On this principle two further considerations are to be discussed. First the structure of the [701] fan itself, and secondly the combination of succeeding fans into a common genealogic tree.

The composition of the fan as a whole includes more than is directly indicated by the facts concerning the birth of new species. They arise in considerable quantities, and each of them in large numbers of individuals, either in the same or in succeeding years. This multiple origin must obviously have the effect of strengthening the new types, and of heightening their chances in the struggle for life. Arising in a single specimen they would have little chance of success, since in the field among thousands of seeds perhaps one only survives and attains complete development. Thousands or at least hundreds of mutated seeds are thus required to produce one mutated individual, and then, how small are its chances of surviving! The mutations proceed in all directions, as I have pointed out in a former lecture. Some are useful, others might become so if the circumstances were accidentally changed in definite directions, or if a migration from the original locality might take place. Many others are without any real worth, or even injurious. Harmless or even slightly useless ones have been seen to maintain themselves in the field during the seventeen years of my research, as proved by Oenothera laevifolia and Oenothera [702] brevistylis. Most of the others quickly disappear.

This failure of a large part of the productions of nature deserves to be considered at some length. It may be elevated to a principle, and may be made use of to explain many difficult points of the theory of descent. If, in order to secure one good novelty, nature must produce ten or twenty or perhaps more bad ones at the same time, the possibility of improvements coming by pure chance must be granted at once. All hypotheses concerning the direct causes of adaptation at once become superfluous, and the great principle enunciated by Darwin once more reigns supreme.

In this way too, the mutation-period of the evening-primrose is to be considered as a prototype. Assuming it as such provisionally, it may aid us in arranging the facts of descent so as to allow of a deeper insight and a closer scrutiny. All swarms of elementary species are the remains of far larger initial groups. All species containing only a few subspecies may be supposed to have thrown off at the outset far more numerous lateral branches, out of which however, the greater part have been lost, being unfit for the surrounding conditions. It is the principle of the struggle for life between elementary species, followed by the survival of the [703] fittest, the law of the selection of species, which we have already laid stress upon more than once.

Our second consideration is also based upon the frequent repetition of the several mutations. Obviously a common cause must prevail. The faculty of producing nanella or lata remains the same through all the years. This faculty must be one and the same for all the hundreds of mutative productions of the same form. When and how did it originate? At the outset it must have been produced in a latent condition, and even yet it must be assumed to be continuously present in this state, and only to become active at distant intervals. But it is manifest that the original production of the characters of Oenothera gigas was a phenomenon of far greater importance than the subsequent accidental transition of this quality into the active state. Hence the conclusion that at the beginning of each series of analogous mutations there must have been one greater and more intrinsic mutation, which opened the possibility to all its successors. This was the origination of the new character itself, and it is easily seen that this incipient change is to be considered as the real one. All others are only its visible expressions.

Considering the mutative period of our evening-primrose [704] as one unit-stride section in the great genealogic tree, this period includes two nearly related, but not identical changes. One is the production of new specific characters in the latent condition, and the other is the bringing of them to light and putting them into active existence. These two main factors are consequently to be assumed in all hypothetic conceptions of previous mutative periods.

Are all mutations to be considered as limited to such periods? Of course not. Stray mutations may occur as well. Our knowledge concerning this point is inadequate for any definite statement. Swarms of variable species are easily recognized, if the remnants are not too few. But if only one or two new species have survived, how can we tell whether they have originated-alone or together with others. This difficulty is still more pronounced in regard to paleontologic facts, as the remains of geologic swarms are often found, but the absence of numerous mutations can hardly be proved in any case.

I have more than once found occasion to lay stress on the importance of a distinction between progressive and retrograde mutations in previous lectures. All improvement is, of course, by the first of these modes of evolution, but apparent losses of organs or qualities are [705] perhaps of still more universal occurrence. Progression and regression are seen to go hand in hand everywhere. No large group and probably even no genus or large species has been evolved without the joint agency of these two great principles. In the mutation-period of the evening-primroses the observed facts give direct support to this conclusion, since some of the new species proved, on closer inspection, to be retrograde varieties, while others manifestly owe their origin to progressive steps. Such steps may be small and in a wrong direction; notwithstanding this they may be due to the acquisition of a wholly new character and therefore belong to the process of progression at large.

Between them however, there is a definite contrast, which possibly is in intimate connection with the question of periodic and stray mutations. Obviously each progressive change is dependent upon the production of a new character, for whenever this is lacking, no such mutation is possible. Retrograde changes, on the other hand, do not require such elaborate preliminary work. Each character may be converted into the latent condition, and for all we know, a special preparation for this purpose is not at all necessary. It is readily granted that such special preparation may occur, because the [706] great numbers in which our dwarf variety of the Oenothera are yearly produced are suggestive of such a condition. On the other hand, the laevifolia and brevistylis mutations have not been repeated, at least not in a visible way.

From this discussion we may infer that it is quite possible that a large part of the progressive changes, and a smaller part of the retrograde mutations, are combined into groups, owing their origin to common external agencies. The periods in which such groups occur would constitute the mutative periods. Besides them the majority of the retrograde changes and some progressive steps might occur separately, each being due to some special cause. Degressive mutations, or those which arise by the return of latent qualities to activity, would of course belong with the latter group.

This assumption of a stray and isolated production of varieties is to a large degree supported by experience in horticulture. Here there are no real swarms of mutations. Sudden leaps in variability are not rare, but then they are due to hybridization. Apart from this mixture of characters, varieties as a rule appear separately, often with intervals of dozens of years, and without the least suggestion of a common cause. It is quite superfluous to go into details, as we have dealt with the horticultural [707] mutations at sufficient length on a previous occasion. Only the instance of the peloric toadflax might be recalled here, because the historic and geographic evidence, combined with the results of our pedigree-experiment, plainly show that peloric mutations are quite independent of any periodic condition. They may occur anywhere in the wide range of the toad-flax, and the capacity of repeatedly producing them has lasted some centuries at least, and is perhaps even as old as the species itself.

