The philosophy of biology

by James Johnstone

The morphological resemblance between the individuals, either in the natural or the artificial populations, is not absolute. If we take any single character capable of measurement we shall find that it is variable from organism to organism. This important concept of organic variability may be made more clear by a concrete example. Examination of a large number of cockle shells taken from the same restricted part of the sea-shore, and therefore belonging presumably to the same race, will show that the number of the radiating ridges on the shell varies from 19 to 27, and that the ratio of the length to the depth of the shell also varies from 1 : 0.59 to 1 : 0.85. In the former case the most common number of ridges is 23, and in the latter case the most common ratio of length to depth is 1 : 0.71. These are the characteristic or modal values of the morphological characters in question, and the other or less commonly occurring values are distributed symmetrically on either side of the mean or modal value, forming “frequency distributions.”[29] The value of the first character changes by unity in any distribution: obviously there cannot be a fraction of a ridge; and this kind of variation is called “discontinuous.” The value of the second character may change imperceptibly, and it is therefore called “continuous,” a term which is not strictly accurate, since in applying it we assume that the numerical difference between two variates may be less than any finite number, however small. In this assumption we postulate for biology the distinctive mathematical concept of infinite divisibility.

The difference from the mode, or mean, with respect to a definite character in a fully grown organism may be due to the direct action of the environment, in the sense in which we have regarded the environment as influencing the organism; or it may be due to the changes in the organism resulting from the increased or decreased use of some of its parts. The conditions with regard to nutrition, for instance, will not be the same for all the individuals composing a cluster of mussels growing on the sea-bottom. Those in the interior of the cluster do not receive so abundant a supply of sea-water as those on the outside of the cluster; and since the amount of food received by any individual depends on the quantity of water streaming over it in unit time, we shall find that the internally situated individuals will be stunted or dwarfed, while those on the outside will be well grown. Such variations are acquired ones, but even when we allow for them, even if we take care that all the organisms studied live under conditions which are as nearly uniform as possible, there will still be some degree of variability. We cannot be sure that this absolute uniformity ever exists; and the notion of the environment of an organism may be extended so as to include the medium in which embryonic development took place, and even the parental body which formed the environment for the germ-cells from which embryonic development began. But it is probably the case that even with an uniform environment, or with one in which the differences were insignificant, variability would still exist. The variations that might be observed in such a case would belong to two kinds—“fluctuating variations,” and “mutations.”

Fig. 21.

Whether the variations observed in a population of organisms are fluctuations or mutations can only be determined by experiment. Let us suppose that we are dealing with a human population, and that the variation studied is that of stature. Let the men with statures considerably over the mean value marry the women who are correspondingly tall, then it will be found that the children from these unions will, when grown up, exhibit a stature which is greater than that of the whole population, but not so great as that of their parents—that is, regression towards the mean of the whole population takes place.

This is shown in the above diagram, where the lines above and below the mean one indicate the proportion (relative to the value or frequency of the mean) of people of each grade of stature. The latter is proportional to the distance from the mean measured along the vertical line, distances below this line indicating statures below the mean, and vice versa.

If, on the other hand, the men and women with statures considerably below the mean marry, their children will ultimately exhibit statures which are greater than that of their parents, but which are less than that of the whole population. Regression again occurs, but in the opposite direction, and such a case would be represented by the above diagram reversed. Continued selection of this kind would lead to an immediate increase in the mean stature (or the opposite, if the “sign” of the selection were reversed) in one or two generations, but after that the amount of change would be very small, while if the selection were to cease the race produced would slowly revert to the mean, which is characteristic of the whole population from which it arose. It is very important to grasp this result of the practical and theoretical study of heredity—the selection of the ordinary variations shown by a general population leads at once to a small change in the mean value of the character which is selected, but continued selection thereafter makes very little difference to this result, while the race slowly reverts to the value of that from which it arose on the cessation of the selection.

Races which “breed true” do, of course, exist; thus the mean height of the Galloway peasant is greater than that of the Welsh. In the cases of “pure races”—that is, races which breed true with respect to one or more characters, we have to deal with another kind of variation, one which shows no tendency to revert to the value from which it arose. Let the observed variability of stature in a human population be represented by the frequency distribution A, and let the individuals at N—that is, those in which the stature was greater than the mean by the deviation ON—intermarry. It might then happen that the variability of the offspring of these unions would be represented by the frequency distribution B, in which the value of the mean is also that of the stock, at N, from which the race originated. It does not matter now from what variants in B a progeny of the third generation arises: the mean height of the latter will be that of the pure race. In this case the individuals from which the pure race originated (those at N in A) have exhibited a mutation. The stature of the individuals of this new race will continue to exhibit fluctuating variations, and the range of this variability may be as much as that of the stock from which it arose, but the mean stature of the new race will continue to be that of the original mutants.

Fig. 22.