the germ cells in a simple case of Mendelian heredity, such
as that of color as shown in Figs. 7 and 8. The spaces
between the large circles represent the bodies of the
individuals while the small circles within each represent the
germ cells formed by those individuals. _P_, parental
generation; each individual forms a single kind of germ
cells. _G. F1_, germs of the first filial or hybrid
generation, each composed of two different kinds of germ
cells, one from each parent. _F1_, individuals of the first
filial or hybrid generation, developed from _G. F1_. Each
member of this generation forms two kinds of germ cells in
approximately equal numbers. _G. C. F1_, germ cells of _F1_,
showing possible combinations resulting from the mating of
two members of _F1_. Each of these combinations occurs with
equal probability. _G. F2_, germs of second filial generation
resulting from the above random combinations. _F2_,
individuals of second filial generation. Each now forms germ
cells like those which constituted its own germ.]
Another possible type of mating is that between a member of a pure
race, either dominant or recessive, and a hybrid individual. This form
of mating is very common in some of the pedigrees that we shall
examine later. The results of such a mating, first between a hybrid
and a recessive individual can be most easily described by considering
a cross between black and white forms and expressing the result
algebraically.
Germ cells of first parent (white or recessive) _W_ + _W_
Germ cells of second parent (hybrid) _B_ + _W_
-------------
_BW_ + _BW_
_WW_ + _WW_
---------------------
_2BW_ + _2WW_
That is, returning to the example of the Andalusian fowls, the progeny
will be one half hybrid blues and one half whites--no black at all.
If the cross had been between black hybrid guinea pigs and white
recessive specimens the result would have been half hybrid blacks and
half pure whites.
Or supposing the mating to have occurred between the pure dominant
(black) and the hybrid the result would have been, in the fowls half
pure black and half hybrid blue; in the guinea pig all the progeny
would have been black, half pure blacks and half hybrid blacks.
Germ cells of first parent (black or dominant) _B_ + _B_
Germ cells of second parent (hybrid) _B_ + _W_
-------------
_BB_ + _BB_
_BW_ + _BW_
----------------------
_2BB_ + _2BW_
In the case of the guinea pigs, although the progeny all look alike
(black) their history would show that they were fundamentally unlike,
for if crossed with white again the result would be the production of
all black looking guinea pigs from the cross with the _BB_ forms, and
half black and half white from the _BW_ cross.
On account of the fact of variation every individual is in a certain
sense a hybrid. One's two parents have the species characters in
common but there are certain distinctive traits that hybridize and
follow Mendel's law of heredity. By no means is it to be understood
that all individual distinctive traits follow this rule in heredity.
Many individual characteristics are what we have learned to call
fluctuations--small deviations above or below an average condition of
a group. Such differences play no part in Mendelian heredity. Other
characteristics may be bodily modifications resulting from the direct
reaction between the body tissues and the environing conditions; such
traits would not be represented in the organization of the germ cells
and consequently would not be inherited at all. At present it seems
that the only characteristics that "Mendelize" are those known as
"unit characters." Such characters seem to have their origin in real
variations or mutations and though each may show fluctuations, these
fluctuations in themselves are not hereditary.
This conception of the unit character is an extremely important
element in the whole Mendelian theory and it has extended beyond the
field of heredity and led to a radical change in our notions of what
an organism really is. It is, of course, true in a sense that an
organism is a unit, an organism is one thing; but at the same time it
is true that an organism is fundamentally a collection of units, of
structural and functional characteristics which are really separable
things. A few of these units were mentioned in the first pages of this
chapter and others are mentioned on a later page. They serve as the
building blocks of organisms: individuals of the same species may be
made up of similar combinations or of different combinations. One unit
or a group of units may be taken out and replaced by others.
From the standpoint of heredity, and particularly from our eugenic
point of view, the most important results of the unit composition of
the organism lie in the fact that these units remain units throughout
successive generations and throughout successive and varying
combinations, whatever their associations may be from generation to
generation. It is a fact of the greatest eugenic significance that a
pure bred individual may be produced by a hybrid mated either with a
pure bred or with another hybrid; and that the pure bred resulting
will be just as pure bred as any. "Pure bred" now means pure bred with
respect to certain traits only. An individual may be pure bred in
certain of its characteristics, hybrid in others. Practically there is
no such thing as an individual which is either pure bred or hybrid in
_all_ its traits. One of the chief contributions, then, of Mendelism
to the subjects of Heredity and Eugenics is this--that a pure bred may
be derived from a hybrid in one generation: the pure bred produced by
a long series of hybrid individuals is just as pure as the pure bred
which has never had a hybrid in its ancestry. Another important
consequent is, that among the offspring of the same parents some
individuals may be pure bred and others hybrid. Community of parentage
does not necessarily denote community of characteristics among the
offspring. Yet by knowing the ancestry for one or two generations we
can know the qualities of the individual. Guesswork is eliminated and
the importance of the qualities of the individual is enormously
emphasized. It is necessary only to suggest the social and eugenic
significance of such facts relating to characteristics that are of
social or racial importance.