Leaving aside such stray mutations, we may now consider the probable constitution of the great lines of the genealogic tree of the evening primroses, and of the whole vegetable and animal kingdom at large. The idea of drawing up a pedigree for the chief groups of living organisms is originally due to Haeckel, who used this graphic method to support the Darwinian theory of descent. Of course, Haeckel's genealogic trees are of a purely hypothetic nature, and have no other purpose than to convey a clear conception of the notion of descent, and of the great lines of evolution at large. Obviously all details are subject to doubt, and many have accordingly been changed by his successors. These changes may be considered as partial improvements, and the somewhat picturesque form of Haeckel's pedigree might well be replaced by [708] more simple plans. But the changes have by no means removed the doubts, nor have they been able to supplant the general impression of distinct groups, united by broad lines. This feature is very essential, and it is easily seen to correspond with the conception of swarms, as we have deduced it from the study of the lesser groups.

Genealogic trees are the result of comparative studies; they are far removed from the results of experimental inquiry concerning the origin of species. What are the links which bind them together? Obviously they must be sought in the mutative periods, which have immediately preceded the present one. In the case of the evening-primrose the systematic arrangement of the allied species readily guides us in the delimitations of such periods. For manifestly the species of the large genus of _Oenothera_ are grouped in swarms, the youngest or most recent of which we have under observation. Its immediate predecessor must have been the subgenus _Onagra_, which is considered by some authors as consisting of a single systematic species, _Oenothera biennis_. Its multifarious forms point to a common origin, not only morphologically but also historically. Following this line backward or downward we reach another apparent mutation-period, which includes the origin of [709] the group called _Oenothera_, with a large number of species of the same general type as the _Onagra-forms, Still farther downward comes the old genus _Oenothera_ itself, with numerous subgenera diverging in sundry characters and directions.

Proceeding still farther we might easily construct a main stem with numerous succeeding fans of lateral branches, and thus reach, from our new empirical point of view, the theoretical conclusion already formulated.

Paleontologic facts readily agree with this conception. The swarms of species and varieties are found to succeed one another like so many stories. The same images are repeated, and the single stories seem to be connected by the main stems, which in each tier produce the whole number of allied forms. Only a few prevailing lines are prolonged through numerous geologic periods; the vast majority of the lateral branches are limited each to its own storey. It is simply the extension of the pedigree of the evening-primroses backward through ages, with the same construction and the same leading features. There can be no doubt that we are quite justified in assuming that evolution has followed the same general laws through the whole duration of life on earth. Only a moment of their lifetime is disclosed to us, but it [710] is quite sufficient to enable us to discern the laws and to conjecture the outlines of the whole scheme of evolution.

A grave objection which has, often, and from the very outset, been urged against Darwin's conception of very slow and nearly imperceptible changes, is the enormously long time required. If evolution does not proceed any faster than what we can see at present, and if the process must be assumed to have gone on in the same slow manner always, thousands of millions of years would have been needed to develop the higher types of animals and plants from their earliest ancestors.

Now it is not at all probable that the duration of life on earth includes such an incredibly long time. Quite on the contrary the lifetime of the earth seems to be limited to a few millions of years. The researches of Lord Kelvin and other eminent physicists seem to leave no doubt on this point. Of course all estimates of this kind are only vague and approximate, but for our present purposes they may be considered as sufficiently exact.

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.

Uniting the heads of the vertical rows of figures by a line, the form corresponding to Quetelet's law is easily seen. In the main it is always the same as the line shown by the measurements of beans and seeds. It proves a dense crowding of the single instances around the average, and on both sides of the mass of the observations, a few wide deviations. These become more rare in proportion to the amount of their divergency. On both sides of the average the line begins by falling very rapidly, but then bends slowly so as to assume a nearly horizontal direction. It reaches the basal line only beyond the extreme instances.

It is quite evident that all qualities, which can be expressed by figures, may be treated in this way. First, of all the organs occurring in varying numbers, as for instance the ray-florets of composites, the rays of umbels, the blades of pinnate and palmate leaves, the numbers of veins, etc., are easily shown to comply with the same general rule. Likewise the amount of chemical substances can be expressed in percentage numbers, as is done on a large [731] scale with sugar in beets and sugar-cane, with starch in potatoes and in other instances. These figures are also found to follow the same law.

All qualities which are seen to increase and to decrease may be dealt with in the same manner, if a standard unit for their measurement can be fixed. Even the colors of flowers may not escape our inquiry.

If we now compare the lines, compiled from the most divergent cases, they will be found to exhibit the same features in the main. Ordinarily the curve is symmetrical, the line sloping down on both sides after the same manner. But it is not at all rare that the inclination is steep on one side and gradual on the other. This is noticeably the case if the observations relate to numbers, the average of which is near zero. Here of course the allowance for variation is only small on one side, while it may increase with out distinct limits on the alternate slope. So it is for instance with the numbers of ray-florets in the example given on p. 729. Such divergent cases, however, are to be considered as exceptions to the rule, due to some unknown cause.

Heretofore we have discussed the empirical side of the problem only. For the purpose of experimental study of questions of heredity this is ordinarily quite sufficient. The inquiry [732] into the phenomenon of regression, or of the relation of the degree of deviation of the progeny to that of their parents, and the selection of extreme instances for multiplication are obviously independent of mathematical considerations. On the other hand an important inquiry lies in the statistical treatment of these phenomena, and such treatment requires the use of mathematical methods.

Statistics however, are not included in the object of these lectures, and therefore I shall refrain from an explanation of the method of their preparation and limit myself to a general comparison of the observed lines with the law of chance. Before going into the details, it should be repeated once more that the empirical result is quite the same for individual and for partial fluctuations. As a rule, the latter occur in far greater number, and are thus more easily investigated, but individual or personal averages have also been studied.

