Chapter 40

In a paper published in 1862 Sir William Thomson (now Lord Kelvin) first endeavored to show that great limitation had to be put upon the enormous demand for time made by Lyell, Darwin and other biologists. From a consideration [711] of the secular cooling of the earth, as deduced from the increasing temperature in deep mines, he concluded that the entire age of the earth must have been more than twenty and less than forty millions of years, and probably much nearer twenty than forty. His views have been much criticised by other physicists, but in the main they have gained an ever-increasing support in the way of evidence. New mines of greater depth have been bored, and their temperatures have proved that the figures of Lord Kelvin are strikingly near the truth. George Darwin has calculated that the separation of the moon from the earth must have taken place some fifty-six millions of years ago. Geikie has estimated the existence of the solid crust of the earth at the most as a hundred million years. The first appearance of the crust must soon have been succeeded by the formation of the seas, and a long time does not seem to have been required to cool the seas to such a degree that life became possible. It is very probable that life originally commenced in the great seas, and that the forms which are now usually included in the plankton or floating-life included the very first living beings. According to Brooks, life must have existed in this floating condition during long primeval epochs, and evolved nearly all the main branches of the animal and vegetable kingdom [712] before sinking to the bottom of the sea, and later producing the vast number of diverse forms which now adorn the sea and land.

All these evolutions, however, must have been very rapid, especially at the beginning, and together cannot have taken more time than the figures given above.

The agency of the larger streams, and the deposits which they bring into the seas, afford further evidence. The amount of dissolved salts, especially of sodium chloride, has been made the subject of a calculation by Joly, and the amount of lime has been estimated by Eugene Dubois. Joly found fifty-five and Dubois thirty-six millions of years as the probable duration of the age of the rivers, and both figures correspond to the above dates as closely as might be expected from the discussion of evidence so very incomplete and limited.

All in all it seems evident that the duration of life does not comply with the demands of the conception of very slow and continuous evolution. Now it is easily seen, that the idea of successive mutations is quite independent of this difficulty. Even assuming that some thousands of characters must have been acquired in order to produce the higher animals and plants of the present time, no valid objection is raised. The demands of the biologists and the results of [713] the physicists are harmonized on the ground of the theory of mutation.

The steps may be surmised to have never been essentially larger than in the mutations now going on under our eyes, and some thousands of them may be estimated as sufficient to account for the entire organization of the higher forms. Granting between twenty and forty millions of years since the beginning of life, the intervals between two successive mutations may have been centuries and even thousands of years. As yet there has been no objection cited against this assumption, and hence we see that the lack of harmony between the demands of biologists and the results of the physicists disappears in the light of the theory of mutation.

Summing up the results of this discussion, we may justifiably assert that the conclusions derived from the observations and experiments made with evening-primroses and other plants in the main agree satisfactorily with the inferences drawn from paleontologic, geologic and systematic evidence. Obviously these experiments are wonderfully supported by the whole of our knowledge concerning evolution. For this reason the laws discovered in the experimental garden may be considered of great importance, and they may guide us in our further inquiries. Without doubt many minor [714] points are in need of correction and elaboration, but such improvements of our knowledge will gradually increase our means of discovering new instances and, new proofs.

The conception of mutation periods producing swarms of species from time to time, among which only a few have a chance of survival, promises to become the basis for speculative pedigree-diagrams, as well as for experimental investigations.

[715]

LECTURE XXV

GENERAL LAWS OF FLUCTUATION

The principle of unit-characters and of elementary species leads at once to the recognition of two kinds of variability. The changes of wider amplitude consist of the acquisition of new units, or the loss of already existing ones. The lesser variations are due to the degree of activity of the units themselves.

Facts illustrative of these distinctions were almost wholly lacking at the time of the first publication of Darwin's theories. It was a bold conception to point out the necessity for such distinction on purely theoretical grounds. Of course some sports were well known and fluctuations were evident, but no exact analysis of the details was possible, a fact that was of great importance in the demonstration of the theory of descent. The lack of more definite knowledge upon this matter was keenly felt by Darwin, [716] and exercised much influence upon his views at various times.

Quetelet's famous discovery of the law of fluctuating variability changed the entire situation and cleared up many difficulties. While a clear conception of fluctuations was thus gained, mutations were excluded from consideration, being considered as very rare, or non-existent. They seemed wholly superfluous for the theory of descent, and very little importance was attached to their study. Current scientific belief in the matter has changed only in recent years. Mendel's law of varietal hybrids is based upon the principle of unit-characters, and the validity of this conception has thus been brought home to many investigators.