We shall have occasion in the next chapter to enumerate some of the
human unit characters whose heredity has been traced and which have
been found to Mendelize, but we may mention here a few Mendelizing
units in other organisms in order to give some idea of the kind of
character which behaves as a unit and of the range of the forms which
have been found to show Mendelian phenomena in their heredity. Among
the higher animals one might mention the absence of horns in cattle
and sheep; the "waltzing" habit of mice and the pacing gait of the
horse; length of hair and smoothness of coat in the rabbit and guinea
pig; presence of an extra toe in the cat, guinea pig, rabbit, fowl;
length of tail in the cat; and in the common fowl such characters as
the shape and size of the comb, presence of a crest or a "muff," a
high nostril, rumplessness, feathering of the legs, "frizzling" of the
feathers, certain characters of the voice, and a tendency to brood.
Among plants may be mentioned such characters as dwarfness in garden
peas, sweet peas, and some kinds of beans; smoothness or prickliness
of stem in the jimson weed and crowfoot; leaf characters in a great
variety of plants; in the cotton plant a half dozen characters have
been found to Mendelize; seed characters such as form and amount of
starch, sugar, or gluten; flat or hooded standard in the sweet pea;
annual or biennial habit in the henbane; susceptibility to a rust
disease in wheat. We should not fail to mention that scores of color
characters are known to Mendelize, such as hair or coat color and eye
color in animals and the colors of flowers, stems, seeds, seed-coats,
etc., in plants. The list of Mendelizing traits in different organisms
now extends into the hundreds and is increasing almost weekly.
Before leaving the subject of Mendelism we should say that the
phenomena, as described above in the Andalusian fowl and guinea pig,
are among the simplest known. And while such simple formulas serve to
describe the phenomena of heredity in a large number of instances, yet
in a great many other cases the descriptive formulas are more
complicated. We cannot in this place describe any of these
complications. For a full discussion of these and of the whole subject
of Mendelism the interested reader is referred to Professor Bateson's
work on "Mendel's Principles of Heredity" (1909). It must suffice to
say here that in color heredity, for example, such ratios as 9:3:4 or
12:3:1 in the second filial generation instead of the more frequent
1:2:1 or 3:1 are explainable upon essentially the same relations as
these simpler and more typical ratios. And further, many less usual
Mendelian phenomena, which we cannot undertake to describe here,
are associated with what the specialist technically terms "sex
limitation," "gametic coupling," and the like.
It is often said that the Mendelian formula has a very limited
applicability to human heredity. This is probably true if we consider
carefully the grammatical tense in which this statement is made. And
yet it is almost certainly true that heredity in man is to be
described by this law. This apparent paradox is easily explained. The
only characters whose history in heredity follows this formula are the
unit characters. A complex trait is not heritable, as a whole, but its
components behave in heredity as the separate units. It is perfectly
well known that we are deeply ignorant regarding this phase of human
structure. Our ignorance here is not the necessary kind, however, it
is merely due to the newness of the subject--we have not had time to
find out. How can we say that a complex trait is or is not inherited
according to some form of Mendel's law when we do not know the nature
of the units of which it is composed? We can make no statements about
the Mendelian inheritance of such a trait until it is factored into
its units. A considerable number of human characteristics are really
known to be heritable according to this formula, enough so that
several general rules of human heredity have been formulated. But it
is also quite within the range of possibility that some traits really
do not follow this law, although it cannot yet be said definitely
that this is or is not the case. On the whole, then, we cannot, for
the next few years, expect too much from the application of Mendel's
laws to human heredity, however much this is to be regretted.
Shall we then decline to say anything about the heredity of the great
bulk of human characteristics? By no means: we have seen that in our
bagatelle board we talk very definitely about the distribution of all
the peas, though only about the probable history of one pea. Mendel's
law deals with individual inheritance. When we cannot apply this
formula we have left still the possibility of talking about human
heredity in the group as a whole. That is to say, we have left the
opportunity of describing heredity by the statistical methods, with
the crowd, not the individual, as the unit. Since we are forced into
extensive use of this formula by our present and temporary ignorance
of the applicability of Mendel's rule we must get a clear notion of
how the statistical method is applied in this matter.