Newton discovered that the law of chance can be expressed by very simple mathematical calculations. Without going into details, we may at once state that these calculations are based upon his binomium. If the form (a + b) is calculated for some value of the exponent, and if the values of the coefficients after development are alone considered, they yield the basis [733] for the construction of what is called the line or curve of probability. For this construction the coefficients are used as ordinates, the length of which is to be made proportionate to their value. If this is done, and the ordinates are arranged at equal distances, the line which unites their summits is the desired curve. At first glance it exhibits a form quite analogous to the curves of fluctuating variability, obtained by the measurements of beans and in other instances. Both lines are symmetrical and slope rapidly down in the region of the average, while with increasing distance they gradually lose their steep inclination, becoming nearly parallel to the base at their termination.

This similarity between such empirical and theoretical lines is in itself an empirical fact. The causes of chance are assumed to be innumerable, and the whole calculation is based on this assumption. The causes of the fluctuations of biological phenomena have not as yet been critically examined to such an extent as to allow of definite conceptions. The term nourishment manifestly includes quite a number of separate factors, as light, space, temperature, moisture, the physical and chemical conditions of the soil and the changes of the weather. Without doubt the single factors are very numerous, but whether they are numerous enough to be treated [734] as innumerable, and thereby to explain the laws of fluctuations, remains uncertain. Of course the easiest way is to assume that they combine in the same manner as the causes of chance, and that this is the ground of the similarity of the curves. On the other hand, it is manifestly of the highest importance to inquire into the part the several factors play in the determination of the curves. It is not at all improbable that some of them have a larger influence on individual, and others on partial, fluctuations. If this were the case, their importance with respect to questions of heredity might be widely different. In the present state of our knowledge the fluctuation-curves do not contribute in any large measure to an elucidation of the causes. Where these are obvious, they are so without statistics, exactly as they were, previous to Quetelet's discovery.

In behalf of a large number of questions concerning heredity and selection, it is very desirable to have a somewhat closer knowledge of these curves. Therefore I shall try to point out their more essential features, as far as this can be done without mathematical calculations.

At a first glance three points strike us, the average or the summit of the curve, and the extremes. If the general shape is once denoted by the results of observations or by the coefficients [735] of the binomium, all further details seem to depend upon them. In respect to the average this is no doubt the case; it is an empirical value without need of any further discussion. The more the number of the observations increases, the more assured and the more correct is this mean value, but generally it is the same for smaller and for larger groups of observations.

This however, is not the case with the extremes. It is quite evident that small groups have a chance of containing neither of them. The more the number of the observations increases, the larger is the chance of extremes. As a rule, and excluding exceptional cases, the extreme deviations will increase in proportion to the number of cases examined. In a hundred thousand beans the smallest one and the largest one may be expected to differ more widely from one another than in a few hundred beans of the same sample. Hence the conclusion that extremes are not a safe criterion for the discussion of the curves, and not at all adequate for calculations, which must be based upon more definite values.

A real standard is afforded by the steepness of the slope. This may be unequal on the two sides of one curve, and likewise it may differ for different cases. This steepness is usually measured by means of a point on the half curve and [736 ] for this purpose a point is chosen which lies exactly half way between the average and the extreme. Not however half way with respect to the amplitude of the extreme deviation, for on this ground it would partake of the uncertainty of the extreme itself. It is the point on the curve which is surpassed by half the number, and not reached by the other half of the number of the observations included in the half of the curve. This point corresponds to the important value called the probable error, and was designated by Galton as the quartile. For it is evident that the average and the two quartiles divide the whole of the observations into four equal parts.

Choosing the quartiles as the basis for calculations we are independent of all the secondary causes of error, which necessarily are inherent in the extremes. At a casual examination, or for demonstrative purposes, the extremes may be prominent, but for all further considerations the quartiles are the real values upon which to rest calculations.

Moreover if the agreement with the law of probability is once conceded, the whole curve is defined by the average and the quartiles, and the result of hundreds of measurements or countings may be summed up in three, or, in [737] the case of symmetrical curves, perhaps in two figures.

Also in comparing different curves with one another, the quartiles are of great importance. Whenever an empirical fluctuation-curve is to be compared with the theoretical form, or when two or more cases of variability are to be considered under one head, the lines are to be drawn on the same base. It is manifest that the averages must be brought upon the same ordinate, but as to the steepness of the line, much depends on the manner of plotting. Here we must remember that the mutual distance of the ordinates has been a wholly arbitrary one in all our previous considerations. And so it is, as long as only one curve is considered at a time. But as soon as two are to be compared, it is obvious that free choice is no longer allowed. The comparison must be made on a common basis, and to this effect the quartiles must be brought together. They are to lie on the same ordinates. If this is done, each division of the base corresponds to the same proportionate number of individuals, and a complete comparison is made possible.

On the ground of such a comparison we may thus assert that, fluctuations, however different the organs or qualities observed, are the same whenever their curves are seen to overlap one [738] another. Furthermore, whenever an empirical curve agrees in this manner with the theoretical one, the fluctuation complies with Quetelet's law, and may be ascribed to quite ordinary and universal causes. But if it seems to diverge from this line, the cause of this divergence should be inquired into.

Such abnormal curves occur from time to time, but are rare. Unsymmetrical instances have already been alluded to, and seem to be quite frequent. Another deviation from the rule is the presence of more than one summit. This case falls under two headings. If the ray florets of a composite are counted, and the figures brought into a curve, a prominent summit usually corresponds to the average. But next to this, and on both sides, smaller summits are to be seen. On a close inspection these summits are observed to fall on the same ordinates, on which, in the case of allied species, the main apex lies. The specific character of one form is thus repeated as a secondary character on an allied species. Ludwig discovered that these secondary summits comply with the rule discovered by Braun and Schimper, stating the relation of the subsequent figures of the series. This series gives the terms of the disposition of leaves in general, and of the bracts and flowers on the composite flower [739] heads in our particular case. It is the series to which we have already alluded when dealing with the arrangement of the leaves on the twisted teasels. It commences with 1 and 2 and each following figure is equal to the sum of its two precedents. The most common figures are 3, 5, 8, 13, 18, 21, higher cases seldom coming under observation. Now the secondary summits of the ray-curves of the composites are seen to agree, as a rule, with these figures. Other instances could readily be given.