A study of fluctuating or individual variability, as it was formerly called, is now carried on chiefly by mathematical methods. It is not my purpose to go into details, as it would require a separate course of lectures. I shall consider the limits between fluctuation and mutation only, and attempt to set forth an adequate idea of the principles of the first as far as they touch these limits. The mathematical treatment of the facts is no doubt of very great value, but the violent discussions now going on between mathematicians such as Pearson, Kapteyn and others should warn biologists to abstain [717] from the use of methods which are not necessary for the furtherance of experimental work.

Fortunately, Quetelet's law is a very clear and simple one, and quite sufficient for our considerations. It claims that for biologic phenomena the deviations from the average comply with the same laws as the deviations from the average in any other case, if ruled by chance only. The meaning of this assertion will become clear by a further discussion of the facts. First of all, fluctuating variability is an almost universal phenomenon. Every organ and every quality may exhibit it. Some are very variable, while others seem quite constant. Shape and size vary almost indefinitely, and the chemical composition is subject to the same law, as is well known for the amount of sugar in sugar-beets. Numbers are of course less liable to changes, but the numbers of the rays of umbels, or ray-florets in the composites, of pairs of blades in pinnate leaves, and even of stamens and carpels are known to be often exceedingly variable. The smaller numbers however, are more constant, and deviations from the quinate structure of flowers are rare. Complicated structures are generally capable of only slight deviations.

From a broad point of view, fluctuating variability [718] falls under two heads. They obey quite the same laws and are therefore easily confused, but with respect to questions of heredity they should be carefully separated. They are designated by the terms individual and partial fluctuation. Individual variability indicates the differences between individuals, while partial variability is limited to the deviations shown by the parts of one organism from the average structure. The same qualities in some cases vary individually and in others partially. Even stature, which is as markedly individual for annual and biennial plants as it is for man, becomes partially variant in the case of perennial herbs with numbers of stems. Often a character is only developed once in the whole course of evolution, as for instance, the degree of connation of the seed-leaves in tricotyls and in numerous cases it is impossible to tell whether a character is individual or partial. Consequently such minute details are generally considered to have no real importance for the hereditary transmission of the character under discussion.

Fluctuations are observed to take place only in two directions. The quality may increase or decrease, but is not seen to vary in any other way. This rule is now widely established by numerous investigations, and is fundamental to [719] the whole method of statistical investigation. It is equally important for the discussion of the contrast between fluctuations and mutations, and for the appreciation of their part in the general progress of organization. Mutations are going on in all directions, producing, if they are progressive, something quite new every time. Fluctuations are limited to increase and decrease of what is already available. They may produce plants with higher stems, more petals in the flowers, larger and more palatable fruits, but obviously the first petal and the first berry, cannot have originated by the simple increase of some older quality. Intermediates may be found, and they may mark the limit, but the demonstration of the absence of a limit is quite another question. It would require the two extremes to be shown to belong to one unit, complying with the simple law of Quetelet.

Nourishment is the potent factor of fluctuating variability. Of course in thousands of cases our knowledge is not sufficient to allow us to analyze this relation, and a number of phases of the phenomenon have been discovered only quite recently. But the fact itself is thoroughly manifest, and its appreciation is as old as horticultural science. Knight, who lived at the beginning of the last century, has laid great stress upon it, and it has since influenced practice in a [720] large measure. Moreover, Knight pointed out more than once that it is the amount of nourishment, not the quality of the various factors, that exercises the determinative influence. Nourishment is to be taken in the widest sense of the word, including all favorable and injurious elements. Light and temperature, soil and space, water and salts are equally active, and it is the harmonious cooperation of them all that rules growth.

We treated this important question at some length, when dealing with the anomalies of the opium-poppies, consisting of the conversion of stamens into supernumerary pistils. The dependency upon external influences which this change exhibited is quite the same as that shown by fluctuating variability at large. We inquired into the influence of good and bad soil, of sunlight and moisture and of other concurrent factors. Especial emphasis was laid upon the great differences to which the various individuals of the same lot may be exposed, if moisture and manure differ on different portions of the same bed in a way unavoidable even by the most careful preparation. Some seeds germinate on moist and rich spots, while their neighbors are impeded by local dryness, or by distance from manure. Some come to light on a sunny day, and increase their first leaves rapidly, while on [721] the following day the weather may be unfavorable and greatly retard growth. The individual differences seem to be due, at least in a very great measure, to such apparent trifles.