The method is the same as that employed by the statistician in
measuring the relatedness of any two series of varying phenomena. If
two quantities or characteristics are so related that fluctuations in
the one are accompanied in a regular manner by fluctuations in the
other, the two quantities or characters are said to be correlated. For
instance, the temperature and the rate of growth of sprouting beans
are related in such a way that increase in the former is accompanied
in a regular way by increase in the latter; or the width and height of
the head, or the total stature and the length of the femur similarly
vary regularly together so that they are said to be correlated to a
certain extent which can be measured. This correlation may result from
the fact that one condition is a cause, either direct or indirect, of
the other; or there may be no such causal relation between the two
phenomena, both resulting more or less independently from a common
antecedent condition or cause.
This phenomenon of correlation is not limited among organisms to the
comparison of two or more different characters in a single series of
individuals; it is applicable also to the comparison of two series of
individuals with respect to the same characteristic. Thus we may
compare the stature of a series of fathers with the same measurement
in their sons. It is this form of correlation with which we are
particularly to deal here. While it is not necessary to understand
just how this subject is dealt with by the statistician we should know
one or two of the elementary principles involved, in order to
appreciate the statistical form of many statements about heredity.
The stature of men may be said to vary usually between limits of 62
and 76 inches, the average height being about 69 inches. In the
complete absence of heredity in stature we should find that fathers of
any given height, say 62 or 63 or 76 inches would have sons of no
particular height but of all heights with an average of 69 inches, the
same as in the whole group. Or if stature were completely heritable
from one generation to the next the _total generations being the units
compared_, then 62 or 63 or 76 inch fathers would have respectively
sons all 62, 63, and 76 inches tall. When we examine the actual
details of the resemblance we find, as a matter of fact, that neither
of these possibilities is actually realized. What we do find is that
fathers below or above the average height have sons whose average
height is also below or above the general average but not so far below
or above the general average as were the fathers. If we measured a
large number of pairs of fathers and sons with respect to stature we
should find each generation with a variability such as that
illustrated in Fig. 3 of the stature of mothers, the limits here,
however, being about 62 and 76 inches. But if we measured all the sons
of 62-inch fathers they would be found to vary say from 62 to only 69
inches, averaging about 66 inches. Similarly 63-inch fathers would
have sons from 62 to 70 inches tall, averaging about 66.5 inches, or
76-inch fathers might have sons from 69 to 76 inches in height,
averaging about 72 inches, and so on for fathers of all heights. In
general, then, we may say that fathers with a characteristic of a
certain plus or minus deviation from the average of the whole group
have sons who on the whole deviate in the same direction but less
widely than the fathers, although the fact of variability comes in so
that some few of the sons deviate as widely as, or even more widely
than, the fathers, others deviate less widely than the fathers from
the average of the whole group. This is the general and very important
statistical fact of _regression_.
The phenomenon of regression may be made somewhat clearer by the aid
of a simple diagram--Fig. 10. Here are plotted first the heights, by
inches, of a group of fathers, giving the series of dots joined by the
diagonal _AB_. Next are plotted the average heights of the sons of
each class of fathers: 62-inch fathers give 66-inch sons, 63-inch
fathers 66.5-inch sons, 64-inch fathers 67-inch sons, and so for all
the classes of fathers. These dots are then joined by the line _EF_.
This is the _regression line_. Had it been the case that there was no
regression in stature the different classes of fathers would have had
sons averaging just the same as themselves and the line representing
the heights of the sons would have coincided with the line _AB_. Or if
regression had been complete the fathers of any class would have had
sons averaging about 69 inches--just the same as the average of the
whole group--and the line representing their heights would have had
the position of _CD_ in the diagram. As a matter of fact, however,
neither of these possibilities is actually realized and the regression
line _EF_ is approximated in an actual series of data. A similar
relation has been found for many characters other than stature.
[Illustration: FIG. 10.--Diagram illustrating the phenomenon
of regression. Explanation in text.]
The fact of regression is of considerable importance for the theory of
evolution as well as for the subject of Eugenics when describing the
phenomena of heredity in this statistical manner in whole groups
without paying attention to particular individuals. Regression is
found in all characteristics observed in this way, psychic as well as
purely physical. "The father [i. e., fathers] with a great excess of
the character contributes [contribute] sons with an excess, but a less
excess of it; the father [fathers] with a great defect of the
character contributes [contribute] sons with a defect, but less defect
of it."