Our second heading includes those cases which exhibit two summits of equal or nearly equal height. Such cases occur when different races are mixed, each retaining its own average and its own curve-summit. We have already demonstrated such a case when dealing with the origin of our double corn-chrysanthemum. The wild species culminates with 13 rays, and the grandiflorum variety with 21. Often the latter is found to be impure, being mixed with the typical species to a varying extent. This is not easily ascertained by a casual inspection of the cultures, but the true condition will promptly betray itself, if curves are constructed. In this way curves may in many instances be made use of to discover mixed races. Double curves may also result from the investigation [740] of true double races, or ever-sporting varieties. The striped snapdragon shows a curve of its stripes with two summits, one corresponding to the average striped flowers, and the other to the pure red ones. Such cases may be discovered by means of curves, but the constituents cannot be separated by culture-experiments.

A curious peculiarity is afforded by half curves. The number of petals is often seen to vary only in one direction from what should be expected to be the mean condition. With buttercups and brambles and many others there is only an increase above the typical five; quaternate flowers are wanting or at least are very rare. With weigelias and many others the number of the tips of the corolla varies downwards, going from five to four and three. Hundreds of flowers show the typical five, and determine the summit of the curve. This drops down on one side only, indicating unilateral variability, which in many cases is due to a very intimate connection of a concealed secondary summit and the main one. In the case of the bulbous buttercup, Ranunculus bulbosus, I have succeeded in isolating this secondary summit, although not in a separate variety, but only in a form corresponding to the type of ever-sporting varieties.

[741] Recapitulating the results of this too condensed discussion, we may state that fluctuations are linear, being limited to an increase and to a decrease of the characters. These changes are mainly due to differences in nourishment, either of the whole organism or of its parts. In the first case, the deviations from the mean are called individual; they are of great importance for the hereditary characters of the offspring. In the second case the deviations are far more universal and far more striking, but of lesser importance. They are called partial fluctuations.

All these fluctuations comply, in the main, with the law of probability, and behave as if their causes were influenced only by chance.

[742]

LECTURE XXVI

ASEXUAL MULTIPLICATION OF EXTREMES

Fluctuating variability may be regarded from two different points of view. The multiformity of a bed of flowers is often a desirable feature, and all means which widen the range of fluctuation are therefore used to enhance this feature, and variability affords specimens, which surpass the average, by yielding a better or larger product.

In the case of fruits and other cultivated forms, it is of course profitable to propagate from the better specimens only, and if possible only from the very best. Obviously the best are the extremes of the whole range of diverging forms, and moreover the extremes on one side of the group. Almost always the best for practical purposes is that in which some quality is strengthened. Cases occur however, in which it is desirable to diminish an injurious peculiarity as far as possible, and in these instances the opposite extreme is the most profitable one.

These considerations lead us to a discussion [743] of the results of the choice of extremes, which it may be easily seen is a matter of the greatest practical importance. This choice is generally designated as selection, but as with most of the terms in the domain of variability, the word selection has come to have more than one meaning. Facts have accumulated enormously since the time of Darwin, a more thorough knowledge has brought about distinctions, and divisions at a rapidly increasing rate, with which terminology has not kept pace. Selection includes all kinds of choice. Darwin distinguished between natural and artificial selection, but proper subdivisions of these conceptions are needed.

In the fourth lecture we dealt with this same question, and saw that selection must, in the first place, make a choice between the elementary species of the same systematic form. This selection of species or species-selection was the work of Le Couteur and Patrick Shirreff, and is now in general use in practice where it has received the name of variety-testing. This clear and unequivocal term however, can hardly be included under the head of natural selection. The poetic terminology of selection by nature has already brought about many difficulties that should be avoided in the future. On the other hand, the designation of the process as a natural [744] selection of species complies as closely as possible with existing terminology, and does not seem liable to any misunderstanding.

It is a selection between species. Opposed to it is the selection within the species. Manifestly the first should precede the second, and if this sequence is not conscientiously followed it will result in confusion. This is evident when it is considered that fluctuations can only appear with their pure and normal type in pure strains, and that each admixture of other units is liable to be shown by the form of the curves. More over, selection chooses single individuals, and a single plant, if it is not a hybrid, can scarcely pertain to two different species. The first choice therefore is apt to make the strain pure.

In contrasting selection between species with that within the species, of course elementary species are meant, including varieties. The terms would be of no consequence if only rightly understood. For the sake of clearness we might designate the last named process with the term of intra-specific selection, and it is obvious that this term is applicable both to natural and to artificial selection.

Having previously dealt with species-selection at sufficient length, we may now confine ourselves to the consideration of the intra-specific [745] selection process. In practice it is of secondary importance, and in nature it takes a very subordinate position. For this reason it will be best to confine further discussions to the experience of the breeders.

Two different ways are open to make fluctuating variability profitable. Both consist in the multiplication of the chosen extremes, and this increase may be attained in a vegetative manner, or by the use of seeds. Asexual and sexual propagation are different in many respects, and so they are also in the domain of variability.

In order to obtain a clear comprehension of this difference, it is necessary to start from the distinction between individual and partial fluctuations, as given in the last lecture. This distinction may be discussed more understandingly if the causes of the variability are taken into consideration. We have dealt with them at some length, and are now aware that inner conditions only, determine averages, while some fluctuation around them is allowable, as influenced by external conditions. These outward influences act throughout life. At the very first they impress their stamp on the whole organism, and incite a lasting change in distinct directions. This is the period of the development of the germ within the seed; it begins with the fusion of the sexual cells, and each of them may be influenced [746] to a noticeable degree before this union. This is the period of the determination of individual variability. As soon as ramifications begin, the external conditions act separately on every part, influencing some to a greater and others to a lesser degree. Here we have the beginning of partial variability. At the outset all parts may be affected in the same way and in the same measure, but the chances of such an agreement, of course, rapidly diminish. This is partly due to differences in exposure, but mainly to alterations of the sensibility of the organs themselves.

