Our Knowledge of Heredity Derived Along Three Lines.—Our modern conceptions of heredity have been derived mainly from three distinct lines of investigation: First, from the study of embryology, in which the biologist concerns himself with the genesis of the various parts of the individual, and the mechanism of the germs which convey the actual materials from which these parts spring; second, through experimental breeding of plants and animals to compare particular traits or features in successive generations; and third, through the statistical treatment of observations or measurements of a large number of parents and their offspring with reference to a given characteristic in order to determine the average extent of resemblance between parents and children in that particular respect.
The Method of Experimental Breeding.—A tremendous impetus was given to the method of experimental breeding when it was realized that we can itemize many of the parts or traits of an organism into entities which are inherited independently one of another. Such traits, or as we have already termed them, unit-characters, may be not only independently heritable but independently variable as well. The experimental method seeks to isolate and trace through successive generations the separate factors which determine the individual unit-characters of the organism. In this attempt cross-breeding is resorted to. Forms which differ in one or more respects are mated and the progeny studied. Next these offspring are mated with others of their own kind or mated back with the respective parent types. In this way the behavior of a particular character may often be followed and the germinal constitutions of the individuals concerned can be formulated with reference to it. Inasmuch as we shall give much consideration to this method in the chapter on Mendelism we need not consider it further here.
The Statistical Method.—The statistical method seeks to obtain large bodies of facts and to deal with evidence as it appears through mathematical analysis of these facts. The attempt of its followers is to treat quantitatively all biological processes with which it is concerned. Historically Sir Francis Galton was the first to make any considerable application of statistical methods to the problems of heredity and variation. In his attempts to determine the extent of resemblance between relatives of different degree as regards bodily, mental and temperamental traits, he devised new methods of statistical analysis which constitute the basis of modern statistical biology, or biometry as it is termed by its votaries. Professor Karl Pearson in particular has extended and perfected the mathematical methods of this field and stands to-day as perhaps its most representative exponent. The system is in the main based on the calculus of probability. The methods often are highly specialized, requiring the use of higher mathematics, and are therefore only at the command of specially trained workers.
Just as insurance companies can tell us the probable length of human life in a given social group, since although uncertain in any particular case, it is reducible in mass to a predictable constant, so the biometrician with even greater precision because of his improved methods can often, when a large number of cases are concerned, give us the intensity of ancestral influence with reference to particular characters.
For example, it is clear that by measuring a large number of adult human beings one can compute the average height or determine the height which will fit the greatest number. There will be some individuals below and some above it, but the greater the divergence from this standard height the fewer will be the individuals concerned.
Galton compared the heights of 204 normal English parents and their 928 adult offspring. In order to equalize the measurements of men and women he found he had to multiply each female height by 1.08. Then, to take both parents into account when comparing height of parents to that of children he added the height of the father to the proportionately augmented height of the mother and divided by two, thus securing the height of what he termed the “mid-parent.” He found that the mid-parental heights of his subjects ranged from 64.5 to 72.5 inches, and that the general mode was about 68.5 inches. It should be mentioned that the mode, in a given population, represents the group containing the largest number of individuals of one kind; it may or may not coincide with the average. The children of all mid-parents having a given height were measured next and tabulated with reference to these mid-parents. The results of Galton’s measurements may be expressed simply as follows:
| MODE | |||||||||
| Height of mid-parent in inches | 64.5 | 65.5 | 66.5 | 67.5 | 68.5 | 69.5 | 70.5 | 71.5 | 72.5 |
| Average height of offspring | 65.8 | 66.7 | 67.2 | 67.6 | 68.3 | 68.9 | 69.5 | 69.9 | 72.2 |
The Law of Regression.—It is plain from this table that the offspring of short mid-parents tend to be under average or modal height though not so far below as their parents. Likewise children of tall parents tend to be tall but less tall than their parents. This fact illustrates what is known as Galton’s law of regression; namely, that if parents in a given population diverge a certain amount from the mode of the population as a whole, their children, while tending to resemble them, will diverge less from this mode. It is clear that the extent of regression is an inverse measure of the intensity of inheritance from the immediate parents; if the deviation of the offspring from the general mode were nearly as great as that of their parents then the intensity of the inheritance must be high; if but slight—that is, if the offspring regressed nearly to the mode—then the intensity of the inheritance must be ranked as low. In the example in question it must be ranked as relatively high. Computations show that as regards stature the fraction two-thirds represents approximately the amount of resemblance between the two generations where both parents are considered.
Correlations Between Parents and Offspring.—In modern researches the conception of mid-parent and mid-grandparent as utilized by Galton has been largely abandoned. It has been found more convenient as well as more accurate to keep the measurements of the two parents separate and to deal with correlations between fathers and sons, fathers and daughters, mothers and sons, mothers and daughters, brother and brother, etc. Professor Pearson and his pupils have found for a number of characters that the correlation between either parent and children, whether sons or daughters, is relatively close. The correlation between brother and brother, sister and sister, and brother and sister, usually ranges a little higher than the corresponding relation between parents and children.
The Biometrical Method, Statistical, Not Physiological.—While biometry may in certain cases go far toward showing us the average intensity of the inheritance of certain characters it can not replace the method of the experimental breeder which deals with particular characters in individual pedigrees. It must be borne in mind that the biometrical method is a statistical and not a physiological one and that it is applicable only when large numbers of individuals are considered in mass. It is most valuable in cases where we are unable sharply to define single characters, due probably to the concurrent action of a number of independent causes, or where experiment is impossible so that we have to depend solely on numerical data gained by observation.