼|3½| 3¾| 4 |4¼|4½|4¾| 5|5¼| | | | +--------+--+--+--+--+---+---+--+--+--+--+--+-------+------+-----------+ | 3¾ | | | | | 4| 20| 7| 4| | | | 35 | 3.83 | -.08 | | 3⅞ | | | | 2| 19| 17| 6| 2| 2| | | 48 | 3.96 | .09 | | 4 | | 1| 1|10| 53| 59|12| 5| 1| 1| 2| 145 | 3.93 | .07 | | 4⅛ | 1| | 2|17| 86| 83|28| 6| 3| 1| | 227 | 3.91 | .21 | | 4¼ | | 1| | 7| 19| 29|11| 3| 1| | | 71 | 3.94 | .31 | | 4⅜ | | | | 3| 6| 14|10| 7| 3| 1| 1| 45 | 4.13 | .24 | | 4½ | | | | | 1| 4| 1| | | 1| | 7 | 4.14 | .36 | | 4⅝ | | 1| | | 3| 4| 3| | | | | 11 | 3.90 | .72 | | 5 | | | | | | | | | 1| | | 1 | 4.75 | .25 | | +--+--+--+--+---+---+--+--+--+--+--+-------+------+-----------+ |Totals | | | | | | | | | | | | | | | | or | | | | | | | | | | | | | | | |means, | | | | | | | | | | | | | | | | 4.09| 1| 3| 3|43|207|217|75|23|11| 4| 3| 590 | 3.94 | .17 | +--------+--+--+--+--+---+---+--+--+--+--+--+-------+------+-----------+

TABLE 13.—_Classification of generation 13, plus selection series._

+--------+-----------------------+-------+------+-----------+ | Grade | Grade of offspring. | | | | | of +--+--+--+--+--+--+--+--+Totals.|Means.|Regression.| |parents.|2¾|3¼|3½|3¾| 4|4¼|4½|4¾| | | | +--------+--+--+--+--+--+--+--+--+-------+------+-----------+ | 4 | | 4|17|23|19| 2| | | 65 | 3.67 | .31 | | 4⅛ | | | 1| 8|16| 5| 1| | 31 | 3.97 | .15 | | 4¼ | 1| | 5|10|20| 6| | 1| 43 | 3.93 | .32 | | 4⅜ | | | 1| 5| 3| 1| | | 10 | 3.85 | .52 | | 4½ | | | 1|14|15| 7| 3| | 40 | 3.98 | .52 | | 4⅝ | | | | 3| 1| | 1| | 5 | 3.95 | .80 | | +--+--+--+--+--+--+--+--+-------+------+-----------+ |Totals | | | | | | | | | | | | | or | | | | | | | | | | | | |means, | | | | | | | | | | | | | 4.22| 1| 4|25|63|74|21| 5| 1| 194 | 3.88 | .34 | +--------+--+--+--+--+--+--+--+--+-------+------+-----------+

TABLE 14.—_Summary of the results of thirteen generations of plus selection based on Tables 1-13._

+-------------------------------------------------------------------+ |Generation. | |No. of offspring. | | |Mean, parents. | | | |Mean, offspring. | | | | |Standard deviation, | | | | |parents. | | | | | |Standard deviation, | | | | | |offspring. | | | | | | |Correlation, | | | | | | |parents-offspring. | | | | | | | |Absolute regression of | | | | | | | |offspring on parents. | | | | | | | | |Advance of | | | | | | | | |parents. | | | | | | | | | |Advance of | | | | | | | | | |offspring. +------+------+------+------+------+------+------+-----+-----+------+ | 1 | 150 | 2.51 | 2.05 | .313 | .541 | .298 | .46 | | | | 2 | 471 | 2.52 | 1.92 | .307 | .732 | .317 | .60 | .01 | -.13 | | 3 | 341 | 2.73 | 2.51 | .285 | .531 | .331 | .22 | .21 | .59 | | 4 | 444 | 3.09 | 2.73 | .215 | .468 | .066 | .36 | .36 | .22 | | 5 | 610 | 3.33 | 2.90 | .240 | .505 | .160 | .43 | .24 | .17 | | 6 | 861 | 3.52 | 3.11 | .209 | .490 | .180 | .41 | .19 | .21 | | 7 |1,077 | 3.56 | 3.20 | .212 | .555 | .215 | .36 | .04 | .09 | | 8 |1,408 | 3.75 | 3.48 | .246 | .439 | .099 | .27 | .19 | .28 | | 9 |1,322 | 3.78 | 3.54 | .112 | .346 | .210 | .24 | .03 | .06 | | 10 | 776 | 3.88 | 3.73 | .112 | .362 | .116 | .15 | .10 | .19 | | 11 | 697 | 3.98 | 3.78 | .113 | .289 | .233 | .20 | .10 | .05 | | 12 | 590 | 4.09 | 3.94 | .176 | .302 | .161 | .15 | .11 | .16 | | 13 | 194 | 4.22 | 3.88 | .433 | .270 | .132 | .34 | .13 | -.06 | +------+------+------+------+------+------+------+-----+-----+------+ |Total |8,941 | | | | | | | | | +------+------+------+------+------+------+------+-----+-----+------+

TABLE 15.—_Mean grade and number of offspring produced by parents of a particular grade in each generation of the plus selection series, based on Tables 1-13. The grade of the parents is indicated at the head of each column. In the body of the table is recorded the grade of the offspring (in light-faced figures) and the number of offspring (in =heavy-faced figures=)._

+------+-----------------------------------------------------+----------+ |Generation. | | | | Grade of parents; below, | | | | grade and number of their | Total | | | offspring. | number | | +-----+-----+-----+-----+-----+-----+-----+-----+-----+ of | | | 2 | 2⅛ | 2¼ | 2⅜ | 2½ | 2⅝ | 2¾ | 2⅞ | 3 |offspring.| +------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----------+ | 1 |1.76 | |1.87 | |2.06 |2.15 |2.12 | |2.35 | | | | =18=| | =20=| | =37=| =5=| =51=| | =12=| =150= | | 2 |1.70 |1.28 |1.87 |1.92 |1.80 |2.11 |1.92 |2.41 |2.47 | | | | =46=| =56=| =8=| =45=|=133=| =44=| =52=| =23=| =59=| =471= | | 3 | |2.06 | |2.15 |2.32 |2.63 |2.46 |2.70 |2.49 | | | | | =21=| | =17=| =54=| =64=| =43=| =47=| =71=| =341= | | 4 | | | | |2.55 | |2.65 |2.97 |2.60 | | | | | | | | =11=| | =18=| =37=|=143=| =444= | | 5 | | | | | | |3.00 |2.87 |2.81 | | | | | | | | | | =12=| =21=| =15=| =610= | | 6 | | | | | | | | |3.25 | | | | | | | | | | | | =2=| =861= | +------+-----+-----+-----+-----+-----+-----+-----+-----+-----+----------+