It is difficult to gain a clear conception of the contrast between individual and partial variability, and neither is it easy to appreciate their cooperation rightly. Perhaps the best way is to consider their activity as a gradual narrowing of possibilities. At the outset the plant may develop its qualities in any measure, nothing being as yet fixed. Gradually however, the development takes a definite direction, for better or for worse. Is a direction once taken, then it becomes the average, around which the remaining possibilities are grouped. The plant or the organ goes on in this way, until finally it reaches maturity with one of the thousands of degrees of development, between which at the beginning it had a free choice.

[747] Putting this discussion in other terms, we find every individual and every organ in the adult state corresponding with a single ordinate of the curve. The curve indicates the range of possibilities, the ordinate shows the choice that has been made. Now it is clear at once that this choice has not been made suddenly but gradually. Halfway of the development, the choice is halfway determined, but the other half is still undefined. The first half is the same for all the organs of the plant, and is therefore termed individual; the second differs in the separate members, and consequently is known as partial. Which of the two halves is the greater and which the lesser, of course depends on the cases considered.

Finally we may describe a single example, the length of the capsules of the evening-primrose. This is highly variable, the longest reaching more than twice the length of the smallest. Many capsules are borne on the same spike, and they are easily seen to be of unequal size. They vary according to their position, the size diminishing in the main from the base upwards, especially on the higher parts. Likewise the fruits of weaker lateral branches are smaller. Curves are easily made by measuring a few hundred capsules from corresponding parts of different plants, or even by limiting the [748] inquiry to a single individual. These curves give the partial variability, and are found to comply with Quetelet's law.

Besides this limited study, we may compare the numerous individuals of one locality or of a large plot of cultivated plants with one another. In doing so, we are struck with the fact that some plants have large and others small fruits. We now limit ourselves to the main spike of each plant, and perhaps to its lower parts, so as to avoid as far as possible the impression made by the partial fluctuations. The differences remain, and are sufficient to furnish an easy comparison with the general law. In order to do this, we take from each plant a definite number of capsules and measure their average length. In some experiments I took the twenty lowermost capsules of the main spikes. In this way one average was obtained for each plant, and combining these into a curve, it was found that these fluctuations also came under Quetelet's law. Thus the individual averages, and the fluctuations around each of them, follow the same rule. The first are a measure for the whole plant, the second only for its parts. As a general resume we can assert that, as a rule, a quality is determined in some degree during the earlier stages of the organism, and that this determination is valid throughout its [749] life. Afterwards only the minor points remain to be regulated. This makes it at once clear that the range of individual and partial variability together must be wider than that of either of them, taken alone. Partial fluctuations cannot, of course, be excluded. Thus our comparison is limited to individual and partial variability on one side, and partial fluctuations alone on the other side.

Intra-specific selection is thus seen to fall under two heads: a selection between the individuals, and a choice within each of them. The first affords a wider and the latter a narrower field.

Individual variability, considered as the result of outward influences operative during extreme youth, can be excluded in a very simple manner. Obviously it suffices to exclude extreme youth, in other words, to exclude the use of seeds. Multiplication in a vegetative way, by grafting and budding, by runners or roots, or by simple division of rootstocks and bulbs is the way in which to limit variability to the partial half. This is all we may hope to attain, but experience shows that it is a very efficient means of limitation. Partial fluctuations are generally far smaller than individual and partial fluctuations together.

Individual variability in the vegetable kingdom [750] might be called seed-variation, as opposed to partial or bud-fluctuation. And perhaps these terms are more apt to convey a clear conception of the distinction than any other. The germ within the unripe seed is easily understood to be far more sensitive to external conditions than a bud.

Multiplication of extremes by seed is thus always counteracted by individual variability, which at once reopens all, or nearly all, the initial possibilities. Multiplication by buds is exempt from this danger and thus leads to a high degree of uniformity. And this uniformity is in many cases exactly what the breeder endeavors to obtain.

We will treat of this reopening of previous possibilities under the head of regression in the next lecture. It is not at all absolute, at least not in one generation. Part of the improvement remains, and favors the next generation. This part may be estimated approximately as being about one-third or one-half of the improvement attained. Hence the conclusion that vegetative multiplication gives rise to varieties which are as a rule twice or thrice as good as selected varieties of plants propagated by seeds. Hence, likewise the inference that breeders generally prefer vegetative multiplication of improved forms, and apply it in all possible cases. [751] Of course the application is limited, and forage crops and the greater number of vegetables will always necessarily be propagated by seed.

Nature ordinarily prefers the sexual way. Asexual multiplications, although very common with perennial plants, appear not to offer important material for selection. Hence it follows that in comparing the work of nature with that of man, the results of selection followed by vegetative propagation should always be carefully excluded. Our large bulb-flowers and delicious fruits have nothing in common with natural products, and do not yield a standard by which to judge nature's work.

It is very difficult for a botanist to give a survey of what practice has attained by the asexual multiplication of extremes. Nearly all of the large and more palatable fruits are due to such efforts. Some flowers and garden-plants afford further instances. By far the greatest majority of improved asexual varieties, however, are not the result of pure intra-specific selection. They are due largely to the choice of the best existing elementary species, and to some extent to crosses between them, or between distinct systematic species. In practice selection and hybridization go hand in hand and it is often difficult to ascertain what part of [752] the result is due to the one, and what to the other factor.

The scientist, on the contrary, has nothing to do with the industrial product. His task is the analysis of the methods, in order to reach a clear appreciation of the influence of all the competing factors. This study of the working causes leads to a better understanding of the practical processes, and may become the basis of improvement in methods.

Starting from these considerations, we will now give some illustrative examples, and for the first, choose one in which hybridization is almost completely excluded.

Sugar-canes have long been considered to be plants without seed. Their numerous varieties are propagated only in a vegetative way. The stems are cut into pieces, each bearing one or two or more nodes with their buds. An entire variety, though it may be cultivated in large districts and even in various countries, behaves with respect to variability as a single individual. Its individual fluctuability has been limited to the earliest period of its life, when it arose from an unknown seed. The personal characters that have been stamped on this one seed, partly by its descent, and partly in the development of its germ during the period of ripening, have become the indelible characters [753] of the variety, and only the partial fluctuability, due to the effect of later influences, can now be studied statistically.

