modified by environmental change, replying in terms less easy to predict from knowledge of the nature and amount of the impinging agency. And finally, there are a series of variations, amongst which no doubt are the mutations of de Vries and the disintegrations and recombinations of the unit factors with which Mendel and his followers have worked, in which the external or environmental factor is most remote from the actual result.
Correlated Variation.—Every organism is an individual, its different parts, organs and functions being associated in a degree of intimacy that varies, but that corresponds roughly with the integration of the individual and its place in the ascending scales of animal or vegetable life. One aspect of organic individuality is the correlation of variations, the fact that when one part varies, other parts vary more or less simultaneously. So far, our knowledge of correlation is almost entirely empirical, and the arrangement of the observed facts cannot be brought into exact harmony with our guesses at their causation.
Much correlation is the inevitable result of organic structure. The various parts of a living organism affect each other in adult life and during growth. If, for instance, the testes fail to develop normally, the secretion which they discharge into the blood is abnormal in character and amount, with the result that the characters of the remotest parts of the body are more or less profoundly affected. It is now known that similar internal secretions, or hormones, pass into the blood from every organ and tissue, so reaching and affecting every part of the body. If we reflect on the multitude and complexity of such actions and reactions in operation from the youngest stages to the end of the life of each individual, we cannot be surprised at any correlation. Change in the size of any part or organ, however it may have been produced, must bring with it many others changes, directly or indirectly. A difference in calibre, elasticity or branching of a blood vessel, the smallest variation in a nerve or group of vessel-cells, any anatomical or physiological divergence, is reflected throughout the organism. Much of the character of organisms is due to various symmetries, radial, bilateral, metameric and so forth, and these symmetries arise, partly at least, from the mode of growth by cell division and the marshalling of groups of cells to the places where they are destined to proliferate. Here, again, a variation in the order, nature and number of the divisions, in itself simple, may result in symmetrical or correlated changes in all the progeny of the affected embryonic part.
Every new individual starts life (see Reproduction) as a mass of germinal material derived from one or from two parents, but with a coherent individuality of its own. This individuality is the result of the particular selection of qualities it receives from its parents, a selection that obviously differs in different cases, as, save in the case of “identical twins,” which are supposed to be the product of a single fertilized ovum, no individual pair of brothers, or pair consisting of brother and sister, are alike. We are still ignorant of the causes that determine the associated selection of inherited qualities that go to the making of any individual. Those who have followed up the work of Mendel believe that the qualities of the new individual are a precise selection from and reconstruction of the parental qualities, and that were complete analysis possible, the characters of the new individual could be predicted with chemical accuracy. On other views of inheritance, there would be required for prediction knowledge not only of the immediate parents but of the whole line of ancestry, with the result that prediction could reach only some degree of probability for any single individual and be accurate only for the average of a sufficient number of individuals. But whatever be the theory of the mode of inheritance, or the mechanism by which the germinal plasm of an individual is made up, it is plain that there is correlation between the various qualities of an individual due to the mode of origin of its germ plasm as a selected individual portion of the parental germ plasm.
Observed cases of correlation cover almost every kind of anatomical and physiological fact, and range from simple cases such as the relation between height of body and length of face to such an unexpected nexus as that between, fertility and height in mothers of daughters. The statistical investigation of correlations forms a new branch of biological inquiry, generally termed “Biometrics,” inaugurated by F. Galton and carried on by Karl Pearson and the late W. F. R. Weldon.
We quote from the article “Variation and Selection,” in the tenth edition of this Encyclopaedia, an exposition of the biometric method by Weldon:—
The characters of individual animals or plants depend upon so many complex conditions, most of which are generally unknown to us, that the statements we can make concerning them are of a peculiar kind. We cannot predict with any exactness the characters of a single unborn individual; but if we consider a large number of unborn individuals, we can predict with considerable accuracy the percentage of individuals which will have the mean character proper to their generation, or will differ from that mean character within any assigned limits. So long as we confine our attention to one or two individuals, we fail to detect any order in the occurrence of variations; but when we examine large numbers we find that it is possible to arrange them in an orderly series, which can be easily and simply described. The series into which we can arrange the results of observing phenomena of complex causation, whether exhibited by living organisms or not, have certain properties in common, which are dealt with by the theory of chance. Many of the properties of such series, and the methods of describing them, are dealt with elsewhere (see Probability: Law of Error); and the frequency with which the mean value or any deviation from the mean value of a character occurs in a race of animals or of plants may probably always be expressed in terms of one or other of the series there described. The theory of chance was applied to the study of human variation by Quetelet; but the most important applications of this theory to biological problems are due in the first instance to Francis Galton, who used the theory of correlation in describing the relation between the deviation of one character in an animal body from the mean proper to its race and that of a second character in the same body (correlation as commonly understood), or between deviation of a parent from the mean of its generation and deviation of offspring from the mean of the following generation (inheritance). The conceptions indicated by Galton have been extended and added to by Karl Pearson, who has also developed the theory of chance so as to provide a means of describing many series of complex results in a simpler and more accurate way than was hitherto possible.
The conception of a race of animals or of plants as a group of individuals capable of being arranged in an orderly series with respect to the condition of a particular character enables us to define the “type” of that character proper to the race. Table I. shows the number of female swine which had a given number of “Müller's glands” on the right fore leg, in a sample of 2000 swine observed by Davenport in Chicago. If we take the whole number of glands in the series, and divide this by the whole number of swine, we obtain the mean number of glands per swine. For many purposes this is the most convenient “type” of the series. Two other ways of determining a “type” will be obvious by reference to the diagram, fig. 1, in which the observed results are recorded by the thick continuous line, and the form of Pearson's “generalized probability curve” best fitted to represent them by a dotted line. The ordinate of the dotted curve which contains its “centre of gravity” has, of course, for its abscissa the “mean” number of glands; the maximum ordinate of the curve is, however, at 2.98, or sensibly at 3 glands, showing what Pearson has called the “modal” number of glands, or the number occurring most frequently. The ordinate which divides the area of the dotted curve into two equal areas is the median of Galton; it lies in this case nearly at 3.38 glands. The best simple measure of the frequency of deviations from the mean character is the “standard deviation” or “error of mean square” of the system (see article Probability), in this case equal to 1.68 glands.
Table I.
| Number of Glands. |
Number of Swine. |
| 0 | 15 |
| 1 | 209 |
| 2 | 365 |
| 3 | 482 |
| 4 | 414 |
| 5 | 277 |
| 6 | 134 |
| 7 | 72 |
| 8 | 22 |
| 9 | 8 |
| 10 | 2 |
In cases of nearly symmetrical distribution about the mean, the three “types,” the mean, the median and the mode, may sensibly coincide. For example, in Powis's table of the frequency of statures in male Australian criminals between 40 and 50 years
