The Social Direction of Evolution: An Outline of the Science of Eugenics

by William E. Kellicott

Fig. 4.—Model to illustrate the law of probability or "chance." Description in the text. A, Peas held in container at top of board. B, Peas after having fallen through the obstructions into the vertical compartments below. The curve connecting the tops of the columns of peas is the normal probability curve.

With this model we may illustrate many other essential facts about variability which must be borne in mind when approaching the problems of Eugenics. Before we allow the peas to fall we know quite definitely what the general distribution of them all will be, but we do not know at all the future position of any single pea. Of this we can speak only in terms of probability; the chances are very high that it will fall in one of the three middle compartments, very low that it will be in one of the extreme compartments. But the chances are equal, whatever they are, that it will fall above or below the average or middle position. We see then that in any group there are many more individuals near the average, i. e., mediocre, than there are in the classes removed from the average and the farther the remove of a class from the average the smaller the number of individuals in that class. Yet all the individuals belong to the same whole group. This leads to the very important fact that an individual may belong to a group without representing it fairly. The average individuals are the most representative. But in order to get a correct idea of the whole group we must know, first, to what extent deviations occur in each direction, above and below the group average, and, second, the average amount by which each individual of the group deviates from this group average. That is, we must know the amount of variability as well as the extent of the greatest divergence from the average. The best measure of the amount of variability exhibited by any group of objects or organisms is not the simple average or mean of all the individual deviations from the average of the group; it is the square root of the mean squared deviations from the group average. This is called the index of variability or "standard deviation." In order to make possible the comparison of the variabilities of characteristics measured in unlike units, such as weight and stature, this index must be converted into an equivalent abstract quantity. This is done by reducing the index of variability to per cents of the group average, giving what is called the coefficient of variability. Thus, for example, in stature the index of variability (standard deviation) of certain classes of men is approximately 2.7 inches; that is, in a large group of men the amount of individual variation from the average height of 69 inches amounts to 2.7 inches. This gives an abstract coefficient of about 4.0 per cent, for 2.7 equals 3.9 per cent of 69. Similarly the index of variability of the weight of a group of university students has been found to be about 16.5 pounds; the average weight is about 153 pounds, and the coefficient of variability is therefore about 10.8 per cent (16.5 equals 10.78 per cent of 153). Although pounds and inches may not be compared, these two abstract coefficients may be, and we may say that men are more than twice as variable in weight as in stature.

Turning now to variation of the second type we find what are ordinarily called mutations, or differences quite properly termed variations, in a strict sense, as distinguished from the preceding fluctuations or variability phenomena. Mutations or variations are abrupt changes of the average or type condition to a new condition or value which then becomes a new center of fluctuating variability. The difference between variability and variation may be illustrated through an analogy suggested by Galton (Fig. 5). A polygonal plinth, or better a polyhedron, resting upon one face is easily tipped slightly back and forth, but after slight disturbance it always returns to its first position of stable equilibrium. Each face of the plinth or polyhedron represents an organismal characteristic; these slight backward and forward movements represent fluctuations, always centering about the average condition. An unusually hard push sends the plinth over upon another face in which it has a new position of stability; this represents true variation or mutation. In this new position it is again stable, may again be rocked back and forth showing fluctuations about its new average position.

Fig. 5.—Plinth to illustrate the difference between variability (fluctuation) and variation (mutation).

The essential difference between true variation and fluctuation or variability of an extreme nature, is with reference to the inheritance of such divergence. In the second generation the offspring of extreme variates or fluctuations have not the same average as their own parents but an average much nearer that of the whole group to which their parents belonged; the average stature of the children of unusually short or tall parents is respectively greater or less than that of their own parents—that is, is nearer the average of the whole group of parents, provided the shortness or tallness of the parents is a fluctuation. When the shortness or tallness is a true variation or mutational character, offspring have approximately the same average stature as their immediate parents, although the children of course show fluctuation in height so that some are slightly above and others slightly below the parental height.

Mutations may occur through the addition or the subtraction of single characters of the simple or unit type. Such are the variations from brown or blue eyes to albino, five fingers to six, and the like. These are the familiar "sports" of the horticulturalist and breeder. They are of the greatest value in evolution, for it seems quite likely that it is only through the permanent racial fixation of these mutations that permanent changes in the characters of a breed may be effected, i. e., evolution occurs primarily through mutation.

In connection with the general subject of variation we should mention briefly certain aspects of the recent work of Johannsen and Jennings, showing that many organic specific groups or "species," whose characters, when measured accurately give what is called a normal variability curve similar to that of stature illustrated in Fig. 3, are not really homogeneous groups of fluctuating individuals as the curves would indicate superficially, but that each gross group or species is actually composed of a blend of a number of smaller groups, each with its own average and fluctuating variability. It is only when these are taken all together as a lump that they fuse into a single and apparently simple curve.