This study has for its main object the production of sugar in the stems, and the curves, which indicate the percentage of this important substance in different stems of the same variety, comply with Quetelet's law. Each variety has its own average, and around this the data of the majority of the stems are densely crowded, while deviations on both sides are rare and become the rarer the wider they are. The "Cheribon" cane is the richest variety cultivated in Java, and has an average of 19% sugar, while it fluctuates between 11% and 28%. "Chunnic" averages 14%, "Black Manilla" 13% and "White Manilla" 10%; their highest and lowest extremes diverge in the same manner, being for the last named variety 1% and 15%.

This partial variability is of high practical interest, because on it a selection may be founded. According to the conceptions described in a previous lecture, fluctuating variability is the result of those outward factors that determine the strength of development of the plant or the organ. The inconstancy of the degree of sensibility, combined with the ever-varying weather conditions preclude any close proportionality, but apart from this difficulty there is, in the [754] main, a distinct relation between organic strength and the development of single qualities. This correlation has not escaped observation in the case of the sugar-cane, and it is known that the best grown stocks are generally the richest in sugar. Now it is evident that the best grown and richest stems will have the greater chance of transmitting these qualities to the lateral-buds. This at once gives, a basis for vegetative selection, upon which it is not necessary to choose a small number of very excellent stems, but simply to avoid the planting of all those that are below the average. By this means the yield of the cultures has often noticeably been enhanced.

As far as experience goes, this sort of selection, however profitable, does not conduce to the production of improved races. Only temporary ameliorations are obtained, and the selection must be made in the same manner every year. Moreover the improvement is very limited and does not give any promise of further increase. In order to reach this, one has to recur to the individual fluctuability, and therefore to seed.

Nearly half a century ago, Parris discovered, on the island of Barbados, that seeds might occasionally be gathered from the canes. These, however, yielded only grass-like plants of no real value. The same observation was made [755] shortly afterwards in Java and in other sugar producing countries. In the year 1885, Soltwedel, the director of one of the experiment stations for the culture of sugar-cane in Java, conceived the idea of making use of seedlings for the production of improved races. This idea is a very practical one, precisely because of the possibility of vegetative propagation. If individuals would show the same range as that of partial fluctuability, then the choice of the extremes would at once bring the average up to the richness of the best stocks. Once attained, this average would be fixed, without further efforts.

Unfortunately there is one great drawback. This is the infertility of the best variety, that of the "Cheribon" cane. It flowers abundantly in some years, but it has never been known to produce ripe seeds. For this reason Soltwedel had to start from the second best sort, and chose the "Hawaii" cane. This variety usually yields about 14% sugar, and Soltwedel found among his seedlings one that showed 15%. This fact was quite unexpected at that time, and excited widespread interest in the new method, and since then it has been applied to numerous varieties, and many thousands of seedlings have been raised and tested as to their sugar-production.

[756] From a scientific point of view the results are quite striking. From the practical standpoint, however, the question is, whether the "Hawaii" and other fertile varieties are adequate to yield seedlings, which will surpass the infertile "Cheribon" cane. Now "Hawaii" averages 14% and "Cheribon" 19%, and it is easily understood that a "Hawaii" seedling with more than 19% can be expected only from very large sowings. Hundreds of thousands of seedlings must be cultivated, and their juice tested, before this improvement can be reached. Even then, it may have no significance for practical purposes. Next to the amount of sugar comes the resistance to the disease called "Sereh," and the new race requires to be ameliorated in this important direction, too. Other qualities must also be considered, and any casual deterioration in other characters would make all progress illusory. For these reasons much time is required to attain distinct improvements.

These great difficulties in the way of selecting extremes for vegetative propagation are of course met with everywhere. They impede the work of the breeder to such a degree, that but few men are able to surmount them. Breeding new varieties necessitates the bending of every effort to this purpose, and a clear conception of [757] the manifold aspects of this intricate problem. These fall under two heads, the exigencies of practice, and the physiologic laws of variability. Of course, only the latter heading comes within the limits of our discussion which includes two main points. First comes the general law of fluctuation that, though slight deviations from the average may be found by thousands, or rather in nearly every individual, larger and therefore important deviations are very rare. Thousands of seedlings must be examined carefully in order to find one or two from which it might be profitable to start a new race. This point is the same for practical and for scientific investigation. In the second place however, a digression is met with. The practical man must take into consideration all the varying qualities of his improved strains. Some of them must be increased and others be decreased, and their common dependency on external conditions often makes it very difficult to discover the desired combinations. It is obvious, however, that the neglect of one quality may make all improvement of other characters wholly useless. No augmentation of sugar-percentage, of size and flavor of fruits can counterbalance an increase in sensitiveness to disease, and so it is with other qualities also.

[758] Improved races for scientific investigation can be kept free from infection, and protected against numerous other injuries. In the experimental garden they may find conditions which cannot be realized elsewhere. They may show a luxuriant growth, and prove to be excellent material for research, but have features which, having been overlooked at the period of selection, would at once condemn them if left to ordinary conditions, or to the competition of other species.

Considering all these obstacles, it is only natural that breeders should use every means to reach their goal. Only in very rare instances do they follow methods analogous to scientific processes, which tend to simplify the questions as much as possible. As a rule, the practical way is the combination of as many causes of variability as possible. Now the three great sources of variability are, as has been pointed out on several occasions, the original multiformity of the species, fluctuating variability, and hybridization. Hence, in practical experiments, all three are combined. Together they yield results of the highest value, and Burbank's improved fruits and flowers give testimony to the practical significance of this combination.

From a scientific point of view however, it is [759] ordinarily difficult, if not impossible, to discern the part which each of the three great branches of variability has taken in the origination of the product. A full analysis is rarely possible, and the treatment of one of the three factors must necessarily remain incomplete.

