Very many discontinuous variations are meristic ; the change in the number of rays in a fish's fin or of vertebrae in its vertebral column is necessarily carried out by steps between which there are no conceivable intermediates. But similar discontinuities may occur in characters which might be expected to vary continuously; there is, for example, no series of intermediates connecting the black coat of a melanic jaguar with the normal spotted pattern. It has long been known, from observation of domesticated animals, that such sports appear sporadically without obvious cause, and that they make their appearance fully developed. Precision has been added to these old observations by long-continued breeding experiments, notably those carried out with the fruit fly Droso phila. These have shown that discontinuous variations, mutations (q.v.), arise continuously, that the same mutation appears inde pendently again and again and does so at a uniform rate, differing from that at which other mutations occur. The number of ob served mutations in this form is very large ; it already exceeds 400.
These mutations, although they affect most profoundly some one structure, actually alter many apparently unassociated parts of the animal. They may produce such gross modifications of structure that the resulting mutant is non-viable and dies at some definite point of the life history, or they may have so small an effect that only long experience will enable an observer to recognize their existence. They may even produce no visible effect in indi viduals bred under normal conditions.
There are certain experiments which seem to show that the rate of appearance of mutations may be greatly increased by exposing the animals to X-rays.
Some of the mutations which appear in the species Drosophila melanogaster, which has been most fully investigated, are repeated in exactly the same form in the other species of the genus, and analogy with plants, and the character of the variations which exist in other groups of animals, such as the rodents and land snails, suggest that similar mutations must be capable of arising in all the species included within large groups such as families.
Furthermore, the same part of the animal may, in some cases, be caused to vary in the same direction by a number of inde pendent mutations, whose effects may be cumulative when they are present together in a single individual. In such a case the extreme conditions may be connected by a series of intermediates, each a distinct step, which may be so small that an appearance of continuous variation may exist.
It is, therefore, most difficult to decide whether any apparently continuous variation is truly such, or whether it is not more justly interpreted as the result of a large series of small steps. This difficulty is increased by the fact that the external conditions under which its development has taken place affect to some degree the character of every adult animal. That modifications in struc ture through use do take place is obvious. The highly-developed arm muscles of a blacksmith clearly owe their size to continuous exercise. But the influence of the environment may show itself in much more subtle ways. A single egg of a bee may develop either into a worker or a queen, castes which exhibit great morpho logical differences, according to the food that it is given and the size of the cell in which it is housed. The brine shrimp Artemia
assumes very different forms if it is grown in water of different salinities.
The effect of such variations, which are induced by the action of the environment during the life of a single animal, will be to hide the clear-cut steps which theoretically exist in a series of variates differing by small mutations.
It is, therefore, impossible by mere inspection to decide whether or not an apparent case of continuous variations is truly such. It may represent congenital variation or it may merely depend on "acquired" variations. As the greater part of the variability which is observable in a population appears continuous, it is neces sary to have methods which will allow its character to be recorded, so that it may be studied.
As the problem is one which is concerned with a population, this method must be statistical. The first step in any such investiga tion is to determine the character, the variation of which is to be recorded, and to decide how it is to be expressed in numerical terns. In such a case as the height of man, or the length of any of his parts, measurements in any units with a determined accuracy are possible, but if the character be a mental one, or is concerned with colour, the only possible procedure is to break up the whole range of variation into a series of arbitrary stages. The masses of figures wnich result from the measurement of a great number of individuals may then be arrayed by grouping together all those individuals who, in respect to the character under investigation, fall between two definite numerical points. If, now, the numbers of individuals within each of these groups be entered on a graph, whose coordinates are the number of individuals and the magni tude of the variant character, it will usually be found that these points lie in a curve, which has a maximum height at some definite value and reaches the base line at values which represent the ex treme variations. Such a curve usually conforms to a definite shape, which can be expressed by an equation, and the whole of whose qualities can be determined from two expressions. The character of this curve, that of normal variation, implies that the variations which it records are due to chance events. If they be constrained in any way, either by external circumstances or by a tendency to division of the population into groups, the curve will be distorted and give evidence of the condition.
The statistical study of animal populations has become an inde pendent discipline, biometry, of great value in the investigation, not only of such problems as those which are presented by fishery investigations, but also in relation to the government of human population.
The variations which occur within the limits of a species, defined as a mutually fertile group of animals, are of very great impor tance because they provide the raw material on which evolution is based. Obly such variations as are heritable, that is, can be handed on from parent to offspring, can be of any value in bringing about the divergencies in structure on which evolution depends.
It is thus necessary to consider individually the possibility, and the mode, of inheritance of the three classes of variations which we have recognized.