On the other hand partial differences are often manifestly due to similar causes. Considering the various stems of plants, which multiply themselves by runners or by buds on the roots, the assertion is in no need of further proof. The same holds good for all cases of artificial multiplication by cuttings, or by other vegetative methods. But even if we limit ourselves to the leaves of a single tree, or the branches of a shrub, or the flowers on a plant, the same rule prevails. The development of the leaves is dependent on their position, whether inserted on strong or weak branches, exposed to more or less light, or nourished by strong or weak roots. The vigor of the axillary buds and of the branches which they may produce is dependent upon the growth and activity of the leaves to which the buds are axillary.

This dependency on local nutrition leads to the general law of periodicity, which, broadly speaking, governs the occurrence of the fluctuating deviations of the organs. This law of periodicity involves the general principle that every axis, as a rule, increases in strength when [722] growing, but sooner or later reaches a maximum and may afterwards decrease.

This periodic augmentation and declination is often boldly manifest, though in other cases it may be hidden by the effect of alternate influences. Pinnate leaves generally have their lower blades smaller than the upper ones, the longest being seen sometimes near the apex and sometimes at a distance from it. Branches bearing their leaves in two rows often afford quite as obvious examples, and shoots in general comply with the same rule. Germinating plants are very easy of observation on this point. When they are very weak they produce only small leaves. But their strength gradually increases and the subsequent organs reach fuller dimensions until the maximum is attained. The phenomenon is so common that its importance is usually overlooked. It should be considered as only one instance of a rule, which holds good for all stems and all branches, and which is everywhere dependent on the relation of growth to nutrition.

The rule of periodicity not only affects the size of the organs, but also their number, whenever these are largely variable. Umbellate plants have numerous rays on the umbels of strong stems, but the number is seen to decrease and to become very small on the weakest lateral [723] branches. The same holds good for the number of ray-florets in the flower-heads of the composites, even for the number of stigmas on the ovaries of the poppies, which on weak branches may be reduced to as few as three or four. Many other instances could be given.

One of the best authenticated cases is the dependency of partial fluctuation on the season and on the weather. Flowers decline when the season comes to an end, become smaller and less brightly colored. The number of ray-florets in the flower-heads is seen to decrease towards the fall. Extremes become rarer, and often the deviations from the average seem nearly to disappear. Double flowers comply with this rule very closely, and many other cases will easily occur to any student of nature.

Of course, the relation to nourishment is different for individual and partial fluctuations. Concerning the first, the period of development of the germ within the seed is decisive. Even the sexual cells may be in widely different conditions at the moment of fusion, and perhaps this state of the sexual cells includes the whole matter of the decision for the average characters of the new individual. Partial fluctuation commences as soon as the leaves and buds begin to form, and all later changes in nutrition can only cause partial differences. All leaves, [724] buds, branches, and flowers must come under the influence of external conditions during the juvenile period, and so are liable to attain a development determined in part by the action of these factors.

Before leaving these general considerations, we must direct our attention to the question of utility. Obviously, fluctuating variability is a very useful contrivance, in many cases at least. It appears all the more so, as its relation to nutrition becomes manifest. Here two aspects are intimately combined. More nutrient matter produces larger leaves and these are in their turn more fit to profit by the abundance of nourishment. So it is with the number of flowers and flower-groups, and even with the numbers of their constituent organs. Better nourishment produces more of them, and thereby makes the plant adequate to make a fuller use of the available nutrient substances. Without fluctuation such an adjustment would hardly be possible, and from all our notions of usefulness in nature, we therefore must recognize the efficiency of this form of variability.

In other respects the fluctuations often strike us as quite useless or even as injurious. The numbers of stamens, or of carpels are dependent on nutrition, but their fluctuation is not known to have any attraction for the visiting insects.

[725] If the deviations become greater, they might even become detrimental. The flowers of the St. Johnswort, or _Hypericum perforatum_, usually have five petals, but the number varies from three to eight or more. Bees could hardly be misled by such deviations. The carpels of buttercups and columbines, the cells in the capsules of cotton and many other plants are variable in number. The number of seeds is thereby regulated in accordance with the available nourishment, but whether any other useful purpose is served, remains an open question. Variations in the honey-guides or in the pattern of color-designs might easily become injurious by deceiving insects, and such instances as the great variability of the spots on the corolla of some cultivated species of monkey-flowers, for instance, the _Mimulus quinquevulnerus_, could hardly be expected to occur in wild plants. For here the dark brown spots vary between nearly complete deficiency up to such predominancy as almost to hide the pale yellow ground-color.