Notwithstanding these considerations, I will now give some examples in order to show that fluctuating variability plays a prominent part in these improvements. Of course it is the third in importance in the series. First comes the choice of the material from the assemblage of species, elementary species and varieties. Hybridization comes next in importance. But even the hybrids of the best parents may be improved, because they are no less subject to Quetelet's law than any other strain. Any large number of hybrids of the same ancestry will prove this, and often the excellency of a hybrid variety depends chiefly, or at least definitely, on the selection of the best individuals. Being propagated only in a vegetative way, they retain their original good qualities through all further culture and multiplication.

As an illustrative example I will take the genus Canna. Originally cultivated for its large and bright foliage only, it has since become a flowering plant of value. Our garden strains have originated by the crossing of [760] a number of introduced wild species, among which the Canna indica is the oldest, now giving its name to the whole group. It has tall stems and spikes with rather inconspicuous flowers with narrow petals. It has been crossed with C. nepalensis and C. warczewiczii, and the available historic evidence points to the year 1846 as that of the first cross. This was made by Annee between the indica and the nepalensis; it took ten years to multiply them to the required degree for introduction into commerce. These first hybrids had bright foliage and were tall plants, but their flowers were by no means remarkable.

Once begun, hybridization was widely practiced. About the year 1889 Crozy exhibited at Paris the first beautifully flowering form, which he named for his wife, "Madame Crozy." Since that time he and many others, have improved the flowers in the shape and size, as well as in color and its patterns. In the main, these ameliorations have been due to the discovery and introduction of new wild species possessing the required characters. This is illustrated by the following incident. In the year 1892 I visited Mr. Crozy at Lyons. He showed me his nursery and numerous acquisitions, those of former years as well as those that were quite new, and which were in the process of rapid [761] multiplication, previous to being given to the trade. I wondered, and asked, why no pure white variety was present. His answer was "Because no white species had been found up to the present time, and there is no other means of producing white varieties than by crossing the existing forms with a new white type."

Comparing the varieties produced in successive periods, it is very easy to appreciate their gradual improvement. On most points this is not readily put into words, but the size of the petals can be measured, and the figures may convey at least some idea of the real state of things. Leaving aside the types with small flowers and cultivated exclusively for their foliage, the oldest flowers of Canna had petals of 45 mm. length and 13 mm. breadth. The ordinary types at the time of my visit had reached 61 by 21 mm., and the "Madame Crozy" showed 66 by 30 mm. It had however, already been surpassed by a few commercial varieties, which had the same length but a breadth of 35 mm. And the latest production, which required some years of propagation before being put on the market, measured 83 by 43 mm. Thus in the lapse of some thirty years the length had been doubled and the breadth tripled, giving flowers with broad corollas and with petals [762] joined all around, resembling the best types of lilies and Amaryllis.

Striking as this result unquestionably is, it remains doubtful as to what part of it is due to the discovery and introduction of new large flowered species, and what to the selection of the extremes of fluctuating variability. As far as I have been able to ascertain however, and according to the evidence given to me by Mr. Crozy, selection has had the largest part in regard to the size, while the color-patterns are introduced qualities.

The scientific analysis of other intricate examples is still more difficult. To the practical breeder they often seem very simple, but the student of heredity, who wishes to discern the different factors, is often quite puzzled by this apparent simplicity. So it is in the case of the double lilacs, a large number of varieties of which have recently been originated and introduced into commerce by Lemoine of Nancy. In the main they owe their origin to the crossing and recrossing of a single plant of the old double variety with the numerous existing single-flowered sorts.

This double variety seems to be as old as the culture of the lilacs. It was already known to Munting, who described it in the year 1671. Two centuries afterwards, in 1870, a new description [763] was given by Morren, and though more than one varietal name is recorded in his paper, it appears from the facts given that even at that time only one variety existed. It was commonly called Syringa vulgaris azurea plena, and seems to have been very rare and without real ornamental value.

Lemoine, however, conceived the desirability of a combination of the doubling with the bright colors and large flower-racemes of other lilacs, and performed a series of crosses. The "azurea plena" has no stamens, and therefore must be used in all crosses as the pistil-parent; its ovary is narrowly inclosed in the tube of the flower, and difficult to fertilize. On the other hand, new crosses could be made every year, and the total number of hybrids with different pollen-parents was rapidly increased. After five years the hybrids began to flower and could be used for new crosses, yielding a series of compound hybrids, which however, were not kept separate from the products of the first crosses.

Gradually the number of the flowering specimens increased, and the character of doubling was observed to be variable to a high degree. Sometimes only one supernumerary petal was produced, sometimes a whole new typical corolla was extruded from within the first. In the same [764] way the color and the number of the flowers on each raceme were seen to vary. Thousands of hybrids were produced, and only those which exhibited real advantages were selected for trade. These were multiplied by grafting, and each variety at present consists only of the buds of one original individual and their products. No constancy from seed is assumed, many varieties are even quite sterile.

Of course, no description was given of the rejected forms. It is only stated that many of them bore either single or poorly filled flowers, or were objectionable in some other way. The range of variability, from which the choices were made, is obscure and only the fact of the selection is prominent. What part is due to the combination of the parental features and what to the individual fluctuation of the hybrid itself cannot be ascertained.

So it is in numerous other instances. The dahlias have been derived from three or more original species, and been subjected to cultivation and hybridization in an ever-increasing scale for a century. The best varieties are only propagated in the vegetative way, by the roots and buds, or by grafting and cutting. Each of them is, with regard to its hereditary qualities, only one individual, and the individual characters were selected at the same time with the [765] varietal and hybrid characters. Most of them are very inconstant from seed and as a rule, only mixtures are offered for sale in seed-lists. Which of their ornamental features are due to fluctuating deviation from an average is of course unknown. Amaryllis and Gladiolus are surrounded with the same scientific uncertainties. Eight or ten, or even more, species have been combined into one large and multiform strain, each bringing its peculiar qualities into the mixed mass. Every hybrid variety is one individual, being propagated by bulbs only. Colors and color-patterns, shape of petals and other marks, have been derived from the wild ancestors, but the large size of many of the best varieties is probably due to the selection of the extremes of fluctuating variability. So it is with the begonias of our gardens, which are also composite hybrids, but are usually sown on a very large scale. Flowers of 15 cm. diameter are very showy, but there can be no doubt about the manner in which they are produced, as the wild species fall far short of this size.

