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.