After this hasty survey of the causes of fluctuating variability, we now come to a discussion of Quetelet's law. It asserts that the deviations from the average obey the law of probability. They behave as if they were dependent on chance only.

Everyone knows that the law of Quetelet can [726] be demonstrated the most readily by placing a sufficient number of adult men in a row, arranging them according to their size. The line passing over their heads proves to be identical with that given by the law of probability. Quite in the same way, stems and branches, leaves and petals and even fruits can be arranged, and they will in the main exhibit the same line of variability. Such groups are very striking, and at the first glance show that the large majority of the specimens deviate from the mean only to a very small extent. Wider deviations are far more rare, and their number lessens, the greater the deviation, as is shown by the curvature of the line. It is almost straight and horizontal in the middle portion, while at the ends it rapidly declines, going sharply downward at one extreme and upward at the other.

It is obvious however, that in these groups the leaves and other organs could conveniently be replaced by simple lines, indicating their size. The result would be quite the same, and the lines could be placed at arbitrary, but equal distances. Or the sizes could be expressed by figures, the compliance of which with the general law could be demonstrated by simple methods of calculation. In this manner the variability of different organs can easily be compared. Another method of demonstration consists in [727] grouping the deviations into previously fixed divisions. For this purpose the variations are measured by standard units, and all the instances that fall between two limits are considered to constitute one group. Seeds and small fruits, berries and many other organs may conveniently be dealt with in this way. As an example we take ordinary beans and select them according to their size. This can be done in different ways. On a small piece of board a long wedge-shaped slit is made, into which seeds are pushed as far as possible. The margin of the wedge is calibrated in such a manner that the figures indicate the width of the wedge at the corresponding place. By this device the figure up to which a bean is pushed at once shows its length. Fractions of millimeters are neglected, and the beans, after having been measured, are thrown into cylindrical glasses of the same width, each glass receiving only beans of equal length. It is clear that by this method the height to which beans fill the glasses is approximately a measure of their number. If now the glasses are put in a row in the proper sequence, they at once exhibit the shape of a line which corresponds to the law of chance. In this case however, the line is drawn in a different manner from the first. It is to be pointed out that the glasses may be replaced by lines indicating [728] the height of their contents, and that, in order to reach a more easy and correct statement, the length of the lines may simply be made proportionate to the number of the beans in each glass. If such lines are erected on a common base and at equal distances, the line which unites their upper ends will be the expression of the fluctuating variability of the character under discussion.

The same inquiry may be made with other seeds, with fruits, or other organs. It is quite superfluous to arrange the objects themselves, and it is sufficient to arrange the figures indicating their value. In order to do this a basal line is divided into equal parts, the demarcations corresponding to the standard-units chosen for the test. The observed values are then written above this line, each finding its place between the two demarcations, which include its value. It is very interesting and stimulating to construct such a group. The first figures may fall here and there, but very soon the vertical rows on the middle part of the basal line begin to increase. Sometimes ten or twenty measurements will suffice to make the line of chance appear, but often indentations will remain. With the increasing number of the observations the irregularities gradually [729] disappear, and the line becomes smoother and more uniformly curved.

This method of arranging the figures directly on a basal line is very convenient, whenever observations are made in the field or garden. Very few instances need be recorded to obtain an appreciation of the mean value, and to show what may be expected from a continuance of the test. The method is so simple and so striking, and so wholly independent of any mathematical development that it should be applied in all cases in which it is desired to ascertain the average value of any organ, and the measure of the attendant deviations.

I cite an instance, secured by counting the ray-florets on the flower-heads of the corn-marigold or _Chrysanthemum segetum_. It was that, by which I was enabled to select the plant, which afterwards showed the first signs of a double head. I noted them in this way;

47 47 52 41 54 68 44 50 62 75 36 45 58 65 72 __ 99

Of course the figures might be replaced in this work by equidistant dots or by lines, but experience teaches that the chance of making mistakes is noticeably lessened by writing down [730] the figures themselves. Whenever decimals are made use of it is obviously the best plan to keep the figures themselves. For afterwards it often becomes necessary to arrange them according to a somewhat different standard.