Among vegetables the potatoes afford another instance. Originally quite a number of good species were in culture, most of them having small tubers. Our present varieties are due to hybridization and selection, each of them being propagated only in the vegetative way.

[766] Selection is founded upon different qualities, according to the use to be made of the new sort. Potatoes for the factory have even been selected for their amount of starch, and in this case at least, fluctuating variability has played a very important part in the improvement of the race.

Vegetative propagation has the great advantage of exempting the varieties from regression to mediocrity, which always follows multiplication by seeds. It affords the possibility of keeping the extremes constant, and this is not its only advantage. Another, likewise highly interesting, side of the question is the uniformity of the whole strain. This is especially important in the case of fruits, though ordinarily it is regarded as a matter of course, but there are some exceptions which give proof of the real importance of the usual condition. For example, the walnut-tree. Thousands of acres of walnut-orchards consist of seedling trees grown from nuts of unknown parentage. The result is a great diversity in the types of trees and in the size and shape of the nuts, and this diversity is an obvious disadvantage to the industry. The cause lies in the enormous difficulties attached to grafting or budding of these trees, which make this method very expensive and to a high degree uncertain and unsatisfactory.

[767] After this hasty survey of the more reliable facts of the practice of an asexual multiplication of the extremes of fluctuating variability, we may now return to the previously mentioned theoretical considerations. These are concerned with an estimation of the chances of the occurrence of deviations, large enough to exhibit commercial value. This chance may be calculated on the basis of Quetelet's law, whenever the agreement of the fluctuation of the quality under consideration has been empirically determined. In the discussion of the methods of comparing two curves, we have pointed to the quartiles as the decisive points, and to the necessity of drawing the curves so that these points are made to overlie one another, on each side of the average. If now we calculate the binomium of Newton for different values of the exponent, the sum of the coefficients is doubled for each higher unit of the exponent, and at the same time the extreme limit of the curve is extended one step farther. Hence it is possible to calculate a relation between the value of the extreme and the number of cases required. It would take us too long to give this calculation in detail, but it is easily seen that for each succeeding step the number of individuals must be doubled, though the length of the steps, or the amount of increase of the quality [768] remains the same. The result is that many thousands of seedlings are required to go beyond the ordinary range of variations, and that every further improvement requires the doubling of the whole culture. If ten thousand do not give a profitable deviation, the next step requires twenty thousand, the following forty thousand, and so on. And all this work would be necessary for the improvement of a single quality, while practice requires the examination and amelioration of nearly all the variable characters of the strain.

Hence the rule that great results can only be obtained by the use of large numbers, but it is of no avail to state this conclusion from a scientific point of view. Scientific experimenters will rarely be able to sacrifice fifty thousand plants to a single selection. The problem is to introduce the principle into practice and to prove its direct usefulness and reliability. It is to Luther Burbank that we owe this great achievement. His principles are in full harmony with the teachings of science. His methods are hybridization and selection in the broadest sense and on the largest scale. One very illustrative example of his methods must suffice to convey an idea of the work necessary to produce a new race of superlative excellency. Forty thousand blackberry and raspberry [769] hybrids were produced and grown until the fruit matured. Then from the whole lot a single variety was chosen as the best. It is now known under the name of "Paradox." All others were uprooted with their crop of ripening berries, heaped up into a pile twelve feet wide, fourteen feet high and twenty-two feet long, and burned. Nothing remained of that expensive and lengthy experiment, except the one parent-plant of the new variety. Similar selections and similar amount of work have produced the famous plums, the brambles and the blackberries, the Shasta daisy, the peach almond, the improved blueberries, the hybrid lilies, and the many other valuable fruits and garden-flowers that have made the fame of Burbank and the glory of horticultural California.



[770]

LECTURE XXVII

INCONSTANCY OF IMPROVED RACES

The greater advantages of the asexual multiplication of extremes are of course restricted to perennial and woody plants. Annual and biennial species cannot as a rule, be propagated in this way, and even with some perennials horticulturists prefer the sale of seeds to that of roots and bulbs. In all these cases it is clear that the exclusion of the individual variability, which was shown to be an important point in the last lecture, must be sacrificed.

Seed-propagation is subject to individual as well as to fluctuating variability. The first could perhaps be designated by another term, embryonic variability, since it indicates the fluctuations occurring during the period of development of the germ. This period begins with the fusion of the male and female elements and is largely dependent upon the vigor of these cells at the moment, and on the varying qualities they may have acquired. It comprises in the main the time of the ripening of the seed, and [771] might perhaps best be considered to end with the beginning of the resting stage of the ripe seed. Hence it is clear that the variability of seed-propagated annual races has a wider range than that of perennials, shrubs and trees. At present it is difficult to discern exactly the part each of these two main factors plays in the process. Many indications are found however, that make it probable that embryonic variability is wider, and perhaps of far greater importance than the subsequent partial fluctuations. The high degree of similarity between the single specimens of a vegetative variety, and the large amount of variability in seed-races strongly supports this view. The propagation and multiplication of the extremes of fluctuating variability by means of seeds requires a close consideration of the relation between seedling and parent. The easiest way to get a clear conception of this relation is to make use of the ideas concerning the dependency of variability upon nourishment. Assuming these to be correct in the main, and leaving aside all minor questions, we may conclude that the chosen extreme individual is one of the best nourished and intrinsically most vigorous of the whole culture. On account of these very qualities it is capable of nourishing all of its organs better and also its seeds. In other words, the seeds [772] of the extreme individuals have exceptional chances of becoming better nourished than the average of the seeds of the race. Applying the same rule to them, it is easily understood that they will vary, by reason of this better nourishment, in a direction corresponding to that of their parent.