Now, whatever the actual extent of this regression is in a group we
need to know how uniformly it occurs for all the classes of different
deviations from the general average, that is, we need to know whether
the extreme groups regress to the same relative extent as do those
nearer the general average; and, further, we need to know how nearly
the sons of fathers of any certain height are grouped about their own
average. In other words, we should know, first, whether the regression
of the sons of 62 and 76 or 67 and 71 inch fathers is proportionately
the same in each case, and, second, to what extent the sons of 62-inch
fathers vary, whether they vary as do the fathers of 62-inch sons, and
so for each group. This kind of information we get by calculating what
is called the _coefficient of heredity_. The calculation of this
coefficient is a complicated process which it is unnecessary to
describe here. It must suffice to say that a numerical coefficient can
readily be determined, which will express the average closeness and
regularity of the relationship between all the plus and minus
deviations from the group average in fathers and the corresponding
plus and minus deviations from the group average of their sons with
respect to a given characteristic. This coefficient of heredity may
vary between 0.0 and 1.0. When it is 0.0 there is, on the whole, no
regularity in the relationship, i. e., no heredity; when it is 1.0
there is, on the whole, complete regularity, i. e., heredity is
complete. Neither of these values is ever actually found in
determining coefficients of heredity in the parental relation; these
are usually between 0.3 and 0.5. It should be emphasized again that
this comparison is between whole groups and not between individuals,
and that it fails to allow for the distinction between fluctuations
and true variations. And, further, it should be noted that the
information derived from such a coefficient is defective in that it
takes into account only the relationship between the son and one
parent; the maternal relation is just as important but this has to be
determined separately. There is no satisfactory method of determining
the relation between children and both parents at the same time.
The coefficient of heredity is, therefore, an abstract numerical value
which gives us a fairly precise estimate as to the probable closeness
of the relation between deviations from the group average of any
character in two groups of relatives. The coefficient of _correlation_
is, in general, a measure of the relation between two different
characteristics or conditions in a single group of individuals. The
method of its determination and its limiting values are the same as
for the coefficient of heredity.
By experience the coefficients of heredity and correlation in general
are found to have the following significance:
0.00- no relation.
0.00-0.10--no significant relation.
0.10-0.25--low; relation slight though appreciable.
0.25-0.50--moderate; relation considerable.
0.50-0.75--high; relation marked.
0.75-0.90--very high; relation very marked.
0.90-1.00--nearly complete.
1.00--complete relation.
One further point remains to be considered, which applies not so much
to coefficients of heredity as to coefficients of correlation in
general, i. e., to the relatedness of two different characters or
series of events in a single group of cases or individuals. This is
that coefficients of correlation may be either positive or negative.
That is, the real limits of the value of the coefficient are plus one
and minus one. The example given above of stature of fathers and sons
gives a positive coefficient. Whenever the deviation from the average
of one group is accompanied in the second group by a deviation in the
same direction, the coefficient is positive. A negative correlation
means that deviation from the average in a given direction in the
first group is accompanied in the second group by a deviation in the
opposite direction. If we imagine that as one measurement increased
above its average a second related measurement decreased below its
average the correlation in such a case would be negative. For
instance, if we measured the relation between the number of berry
pickers employed and the quantity of berries remaining unpicked, in a
number of different fields we would get a negative correlation
coefficient. Some organisms are formed in such a way that increase in
one dimension, such as length, is associated with decrease in another,
such as breadth; measurement of the relatedness of these dimensions
would give a coefficient of correlation that might be very high,
indicating a considerable relation in the deviations, but it would be
negative. In an instance of negative correlation the relation is that
of "the more the fewer." As we shall see presently, a negative
correlation may be just as important and significant as a positive
correlation.
The application of the principles of heredity to our subject of
Eugenics is of such great importance that it is reserved for separate
consideration in the next chapter. We may, therefore, devote the
remainder of this chapter to the consideration of data of another
kind, which are commonly treated by this same method of determining
correlation coefficients between two sets of varying phenomena in
order to determine whether there is any actual relation between them
or not. This will serve to illustrate the use of this method.
We shall turn then to the subject of differential or selective
fertility in human beings and consider its relation to Eugenics. As a
starting point we may take the self-evident statement that a group of
organisms will tend to maintain constant characteristics through
successive generations only when all parts of the group are equally
fertile. If exceptional fertility is associated with the presence or
absence of any characteristic the number of individuals with or
without that trait will either increase or diminish in successive
generations, and the character of the distribution of the group as a
whole will gradually become altered, the average moving in the
direction of the more fertile group. Or if infertility is so
associated, then the average of the whole group moves away from that
condition. Eugenically, then, we should ask whether in human society
there is at present any such association of superfertility or
infertility with desirable or undesirable traits. It is obviously the
aim of Eugenics to bring about an association of a high degree of
fertility with desirable traits and a low degree of fertility with
undesirable characteristics.
First, let us look at certain data gathered relative to the size of
the family in both normal and pathological stocks (Table II). In order
that a stock or family should just maintain its numbers undiminished
through successive generations and under average conditions, at least
four children should be born to each marriage that has any children at
all.
TABLE II
_Fertility in Pathological and Normal Stocks._ (From Pearson)
NATURE OF MARRIAGE. NO. IN
AUTHORITY. (Reproductive period.) FAMILY.