Difficult to get Correct Data.—While it must be said that in many cases no simple form of Mendelian tabulation has been unequivocally established, yet the general behavior of the various inheritable traits in question is so obviously related to the conventional Mendelian course that there seems little reason for doubting that they are at bottom the same. Failure to obtain exact proportions may be attributable in part to the probability that what we loosely regard as a character should in reality be analyzed into more elemental components, and above all to the fact that from the very nature of the conditions under which human records must be obtained, there is considerable chance of inaccuracy or error in such accounts. How many human traits follow Mendelian rules remains largely for future investigators to establish.

We are handicapped at the outset in man by the many difficulties of getting correct data from the genealogies on which we must depend, or in fact of getting any genealogy at all, for in this country at least, most families keep imperfect records of births and deaths and many of the institutions for the various kinds of defectives have little in their records that will help us in following out hereditary conditions. Then in matters of disease we meet with the fact that many former diagnoses were erroneous. In yet other cases, and this is particularly true among mental and moral defectives, we are often not sure of the paternity of a given child. Furthermore, one is likely to be misled by the proportions which may occur in the very limited number of children of any given couple.

Still other difficulties exist. Among these is the fact, for example, that in many cases of defect or susceptibility to disease, a given individual in the stock may have the trait in an expressible and transmissible form, yet it never comes to expression because that individual has been fortunate enough to escape the environmental stimulus which would call it forth. Thus one highly susceptible to tuberculosis might escape infection, or persons hovering on the verge of insanity might never receive the precipitating stimulus which would topple them into actual insanity; yet each would be wrongfully recorded in a genealogy looking to such traits as perfectly normal. Or again if it be a question of intellectual brilliancy as shown by accomplishment in the realm of scholarship, or of worldly affairs, the ones who although possessing them have had no chance to display unusual talents would be tabulated as average whereas in fact they should be recorded as of high rank. That this is particularly likely to happen in the case of women is evident.

A Generalized Presence-Absence Formula for Man.—In man as in lower forms some characters or traits are due presumably to the presence of determiners or to their absence. Likewise, dominance and recessiveness are as much in evidence, for in tracing back pedigrees of various traits we find the same forms of tabulation that obtain for these conditions in plants and lower animals hold good. For typical cases in man let us use a generalized presence-absence formula and the arbitrary symbol A for the presence of the determiner of the character (double in the individual, single in the germ) and a for its absence. Thus AA represents a condition in which similar determiners have been derived from both parents and the individual is duplex as regards the character in question; each mature germ-cell will have the determiner. Aa represents a condition in which the individual has received the determiner from only one parent and is therefore simplex with regard to the character; half of the gametes of such an individual will have the determiner and half will lack it. Lastly, aa represents total absence of the determiner. Such an individual is nulliplex. He or she will not have the determiner represented in any of the gametes, and can not, of course, transmit a trait represented by the determiner.

It is evident that six kinds of gametic matings are possible among individuals representing these various formulæ. These matings are as follows:

MatingsPossible
couplings
gametes		 Product
1. Nulliplex x Nulliplex (aa x aa) == == all nulliplex
2. Nulliplex x Simplex (aa x Aa) == == 50 per cent.
with character
nulliplex and
50 per cent.
with it simplex.
3. Nulliplex x Duplex (aa x AA) == == all with
characters
simplex
4. Simplex x Simplex (Aa x Aa) == == 25 per cent.
with characters
duplex, 50 per
cent. with it
simplex and 25
per cent. with
it nulliplex.
5. Simplex x Duplex (Aa x AA) == == 50 per cent.
with character
duplex and 50
per cent. with
it simplex.
6. Duplex x Duplex (AA x AA) == == all duplex.

Indications of Incomplete Dominance.—While in cases of strict Mendelian dominance it is not possible to distinguish directly the simplex from the duplex condition, as a matter of fact the individual of simplex constitution sometimes has the character represented in the single determiner less perfectly developed than in the corresponding character of duplex origin. In studying defects in man due to the absence of a determiner, where theoretically presence of the determiner (normality) is dominant over its absence in individuals of simplex constitution, one finds it recorded with increasing frequency that such individuals are more or less “intermediate” or are “tainted” with the defect; thus showing that the defect though obscured is not wholly in abeyance. Thus individuals carrying epilepsy or feeble-mindedness which are regarded as recessive traits, while not showing specific feeble-mindedness or epilepsy, may nevertheless apparently show a neuropathic taint in the form of migraine, alcoholism or other lapse from normality. The condition is seemingly more akin in some cases to that found in the offspring of certain red flowers crossbred with white flowers, which though red do not show the same intensity of color as the original red parent. Just as here the single determiner or single “dose” of redness is insufficient to produce the intensity of color that appears when the offspring receive two determiners for red, one from each parent, so in man a single determiner for normality of a specific character is inadequate in some cases to make the individual wholly normal. Or possibly some cases are more of the type of those in which the character in question, for instance the red color of some wheats and corn, may be produced by any one of two or three determiners, the intensity of the characters (red color, e. g.) depending on whether one, two or three determiners are present.

Why After the First Generation Only Half the Children May Show the Dominant Character.—If the trait is a simple dominant one it is clear that it will appear in each generation and always spring from an affected individual. By referring back to our tabulation of possible matings on page 100 where the dominant character is represented by the letter A, this can be seen at a glance. If the trait is present in the duplex condition in one parent and absent from the other, then formula 3 applies; all children will show the trait, but in the simplex form (Aa). If the trait is present in the simplex form in one parent and absent in the other, formula 2 applies. Fifty per cent. of the children will have the character in the simplex form (Aa) which means also an even chance of transmitting it to their offspring; fifty per cent. will not inherit it and will be incapable, furthermore, of transmitting it, since they have become nulliplex (aa). In human genealogies if an individual having an unusual trait which is inherited as a dominant marries a normal person and half of the offspring show the trait (and this is common), this means that the parent manifesting the trait had it represented only in the simplex condition, otherwise all of the children would have shown it. Even though the original ancestor who first developed the condition or structure may have had it in a duplex form, it would after the first mating, if this were with an individual lacking the trait, be represented only in the simplex form (see formula 5) and could never become duplex again unless two individuals both having the character married, and then only in twenty-five per cent. of the offspring (see formula 3). If the trait is a defect all the children showing it, even though marrying normal (nulliplex) individuals, will pass it on again to half their children, but those who do not show it may ordinarily marry with impunity since its non-expression in their make-up means, as far as we know at present, that their germ-plasm has been purged of the defect and that they are therefore nulliplex with reference to it.

Eye-Color in Man.—Of normal characters in man which follow the Mendelian formula perhaps eye-color is the best established. Brown or black eye-color is due to a melanin pigment absent from the blue or gray eye. That is, a brown eye is practically a blue eye plus an additional layer of pigment on the outer surface of the iris. The different shades of brown and the black are due to the relative abundance of this pigment. Gray color and the shades of blue seem to be a modification of an original dark blue, due to structural differences in the fibrous tissues of the iris.

In inheritance brown or black is dominant to blue or gray, or in other words the presence and absence of a pigment P constitutes a pair of allelomorphs. Hence two brown-eyed parents, if P is duplex in both (or duplex in one and simplex in the other) can have only brown-eyed children. Thus,